UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Digital simulation of power system protection under transient conditions Garrett, Bretton Wayne 1987

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1987_A1 G36.pdf [ 14.5MB ]
Metadata
JSON: 831-1.0097377.json
JSON-LD: 831-1.0097377-ld.json
RDF/XML (Pretty): 831-1.0097377-rdf.xml
RDF/JSON: 831-1.0097377-rdf.json
Turtle: 831-1.0097377-turtle.txt
N-Triples: 831-1.0097377-rdf-ntriples.txt
Original Record: 831-1.0097377-source.json
Full Text
831-1.0097377-fulltext.txt
Citation
831-1.0097377.ris

Full Text

DIGITAL SIMULATION OF POWER SYSTEM PROTECTION UNDER TRANSIENT CONDITIONS by B R E T T O N W A Y N E G A R R E T T M . A . S c , University of British Columbia, 1978 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF DOCTOR OF P H I L O S O P H Y in THE F A C U L T Y OF G R A D U A T E STUDIES Department of Electrical Engineering We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A Apri l 1987 ® Bretton Wayne Garrett, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at The University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Electrical Engineering The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V 6 T 1W5 Date: Apri l 1987 ABSTRACT This work demonstrates the use of digital simulation for analyzing protec-tion system performance. For studies of complex, multi-relay protection systems, digital simulation provides utility engineers with an attractive alternative to relay testing techniques. The cost of digital simulation facilities can be lower than the cost of comparable testing facilities; relay hardware does not have to be made available for the test laboratory. Digital simulation would ordinarily be impractical for security and dependability studies, due to the thousands of individual simulations involved. The number of simulations needed can be greatly reduced by using a technique called "numerical logic replacement" for implementing the protection scheme logic. This unconventional technique makes near-misoperation visible from individual sim-ulations. The likelihood of overlooking potential misoperation is thus much lower than with the usual direct (Boolean) implementations. 11 T A B L E O F C O N T E N T S Abstract i i List of Figures vii List of Tables viii Acknowledgements ix Chapter I. Introduction 1 Chapter II. Transient Phenomena and Power System Protection 7 A . Introduction 7 B. Transient Effects 7 1. Problems due to power system transients 8 2. Problems due to instrument transformer transients 8 3. Problems due to relay transient behaviour 9 C. Relay Testing Techniques 10 1. High- and medium-power analog simulation 11 2. Low-power analog simulation 12 3. Digital computer simulation 13 D. Limitations of Relay Testing Techniques 14 Chapter III. Digital Simulation of Protection Schemes 17 A . Numerical Logic Replacement 21 1. Replacement operations 23 2. Selection of the pseudo-output 27 Chapter IV. Modelling for Protection Simulation 30 A . Power System Modelling 30 1. Transmission Line Modelling 34 2. Load Modelling 35 3. Transformer Modelling 35 4. Generator Modelling , 36 5. Fault Modelling 37 B. Protection Modelling 38 1. Transducer Modelling 38 2. Relay Modelling 42 3. Protection Scheme Modelling 46 C. Combining Simulations for the Power and Protection Systems 47 Chapter V. Modelling the B.C. Hydro Peace River Scheme 51 A . Introduction 51 B. B.C. Hydro Peace River System 51 1. Portions of the System not Represented 55 C. B .C. Hydro 5L1 Protection 55 1. Phase-fault Protection 56 2. Ground-fault Protection 60 ii i D. Assumptions and Operating Conditions for Study 67 1. Effects of Not Modelling Instrument Transformers . 72 2. Use of Transient Response Processor for Protection Simulation 74 3. Establishing Values for Unknown Relay Parameters .... 76 Chapter VI . Peace River Simulation Results 81 1. Description of Benchmark Cases 81 2. Effect of System Truncation on Protection Response ... 115 Chapter VII . Conclusion 121 A. Difficulty of Creating Power System and Relay Models .. 121 B. Cost of Power System and Protection Simulation 124 C. Summary of Findings 125 D. Directions for Future Work 128 E. Contributions of This Research 130 List of References 131 Appendix A Power System Model 137 A . B .C. Hydro 500 kV System 137 1. Series Capacitors 141 2. Shunt Reactors 143 3. Generator Equivalents 144 4. System Operating Conditions 144 5. Derivation of Two-bus Thevenin Equivalent at Williston and Kelly Lake 144 6. Derivation of Equivalent South of Williston 146 7. Simulation Step Size and Duration 146 8. Listings of Ful l- and Equivalent-case Data for E M T P 147 Appendix B Protection Model 177 A . TRP Protection Simulation 177 B. User Function Descriptions 177 1. A N D 177 2. DIRECTIONAL 186 3. F I L T E R '. 188 4. L A C 188 5. NOT 189 6. OR 190 7. O V E R C U R R E N T . I T 190 8. O V E R C U R R E N T . R 191 9. PERMISSIVE 193 10. PS -F ILTER.A 194 iv 11. S D X 1 H 195 12. SD2H 196 13. TIMER 198 C. Relay Modelling Details 199 1. Assumptions 199 2. Model Initialization 200 3. Accounting for Finite Sensitivity 202 4. Solving State Equations using Central Differences 203 5. Directional Element Modelling 205 6. Transactor Modelling 206 7. Block-average Phase Comparator Model 208 8. Filter/Memory Circuit Modelling 213 9. Inverse-Time Overcurrent Model 218 10. Positive-Sequence-Restrained Overcurrent Relay 223 11. Permissive-Trip Model 226 12. Positive-Sequence Filter Modelling 226 13. Westinghouse SD-2H Modelling 232 14. Modelling for Westinghouse S D X - 1 H Fault-detecting Relay 245 15. Undervoltage Relay 247 16. Negative-sequence Relay 247 17. Load Angle Compensator Modelling 250 18. Delayed-pickup/delayed-dropout timer 255 Appendix C Transient Response Processor 259 A . Introduction 259 B. Summary of Operation 259 C. Structure of the Data 260 D. Commands 262 1. B A T C H 263 2. C O M M E N T 263 3. C O M P U T E 263 4. D E L E T E 264 5. D I S P L A Y 265 6. GET 267 7. P A U S E 269 8. PLOT 269 9. S A V E 274 10. SET 274 11. STOP 277 E . TRP Internal Functions 278 1. A D D 278 2. B A S E 279 3. B L O C K 279 4. C O P Y 280 5. COSINE 281 6. G A T E 281 v 7. I N T E G R A T E 282 8. M A X I M U M 283 9. M I N I M U M 284 10. N E G A T E 284 11. S U B T R A C T 285 12. Z E R O - S E Q U E N C E 286 F. Preparing and Interfacing TRP User Functions 286 G. TRP File Prefixes 297 H . TRP Design Limits 302 vi LIST OF FIGURES 1. Intermediate waveforms for N L R Exclusive-OR operation 26 2. Obtaining N L R pseudo-output for static relay 29 3. CT and C V T equivalent circuits 41 4. Transmission detail for northern Peace River system 53 5. Phase-fault protection (as modelled) 57 6. Details of L A C connection for 21L3 SD-2H voltage input 58 7. Ground-fault protection (as modelled) 61 8. Details for 50LN modelling 62 9. Details for 32F/R modelling 64 10. Phase- and ground-fault combining logic 65 11. General structure of permissive-trip model 66 12. Detailed structure of PT block for permissive-trip model 67 13. Repeat-if-no-block detail for permissive-trip model 71 14. Example showing effect of hysteresis on relay output 83 15. Protection waveforms for case H09012 85 16. Protection waveforms for case H09003 93 17. Protection waveforms for case H10006 99 18. Protection waveforms for case H09002 108 19. Williston phase-fault protection waveforms for case H09011 115 20. 5L1 waveforms for cases H I 1002 and H09012 116 21. One-line diagrams for B.C. Hydro power system, as modelled 138 22. Derivation of two-bus Thevenin equivalent for Williston and Kelly Lake 142 23. Series capacitor detail for 5L1 and 5L2 143 24. Listing of E M T P data for full power system model 148 25. Listing of E M T P data for reduced power system model 167 26. Listing of TRP data for 5L1 protection simulations 178 27. Transactor equivalent circuit 207 28. Input waveforms for phase comparator derivations 212 29. Series R L C filter equivalent circuit 215 30. Input waveforms for amplitude comparator derivations 221 31. Positive-sequence filter equivalent circuit 228 32. SD-2H input circuits 234 33. SD-2H output circuit (as modelled) 244 34. S D X - 1 H general layout 246 35. Negative-sequence filter equivalent circuit 249 36. Load angle compensator equivalent circuit 251 37. Delayed-pickup/delayed-dropout timer 256 38. SR flipflop logic, with S-input dominance 258 39. Listing of skeleton T R P U F X 287 40. Listing of example interface routine U F T I M R 291 41. Listing of example of completed routine T R P U F N 298 vii LIST OF TABLES 1. List of Abbreviations for Simulation Waveforms 68 2. Parameter Values for Relay Models 77 3. List of Abbreviations for Station Names 140 4. Prefix List for TRP Files 302 5. TRP Design Limits 302 viii A C K N O W L E D G E M E N T S The successful completion of this project owes much to K a r l Engelhardt of B.C. Hydro, who served as Industrial Advisor on this project. His technical assistance, discerning eye for peculiar results, and Holmesian knack for deducing their cause, are greatly appreciated. The author would also like to thank B.C. Hydro for assistance with data and aspects of the modelling and simulation of their power system. Special thanks are due to Brent Hughes, Mark Scott, Jack Sawada, and Ernest Chung. Financial assistance for this project was provided by the Natural Sciences and Engineering Research Council of Canada, the Canadian Electrical Association, and B.C. Hydro. A scholarship was generously provided by the North American Life Assurance Company and the Canadian Council of Professional Engineers. Computing facilities were provided by The University of British Columbia, and the Industrial Technology Centre of the Manitoba Research Council. The assistance of Professors L . M . Wedepohl and Hermann Dommel of the University of British Columbia, Dr. Erling Nyborg of the Manitoba Research Council, and Dean Ed Kuffel and Professor Mohan Mathur of the University of Manitoba is gratefully acknowledged. ix C H A P T E R I. I N T R O D U C T I O N Power system response to faults and other sudden disturbances includes both "transient" and "steady-state" components. For low-speed protection systems, the transient component is generally ignored; only the steady-state component is used for analysis. For high-speed protection systems, the transient component must be considered as well, since it creates a serious risk to protection security and dependability.! Sudden changes in power system voltages and currents produce "transient" and "steady-state" components in the relay and instrument transformer responses also. Both of these components must be considered for studies of high-speed protection systems. The complete response (i.e. accounting for all transient and steady-state components) of a protection system is usually determined using sophisticated relay test facilities. These facilities simulate protection response to a disturbance, using analog or digital techniques for modelling the power system, and actual relays for the protection system. While relay test facilities are the most accurate (laboratory) method for determining the responses of individual relays, they have three practical disadvan-tages which limit their use by utility protection engineers. Firstly, test facilities are not readily available. Few utilities could justify the high cost of building, maintaining, and operating a test facility in house. Access to existing external facilities is limited, and too inconvenient except for tSecurity deals with the erroneous operation of a relay in the absence of a fault; dependability deals with the failure of a relay to operate when a fault occurs. 1 2 special studies (e.g. testing a relay of advanced design in a new and difficult application). Secondly, by their very nature test facilities require the relays to be physically on site. This makes it difficult, if not impossible, to use such facilities for the evaluation of conceptual protection schemes, where the relays to be used may exist only in prototype form, if at all. Even the analysis of existing protection systems can be difficult, since enough spare relays must be collected to duplicate the protection in the laboratory. Further, relay test facilities are generally quite limited in the number of relays which can be handled simultaneously. This complicates the evaluation of complete protection schemes, which are usually of more concern to utilities than one or two principal relays. Only by studying the performance of the complete protection scheme is it possible to account for the effects of the scheme logic on dependability and security. The research described in this thesis explores the use of digital simulation techniques, as an alternative to relay testing, for predicting complete protection system response. Digital simulation is free of the three disadvantages of test facilities listed above. As a result, it better addresses the (non-testing) needs of the utility protection engineer. Previous use of digital simulation has been limited to single relays, or to simple combinations of a few relays, such as underreaching transfer-trip schemes for transmission lines. The research described herein successfully applies digital techniques to the simulation of a large, multi-relay protection scheme used by the British Columbia Hydro and Power Authority (B.C. Hydro). Two major restrictions to the wide-spread application of digital simulation 3 are the lack of suitable industrial-grade protection simulation programs, and the high cost of the many simulations needed to reliably establish protection security and dependability. The latter problem is addressed in this research by using an unconventional technique, herein called "numerical logic replacement" (NLR, described in chapter III) to implement the protection scheme logic. N L R provides a numerical measure of how "close" the protection comes to operating during a simulation. This is a major advance over the direct implementation, using Boolean logic, employed for conventional digital and analog simulations. Direct implementations indicate only whether or not the protection operates. No warning is given of near-operation, or more importantly, near-misoperation. N L R provides this warning. The numerical measure of "nearness to operation" provided by N L R not only greatly reduces the likelihood of overlooking potential misoperation, it also provides a direct "index of misoperating tendency". This "index" can be used to identify changes in simulation parameters which increase the risk of misoperation. The operator, or even the computer itself in an automatic mode, can then select only simulations which produce a high risk of misoperation. The number of sim-ulations required to prove protection security and dependability is thus greatly reduced, as is the total simulation time and cost. In order to carry out this research, it was necessary to develop a protec-tion simulator. This provided an excellent opportunity to explore the require-ments of an industrial-grade simulator. Flexibility, ease of use, a wide range of features, the ability to handle large protection schemes, ease of adding user-written relay models, and portability were characteristics which would clearly be 4 required. The simulator produced for this research incorporates these features. Along the same lines, the need to develop a large variety of relay models provided an opportunity to test modelling approaches which would be useful for industrial protection simulation. It was obvious that exact models would not be required for all relays. The less-important relays (e.g. some supervisory relays, relays used for local backup protection, etc.) would require only "generic" models. Generic models share the same general principles of operation as the actual relays (e.g. overcurrent relays based on average current measurement), but omit details such as input filtering or input sensitivity levels. The principal measuring relays in a high-speed protection scheme, in contrast, would require more detailed modelling. This might include the specifics of the input circuitry (e.g. filters), comparator details (e.g. input sensitivity levels), and details of the relay output circuitry (e.g. blocking or latching features); the nature and application of the relay would determine which features were important enough to be included in any specific model. Exact relay modelling, wherein the behaviour of the actual relay is duplicated as accurately as possible for all plausible operating conditions, was not feasible for this research. Exact modelling requires samples of the actual relays, and extensive access to a sophisticated relay test facility for testing them. The latter, in particular, was not available for this research. Modelling detail was therefore restricted to information which could be obtained from the manufacturer's instruction manuals. Testing of the models was limited to situations where the operation of the actual relay was known or predictable. As these restrictions would be expected in a typical utility envir-onment, they effectively demonstrated the practical difficulties which utilities would 5 face when preparing relay models. The remainder of this thesis is organized into six chapters and three appendices. Chapter II discusses transient phenomena which must be considered in protection studies, and the relay test facilities conventionally used to study them. Chapter III discusses the use of digital simulation, as an alternative to rela3T test facilities, for studies of complete protection systems. The theory, prin-ciples, and procedure for N L R are described in detail. Chapter IV discusses power system and protection modelling for digital protection simulations. The two methods by which power system and protection simulations can be combined are compared. Chapter V describes the B.C. Hydro Peace River system and the modelling (in general terms) used for the power system and protection simula-tions. Chapter VI describes the results of simulations of the protection for a key transmission line of the B.C. Hydro Peace River system. A number of benchmark simulations are described in detail, and the resulting protection wave-forms presented. Chapter VII summarizes the results of the research, and suggests direc-tions for future work. Appendix A provides additional detail about the B.C. Hydro Peace River system and the modelling used for the power system simulations. Appendix B describes the protection modelling in detail. Appendix C describes the Transient Response Processor (TRP), which was 6 the simulator developed for the protection simulations. CHAPTER II. TRANSIENT PHENOMENA AND POWER SYSTEM PROTECTION A. INTRODUCTION Reliability is perhaps the most important requirement of power system protection schemes. The reliability of a protection system is determined both by the reliability of the hardware itself, and the reliability of the "decisions" made by the hardware. "Decision" reliability, which is usually divided into "security" and "dependability", becomes increasingly difficult to achieve as relay operating speed increases. The short measurement time during high-speed operation reduces the amount of information the relay has available to make its decision. Transients originating in the power system and the instrument transformers are therefore much more disruptive for high-speed relays (operating in 0.5 cycles or less) than for low- or medium-speed relays. For essentially the same reasons, the transient response of the relay measuring circuit is more important for high-speed relays than for slower relays. Consequently, there has been increasing interest in recent years in the behaviour of protective relays under transient conditions. 7 8 B. TRANSIENT EFFECTS 1. Problems due to power system transients There are basically two types of power system transient which cause problems for protection. The most familiar of these is current offset. Offset currents can cause CT (current transformer) saturation, and relay overreaching. Because current offset affects low- and medium-speed relays as well as high-speed relays, it has been widely studied for many years. The second type of power system transient which can present problems for relays is caused by travelling-wave reflections in transmission networks. Since the resulting high-frequency oscillations generally cause problems only for high-speed relays, travelling-wave reflections attracted little interest prior to the last decade. The most common problem caused by these reflections is delayed operation of distance relays (see, for example, Johns and Aggarwal, 1977). Distance relay inputs are commonly filtered to minimize these delays (Hayden et al., 1971; Souillard, 1978; comments of Suzuki and Chamia during the General Discussion for CIGRE Study Committee 34, 1978; Okamura et al., 1980; Kudo et al., 1985). 2. Problems due to instrument transformer transients The major cause of transients originating in CTs and CVTs (capacitive voltage transformers) is sudden de-energization of the transformer primary. CTs become largely or completely de-energized when internal or nearby-external faults are cleared; CVTs become largely de-energized during faults close to the C V T location. In CTs the de-energization transient is a unipolar "current tail", which can have a long decay time constant. This current tail can delay dropout of "low-set" level-detecting current relays. In CVTs the de-energization transients consist of decaying oscillations of high and low frequency. Although of low amplitude, these oscillations can easily swamp the small power-frequency output during close-up faults. The low-fre-quency oscillation, in particular, can cause incorrect phase comparison in distance relays, leading to improper operation for faults immediately "behind" the relay. 3. Problems due to relay transient behaviour The transient behaviour of the relay itself influences decision reliability just as do power system and instrument transformer transients. The transient response of relay input circuitry is one important factor. With memory-polarized mho relays, for example, the expanded "transient" region of the characteristic is affected by the action of the relay input Filters. The high-Q input filters delay relay operation, during which time the relay memory decays. This decay causes the transient characteristic to be smaller than simple analysis would predict. (In effect, both phase comparator inputs have "memory".) Because of this interaction, it is essential that memory-polarized relays be evaluated under trans-ient conditions whenever the "transient" reach is to be relied upon.t The transient response of relay comparators is also an important factor. The operation of electronic "phase comparators", for example, is based on polarity coincidence between the two inputs. The effect of phase comparison is therefore t Chapter V describes a practical instance of this effect, discovered while testing parameter values for the example simulations. 10 obtained only for periodic inputs of regular form, such as sinusoids. (This is hardly surprising, since the concept of phase has no meaning except for a periodic waveform.) For the complex, non-periodic input signals which exist under transient conditions, the comparator output will depend on the comparator operating prin-ciple. The so-called "block-average" phase comparator, for example, exhibits less sensitivity to offset currents than does the so-called "block-instantaneous" design (Jackson, 1981). The behaviour of these two designs in the presence of high-frequency transients (produced by travelling-wave reflections, for example) is also different. The block-instantaneous comparator resets during the resulting short non-coincidence periods; the block-average comparator exhibits a "dithering" behaviour (Johns and Aggarwal, 1977). C. RELAY TESTING TECHNIQUES Increasing^ over the last decade, the importance of transient effects to the decision reliability of high-speed protection systems has been gaining recogni-tion. This has resulted in increasing use of testing and simulation for evaluating relays and protection systems. According to Chamia and Liberman (closure to discussion, 1978), over 5000 digital and analog simulations were carried out on the A S E A R A L D A relay. G E reportedly conducted over 8000 separate fault tests during laboratory testing of a digital protection system (J.T. Tengdin discu-ssion to Chamia and Liberman, 1978). The most common method of verifying relay behaviour in the presence of transients is through the use of relay test facilities. These facilities are specially 11 designed for observing hardware performance during simulated disturbances. They provide a convenient and practical alternative to field testing using staged faults. The power system voltages and currents are simulated, using either analog or digital techniques, and applied as "synthetic" inputs to the actual relay hardware. The basic simulation approaches are outlined in the following section. A more complete discussion has been prepared by CIGRE Working Group 34-06 (1980). There is also some excellent discussion on relay testing in the CIGRE Group 34 General Discussion (1980). 1. High- and medium-power analog simulation The traditional, and simplest, system for simulating a power system for relay testing uses an adjustable, three-phase Thevenin-equivalent "source" network, and inductances to represent the apparatus (e.g. transmission line) being protect-ed. While too crude for comprehensive testing of modern high-speed protection, these "test benches" were very useful for studying the effects of current offset, and for checking the static characteristics of relays. A significant improvement over the simple test bench is the model power system (or power system simulator), which is better able to account for the dynamics of the power system. The simulator is usually small, consisting of perhaps two synchronous generator sources and two parallel transmission lines (represented by cascaded pi-sections), plus miscellaneous other necessary items (transformers, switches for circuit breakers, etc.).t Model power systems are in common use by relay manufacturers (comments of Smith, Petrov, and Suzuki during CIGRE Group 34 General tSome installations are much larger—see the comments by Ogorelec during the CIGRE Group 34 General Discussion (1978). 12 Discussion, 1978; Hayden et al., 1971; Muller, 1980). They are, however, better suited for studying the effects of medium-term power system dynamics than short-term power system transients. The power system representation used is necessarily approximate, and is not suitable for accurate simulation of travelling-wave effects. This is particularly due to the difficulty of building transmission-line models with wide frequency response at high power levels. The high power levels result from the practice of driving the relays directly from the model, thus requiring the use of relatively high voltages and currents. Network powers of several hundred k V A are required if actual instrument transformers are to be used between the power system model and the relays under test. Even if lower-power model instrument transformers are to be used, network powers of 50 k V A or more can be required (CIGRE Working Group 34-06, 1980). A modern alternative is to conduct the simulation at a low power level, and amplify the voltages and currents for application to the relay hardware. 2 . Low-power analog simulation The modelling complexity required for accurate analog simulation of power systems is practical only at low power levels. For use in relay testing, the low-level simulated voltages and currents must be amplified by high-power, high-quality amplifiers before application to the relay inputs. There are essentially two approaches used for low-power simulation. The first is to construct what is essentially a low-power equivalent of a model power system. This is the approach which has been taken by A S E A (Chamia and Hillstrom, 1983). 13 The second approach is to make use of T N A s (transient network analyzers), which are analog devices designed for the highly-accurate simulation of power system transients. The use of TNAs for power system transient simula-tion is well-established at major T N A sites around the world (e.g. CESI, EREQ), and excellent simulation results can be achieved. For relay testing, the T N A essentially replaces the model power system for the power-system simulation. As with low-power model power systems, the output quantities from the T N A are amplified before application to the relays. The use of a T N A for relay testing has been described by Lionetto et al. (1980), and has also been mentioned by Schumm (CIGRE Group 34 General Discussion, 1978). 3. D ig i t a l computer s imulat ion Digital computer simulation of the power sj^stem is an attractive alternative to the use of low-power analog simulation. Modern digital computer programs, such as the widely-used Bonneville Power Administration (BPA) Electro-magnetic Transients Program (EMTP), are available at modest or no cost for use on many popular computers. Only moderate expertise is required for effective use (as opposed to TNAs, for example), and excellent simulation results can be obtained. Digital simulation offers unexcelled flexibility; changes to base-case simula-tions may be made quickly and conveniently. This is in marked contrast to model power systems and T N A s . The high cost of simulation time on T N A s , in particular, in most cases requires fault waveforms to be recorded and catalogued for later use. Variations on available fault cases are then inconvenient and expensive to obtain due to the need for repatching. Data files for digital sim-ulation, in contrast, are easily stored for later use, and can be readily modified with a text editor. Subsequent individual simulations are thus relatively inexpensive compared with model power systems or TNAs . As with low-power model power systems and T N A s , the voltages and currents obtained from digital computer simulations must be amplified before being applied to the relay under test. In addition they must first be converted from digital values to analog levels using a digital-to-analog converter. The hybrid nature of this approach permits CT and C V T models to be either analog (as with low-power analog simulation) or digital, as desired. One problem with relay test facilities which use digital power system sim-ulation is that the power system simulation does not occur in "real time", as it does with analog simulation. The power system simulation must be performed separately from, and ahead of, the relay test. Consequently, any response of the relay being tested is not automatically and immediately reflected in the power system simulation (i.e. there is no feedback from the relay to the power system during the relay test). For most test purposes, however, this is not a serious limitation (it is, after all, no different than the use of pre-recorded results from T N A s or model power systems). Relay test facilities using digital power system simulation are in use by G E C (Williams and Warren, 1984), some university researchers (e.g. Coish et al., 1980), and at least one utility (Bornard et al., 1984). 15 D. LIMITATIONS OF RELAY TESTING TECHNIQUES Relay testing facilities have serious practical limitations from the perspec-tive of the power system utility. Principally, they are expensive to build, no matter which method is used for simulation of the power system. This is largely due to the need to drive the hardware with full rated voltages and currents. Driving powers are high—several kilowatts for current inputs, where the burden under fault conditions is orders of magnitude larger than the burden at rated input. Either the simulator itself must provide this power, or special high-quality amplifiers must be used. In either case, the cost of providing signal power is high. When the cost of operating and maintaining a test facility is included, the expense of providing an in-house facility is greater than most utilities could justify. External facilities provide only a partial solution, since access is limited and inconvenient. While not serious problems for the occasional special studj', these factors prohibit the use of external facilities for routine work. Where hardware testing is the end objective, there is no reasonable substitute for conventional test facilities. Field testing is clearly more accurate, but it is so expensive, time-consuming, and disruptive to the electricity supply that it is impractical except for spot checks. Laboratory testing is therefore required. As important as hardware testing, however, is protection scheme testing. Protection schemes for modern bulk transmission systems, in particular, are so complex that some sort of evaluation is required before a scheme is put into service, or significantly modified. Relay test facilities have proven to be extremely useful for this type of 16 evaluation. The relays are connected together in the laboratory to duplicate the eventual protection in the field. This type of pre-installation testing, using a model power system, was used for extensive studies of the protection for B.C. Hydro's Peace River system (Hayden et al., 1971). More recently, the protection for B .C . Hydro's 500 kV submarine A C cable, between Cheekye on the mainland and Dunsmuir on Vancouver Island, was tested using a digital-computer-based test facility (Burk and Hindle, 1984). As valuable as they have proven to be, however, relay test facilities are not well-suited for evaluating complete protection schemes. Firstly, test facilities typically drive only a few relays at a time. Yet utilities are understandably more concerned about the performance of the protection system as a whole, rather than just one or two principle relays. The influence of the scheme logic on security and dependability can be found only by studying the performance of the complete protection scheme. A second limitation to the use of test facilities for protection scheme studies is the obvious need for the relay hardware to be physically available for testing. Thus, test facilities cannot be used where the hardware has not yet been constructed, or where it is not readily available for any other reason. This makes it difficult, if not impossible, to use these facilities for studies of conceptual protection schemes. Even the analysis of installed schemes is impossible unless a sufficient number of spares of the installed relays can be found to assemble a duplicate system for testing. Utilities are thus in need of an alternative to relay test facilities for protection scheme studies. CHAPTER III. DIGITAL SIMULATION OF PROTECTION SCHEMES For evaluating protection schemes, digital simulation is an attractive alternative to relay test facilities. The simulated protection can be as extensive and complex as required. There is, for all practical purposes, no limit to the number of relays which can be included in the simulation. Since there is no need for relay hardware, digital simulation is well suited for evaluating new relay designs and concepts, or for similar situations where hardware is not readily available. Setting and design changes are relatively fast and simple. In-house digital simulation capability can be provided at a small fraction of the cost of relay test facilities. Suitable general-purpose computers are widely available, so little or no extra hardware would be required. Capital costs are mainly associated with providing the necessary software. Maintenance costs are not a consideration. Operating costs consist mainly of the computer time used for the simulation, and the manpower required to set up and run studies. With these advantages, the question arises: why have utilities not adopted digital simulation for protection studies? It has been widely used for research, mainly at universities, into the behaviour of general relay designs under specific conditions (Johns and Aggarwal, 1977; Rowbottom and Gillies, 1976; Humpage and Wong, 1978 and 1979; Peng et al., 1985; Klebanowski et al., 1980). It has also been used for evaluation of some new and suggested relay designs (Esztergalyos et al., 1978; Crossley and McLaren, 1983). It has not, however, been used to any significant degree by utilities studying the security and 17 18 dependability of their protection systems. There would seem to be two principal reasons why this is so. The first is the lack of software for protection simulation.! In spite of the number of reported studies in which relays have been simulated, no proven relay models have been presented. Only in the case of Peng et al. (1985), and to a lesser extent Johns and Aggarwal (1977), were modelling details given. Typically, little or no detail is provided about the models used. Without detail it is impossible to judge the suitability of the models for industrial simulations, or to build on the experience gained. The lack of relay models is not a long-term problem, however. Models can been developed. By comparing the behaviour of a relay model with that of the actual hardware, the model can be proven to be accurate.$ The proving of relay models can be greatly aided by the use of relay test facilities, which permit such direct comparison between hardware response and simulated response. Once developed, the collection and cataloging of these models becomes a purely organizational issue. The models can be made widely available, spreading the investment in software development over many users. Apart from the lack of relay models, a suitable protection simulation package is required into which the models can be incorporated. Only Humpage et al. (1974 and 1975) have reported a simulation package which appears to be sufficiently complete to be of industrial use. The program structure is now dated, however. Not enough detail has been provided to judge the practicality of tReliable software is already widely available, at modest or no cost, for power system simulation (e.g. Bonneville Power Administration's Electromagnetic Transients P rogram-EMTP) . tComparison with an actual relay is all that was missing in the Peng et al. work. 19 the methods employed, or the suitability of the techniques for simulation of comprehensive multi-relay protection schemes. Again, however, this is not a long-term problem: a suitable package can be developed. The second, more serious reason why utilities do not use digital protection simulation is the large amount of computer time required. For individual simula-tions, the C P U time required! is comparable with the requirements for other, standard utility simulations (e.g. transient stability). Where only a few simula-tions are required the C P U load is thus acceptable. For protection security and dependability studies, however, thousands of individual simulations are typically required. It is the number of simulations which causes a problem. Souillard, during the 1980 General Discussion of CIGRE Group 34, made the following statement on this point: By its nature, a protection emits an on/off signal. For this reason it is very difficult to know whether an operation which gave a correct state is close to the change of state, or not, we do not have, as in an analog output device, a means of following up as a function of the variation of parameters to permit the application of interpolation or extrapolation prin-ciples, for envisaging the changes and limiting the number of tests. When the output device is of an "on/off" type, it is therefore appropriate to undertake very fine investigation, to detect all points missed in the examination. Even when many tests are conducted, the various relay outputs (and other binary signals) which are combined in the scheme logic must be examined individually. This is because the scheme logic tends to further obscure the tFor the simulations discussed in chapter V I , the C P U time required for simula-tion of both the power system and the protection was about 20 s on a V A X 780 computer. 20 existence of marginal operating conditions. Careful examination of the critical steps in the scheme logic is required to avoid overlooking potential misoperation. This problem appears to be at the core of Muller's statement in a paper (Muller, 1980) presented to the same session of CIGRE: The testing of protection systems is relatively expensive. Apart from the limitations arising from the testing device . . ., there is also a limitation on the complexity of the system being tested. This is determ-ined predominantly by the number of signals which have to be eval-uated. For the new systems which are to be developed, more internal signals result that is the case for combinations of tested elements. When there are too many internal signals the evaluations become too extensive. The computer [by which he means the control computer of the testing facility he is describing] is only of limited use under these circumstances because criteria can arise which are difficult to predict and therefore to programme. None of the published material on relay testing or simulation proposes a solution to these problems. Reducing the number of tests sacrifices the reliability of the conclusions. Yet unless the number of tests is greatly reduced, digital simulation is impractical for security and dependability studies of complex, multi-relay protection schemes. Numer ica l logic replacement, a concept described next, offers a solution. It provides the "analog output" Souillard speaks of. Analog output levels from each relay are carried through the logical combinations which form the scheme logic, all the while preserving the necessary analog form. A reliable indication of marginal operating conditions is thus propagated far "downstream" in the logic flow from the source of the original problem—right to the circuit-breaker trip sig-nals. As a consequence, the number of signals which must be examined—the problem Muller spoke of—is greatly reduced. The number of simulations required—the problem Souillard spoke of—is also greatly reduced. And digital simulation becomes practical, even for complex multi-relay protection schemes, as will be seen in chapter V I . A. NUMERICAL LOGIC REPLACEMENT When relay output contacts are represented directly as Boolean ("on"/"off") quantities, it is not clear from the output how close the relay comes to operating. No warning is given of near-operation, or more importantly, near-misoperation. In an effort to avoid overlooking potential misoperation in security and dependability studies, typical practice is to adjust simulation parameters in small steps. This requires a large number of simulations to cover the required range of operating conditions. Numerical Logic Replacement, or N L R , greatly reduces the need for these small steps. With N L R , the state of the relay output contact is represented as a continuous (as opposed to Boolean) quantity. This continuous quantity, called a pseudo-output, takes on positive values when the contact is closed ("on") and negative values when the contact is open ("off'). The magnitude provides a measure of the margin by which the contact is open (or closed)—indicating how close the relay is, at any instant, to operation. (A small negative value of the pseudo-output, for example, indicates that the contact is open, but not far from closing.) The potential for misoperation can thus be seen directly from the value of the pseudo-output. The idea of using an equivalent analog output for a relay, rather than the actual output contact, is not new. It is relatively common, when simulating individual relays, to display an internal (analog) signal as the "output". A sig-nal is chosen which can be directly related to the state of the output contact. In Johns and Aggarwal (1977), for example, the output of the phase-comparator integrator was used. This "analog-output" technique was also used during model power system tests of relays for the B .C . Hydro Peace River protection (Engelhardt, 1985). A problem arises, however, when the relays are combined into complete protection schemes. Protection scheme logic is implemented using Boolean opera-tions (AND, OR, NOT) to combine the contact outputs of the individual relays. "Analog" levels cannot be used as input for these operations; neither can they be produced as output. The "analog-output" technique must therefore be abandoned to carry out the scheme logic. Protection engineers are thus forced to manually interpret the operation of the scheme logic to decide if misoperation of a particular relay could cause misoperation of the overall protection scheme. This tedious interpretation is excessively subject to human error. The need for interpretation would be greatly reduced if the Boolean opera-tions could be replaced by equivalent "numerical" operations. The equivalent operations would have to use relay pseudo-outputs as input. They would have to produce output of the same (analog) form as the input, so that the output could be used as input to subsequent operations. Finally, the relationship between the input and output for each equivalent operation would have to be directly analogous to the input-output relationship for the Boolean operation being replaced. 23 Such equivalent "numerical" operations exist, and form the basis for N L R . N L R outputs are directly analogous to the outputs of the corresponding Boolean logic elements, just as relay pseudo-outputs are directly analogous to the contact outputs. N L R outputs preserve the measure of operating margin conveyed by the relay pseudo-outputs, and can therefore be treated just like pseudo-outputs for use in subsequent operations. Consequently, it is possible to replace any sequence of logical operations with an equivalent set of N L R operations.! By preserving a one-to-one correspondence between the actual Boolean operations and the replacement operations, the replacement process is made completely transparent to the person running the simulation. There is thus no additional risk of human error due to the replacement process. 1. Replacement operations For relay "analog" outputs to be used in replacement operations, they must be offset (and inverted, if necessary) so that the level will be positive when the associated contacts are closed, and negative otherwise. It is the offset (and possibly inverted) value which becomes the pseudo-output. Consider the logical A N D combination of the output contacts of two relays i and j , with pseudo-outputs f ^ and f ^, respectively. Relay i contact is closed if f ^ > 0 , and similarly for relay j . In terms of pseudo-outputs, the logical state T R U E is represented by f ^ > 0 , and the logical state F A L S E is represented by f ^ < 0 . (Note that f ^ = 0 is neither true nor false, since the logical negation NOT, described following, would not otherwise be equivalent to algebraic negation.) The A N D combination of the output contacts is thus tThe timer model in appendix B uses an SR flipflop model implemented using N L R . represented as AND(f. > 0 , f j > 0) which is true if and only if MINIMUM(f ^ , f j ) > 0. Thus the result of a numerical M I N I M U M operation on the pseudo-outputs implies the result of a Boolean A N D operation on the output contacts. As importantly, the magnitude of the M I N I M U M result indicates the margin by which the result is true or false. Similarly, a logical OR combination of two relay contacts O R ( f i > 0, f j > 0) is true if and only if MAXIMUM(f ^ , f j ) > 0. Thus the result of a numerical M A X I M U M operation on the pseudo-outputs implies the result of a Boolean OR operation on the output contacts. Again, magnitude of the M A X I M U M result indicates the margin by which the result true or false. Finally, the logical negation NOT(f i > 0) is true if and only if 25 - ( f ^ ) > 0 . The result of a numerical negation on a pseudo-output thus implies the result of a Boolean NOT operation on the output contact. As for the A N D and OR operations, the magnitude of the negation result indicates the margin by which the result is true or false. Conversion of N L R results to Boolean results (where desired for display, for example) can be achieved using a simple function which produces a constant high-level output when the input is positive, and a constant low-level output otherwise. The operation of N L R can be better understood by studying fig. 1, which shows the waveforms corresponding to an N L R E X C L U S I V E - O R operation XOR = A" • B + B" • A. The two upper traces show the input signals A and B, both of which are 60 Hz cosines, with B lagging A by 90° . The third trace from the top shows A, which with N L R becomes -A. The fourth and fifth traces from the top are the X • B and B~ • A terms, respectively. With N L R , the logical A N D opera-tion A • B is performed as an instant-by-instant minimum of A and B , as can be seen by studying the traces for A", B , and A" • B . The bottom trace shows the E X C L U S I V E - O R result, which is obtained as an OR result of X • B and B" • A. With N L R , the logical OR operation is performed as an instant-by-instant maximum of A" • B and B • A, as can be seen by studying the lower three traces of fig. 1. Positive values of the X O R output represent a T R U E condition (high state), while negative values represent a F A L S E condition (low 26 TIME (MILLISECONDS) i_ i E X C L U S I V E - O R E X A M P L E i98603i8j Fig. 1. Intermediate waveforms for N L R Exclusive-OR operation state). The X O R in this example serves as a polarity non-coincidence detector. Had an E X C L U S I V E - N O R (XNOR) operation been simulated gust the logical negation of the E X C L U S I V E - O R , and the algebraic negation of the N L R E X C L U S I V E - O R ) , it would serve as a polarity coincidence detector, which is a component of both the static phase comparator (Jackson, 1981) and the A S E A R A L D A directional wave detector (Chamia and Liberman, 1978). In fact, the expression for the R A L D A trip output given in the closure to Chamia and Liberman can be seen to be that of a two-input N L R E X C L U S I V E - O R , and the 27 expression for the block output is that of an N L R E X C L U S I V E - N O R . With a simple shift in the values representing T R U E and F A L S E , N L R operations become identical to the logical operations used with Fuzzy Sets (see Zadeh, 1965). This is not surprising, since N L R can be viewed as an applica-tion of "multiple-valued" logic. This is not to say, however, that we are making use of Fuzzy Sets with N L R . Fuzzy Sets deal with elements which can simultaneously belong to more than one set, due to the "fuzziness" in the definition of the sets themselves. There is no such fuzziness here. A relay either operates or does not operate for a given simulation. The object of using N L R and pseudo-outputs is to gain an indication of the sensitivity of the protection output to changes in relay inputs. For example, if the margin to contact closure is large, a relay is less likely to change state for a given change in input than if the margin is small. More particularly, by observing the magnitude and direction of the change in margin which accom-panies a given change in simulation parameters, tests which will not produce a significantly smaller margin (i.e. risk of protection misoperation) can be avoided. N L R provides the sensitivities which are needed to reduce simulation eff-ort. 2. S e l e c t i o n o f t h e p s e u d o - o u t p u t The selection of the appropriate pseudo-output for a relay is usually more obvious than it may first appear. For all relays, the state of the output con-tact is the result of a comparison between some value derived from current and/or voltage measurements, and a threshold value, often derived (perhaps indirectly) from one of the relay settings. In some cases, several such 28 comparisons may be combined through logic to produce a trip output (e.g. directional comparison schemes). For electromechanical relays of the induction disc/cup type, for example, the angular position of the disc/cup is "compared" with the position of the "a" contact. For static relays, the output of a timer or integrator is applied to a comparator circuit, where it is compared against a threshold (see fig. 2). Digital relaying algorithms generally use an explicit logical comparison between some computed value (impedance estimate, event counter, etc.) and a setting. A timing element, such as would be used for zone 2 delay in distance schemes for example, is treated like an ordinary relay. In this case the measurement is the elapsed time since timer start, and the threshold value is the pickup or dropout delay. In all cases, the pseudo-output is formed by taking the difference between the value derived from the measurements and the threshold value. Hysteresis, where it is used, is automatically accounted for by this procedure, and appears in the output waveform as an instantaneous shift in level as the response passes through zero. Where relay operation requires some combination of events to be true, the detectors for the individual events are treated as individual relay elements, each with an appropriate output. The output for the relay as a whole is then the appropriate logical combination, using N L R operations, of the individual elements. to inverting driver for trip output pseudo-output for NLR Fig. 2. Obtaining N L R pseudo-output for static relay C H A P T E R I V . M O D E L L I N G F O R P R O T E C T I O N S I M U L A T I O N A . POWER SYSTEM MODELLING Usual practice for power system simulations is to use detailed modelling only in the immediate study area. Increasingly approximate representations are used as the (electrical) distance from the study area increases. Modelling in the areas of the fault and the relays should be as detailed as practical, particularly at the voltage level where the fault occurs. (The effects of approximations in the modelling of adjacent higher and lower voltage systems tend to be "swamped", to some extent, by the impedances of the interconnecting transform-ers.) Modelling approximations at a few busbars distance from the fault and relay locations will have a greatly-reduced effect on relay voltages and currents due to the "swamping" effect of the intervening system. For protection studies, the voltage sources and the network must be set up so that the steady-state solution more or less matches results from other types of programs. Without the fault applied, the steady-state solution must produce line flows which are reasonably close to those obtained from a power flow program, for the same loading condition. With the fault applied, the steady-state solution must produce approximately the same short-circuit currents as are obtained from a short-circuit program. This matching of pre-fault and post-fault solutions with results from power-flow and short-circuit programs is required at all relay locations and all fault locations being considered. When portions of the transmission system are replaced with network equivalent circuits, satisfactory matching may be possible only with more com-plicated equivalents than those usually used for switching-surge studies. In the 30 31 latter case the line is assumed to be open at one end; a single-bus Thevenin equivalent circuit for the feeding network is then sufficient to obtain the correct short-circuit currents, and there is no pre-fault power flow to match. For protection studies, however, an equivalenced portion of the network will generally be connected to the retained network at more than one location. The assumption of a radial connection, implicit in the development of single-bus Thevenin equivalent circuits, is thus no longer valid. If the effects of coupling between the various connection points are ignored, it may be impossible to obtain the correct pre- and post-fault power flows. To preserve the coupling, it is necessary to use multi-bus Thevenin equivalents. These equivalents can be large, and are tedious to compute. For a two-bus equivalent,! for example, which would be used where there are two connections from the modelled higher-voltage system to a particular lower-voltage network, twenty-one matrix elements are required (allowing for symmetry) as compared with six for the usual single-bus equivalent. Where four or five connections exist between the modelled voltage level and an underlying lower vol-tage system, the work involved in computing an equivalent can be considerable. Multi-bus Thevenin equivalents will likely be required only for equivalents close to the study area. At a few busbars distance from the study area single-bus equivalents are likely to cause insignificant errors in the transient response, and only small errors in the steady-state fault levels. Whether equivalents are single- or multi-bus, they must represent not only the proper power-frequency impedance, but the higher-frequency impedances as well. To develop such equivalent circuits with reasonably good frequency t Appendix A describes the derivation of a two-bus Thevenin equivalent used for the simulations described in chapter V I . 32 response is still more of an art than a science. An interesting technique has been described by Morched and Brandwajn (1983). In switching-surge studies, the single-bus Thevenin equivalent circuit is often modelled as an inductance, which produces the correct power-frequency short-circuit current, in parallel with a resistance R = Z /n. This ' ^ surge resistance approximates the impedance seen by travelling waves from the switched bus entering the n transmission lines, each of surge impedance Z _ u _ _ _ , connected to the bus. For protection studies, however, the frequencies of interest are too low for this approximation to hold. Simple single-frequency equivalents must therefore be used at some distance (electrically) from the study area. Typically this will require modelling of the majority of the high voltage system, and at least the local underlying lower-voltage system.! Unfortunately, common practice for protection simulations is to model only that portion of the system which is directly under study (e.g. Johns and Aggarwal, 1976 and 1977; Breingan et al., 1979; Redfern et al., 1980; Girgis and Brown, 1981 and 1983), using a simple single-frequency Thevenin equivalent source connected directly to the study network. This abrupt truncation of the transmission system leads to reflection transients in the modelled system which are unrelated to those of the actual power system, t The reflection transients which arise within these overly-simplified systems tend to be predominantly of single (and relatively high) frequency. Reflection transients which arise in more realistic transmission networks do not necessarily show any single dominant tThis is consistent with the experience of the author, B .C . Hydro, and CESI (Lionetto et al., 1980). t-An example of the effects of truncation on system waveforms and protection response can be found in chapter V I . 33 frequency, and contain components of relatively low frequencies, sometimes below that of a second harmonic. The classic paper by Swift (1979), while informative on the matter of reflection transients, does not fully discuss the effects of transmission-line termina-tions on the frequency and waveshape. The frequency of the transients is determined not solely by the reflections at the end of the line, as Swift's paper implies, but also by reflections occurring deeper within the connected system. Thorp et al. (1979) have published results of studies with a laboratory model of the American Electric Power system which show considerable variation in the fre-quency of the dominant resonance with the extent of the connected network. The degree to which the connected network influences the resonance fre-quency depends on the impedance mismatch which the termination presents to the line. A clear limiting case is the perfect match produced when a transmi-ssion line is connected to (i.e. terminated by) an identical line, with nothing connected to the intervening bus. The extent of the "connected network" (the length of the second line) would obviously be as much a determining factor in the resonance frequency as the study line. In this case there is no energy reflected at the interface, so the resonance is entirely due to energy crossing the interface into the termination and reflecting back across the interface into the study line. For the resonant frequency to be correct, an equivalent must present the study network with an essentially-correct impedance at all frequencies. Thus, except where the study line connects to a stiff bus (in which case it becomes essentially decoupled from the remainder of the system beyond that bus), the use of simple single-frequency equivalents in the immediate study area should be 34 avoided. Even geographically-small areas, such as Japan, can experience "large-sys-tem" reflection transients (Okamura et al., 1980; Kudo et al., 1985; comments of Suzuki during General Discussion of CIGRE Group 34, 1978) due to mixed overhead-line/cable systems, since lower cable propagation velocities reduce the resonance frequency. Thus even when dealing with geographically-small areas, the extent of the system to be modelled must be considered carefully. 1. Transmission Line Modelling The simple R L line model used for classical steady-state protection calculations is entirely inadequate for transient simulations. A better representa-tion is a cascade connection of short nominal-pi sections, with mutual coupling represented between phases and between parallel lines on the same right-of-way. A double-circuit line would thus be modelled as cascaded six-phase pi-circuits. The length of each section is determined by the highest frequency of interest in the transient simulation. Distributed-parameter models are preferable to pi-circuits because they give the proper response over the entire frequency range. Ideally, frequency-dependent effects should be modelled for at least the ground-return mode. To model the complete line with sections of untransposed lines is straightforward with nominal pi-circuits; reliable distributed parameter models for untransposed lines are still in the development stage. 35 2 . Load Modelling Load modelling for transient simulation is still at an early stage. The minimum acceptable load representation is a three-phase power-frequency Thevenin equivalent, which at least ensures that steady-state fault and pre-fault flows will be correct. For loads close to the relay location, and which experience depressed vol-tage during the faults under study, some attempt at modelling the voltage behaviour of the load may be justified for medium term (e.g. reclosing) simula-tions. For short term simulations (e.g. fault application), it may only be necessary to model the frequency behaviour of the load. Ontario Hydro have made measurements of the frequency behaviour of representative distribution feeders by applying signal-processing techniques to trans-ient responses recorded during staged system disturbances (Morched, 1985). The results were used to synthesize models for the feeders. These models were of the form of a parallel connection of R and L, connected to the system through a cascade connection of pi-sections (in one case using non-zero shunt conductance to represent tapped loads). In the cases studied, excellent matches were achieved between the measured frequency behaviour and that of the synthesized models. 3. Transformer Modelling Power transformers in protection studies can usually be adequately represented as coupled windings with constant resistances and constant self and mutual inductances. The resistances and inductances can be derived from the power-frequency interwinding impedances, as for steady-state calculations. Where 36 the operation of transformer protection is under study, and it is important to account for inrush currents or harmonics from saturation effects, a more elab-orate representation can be used, at least accounting for the non-linearity of the magnetization curve. Brandwajn et al. (1982) have shown how a coupled multi-winding transformer model can be produced from readily-available data. Nakra and Barton (1974) presented results for a coupled multi-winding transformer model which included saturation and hysteresis effects. 4. G e n e r a t o r M o d e l l i n g Generators can usually be modelled adequately as equivalent voltage sources E " behind subtransient inductances L ^ ' (analogous to the representation used with short-circuit programs) for the short time spans involved in fault-clearing studies. This is particularly true where the relay location is separated from the generation by the generator transformers, or the transformers plus some transmission, so that the generator impedance is somewhat masked by the intervening impedance. For studies of longer duration, where the dynamics of the generator and exciter must be accounted for, or for studies of the generator or generator transformer protection, more exact generator modelling will be required. Detailed generator models have been developed for sub-synchronous resonance studies using the Bonneville Power Administration E M T P , which also has the capability to represent exciter and governor dynamics (Brandwajn and Dommel, 1979). Transient programs with detailed generator and exciter models provide a particularly accurate way of determining the effect of generator swings on the 37 protection. Although some transient stability programs have rudimentary protec-tion modelling capability, the absence of any zero-sequence representation limits their use to phase faults. Transient programs such as the E M T P allow all types of faults to be considered. For long duration studies, it should not be necessary to consider the effects of electromagnetic transients over the entire interval, so that large step sizes can be used. Aggarwal and Johns (1980) advocated continuing the trans-ient simulation over the entire sequence from fault incidence through to auto-reclosure. This is unnecessary, since realistic reclosing times are of the order of tens of cycles for practical power systems (Ellis et al., 1966, for example, found a value of =0.5 seconds for the early B.C. Hydro Peace River system). By this time, electromagnetic transients will have decayed to insignificance, so that, from the transient point of view, reclosure is essentially from a new steady-state condition. 5. Faul t Mode l l i ng Fault impedance is commonly modelled using a linear resistance to represent tower footing resistance (for ground faults), and a non-linear resistance (similar to, for example, a zener diode characteristic, except bipolar) to represent arc impedance (Hayden et al., 1971; Marsman, 1980). It may be acceptable to ignore the nonlinear characteristic for some studies. The I E E E Power System Relaying Committee (1985), for example, have suggested that "the nonlinear nature of the arc generally merits consideration only for the lower voltages or for time delay backup relaying at any voltage". Where ground wires are not used, tower footing resistance will likely dominate any arc "resistance" for ground 38 faults; a linear resistance will thus suffice in these cases. Where the arc voltage is to be represented, an empirical expression devel-oped by Warrington (1931) can be used to estimate the arc voltage for a given fault current level: V = 8750 1 / I 0 * 4 where 1 is the arc length in feet, in still air, I is the fault current level in amperes, and V is the arc voltage in volts. It is apparent from the data presented in the original paper that the voltage and current in this expression are R M S values. (Warrington does not explain how the RMS values were computed from the distorted waveforms.) B. PROTECTION MODELLING 1. Transducer Model l ing The digital modelling of instrument transformers has been discussed in a number of published papers (e.g. Wright and Rhodes, 1974; Rowbottom and Gillies, 1976; Wong and Humpage, 1978). The main effects which must be accounted for by instrument transformer models are: core saturation effects, including remanence and hysteresis for best modelling of current transformers (CTs). The effect of the magnetic core non-linearities may generally be ignored for capacitive voltage transformers (CVTs), except where ferroresonant possibilities are of concern. 39 relaxation transients, which occur with both CTs and CVTs when the primary energization collapses to zero, due to the decay of charge and flux from the energy-storage mechanisms intrinsic to these devices. Related to relaxation transients are the energization transients which occur when de-energized instrument transformers are suddenly re-energized, such as occurs after a line is reclosed. Relaxation trans-ients in CTs can cause slow dropout of overcurrent relays, while C V T relaxation transients can cause incorrect operation of distance relays for close-up faults. bandwidth effects, particularly C V T resonances due to the interaction of the capacitive voltage divider with the compensating inductance. Douglass (1981) has published the results of measurements on CTs, which show the frequency response to be essentially flat to beyond 20 kHz when the CTs are properly applied. Bandwidth is thus not an issue for CTs (per se—see next point). For CVTs the situation is more complex due to the tuning inductance used for reducing power-frequency phase error. Chamia (1980) gives the useful frequency range for a C V T as being from 20 to a "few hundred" Hertz. CIGRE Working Group 36-05 have published (1984) a plot of relative transformation ratio versus frequency for a 220 kV C V T for 50 Hz systems, which shows a narrow peak of 2.7 (relative to 1.0 at 50 Hz) at about 170 Hz, and another broad peak of over 3.1 at about 800 Hz. burden effects, particularly under transient conditions. Apart from the 40 well-known effects which the burden can have on its transducer under steady-state power-frequency operating conditions, the transient response of the transducer will clearly be affected by the transient behaviour of the burden. Since the exact burden composition is almost never known (particularly for CVTs, which supply a collection of relays, etc.), some assumption must be made. The usual assumption of a Thevenin equivalent (power-frequency) impedance at least ensures that power-frequency modelling is correct. The value of detailed CT and C V T models is debatable, however, when the burdens are represented so imperfectly. Sensitivity studies are required in this area, along with measurements of the transient characteristics of typical installed CT and C V T burdens (total burden, that is, including wiring and composite relay/metering burdens). It is essential that burden representations be developed which can be used with greater confidence than can the present power-frequency "equivalent" burdens. Figure 3 shows equivalent circuits which can be used for CT and C V T modelling. Neither is very sophisticated, but data for both can be either derived or estimated from available information, and at least the most important transdu-cer effects are represented. The CT magnetizing branch uses a non-linear inductance as a core model to account for saturation effects. Wright and Rhodes (1974) have reported good results using the common "two-slope" model. Rowbottom and Gillies (1976) used a more complex model which accounts for saturation, hysteresis, and remanence. This latter model appears to be a good compromise between accuracy of representation and practicality of implementation. 41 i dea l m a g n e t i z i n g b r a n c h leakage, w ind ing , and b u r d e n i m p e d a n c e s ideal (a) CT model burden i m p e d a n c e (b) C V T model Fig. 3. CT and C V T equivalent circuits. The linear resistance shown in the CT magnetizing branch is used to produce eddy-current-like loss effects. This is a commonly-used artifice. The CT burden is a composite of the usual series R L power-frequency equivalents of the burden impedance, secondary winding resistance, and leakage inductance. The C V T model includes a series R L C branch representing the equivalent input capacitance of the capacitive voltage divider, the phase-shift compensating inductance, and the damping resistance. This determines the major frequency response of the C V T , and the high-frequency capacitive relaxation transients. The shunt linear inductance provides an approximation to the magnetizing induc-tance of the internal magnetic VT, and permits representation of the low-fre-quency inductive relaxation transients. The burden has the format required for the A N S I transient tests for CVTs , and is intended to permit "tuning" of the damping resistance to obtain reasonable transient characteristics. The series R L limb would ordinarily be used in the simulations, being set to the power-frequency equivalent burden impedance. 2. Relay Modelling Protective relays may be modelled in varying degrees of detail. Where digital models of relays have been used for published work, they appear to be mostly "generic" (e.g. Johns and Aggarwal, 1978). Generic models share the same general principles of operation as the actual relays (e.g. mho relays based on block-average phase comparison), but omit details such as input filtering or input sensitivity levels. Generic modelling can be quite useful for studying basic protection concepts, and can be used for modelling the less-important relays in a protection scheme (e.g. some supervisory relays, relays used for local backup protection, etc.) The principal measuring relays in a high-speed protection scheme are likely to require more detailed modelling. This could include the specifics of the input circuitry (including filters), comparator details (such as input sensitivity levels), and specifics of the relay output circuitry (such as the blocking and 43 latching features used in the Westinghouse SD-2H relay described in appendix B). This more-detailed modelling naturally requires specific knowledge about the relays in question. The most advanced level of detail requires not only extensive information about the relay circuitry, but also an actual relay and access to a sophisticated facility for testing it. The testing is needed to verify the digital model by subjecting both the actual relay and the model to identical input waveforms and comparing the output (and selected internal) signals for the two. Of the two basic problems associated with relay modelling—collecting the necessary detailed data about the relay, and preparing the actual digital model—collecting and interpreting the data may be the most difficult task. Manufacturers' descriptive bulletins and instruction manuals do not necessarily contain all required details. For example, although the manufacturer's instruction booklet was very helpful when modelling the SD-2H relay described in appendix B , the "Q" or "quality factor" of the memory and input filter were not given. A n alternate method had to be used to find acceptable values. Because of the difficulty of obtaining data, specific models should be used only where absolutely necessary (e.g. principal measuring relays); generic modelling is appropriate for the remaining relays. Once the necessary information has been collected, the actual modelling is generally straightforward. The relay input circuits, which transform the measured currents and voltages into the quantities needed by the comparator, are generally linear and can be modelled using state equations. Although various techniques are available for solving state equations numerically, the excellent numerical stability of central difference equations (which form the basis for implicit trapezoidal integration) make this the technique of choice for power sys-tem transient applications (Dommel, 1969). While other techniques theoretically offer better accuracy, experience has shown that these techniques are mostly unsuitable, being numerically unstable unless used with impractically-small step sizes. The comparators themselves are generally non-linear, and are of varying difficulties to model. Polarity-coincident (static) two-input phase comparators, for example, require only straightforward E X C L U S I V E - N O R logic. Some two-input amplitude comparators, by way of contrast, require modelling of a multi-rectifier bridge circuit with an RC load circuit, which is a much more difficult modelling task. No single approach can be recommended. Initialization of the comparator, particularly where integration of some kind is used at the output stage, can be a more complex task than the development of the iterative equations. This task is simplified by making use of the max-imum and minimum limits on the output range. It is usually possible to iden-tify the input conditions which cause the output to leave one limit and move into the "active region" toward the other. (The output will reach one of the two limits at least once per power-frequency cycle if the initial condition is from the steady state, since the relay cannot drift in the "undecided" intermediate region indefinitely.) The examples in appendix B clarify the procedure. In extreme cases, the initialization can be performed by a "silent simula-tion", wherein a "pre-simulation" of one or two (power frequency) cycles duration is performed using the same equations as the main simulation. The pre-simula-tion is started from some assumed initial condition. Only the final value reached in the pre-simulation is retained (hence the term "silent"), this being the initial condition for the main simulation. The error in the pre-simulation due to the assumed initial condition will be corrected when the comparator reaches the appropriate output l imit . ! The comparator output will then be reset to the correct value, and will leave the limit again at the correct time. The remainder of the pre-simulation will then be correct. Provided that the appropriate output limit is reached at least once during the pre-simulation, the initial condition for the main simulation will be correct. Although silent-simulation is a brute force technique, it may be the most practical method of initializing highly non-linear comparators. Another important aspect of relay modelling is establishing the integrator gain for relays with integrating (averaging) comparators. For a fixed output trip threshold, the speed of integrator-type relays is directly proportional to the integrator gain. The maximum value of integrator gain (which determines the theoretical maximum operating speed for the relay) is determined by the measurement uncertainty inherent in the comparator. Measurement uncertainty shows up as a ripple in the comparator output—the rectifier ripple for an amplitude comparator, for example. The max-imum gain must be low enough to ensure that the relay does not operate on this ripple for steady-state inputs just below setting. Since the gain may have to be reduced below this value to ensure security under transient conditions, a ! I f the steady-state inputs are such that the comparator would be high, the appropriate limit would be the high limit. Otherwise, the appropriate limit would be the low limit. 46 convenient model parameter is the fraction of the maximum gain which is to be used. A detailed example of the calculation of the maximum integrator gain is given in appendix B for the single-input amplitude comparator used in the over-current relay model. 3. Protection Scheme Mode l l ing a. Accounting for pilot channel delay time Since most protection applications use communication between relays at different locations (usually at the two ends of a transmission line), it will usually be necessary to account for the delay associated with the pilot channels. During the later portion of the simulation, the signals at the receiving ends of the pilot channels will be identical to the signals at the sending ends, except delayed by the channel time. The delay can be easily handled in the simulation by "reaching back" in time (time-delaying the sending-end signals) by the amount of the delay. At the start of the simulation, however, "reaching back" requires knowl-edge of the signals at the sending-end before the start of the simulation. Since the pilot channel signals are derived from the relay outputs, it is necessary to determine the output of the relays before the start of the simulation (during the steady-state operating period). The only way of finding the relay outputs is to perform a "pre-simulation", identical to the main simulation except that the results would be used only for computation, and not for display. The pre-sim-ulation would have to cover one full delay period before the start of the main simulation. The need for the "pre-simulation" can be avoided if the pilot channels can be assumed to be completely quiescent during the initial delay period. If the protection system is known to be in an inactive, steady-state condition prior to the start of simulation, the assumption of complete quiescence would be reasonable for permissive- and transfer-trip channels. C. COMBINING SIMULATIONS FOR THE POWER AND PROTECTION SYSTEMS Two possible approaches can be used for combining the power system sim-ulation with the protection simulation. The first approach is analogous to that used with analog relay test facilities, where the power system and protection function together at every instant in time. In digital simulation, both systems would be solved simultaneously at each time step before advancing to the next. This is the simultaneous approach. The second approach is analogous to the one generally used with test facilities which use digital power system simulation. In these facilities, the vol-tage and current waveforms are often recorded on magnetic tape and played back through amplifiers for testing the relays. In this sequential approach, the power system and protection function separately, one after the other. The simultaneous approach has the advantage of directly accounting for the effects of protection operation on the power system (circuit breaker opening and closing). These effects cause some difficulty with the sequential approach, since circuit breaker operations must be predicted when setting up the power flow simulation. This is possible in simple cases (e.g. fault clearing on a 48 parallel line) by running a preliminary simulation to determine when the opera-tions take place (e.g. circuit-breaker set to open after 70 ms, with the time of 70 ms obtained from a preliminary simulation). A related problem with the sequential approach is the need to prepare special models wherever feedback loops are encountered within the scheme logic. The reason the special models are needed is that feedback can only be accounted for when everything encompassed by the feedback loop is simulated together (simultaneously). With the sequential approach, only individual models (which could be of relays, timers, logic blocks, or selected portions of the scheme logic) are simulated simultaneously. In practice, however, the need to produce special models is not a serious disadvantage, since feedback loops in the protection scheme logic generally occur only where pilot channels are used. The required models are thus of relatively standard form (e.g. permissive trip logic) in most cases. In the author's view, the advantage of the simultaneous approach is outweighed by several practical disadvantages. Firstly, the simultaneous approach requires a very large and complex program for the joint simulation of the power system and protection. The relay models must be re-entrant, complicating the programming and increasing storage requirements. The large number of subroutine calls required (one for each use of the model, at each time step) reduces program efficiency. In general, programming, program additions, and program maintenance are considerably more complex than with the sequential approach, which uses more-or-less independent program segments. Secondly, the simultaneous approach provides only a limited choice of solution techniques. The entire power system and protection simulation must be either digital or analog. Digital simulation may use only time-domain methods. Further, if the parts of the program dealing with power system simulation are intricately interwoven with the protection simulation portions, the power system simulation method will be "locked-in" to the final program. The sequential approach is virtually free of limitations of this nature. Digital or analog simulation may be freely intermixed, as suits the circumstances; in a hybrid simulation facility, actual relays and digital models of relays can be used interchangeably. This is possible because the inputs for each model are pre-computed, so that rather than simulating the entire protection scheme in real-time, it is only necessary to be able to transfer data at real-time rates from memory to the necessary digital-to-analog converters, and from the necessary analog-to-digital converters to memory. This is quite a modest requirement, employing well-tested technology. The advantage of this capability is that accurate digital models can be developed and tested against the actual hardware under identical conditions. Since both model and hardware can have identical appearance to the remainder of the simulation package, either can be "dropped in" to the overall protection simulation with little effort. Either Fourier-transform or time-domain solution methods can be used for digital models of either protection system components or the power system. Power system voltages and currents do not even have to be simulation results—recordings of actual power system voltages and currents can be used if available. A further advantage offered by the sequential technique is that the various independent portions of the protection (phase and ground relaying, for example) can be simulated independently. This feature can offer considerable savings in computation when investigating the effects of changing the parameters of a relay (or set of relays) on protection performance, since all portions of the protection which are not dependent on the output of the relay under study can be simulated separately and stored. For most security and dependability simulations, circuit breaker operations due to the protection are either irrelevant to the study or easily predetermined. The sequential approach is therefore usually the best choice for these studies. CHAPTER V. MODELLING THE B.C. HYDRO P E A C E RIVER SCHEME A. INTRODUCTION This chapter describes the modelling used for digital simulations of the B. C. Hydro Peace River system. The simulations were performed, using the techniques described in the previous chapter, to demonstrate the feasibility of digital protection simulation using N L R . The modelled protection is that used on the B .C . Hydro 500 kV transmission line designated 5L1, part of the Peace River transmission system. The protection is comprehensive enough to show that digital simulation using N L R is feasible for practical protection schemes. While the simulations are for a transmission protection scheme, the principles involved are sufficiently general not to limit the conclusions drawn from this research. The simulations have been designed to demonstrate the operation of the 5L1 protection for critical benchmark faults. The simulation procedure is very similar to that which would be used in checking out a proposed protection scheme during the planning process. Some relay parameters have been determ-ined experimentally. B. B.C. HYDRO PEACE RIVER SYSTEM The B.C. Hydro power system consists of some 10.5 GW (nameplate) of generation, of which 9.3 GW is hydroelectric. The majority of the generation is located at sites remote from the major load centre at Vancouver, in the southwest corner of the province. The bulk of the power generated at these remote hydroelectric sites is carried by 5088 circuit-km of 500 kV transmission (including 38.5 km of submarine cable), which spans the width of the province 51 52 from Vancouver Island to the Rocky Mountains (there interconnecting with the Trans Alta Utilities system in Alberta), and some 60% of the length of the province from the U.S . border in the south (there interconnecting with Bonneville Power Administration (BPA) in the state of Washington), to the G . M . Shrum and Peace Canyon generating stations of the Peace River system, 800 km to the north, t The Peace River portion of the B.C. Hydro power system was the first of the B.C. Hydro 500 kV system to be developed (Ellis et al., 1966), coming on-line in 1968. This installation featured the use of braking resistors, fast solid-state exciters, and series compensation, in order to ensure the stability of over 900 km of radial 500 kV system. Even now, some 600 km of this sys-tem, from Kelly Lake substation (southwest of 100 Mile House) north to G . M . Shrum and Peace Canyon generating stations (near Fort St. John), is essentially radial. It is the northern-most portion of this system which is of immediate interest for this study, from the 2730 M W G . M . Shrum and 700 M W Peace Canyon generating stations south to the Williston substation near Prince George, at the end of 277 km of 500 kV transmission. Details of this area of immediate interest, as modelled, can be found on the one-line diagram of fig. 4. (A list of the three-letter station abbreviations can be found in appendix A.) The protection under study is for transmission line 5L1, a 277 km 500 k V line of flat single-circuit construction, running from G . M . Shrum to Williston. Neighbouring 500 k V lines are 5L4, 14 km long (modelled as tOne-line diagrams of the majority of the 500 k V system, as modelled, along with details of the power system modelling, and complete listings of the E M T P input data used for this study, can be found in appendix A . Fig. 4. Transmission detail for northern Peace River system 19 km—see appendix A) from G . M . Shrum to Peace Canyon; 5L2 and 5L3, the 277 km long lines running parallel to 5L1; and 5L11 and 5L12, the 329 km long parallel lines connecting Williston with Kelly Lake. Series capacitor banks provide 50% compensation in the three lines between G . M . Shrum and Williston (at Kennedy station), and in the two lines between Williston and Kelly Lake (at McLeese station). The series capacitor banks are equipped with protective gaps which bypass dangerously high currents (Batho et al., 1977; Mansour et al., 1983). These gaps have been modelled only at Kennedy (for 5L1, 5L2, and 5L3; see appendix A); all other series capacitor installations have only the effective series capacitance modelled (i.e. gap flashing is inactive). Shunt reactors are used throughout the B.C. Hydro 500 kV system. For the Peace River transmission, these consist of standard-rated (X = 20400) single-phase units, connected in a grounded-wye configuration. Integral numbers of these standard banks can be connected to the transmission lines (rather than the bus), as required. For the study at hand, one of these standard banks is in service at the north ends of each of 5L1, 5L2, and 5L3. (Reactors have been modelled on the associated bus for all lines except 5L1 and 5L2, for which the exact location is significant for this study.) The power system model used in this study does not include the G . M . Shrum braking resistance (used to enhance stability during loss of one of the 500 kV lines to Williston). Nor has any detail of the generators (exciters, governors, etc.) been included for this study. Generation is modelled as E " behind L 7 , as for conventional (steady-state) fault studies. 55 1. Portions of the System not Represented For buses remote from the immediate study area, lower voltage portions of the system are represented by single-bus (three-phase) Thevenin equivalents at 60 Hz, so that steady-state fault and pre-fault flows will be correct. There is an error associated with this approach where the lower voltage system is not radial from the high voltage bus, which is the case here for many of the buses south of Kelly Lake (the 230 kV system underlies the 500 kV system in this area). Comparisons between transient model steady-state fault results and results from a conventional (steady-state) fault study program showed the error produced by single-bus Thevenin equivalents south of Kelly Lake to be acceptably small for faults within the study area. Between Williston and Kelly Lake, however, the 500 kV system is essentially in parallel with a portion of the 230 kV sys-tem. To reduce steady-state errors for faults near Williston, a two-bus Thevenin equivalent was required at Williston and Kelly Lake when equivalencing this underlying 230 kV system. C. B.C. HYDRO 5L1 PROTECTION A detailed description of the Peace River protection is given in Hayden et al. (1971); only a general description is given here. Details of the relay models and a listing of the Transient Response Processor (TRP) commands used to simulate the protection can be found in appendix B . The scheme consists of nearly identical primary and secondary protection. Only the primary protection and the unique aspects of the secondary protection will be discussed here. The protection is basically arranged as two independent configurations (underreaching direct transfer trip and over- and underreaching permissive trip with reverse blocking) for both ground and phase faults. The reverse blocking, which is equipped with a 100 ms memory (dropout delay), is essential to ensure security for faults clearing on parallel lines. Without reverse blocking, the sequential clearing of the two ends of a faulted parallel line could cause the permissive trip scheme to mistakenly indicate an internal fault. The reverse blocking feature will be demonstrated in chapter VI . 1. Phase-fault Protect ion The phase-fault protection, for which the A B phase-pair elements are shown in logic-diagram form in fig. 5, is built up from three Westinghouse Canada type SD-2H memory-polarized mho relays. The underreaching elements, designated 21L1, are set to reach 77% of the compensated line "length" (35.40 at 85°), with a "lens" impedance characteristic obtained by requiring phase coincidence within ± 8 2 . 5 ° rather than the usual ± 9 0 ° . The overreaching elements, designated 21L2, are set to reach 134% of the uncompensated line length (1230 at 85°), with a lens impedance characteristic identical to 21L1. These units also provide zone 2 operation after a 250 ms delay. The zone 2 operation has not been included in this study since the delay is longer than the study time. The reverse-looking blocking elements, designated 21L3, are set to reach back into the protected line by 33.70 at 85° , and out of the protected line by 1270 at 85° . This offset characteristic is produced by a "Load Angle Compensator", Westinghouse Canada type L A C - 1 H , and designated L A C for this study (see fig. 6). The principal function of the L A C is to ensure that the 57 v ab v b c 21LX INSDLY SWQ v ab 'ab 21L1 ab 21L1 D C . 21L1 c a -PFDT PFPT = 0 0 PRB Fig. 5. Phase-fault protection (as modelled) (Signal abbreviations are defined in table 1. Relays are described in text. Inputs to 21L2 and 21L3 are similar to 21L1, except as shown.) 58 'a LACG v a 'b LAC b Fig. 6. Details of L A C connection for 21L3 SD-2H voltage input transient characteristics of 21L3 coordinate with those of the remote 21L2 unit when the protected line is carrying significant pre-fault current. (Pre-fault current modifies the transient characteristic of memory-polarized mho relays.) The L A C (which is essentially three independent transactors) uses the line currents to produce output voltages which are phase-shifted + 9 0 ° with respect to the currents. The L A C output voltages are added to the input voltages of 21L3. The modified 21L3 voltages compensate for the phase angle differences between the memory voltages of 21L3 and the remote 21L2, caused by the vol-tage drop across the intervening line impedance. The net effect is to align the transient characteristic of 21L3 to that of the remote 21L2, thus ensuring that 21L2 will not operate for a fault beyond 21L3 which 21L3 can not see (and therefore block). A full description of the operation of the L A C is given in the 59 manufacturer's instruction manual (Westinghouse Canada Inc., 1979). Although the reach values are correct, the specific settings used for 21L3 and the L A C in this study are different from those used with the actual devices. The reason for this is that the burden of the 21L3 voltage circuit causes a voltage drop across the L A C , which modifies the actual characteristics from those which would otherwise be expected. The effect of the 21L3 burden is not modelled for this study, so that no compensating adjustments were needed in the settings. A l l of the reach values given above have been those which apply under static conditions. The use of memory polarizing gives a characteristic which, for internal faults, is greatly expanded for a short time after fault incidence for 21L1 and 21L2, and greatly reduced for 21L3 (closure to Hayden et al., 1971). To reduce sensitivity to transients, the SD-2H relay employs an input fil-ter in the "IZ-V" circuit. The Q of this filter is low under normal conditions so as to avoid operating delays, which are especially severe for faults near the limit of reach due to the low operating energy then available. Some 2-4 ms after a transient disturbance is detected, the Q of the filter is switched to a higher value, providing improved filtering against post-fault transients. To prevent misoperation caused by switching transients, a pickup delay of 35-45 ms (modelled as 40 ms) is inserted into the output of 21L1 and 21L2 (provided that they have not already operated). The delay-insertion feature is inhibited for 30-40 ms (modelled as 35 ms) after fault detection to permit rapid relay operation for true faults. The filter-switching and insert-delay signals are provided by a fault-6 0 detecting relay, Westinghouse Canada type SDX-1H, designated 21LX. This relay operates when a negative sequence voltage of 22.5 k V or greater (primary value) is detected, or when the primary voltage drops below 360 k V line-to-line (thus ensuring continued operation for three-phase faults). A l l phase-fault relays are supervised by a three-phase, low-set line current relay set at 268 A (primary), designated 50L. The setting is high enough to allow the relay to reset on steady-state line charging current. (For this study, 50L has been modelled as three single-phase overcurrent elements with OR-connected outputs.) 2. Ground-fault Protect ion Ground wires are used only within a short distance of the substations, so that for the vast majority of ground faults, the fault resistance is determined by the tower footing resistance. The design value of fault resistance is 300fi, although tower footing resistances of over 1000O have been measured. As a consequence of the high fault resistances, residual overcurrent protec-tion is used for ground faults. Figure 7 shows the ground fault relaying in logic-diagram form. The principal ground overcurrent device is a Westinghouse Canada type S1G-1H positive-sequence-restrained instantaneous overcurrent relay, designated 5 0 L N . This device includes three independent overcurrent elements with individ-ual setpoints (see fig. 8). The positive-sequence restraint prevents operation on load-derived zero-sequence current, such as occurs during conditions of unsymmet-rical bypass of the series capacitor bank. The high-set element, designated 50LN/IOD, is the underreaching element 61 32F 50LN1S 50LNIOD 50LNIOH 50LNI0L GFDT GFPT GRB Fig. 7. Ground-fault protection (as modelled) (Signal abbreviations are defined in table 1. Relays are described in text.) used for direct tripping in the transfer trip scheme. This element is set to pick up when 311oI - 0 - 211,| £ 1 400 A (primary) No directional supervision is used with 50LN/IOD. 62 50LN /IOD /IOH /IOL Fig. 8. Details for 50LN modelling A second element of 50LN, designated 50LN/IOH, is set to pick up when 3 1 1 o I " 0 . 2 ( 1 , 1 > 300 A ( p r i m a r y ) This is the overreaching element used in the permissive trip scheme, and is supervised by the forward directional element designated 32F. The final (low-set) element of 50LN, designated 50LN/IOL, is set to pick up when 3 | X oI " 0 . 2 | I , | £ 100 A ( p r i m a r y ) This is the reverse-blocking element used in the permissive trip scheme, and is supervised by the reverse directional element designated 32R. The forward and reverse directional elements 32F and 32R are 63 Westinghouse Canada type SRG-1H devices, potential-polarized from an auxiliary transformer with a broken-delta secondary. These devices remain muted (in the unoperated state) until the input current exceeds 50 A (primary). The muting helps prevent misoperation of the permissive trip scheme due to slow reset of 32F/R. Element 32F is set for a maximum torque angle (MTA) of -90° , with an operate zone of ± 8 5 ° about the M T A . Element 32R is set to overlap 32F, with an M T A of + 9 0 ° and an operate zone of ± 9 6 ° about the M T A . The directional element models which form the basis of the 32F/R models are of "infinite" sensitivity, viz. they do not require any threshold magnitude of current or voltage to operate. Consequently, the muting has been obtained by using an instantaneous overcurrent element to gate the current input to the directional elements (see fig. 9). This approximates the effect of finite sensitiv-ity. (Note that finite sensitivity could also have been included directly in the directional element model, making external manipulation unnecessary. It was included separately here to demonstrate the technique.) In addition to the main ground fault relaying just described, the secondary protection includes an extra inverse-time overcurrent relay, A S E A type RRIDE-41, designated 50LN1S. This relay has a "very-inverse" characteristic with a time dial setting of 0.13, which produces a time-overcurrent curve described by t = 1.8 / ( I - 1) s e c o n d s , where I is the ratio of input current to setting current. The setting is 200 A (primary). This relay is directionally supervised by 32F, and operates in a direct tripping mode. 64 3V0 32F out | \ control Fig. 9. Details for 32F/R modelling The combination of phase- and ground-fault protection, shown in fig. 10, is entirely straightforward. The reverse-blocking is held, once set, for a minimum of 100 ms. The transfer- and permissive-trip logic is shown, as modelled, in figs. 11 and 12. The Williston circuit breaker trip signal is obtained in the simulations as an OR combination of the Williston and G . M . Shrum transfer-trip outputs from the permissive trip block. The actual scheme logic generates the trip sig-nal somewhat differently (see appendix B , part A), although the two are logically equivalent. The transfer-trip signal is developed from the OR combination of the direct local trip (DLT) signal and the confirmed permissive trip. This latter signal is obtained from an A N D combination of the local forward permissive (LFP) signal 65 PFDT blocking memory 0 / / 1 0 0 • > msec CPT DLT GFPT Fig. 10. Phase- and ground-fault combining logic and the received permissive signal transmitted from the remote end (GMS.TTT for Williston-end protection). (Table 1 lists the signal abbreviations used in the TRP listing in appendix B and the logic drawings.) For increased security, the permissive trip logic incorporates three special features: direct local trip signals key both the permissive- and transfer-trip tones, when a permissive-trip situation is confirmed, a transfer-trip tone is keyed, and when a permissive-trip tone is received, but no local permissive 66 LFR a DLT, a N R B a PTTXh R I N B Q T E R M I N A L A TTTX a PTTX, channel delay <zzz> PTTX a TERMINAL B channel delay <zzz> Fig. 11. General structure of permissive-trip model 67 PT RINB DLT RPT LFP 4 > > TTTX PTTX Fig. 12. Detailed structure of PT block for permissive-trip model condition exists, the permissive tone is repeated provided no local blocking condition exists. This feature, designated repeat-if-no-block (RINB), permits relatively fast clearing for faults (particularly high-resistance ground faults) which do not create sufficient infeed from both ends of the line. Details of this feature are shown in fig. 13. D. ASSUMPTIONS AND OPERATING CONDITIONS FOR STUDY Frequency-dependence of the transmission-line parameters has been ignored; line constants have been computed at 60 Hz. Steady-state results should thus be correct, while aerial-mode transients should be only slightly in error. Ground-mode transients, which are significant only for ground faults, will have insufficient damping at the higher frequencies. For relays modelled with 68 T A B L E 1 List of Abbreviations for Simulation Waveforms Abbreviation Waveform CPT combined permissive trip (phase- and ground-overreaching DGOC directional ground overcurrent D L T direct local trip signal F I L T E R X delayed-dropout filter-switching control signal for 21L3 G A T E gating control signal for 32F/R input gate (to account for finite sensitivity) GFDT ground-fault direct trip logic signal GFPT ground-fault permissive trip logic signal GIAB G . M . Shrum A B delta current GIBC G . M . Shrum BC delta current GICA G . M . Shrum C A delta current G M S D L T G . M . Shrum direct local trip logic signal G M S N R B G . M . Shrum no reverse blocking logic signal G M S L F P G . M . Shrum local forward permissive logic signal GMS.IA G . M . Shrum delayed phase A current GMS.IB G . M . Shrum delayed phase B current GMS.IC G . M . Shrum delayed phase C current GMS.TTT G . M . Shrum transfer-trip transmit signal G M S . V A G . M . Shrum delayed phase A voltage G M S . V B G . M . Shrum delayed phase B voltage G M S . V C G . M . Shrum delayed phase C voltage GRB ground-fault reverse blocking logic signal G V A B G . M . Shrum delayed A B inter-phase voltage G V B C G . M . Shrum delayed BC inter-phase voltage G V C A G . M . Shrum delayed C A inter-phase voltage G3I0 gated residual current 3I 0 for input to 32R IA phase A current to L A C IAB A B delta current for 21L3 IB phase B current to L A C IBC B C delta current for 21L3 IC phase C current to L A C ICA C A delta current for 21L3 I N S D L Y insert-delay control signal for SD-2H L A C A phase A L A C output voltage L A C B phase B L A C output voltage L A C C phase C L A C output voltage L F P local forward permissive signal NG3I0 negation of G3I0 for input to 32F N R B no reverse blocking logic signal P E R M output from permissive-trip block PFDT phase-fault direct trip logic signal PFPT phase-fault permissive trip logic signal 69 T A B L E 1 (cont'd) PRB phase-fault reverse blocking logic signal P S F I L T E R positive-sequence filter output PT permissive trip P T T X permissive-trip transmit signal RB reverse blocking logic signal R E S T R A I N positive-sequence restraining voltage for 5 0 L N RINB repeat-if-no-block logic signal RPT received permissive trip signal SWQ Q-switching control signal for SD-2H T M P temporary (intermediate waveform) TMPO temporary (intermediate waveform) T M P l temporary (intermediate waveform) TTTX transfer-trip transmit signal V A phase A input voltage for 21L3 after inclusion of L A C output V B phase B input voltage for 21L3 after inclusion of L A C output V C phase C input voltage for 21L3 after inclusion of L A C output V A B A B inter-phase voltage for 21L3 V B C BC inter-phase voltage for 21L3 V C A C A inter-phase voltage for 21L3 WIAB Williston A B delta current WIBC Williston BC delta current WICA Williston C A delta current W S N D L T Williston direct local trip logic signal W S N L F P Williston local forward permissive logic signal W S N N R B Williston no reverse blocking logic signal WSN.CB Williston circuit breaker trip signal WSN.TTT Williston transfer-trip transmit signal W V A B Williston A B inter-phase voltage W V B C Williston BC inter-phase voltage W V C A Williston C A inter-phase voltage 310 residual current 3I 0 3V0 residual voltage 3 V 0 21LX 21LX outputs 21L1 21L1 output 21L1AB 21L1 "phase" A B element output 21L1BC 21L1 "phase" BC element output 21L1CA 21L1 "phase" C A element output 21L2 21L2 output 21L2AB 21L2 "phase" A B element output 21L2BC 21L2 "phase" BC element output 21L2CA 21L2 "phase" C A element output 21L3 21L3 output 21L3AB 21L3 "phase" A B element output 21L3BC 21L3 "phase" BC element output 21L3CA 21L3 "phase" C A element output 70 T A B L E 1 (cont'd) 32F 32R 50L 5 OLA 50LB 50LC 50LNIOD 50LNIOH 50LNIOL 50LN1S 32F forward directional element output 32R reverse directional element output 50L distance supervision overcurrent output 50L distance supervision phase A output 50L distance supervision phase B output 50L distance supervision phase C output 5 0 L N ground overcurrent direct trip output 50LN ground overcurrent permissive trip output 5 0 L N ground overcurrent blocking output 50LN1S secondary ground overcurrent output filters in the input circuits (such as the directional elements), the effect on opera-tion will be minimal. There should also be little effect on the ground-fault over-current relay models since the amplitude comparators used are of the integrating type, which are less sensitive to higher frequencies. Thus the overall protection performance should not be seriously affected by the constant-parameter modelling. The generator models are E " behind L ^ ' Thevenin equivalents. The effect on transients will likely be small, since this assumption is reasonably accurate for the short time span over which transients are significant. There may be some error at G . M . Shrum due to the fact that the fast static exciters have been neglected. The G . M . Shrum braking resistance has been ignored. Since this only comes into action at fault clearing, it will affect only the fault-clearing simula-tion, case H09002 . t The operating conditions for the simulations correspond to heavy load conditions for the Peace River system. The corresponding loading on 5L1 is 1200 M V A at a 95% power factor (as measured at the G . M . Shrum end). tThe various simulations are described in chapter V I . 71 The simulations are benchmark tests, intended to exercise key portions of the protection rather than reproduce some observed operating conditions. Consequently, fault resistance has been ignored for inter-phase faults, and for all ground faults near stations. This is a natural limiting case, and gives the worst-case fault conditions (maximum voltage transient, maximum fault current, and maximum time constant for the transient components of the fault current). It also results in the minimum self-polarizing voltage for the mho relays, ensur-ing maximum dependence on memory polarizing. The high tower footing resistance experienced on the Peace River system limits sensitivity to ground faults remote from the substations. Since this presents a performance limit for the ground protection (and was a major factor in the scheme design), a linear resistance of 250Q has been used for remote ground faults. The effect of ignoring the nonlinear effects of arc voltage should 72 be insignificant compared with the voltage developed across the 250O resistance. This is consistent with the recommendations of the I E E E Power System Relaying Committee (1985). The microwave channel delay between G . M . Shrum and Williston is taken to be 9 ms. The principal relays (SD-2H distance relays for phase faults, and 50LN restrained-overcurrent relay for ground faults) have been modelled using specific relay models. The remaining models (e.g. the 50L current supervisory relay, 32F/R directional relays) are generic (see chapter IV). The use of generic modelling for these less-important relays eliminated the need for detailed knowl-edge about the relays, and the dedication of a substantial amount of time to the preparation of special models. The use of generic modelling for the less-critical relays is not expected to adversely affect the simulation results. The instrument transformers have not been modelled; the effect of their omission is discussed in the following subsection. 1. Effects of Not Modelling Instrument Transformers One reason for ignoring the instrument transformers for this study is that the modelling of instrument transformers for transient simulations has received thorough study elsewhere (Wong and Humpage, 1978; Krishnamoorthy and Venugopal, 1974; Wright and Rhodes, 1974; Germay et al., 1974). It was considered unnecessary to complicate this study by including the extra detail. There are also good reasons to expect that the instrument transformer effects, described in detail in chapter IV, will not be of serious concern for the simulations described herein: 73 a. Current transformers None of the three principal causes of measurement error due to current transformers are of major concern for the studies described herein. Core saturation, the first of these causes, is unlikely to cause serious errors since the CTs were originally specified to produce no more than 10% ratio error under worst-case conditions (Hayden et al., 1971). The second principal cause of CT measurement error, the relaxation trans-ients which arise when the CT primary current is suddenly interrupted, also should not be of concern for the simulations considered here. The only situation which can cause a complete collapse in primary current is the clearing of 5L1, which does not occur in these simulations. (Load currents should mask the relaxation transients for case H09002, in which a 5L2 fault is cleared.) The third principal cause of CT measurement errors, limited frequency bandwidth, would not present a serious source of error even if it were as low as the 1 to a "few thousand" Hertz given by Chamia (1980). This is partic-ularly so when the effects of input filters, used on all of the principal relays, are taken into account. b. Capacitiue voltage transformers Neglecting ferroresonance, which can be prevented by correctly sizing the core ,of the internal magnetic V T , there are two remaining major causes of measurement errors due to capacitive voltage transformers. Relaxation transients, the first of these, are unlikely to cause serious errors for this study due to the memory polarization of the distance relays. The relaxation transients arise when a fault occurs close to the C V T location, causing the primary voltage to collapse 74 suddenly. The memory polarizing of the SD-2H ensures that the relaxation transients are insignificant with respect to the total polarizing voltage applied to the phase comparator. (Since the current is high in the "IZ-V" input circuit under fault conditions, C V T relaxation transients are not significant for this input either.) The second principal cause of C V T measurement errors, limited bandwidth, would seem the most likely to affect relay operation. For the principal relays, however, the 20 to a "few hundred" Hertz range given by Chamia (1980) is less likely to limit signals applied to the relay measuring circuitry than are the high-Q input filters and memory circuits. This effect too, then, can reasonably be ignored for the benchmark simulations used herein. Tests conducted by Hayden et al. (1971) proved that "CVT performance would not jeopardize the relay operation", supporting the above statements. 2. Use of Transient Response Processor for Protect ion Simulat ion The Transient Response Processor (TRP), described in some detail in appendix C, provides a powerful tool for the simulation of protection schemes under transient conditions. Input data (power system transient responses, gen-erally) can be from any source, the only requirements being that the data be complete (i.e. no missing pertinent information) and digitized. Typical sources would be digital simulation programs (such as the widely-popular E M T P used for this study) or digitized Transient Network Analyser (TNA) waveforms or fault recordings. The design of the TRP is such that, with the provision of suitable library software (user functions), the T R P command language can serve as a high-level 75 simulation language. This feature has been used, along with a comprehensive library of protective relay models, to permit the TRP to function as a sophis-ticated transient protection simulator.! A number of TRP user functions have been added to allow modelling the protection. Two types of functions have been provided: processing functions to provide the logical operations A N D , OR, and NOT, and model functions which simulate an R L C filter, delayed pickup/dropout timer, positive-sequence filter, the permissive-trip logic (including the transfer-trip logic, since the two are cross-coupled in the Peace River scheme), load-angle compensator, and the directional, inverse-time over-current, instantaneous overcurrent (obtained as an option of the inverse-time overcurrent model), restrained overcurrent, SDX-1H, and SD-2H relays and relay elements. Two approaches have been used with the model functions. In some cases (e.g. SD2H, SDX1H) the TRP function represents a complete relay. This approach has generally been taken only for very specific models. In the remaining cases (e.g. directional units 32F/R, ground fault relays 50LN) the TRP function represents only a portion of the relay, several functions being used for a complete model. This approach has the advantage of flexibility, and minimizes the number of special-purpose functions required, since functional equivalents of tWhile intended for use with digital models of relays and transducers, the TRP design permits analog devices to be substituted for the digital models, provided, of course, that suitable hardware (reasonably high-speed digital-to-analog and analog-to-digital converters, wide-bandwidth high-power amplifiers, etc.) is available. This feature was not used for this research. 76 specific relays can be built up of standard functions. The first approach, howev-er, offers the greatest clarity of the final protection "program". Individual descriptions of the special TRP functions and details of the model functions may be found in appendix B . The values of the parameters used for the various relay models are listed in table 2. 3. Es tabl ishing Values for U n k n o w n Relay Parameters When collecting data for practical studies, it is inevitable that utility protection engineers will be confronted with some relay parameters which are not known. Where the needed information can be readily determined from instruction manuals or similar sources, this is certainly the best solution. Where the information cannot be obtained, however, it must be estimated with the aid of test simulations. (This is necessarily the case when doing simulations for protec-tion planning, before the protection design has been finalized.) For the simula-tions reported herein, test simulations were required to estimate memory and filter Q values for various relays. When testing for the memory and filter Q values, it was decided that they should be made no greater than was absolutely necessary to obtain correct protection performance. Test simulations showed that the directional element (32F and 32R) input filters needed a minimum value of Q = 1 to reduce the "dithering" (characteristic of block-average phase comparators subjected to high frequency transients) to acceptable amounts. Similarly, the zero-sequence filters in the ground-fault overcurrent relays were found to require a minimum value of Q = l to prevent serious transient overreach. A n interesting problem arose with the SD-2H model during tests to find 77 T A B L E 2 Parameter Values for Relay Models (Values are the same at both Williston and G . M . Shrum) (Unspecified values are model defaults) Relay TRP Model Parameter Value 21LX S D X 1 H primary phase-to-phase 360 K V undervoltage setting primary negative sequence 22.5 K V voltage setting undervoltage sequence 33% hysteresis negative sequence hysteresis 33% 21L1 SD2H replica impedance 35.40 replica impedance angle 85° input filter high-Q value 10 input filter low-Q value 1 memory Q value 5 delay 40 ms phase-coincidence angle 82.5° hysteresis level 33% 21L2 SD2H replica impedance 1230 replica impedance angle 85° input filter high-Q value 10 input filter low-Q value 1 memory Q value 5 delay 40 ms phase-coincidence angle 82.5° hysteresis level 33% 21L3 SD2H replica impedance 160.70 replica impedance angle 87.1° input filter high-Q value 10 input filter low-Q value 1 memory Q value 5 delay none phase-coincidence angle 82.5° hysteresis level 33% TIMER Filter dropout delay 60 ms Filter pickup delay none L A C L A C impedance setting 33.770 50L O V E R C U R R E N T . I T primary pickup setting 268 A time-multiplier setting 1 hysteresis level 33% 32F D I R E C T I O N A L 3 V Q filter Q 1 3 I Q filter Q 1 78 T A B L E 2 (cont'd) 32R O V E R C U R R E N T . I T D I R E C T I O N A L 50LN1S 50LN/IOD O V E R C U R R E N T . I T O V E R C U R R E N T . I T O V E R C U R R E N T . R 50LN/IOH O V E R C U R R E N T . R 50LN/IOL O V E R C U R R E N T . R blocking T I M E R memory timer channel delay D E L A Y permissive-trip P E R M I S S I V E logic maximum torque angle operating zone hysteresis level primary pickup setting time-multiplier setting hysteresis level 3 V Q filter Q 3 I Q filter Q maximum torque angle operating zone hysteresis level primary pickup setting time-multiplier setting hysteresis level primary pickup setting time-multiplier setting hysteresis level positive sequence restraint factor primary pickup setting maximum restraining amplitude hysteresis level positive sequence restraint factor primary pickup setting maximum restraining amplitude hysteresis level positive sequence restraint factor primary pickup setting maximum restraining amplitude hysteresis level pickup delay dropout delay delay amount A l l values are model defaults -89.5° 85° 33% 50 A 1 none 1 -89.5° 96° 33% 50 A 1 none 200 A 1000 33% 0.2 1400 A 630 A 33% 0.2 300 A 630 A 33% 0.2 100 A 630 A 33% none 100 ms 9 ms 79 Q values for the memory and "IZ-V" input filter. The memory Q had been set just large enough (Q]y[ = 5) to ensure relay operation for close-up forward faults, and relay blocking for close-up reverse faults. The "IZ-V" input filter Q was similarly set just large enough (Qpj= 10) to prevent the zone 1 underreaching elements from operating for bolted faults at the remote-end bus (due mainly to series capacitor transients). Ordinarily these values would be expected to produce correct transient coverage of the remote side of the series capacitors at Kennedy, due to the expanded mho characteristic of memory-polarized relays under transient conditions (closure to Hayden et al., 1971). The high-Q of the "IZ-V" input filter, howev-er, was found to produce such a strong memory effect that the polarizing-input memory was rendered largely ineffective. Further testing showed that the memory Q had to be increased to 50 (for an "IZ-V" filter value of Qjj = 5) in order to ensure transient coverage for the remote side of the Kennedy capacitors. The values finally used for the simulations were Q]yj = 5 and QJJ=10. These values would not have been adequate in the case of a multi-phase fault at Kennedy north, since the Williston zone 1 protection would then incorrectly operate. It was not necessary to study this fault here, however,! and for the corresponding Kennedy south fault, the bypassing of the series capacitors pushed the fault beyond the reach of the G . M . Shrum zone 1 relays anyway. This experience demonstrates the importance of either transient testing or t i t might be asked why values were not chosen which were high enough to guarantee correct behaviour for the Kennedy north fault as well. The reason is that the necessary values looked to be unreasonably large, and there was no information as to the "correct" Q values (the manufacturer's literature does not specify the values for the actual relays, and measurements were not practical). This shows the weakness of a purely empirical approach, and the importance of using any other sources of data which may be available. 80 transient simulation for proving the performance of relays using memory polarizing, t The value of 630 A used for the maximum restraining amplitude for 5 0 L N (/IOD, / IOH, and /IOD) is 20% of the maximum positive-sequence current which could flow on 5L1 for a 500 kV sending-end voltage (i.e. into a three-phase short circuit at the receiving end). Testing showed this value would produce relay operating times consistent with the specifications for 50LN. tThe same statement can probably be made for any externally-polarized mho relays, but the author has no experience to support this. C H A P T E R V I . P E A C E R I V E R S I M U L A T I O N R E S U L T S The simulations described in this chapter are selected benchmark cases for the Peace River protection. There are four principal cases: H09002-external A-phase S L G fault at the Williston end of 5L2, including clearing of 5L2. H09003—internal A-phase S L G fault on the north side of Kennedy series capacitor bank. H09012 and H I 1002—internal A B phase-to-phase fault on the south side of Kennedy series capacitor bank. H10006—external A C phase-to-phase fault on the Williston bus. Both full and reduced system models (see appendix A) have been used for the simulations. Cases H10006 and H I 1002 use the reduced system model with the equivalent south of Williston. The other cases all use the full system model. Simulation results for the two models are compared (for cases H09012 and H I 1002) at the end of the chapter. 1. Descr ipt ion of Benchmark Cases The faults in the benchmark cases were applied at a point-on-wave angle t of 143°, referenced to the fault location phase-to-ground voltage for S L G faults, or phase-to-phase voltage for inter-phase faults. This angle has the tAngle specifications used herein are based on the use of a cosine source func-tion (some authors use sine sources). 81 advantage of simultaneously producing a current offset of approximately -sin(143°)X100% = -60% and a voltage transient of -cos(143°)X 100%' = 80% (of the peak pre-fault voltage). The fault is purposely placed on the leading (rising) edge of the voltage waveform so as to be physically-plausible. Faults due to flashovers are most likely to occur during portions of the voltage cycle where the voltage is increas-ing, and within some 45° of voltage maximum (Warrington, 1968, pp. 205-7). The value of 143° used herein satisfies these requirements while producing relatively high values of both voltage and current transients. The hysteresis level for all relay models has been set at 1/3 of the max-imum output range. The effect of the hysteresis can be seen from comparison of fig. 14(a) and (b), which are for identical situations (behaviour of Williston ground-fault protection during a phase-A S L G bus fault at G . M . Shrum) except for relay hysteresis (also note the difference in scales). For the no-hysteresis case of fig. 14(a), the waveforms cross smoothly through the threshold at zero. For the hysteresis case of fig. 14(b), the waveforms jump suddenly (when the hysteresis comes into action) as they cross the threshold. Note also that hysteresis tends to maintain a state for a longer period of time (this is how hysteresis prevents "chattering" and improves noise immunity) so that the hysteresis and no-hysteresis waveforms may exhibit significant differences after the first threshold crossing. WSN 50LN/100 1 0 WSN 32R 16 24 64 72 32 40 48 56 TIME (MILL I SECONDS) H10002: EXTERNAL GMS A - G N O BUS FAULT 80 88 96 19860.315j Fig. 14(a). Ground-fault protection waveforms with no relay hysteresis. 2 0 _ WSN 50LN/IOD WSN 50LN/IOH WSN 50LN/IOL WSN 50LN1S WSN 32F -20 WSN 32R 16 24 64 72 32 40 48 56 TIME (MILLISECONDS) H10002: EXTERNAL GMS A - G N D BUS FAULT 80 68 96 19860315) Fig. 14(b). Ground-fault protection waveforms with hysteresis. Fig. 14. Example showing effect of hysteresis on relay output 84 a. Case H09012 Case H09012 is for an internal A B phase-to-phase fault on the south side of the Kennedy series capacitor bank. The large power system model was used for this simulation. The fault was applied 3.78 ms after the start of the sim-ulation. This corresponds to a point-on-wave angle of 143°, referenced to the voltage between the faulted phases, measured at the fault location. Fault resistance is ignored, t The 5L1 series capacitor protective gaps flash at 9.2 ms. The protection waveforms are shown in fig. 15(a-j). Referring to fig. 15(a), the Williston fault-detecting relay 21LX responds with a high output for the SD-2H Q-switching control signal within 3 ms of the fault, followed 35 ms later by a high output for the SD-2H pickup-delay-insertion control signal. Relays 21L1 and 21L3 remain quiescent, since the fault is a forward fault and outside of the zone 1 (direct-trip) reach. The measurement ripple can be clearly seen in the 21L3 output waveform, but at all times is well below the threshold, indicating no tendency toward false blocking on transients. The overreaching distance relay 21L2 picks up 20 ms after the fault, which is within the zone 2 reach. The clean step in output as the threshold is crossed is due to the effect of hysteresis. The distance supervision relay 50L remains high on load and fault current throughout. Referring now to fig. 15(b), all ground-fault relays (50LN/IOD, / IOH, and /IOL; and 50LN1S) correctly remain quiescent. (The directional elements 32F/R thus are inconsequential.) TNote that for this fault the arc resistance would be approximately 3-6 0 by Warrington's formula—this is comparable with the resistance of about 6 0 due to the line itself. 20 WSN 50L 85 o • -20 20 - WSN 21L1 -20 1 20 i 0 • -20 -20 -WSN 21L2 WSN 21L3 -20 • 20 • -20 • 20 • -20 • WSN 21LX Q-SWITCHING OUTPUT WSN 21LX INSERT DELRT OUTPUT 16 24 32 40 48 56 TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 R - B F R U L T RT KDY SOUTH 64 72 80 0 OHMS Fig. 15(a). Williston phase-fault protection waveforms WSN 50LN/IOD 96 19861004; 16 24 32 40 48 56 TIME (MILLISECONDS) 5L1 R - B F R U L T RT KDY S O U T H . 64 72 80 88 H 0 9 0 1 2 : 1 S . 0 OHMS Fig. 15(b). Williston ground-fault protection waveforms Fig. 15. Protection waveforms for case H09012 96 1986I004j 86 20 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 WSN PHASE FAULT DIRECT TRIP WSN GROUND FAULT OIRECT TRIP WSN PHASE FAULT PERMISSIVE TRIP WSN GROUND FAULT PERMISSIVE TRIP WSN PHASE FAULT REVERSE BLOCKING WSN GROUND FAULT REVERSE BLOCKING 16 2d 32 40 48 56 TIME (MILLISECONDS) H 0 9 0 1 2 : 5 L 1 R - B F R U L T RT KDY S O U T H . 64 72 80 8B 96 0 OHMS 19861001) Fig. 15(c). Williston phase- and ground-fault direct, permissive, and blocking sig-nals 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 WSN DIRECT LOCAL TRIP WSN LOCAL FORWARD PERMISSIVE WSN NO REVERSE BLOCKING WSN COMBINED PERMISSIVE TRIP 8 16 24 64 72 80 88 96 i_ 4 H U a U I Z : D L l H-t) l-HULI Hi KUT SOU IH. 0 OHMS I986i004j Fig. 15(d). Williston local reverse blocking and direct- and permissive-trip signals 32 40 48 56 TIME (MILLISECONDS) 0 9 0 1 2  5 1 R - B F R T RT DY S TH GMS SOL GMS 21L1 GMS 21L2 GMS 21L3 GMS 21LX Q-SWITCHING OUTPUT GMS 21LX INSERT DELAY OUTPUT 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 F l -B FPULT AT KDY SOUTH. 0 OHMS i986ioo4j Fig. 15(e). G . M . Shrum phase-fault protection waveforms GMS 50LN/IOD GMS 50LN/IOH GMS 50LN/ IOL GMS 50LN1S GMS 32F 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 R - B FRULT RT KDY SOUTH. 0 OHMS i986ioo4j Fig. 15(0- G . M . Shrum ground-fault protection waveforms 20 • 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 GMS PHASE FAULT DIRECT TRIP GMS GROUND FAULT DIRECT TRIP GMS PHRSE FAULT PERMISSIVE TRIP GMS GROUNO FAULT PERMISSIVE TRIP GMS PHASE FAULT REVERSE BLOCKING GMS GROUND FAULT REVERSE BLOCKING 16 24 32 40 48 56 TIME (MILLISECONDS) H 0 9 0 1 2 : 5 L 1 R - B F R U L T RT KDY S O U T H . 64 72 80 88 96 0 OHMS 19861004, 15(g). G . M . Shrum phase- and ground-fault direct, permissive, and blocking signals 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 GMS DIRECT LOCAL TRIP GMS LOCAL FORWARD PERMISSIVE GMS NO REVERSE BLOCKING GMS COMBINED PERMISSIVE TRIP 8 16 24 32 40 48 56 „ „ „ „ ^ TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 R - B F A U L T RT KDY SOUTH 64 72 80 88 96 0 OHMS 19861004, 15(h). G . M . Shrum local reverse blocking and direct- and permissive-trip sig-nals 89 l_10 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 .0 -20 WSN PERMISSIVE TRIP TRANSMIT 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 GMS PERMISSIVE TRIP TRANSMIT WSN R E P E A T - I F - N 0 - B L 0 C K GMS REPEAT- IF-NQ-BLQCK 16 24 32 40 48 56 TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 R - B F R U L T RT KDY SOUTH 64 72 80 88 96 0 OHMS 19861004j Fig. 15(i). Permissive trip and repeat-if-no-block waveforms WSN CIRCUIT BREAKER TRIP GMS CIRCUIT BREAKER TRIP WSN TRANSFER TRIP TRANSMIT GMS TRANSFER TRIP TRANSMIT 8 16 24 32 40 48 56 _ TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 fl-B F R U L T RT KDY SOUTH 64 96 72 80 88 0 OHMS 19861004, Fig. 15(j). Transfer trip and Williston circuit breaker trip waveforms 90 Referring to fig. 15(c), both phase- and ground-fault reverse blocking correctly remains low, as do both direct-trip signals. Of the permissive-trip (overreaching) signals, only the phase-fault component responds, due to 21L2 and the supervisory relay 50L. Referring to fig. 15(d), the combined phase- and ground-fault permissive signal is high due to the phase-fault component. The lack of blocking permits this combined permissive signal to raise a loca l forward permissive signal, enabling permissive tripping from the Williston end. The direct loca l tr ip correctly remains quiescent. Figure 15(e) shows the waveforms for the G . M . Shrum phase-fault protec-tion. The 21LX Q-switching output has responded 3 ms after the fault. The zone 2 overreaching relay 21L2 picks up briefly 19 ms after the fault and then permanently 7 ms later (on phase coincidence during the next half-cycle).t The distance supervision relay 50L is held high first by load current and later by fault current. Since the fault is on the opposite (i.e. Williston) side of the Kennedy series capacitor bank, the underreaching distance relay 21L1 would ordinarily be expected to pick up. The bypassing of the series capacitors due to the flashing of the protective gaps has shifted the fault out of zone 1 reach, however, before 21L1 has had time to operate. Figure 15(f) shows the waveforms for the G . M . Shrum ground-fault protec-tion. A l l overcurrent relays properly remain quiescent. It is interesting to note that directional element 32F has been picked up by load current (ordinarily it tThe temporary dropout here and in the output of SD-2H relays in other cases was due to an oversight in the modelling- of the SD-2H relay—in the actual relay the output is latched for approximately one cycle. 91 would be muted as was the case with the Williston directional elements). Figure 15(g) shows the direct-trip, permissive-trip, and reverse blocking waveforms for G . M . Shrum-end protection. Only the p h a s e - f a u l t p e r m i s s i v e sig-nal becomes high (due to 21L2 pickup and distance supervision 50L). The combined phase- and ground-fault waveforms for G . M . Shrum are shown in fig. 15(h). The lack of reverse blocking has enabled the c o m b i n e d -p e r m i s s i v e signal (high due to the p h a s e - f a u l t p e r m i s s i v e component) to estab-lish a l o c a l f o r w a r d p e r m i s s i v e condition, enabling permissive tripping from the G . M . Shrum end. The p e r m i s s i v e - t r i p t r a n s m i t and r e p e a t - i f - n o - b l o c k signals are shown in fig. 15(i) for both Williston and G . M . Shrum. Note that the transmission of a permissive-trip signal from Williston has started timing for the G . M . Shrum r e p e a t - i f - n o - b l o c k signal. Similarly, G . M . Shrum permissive trip has started Williston r e p e a t - i f - n o - b l o c k . The Williston and G . M . Shrum t r a n s f e r - t r i p t r a n s m i t and c i r c u i t b r e a k -e r t r i p signals are shown in fig. 15(j). Since the trip is due to a permissive operation, these waveforms arise from the A N D combination of the p e r m i s s i v e -t r i p t r a n s m i t signals, as can be seen by comparison of figs. 15(i) and (j).t The Williston circuit breaker thus gets a trip command 27 ms after the fault as a result of a permissive-trip operation. tWhen making the comparison, the signal from the remote end must be delayed by the 9 ms channel propagation time before being combined with the signal from the local end. 92 b. Case H09003 Case H09003 is for an internal A-phase S L G fault on the north side of the Kennedy series capacitor bank. The large power system model was used for this simulation. The fault was applied 5.61 ms after the start of the simula-tion, corresponding to a point-on-wave angle of 143° between the faulted phase and ground. The fault resistance is 250J2. The duration of this simulation was extended to 105 ms to fully show the operation of the protection. The protection waveforms are shown in fig. 16(a-j). Apart from the operation of fault-detecting relay 21LX and the current supervision relay 50L, the Williston phase-fault relays remain quiescent, as can be seen from fig. 16(a). Referring to fig. 16(b), the directional elements 32F/R remain muted until 32F picks up 7 ms after the fault. The low-set blocking element 50LN/IOL picks up 11 ms after the fault, and the 50LN/IOH permissive element picks up 7 ms later. The fault current is too low to cause the direct-tripping 50LN/IOD element to react, and 50LN1S is too slow to be of consequence here. Since the reverse directional element 32R does not pick up, reverse blocking is inhibited in spite of 50LN/IOL, as can be seen from fig. 16(c). The g r o u n d - f a u l t p e r m i s s i v e signal is enabled by the operation of 50LN/IOH with 32F picked-up. Referring to fig. 16(d), the c o m b i n e d p e r m i s s i v e signal, enabled by the ground permissive component, raises a l o c a l f o r w a r d p e r m i s s i v e condition due to the lack of reverse blocking, thus enabling permissive tripping from the Williston end. Figure 16(e) shows no activity of the phase-fault protection at G . M . Shrum. For the ground-fault protection shown in fig. 16(0, directional I_ 1 L 2 WSN 50L 20 • 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 93 WSN 21L1 WSN 21L2 WSN 21L3 WSN 21LX Q-SWITCHING OUTPUT WSN 21LX INSERT DELAY OUTPUT 80 40 50 60 70 TIME (MILLISECONDS) H 0 9 0 0 3 : 5L1 fl-GND F A U L T RT KDY N O R T H . 90 100 110 120 2 5 0 OHMS 19861018J Fig. 16(a). Williston phase-fault protection waveforms WSN 50LN/IOD WSN 50LN/IOH WSN 50LN/ IOL WSN 50LN1S WSN 32F WSN 32R 10 20 30 80 40 50 60 70 TIME (MILLISECONDS) H 0 9 0 0 3 : 5L1 R - G N D F R U L T RT KDY N O R T H . 90 100 110 120 2 5 0 OHMS i986ioi8j Fig. 16(b). Williston ground-fault protection waveforms Fig. 16. Protection waveforms for case H09003 94 20 -20 20 WSN PHASE FAULT DIRECT TRIP WSN GROUND FAULT DIRECT TRIP L 3 -20 20 0 WSN PHASE FAULT PERMISSIVE TRIP WSN GROUND FAULT PERMISSIVE TRIP WSN PHASE FAULT REVERSE BLOCKING WSN GROUND FAULT REVERSE BLOCKING 40 50 60 70 80 TIME (MILLISECONDS) H 0 9 0 0 3 ; 5 L 1 fl-GND F A U L T AT KDY N O R T H . 90 100 110 120 2 5 0 OHMS 198E1018J Fig. 16(c). Williston phase- and ground-fault direct, permissive, and blocking sig-nals 40 20 0 -20 40 20 0 -20 40 20 0 -20 WSN DIRECT LOCAL TRIP WSN LOCAL FORWARD PERMISSIVE WSN NO REVERSE BLOCKING WSN COMBINED PERMISSIVE TRIP 80 40 50 60 70 ,_ TIME (MILLISECONDS) H 0 9 0 0 3 : 5 L 1 A - G N D F A U L T AT KDY N O R T H . 90 100 110 120 L c n u a u u j : J  H b U l - H L I H I ftUT N U K I H  2 5 0 OHMS 19861018, Fig. 16(d). Williston local reverse blocking and direct- and permissive-trip signals 95 20 GMS 50L -20 -20 • GMS 21L1 -20 • 20 - GMS 21L2 -20 • 20 • GMS 21L3 -20 • 20 • GMS 21LX Q-SWITCHING OUTPUT -20 • 20 -0 --20 -GMS 21LX INSERT DELAY OUTPUT 20 • 10 20 30 80 40 50 60 70 TIME (MILLISECONDS) H 0 9 0 0 3 : 5 L 1 R - G N D F R U L T RT KDY N O R T H . 90 100 110 2 5 0 OHMS 120 19861018j Fig. 16(e). G . M . Shrum phase-fault protection waveforms GMS 50LN/IQD -20 • 20 • GMS 50LN/IOH -20 • 20 • GMS 50LN/ IOL -20 J 20 - GMS 50LN1S -20 • 20 • GMS 32F -20 • 20 • GMS 32R l_ 6 -20; 10 20 30 BO 40 50 60 70 TIME (MILLISECONDS) H 0 9 0 0 3 : 5L1 R - G N D F R U L T RT KDY N O R T H . 90 100 UO 2 5 0 OHMS Fig. 16(f)- G . M . Shrum ground-fault protection waveforms 120 19861018j 20 -20 20 -20 20 -20 20 -20 20 -20 20 -20 GMS PHASE FAULT DIRECT TRIP 96 GMS GROUND FAULT DIRECT TRIP GMS PHASE FAULT PERMISSIVE TRIP GMS GROUND FAULT PERMISSIVE TRIP GMS PHASE FAULT REVERSE BLOCKING GMS GROUND FAULT REVERSE BLOCKING 10 20 30 40 50 60 70 80 90 100 110 120 TIME (MILLISECONDS) H 0 9 0 0 3 : 5L1 A - G N D F A U L T AT KDY N O R T H . 2 5 0 OHMS igaeioiBj 16(g). G . M . Shrum phase- and ground-fault direct, permissive, and blocking signals 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 GMS DIRECT LOCAL TRIP GMS LOCAL FORWARO PERMISSIVE GMS NO REVERSE BLOCKING GMS COMBINED PERMISSIVE TRIP 10 20 30 40 50 60 70 80 90 100 110 120 TIME (MILLISECONDS) H 0 9 0 0 3 : 5 L 1 A - G N D F A U L T AT KDY N O R T H . 2 5 0 OHMS lsaeioigj 16(h). G . M . Shrum local reverse blocking and direct- and permissive-trip sig-nals 97 1_!0 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 WSN PERMISSIVE TRIP TRANSMIT 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 GMS PERMISSIVE TRIP TRANSMIT WSN REPEAT- IF-NO-BLOCK GMS REPEAT- IF -NO-BLOCK r~ 10 20 30 80 40 50 60 70 , TIME (MILLISECONDS) H 0 9 0 0 3 : 5L1 A - G N D F A U L T AT KDY N O R T H . 90 100 110 120 2 5 0 OHMS i986ioi8j Fig. 16(i). Permissive trip and repeat-if-no-block waveforms WSN CIRCUIT BREAKER TRIP GMS CIRCUIT BREAKER TRIP WSN TRANSFER TRIP TRANSMIT GMS TRANSFER TRIP TRANSMIT 10 20 30 90 100 UO 120 2 5 0 OHMS 19861018J Fig. 16(j). Transfer trip and Williston circuit breaker trip waveforms 40 50 60 70 80 TIME (MILLISECONDS) H 0 9 0 0 3 : 5L1 A - G N D F A U L T AT KDY NORTH. 98 element 32F is initially high due to load current. Only the low-set blocking element 50LN/IOL picks up, 39 ms after the fault. Since the reverse directional element is low, however, no reverse blocking will result, as can be seen from fig. 16(g). It is also clear from this and the following figure that none of the G . M . Shrum elements have detected the fault. Ordinarily this would mean that the fault would have to be cleared by the secondary ground-overcurrent relay 50LN1S, which is very slow to operate for this level of current. The repeat-if-no-block feature, however, allows the Williston permissive-trip transmit signal to cause a trip after being repeated from the G . M . Shrum end, as can be seen in fig. 16(i). Thus the breaker is tripped locally at Williston, with a transfer-trip to G . M . Shrum, 91 ms after the fault. This shows the advantage of the repeat-if-no-block feature. c. Case HI 0006 Case H10006 is for an external A C phase-to-phase fault on the Williston bus, immediately behind the Williston-end protection. The reduced power-system model was used for this simulation. The fault was applied at 7.04 ms, corresponding to a point-on-wave angle of 143° between the faulted-phase vol-tages. Fault resistance is ignored. The protection waveforms are shown in fig. 17(a-j). The Williston fault-detecting relay 21LX responds with a high Q-switching control signal within 2 ms of the fault, as can be seen from fig. 17(a). The reverse blocking dis-tance relay 21L3 picks up temporarily 10 ms after the fault, and permanently 8 ms later on the next half-cycle phase coincidence. The distance supervision WSN SOL l_ ' L 2 99 16 24 64 72 32 40 48 56 TIME (MILLISECONDS) H 1 0 0 0 6 : E X T E R N A L WSN A - C B U S F A U L T 80 88 96 19861004j Fig. 17(a). Williston phase-fault protection waveforms WSN 50LN/IOD 64 32 40 48 56 TIME (MILLISECONDS) E X T E R N A L WSN A - C BUS F A U L T 80 16 24 H 1 0 0 0 6 : Fig. 17(b). Williston ground-fault protection waveforms Fig. 17. .Protection waveforms for case H10006 96 19861004, 100 WSN PHASE FAULT DIRECT TRIP WSN GROUND FAULT DIRECT TRIP 20 0 -20 20 0 -20 20 0 -20 20 0 -20 2 0 . WSN PHASE FAULT REVERSE BLOCKING WSN PHASE FAULT PERMISSIVE TRIP WSN GROUND FAULT PERMISSIVE TRIP 0 -20 2 0 . WSN.GROUND FAULT REVERSE BLOCKING 0 -20 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H I 0 0 0 6 : E X T E R N A L WSN A - C BUS F A U L T isseipou 17(c). W i l l i s t o n p h a s e - a n d g r o u n d - f a u l t d i rec t , p e r m i s s i v e , a n d b l o c k i n g s i g -n a l s WSN DIRECT LOCAL TRIP 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 WSN LOCAL FORWARD PERMISSIVE WSN NO REVERSE BLOCKING WSN CQMBINEO PERMISSIVE TRIP 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H 1 0 0 0 6 : E X T E R N A L WSN A - C BUS F A U L T i986ioo4j 17(d). W i l l i s t o n loca l r e v e r s e b l o c k i n g a n d d i rec t - a n d p e r m i s s i v e - t r i p s i g n a l s 101 GMS 50L GMS 21L1 GMS 21L2 GMS 21L3 GMS 21LX 0-SWITCHING OUTPUT GMS 21LX INSERT DELAY OUTPUT I 0 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H 1 0 0 0 6 : E X T E R N A L WSN A - C BUS F A U L T Fig. 17(e). G . M . Shrum phase-fault protection waveforms GMS 50LN/IOD GMS 50LN/ I0H 19861004) GMS 50LN/ IOL GMS 50LN1S GMS 32F GMS 32R 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H I 0 0 0 6 : E X T E R N A L WSN A - C B U S F A U L T i986ioo4j Fig. 17(f). G . M . Shrum ground-fault protection waveforms 20 0 -20 20 0 -20 20 0 -20 20 GMS PHASE FAULT DIRECT TRIP 1 0 2 GMS GROUND FAULT OIRECT TRIP GMS PHASE FAULT PERMISSIVE TRIP GMS GROUND FAULT PERMISSIVE TRIP -20 20 1 GMS PHASE FAULT REVERSE BLOCKING -20 20 -20 GMS GROUND FAULT REVERSE BLOCKING 16 24 64 72 32 40 48 56 TIME (MILLISECONDS) H 1 0 0 0 6 : E X T E R N A L WSN A - C B U S F A U L T 80 88 96 19861004) Fig. 17(g). G . M . Shrum phase- and ground-fault direct, permissive, and blocking signals 40 -20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 GMS DIRECT LOCAL TRIP GMS LOCAL FORWARD PERMISSIVE GMS NO REVERSE BLOCKING GMS COMBINED PERMISSIVE TRIP 8 16 24 64 72 32 40 48 56 TIME (MILLISECONDS) H 1 0 0 0 6 : E X T E R N A L WSN A - C B U S F A U L T 80 88 96 i_ 8 l U U U b : t l t K N H  b  H - L tS b r H  I I986l004j Fig. 17(h). G . M . Shrum local reverse blocking and direct- and permissive-trip sig-nals 103 1_ 9 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 WSN PERMISSIVE TRIP TRANSMIT 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 GMS PERMISSIVE TRIP TRANSMIT WSN REPEAT- IF -NO-BLOCK GMS REPEAT- IF -NO-BLOCK 16 24 H 1 0 0 0 6 : 64 72 32 40 48 56 TIME (MILLISECONDS) EXTERNAL WSN A-C BUS FAULT 80 88 96 19861004j Fig. 17(i). Permissive trip and repeat-if-no-block waveforms WSN CIRCUIT BREAKER TRIP GMS CIRCUIT BREAKER TRIP WSN TRANSFER TRIP TRANSMIT GMS TRANSFER TRIP TRANSMIT 16 24 64 72 32 40 48 56 TIME (MILLISECONDS) EXTERNAL WSN A-C BUS FAULT 80 88 96 L i o H 1 0 0 0 6 : L I t K H b  H L tS b rH I 19861004, Fig. 170. Transfer trip and Williston circuit breaker trip waveforms 104 relay 50L is high throughout. Note that there is a slight tendency for 21L2 to operate on transients until the insert-delay control signal from the 21LX causes the insertion of a pickup delay. A l l ground-fault relays remain quiescent, as can be seen from fig. 17(b). The combination of 50L and 21L3 high produce a phase-fault reverse b lock ing condition, shown in fig. 17(c). This causes the no reverse b lock ing signal in fig. 17(d) to drop low and hold. (Note that the 100 ms blocking memory prevents the temporary dropout of the phase-fault reverse b lock ing from causing the no reverse b lock ing signal to reset high.) The G . M . Shrum fault-detecting relay 2 1 L X produces a high Q-switching control signal 3 ms after the fault, as can be seen in fig. 17(e). The overreaching distance element 21L2 picks up temporarily 18 ms after the fault and permanently 7 ms later. Note the slight residual tendency of 21L1 to overreach on the series capa-citor transient. N L R makes this tendency clearly visible, showing that it is too little to be of concern. The overreaching tendency could be investigated for other fault conditions (point-on-wave angle, etc.); the relative effect of each condition could be easily seen from the relative levels of the 21L1 response. Without N L R , this kind of comparison would require the evaluation of several internal signals from each of the three phase elements of 21L1. The task can become unmanageable. The reader is referred to the statements by Muller quoted on page 20. The G . M . Shrum ground-fault protection remains quiescent, as can be seen from fig. 17(f). Note the effect of the high-frequency transients on the response 105 of 32F/R, producing the characteristic dithering behaviour of the block-average phase comparator. (Recall that the actual directional elements use a block-instantaneous comparator, which will exhibit a repetitive resetting behaviour under these conditions.) The dithering could have been further reduced by using higher-Q input filters. Dithering is more pronounced with the truncated system model than with the full system model, due to the accentuated reflection trans-ients. Figure 17(g) shows the p h a s e - f a u l t p e r m i s s i v e signal which has been enabled by the combination of 21L2 and the 50L distance supervision. The misoperation tendency of 21L1 is also visible, in the p h a s e - f a u l t d i r e c t t r i p sig-nal. It is this ability of N L R to propagate problem indicators through the scheme logic which makes it so powerful. Only a few of the final signals need be monitored to detect a potential problem, thus permitting a "wide angle" view of protection operation without missing critical details. Where a potential problem is identified, it can be traced back up the logic path in subsequent simulations, "zooming in" on the problem area. This permits a maximum of information to be gleaned from a minimum of waveforms, while reducing user-interpretation to a reliable minimum. Only with the use of N L R is this possible. . The p h a s e - f a u l t p e r m i s s i v e signal enables the c o m b i n e d p e r m i s s i v e sig-nal, which together with the n o r e v e r s e b l o c k i n g establishes a l o c a l f o r w a r d p e r m i s s i v e condition, enabling permissive tripping from the G . M . Shrum end. A l l of this is visible in fig. 17(h). The resulting tripping signals are visible in figures 17(i) and (j). A permissive-trip signal is transmitted from G . M . Shrum. No corresponding 106 permissive-trip condition exists at Williston, however, so no trip condition results. Note also that the blocking at Williston inhibits the r e p e a t - i f - n o - b l o c k feature there. The G . M . Shrum t r a n s f e r - t r i p t r a n s m i t , and thence the Williston c i r c u i t b r e a k e r t r i p signal, still shows the overreaching tendency of 21L1. (The overreaching tendency, incidentally, is controlled by the "IZ-V" input filter in the SD-2H unit, which has been switched into a high-Q state by the operation of 21LX). N L R has permitted the overreaching tendency to be carried through to the final, circuit-breaker trip signal. N L R clearly shows that whatever risk there is to protection security for this fault condition derives from the 21L1 overreaching tendency. It is worth noting at this point that N L R is especially valuable for establishing protection security, which is critical to the stability of power system operation and continuity of supply. Horowitz, in a Special Report for CIGRE Group 34 (1980), stated: The balance between dependability . . . and security . . . has always been biased towards tripping. This is now seriously being called into review and slower tripping (although less false trip [sic]) may be on the horizon. d. Case H09002 Case H09002 is for an external A-phase S L G fault at the Williston end of 5L2. The full power system model was used for this" simulation. The sim-ulation was continued through to clearing of the fault. The protection operating times for 5L2 were determined from the simulation of an identical fault on 5L1 , using the 5L1 protection model. A n omission was subsequently discovered in the protection model, which produced optimistically-fast operation. This was corrected 107 for H09002 but the clearing times for 5L2 were not adjusted. Hence 5L2 clearing is unrealistically prompt. The times used were 26.3 ms to Williston breaker opening after fault initiation, with a 10 ms transfer trip time to G . M . Shrum. The fault was applied at 5.64 ms after the start of simulation. The protection waveforms are shown in fig. 18(a-j). Inspection of fig. 18(a) shows Williston 2 1 L X pickup some 2 ms after the fault. A very small tendency to mis-operate is shown by 21L2. Figure 18(b) shows the Williston ground-fault protection waveforms. Note that directional element 32R correctly picks up after fault inception and holds until the fault is cleared by the Williston-end 5L2 breaker. Low-set relay 50LN/IOL picks up shortly after the fault (as 50LN/IOH very nearly does also). After the fault is cleared from the Williston end, ground-permissive relay 50LN/IOH picks up and holds until the fault is cleared at the G . M . Shrum end as well. The combination of 32R and 50LN/IOL activates a g r o u n d - f a u l t r e v e r s e b l o c k i n g signal during the time the fault is fed via Williston. The reversal of apparent fault direction (which occurs on clearing from Williston end) causes the combination of 32F and 50LN/IOH to activate a ground-permissive signal until the fault is finally cleared from G . M . Shrum. This is all visible in fig. 18(c). The ground-permissive signal produces a c o m b i n e d - p e r m i s s i v e signal, as can be seen in fig. 18(d). Were it not for the blocking memory, this signal would produce a l o c a l f o r w a r d p e r m i s s i v e condition at Williston which would overlap with the G . M . Shrum l o c a l f o r w a r d p e r m i s s i v e condition shown in fig. 18(h), causing an incorrect permissive-trip operation. As it is, however, the g r o u n d - f a u l t r e v e r s e b l o c k i n g condition is maintained well past the apparent l_ 1 L 2 20 -20 20 -20 20 -20 20 -20 20 -20 20 WSN 50L 108 WSN 21 LI WSN 21L2 WSN 21L3 WSN 21LX Q-SWITCHING OUTPUT -20 WSN 21LX INSERT DELAY OUTPUT o 8 H 0 9 0 0 2 : 16 2 0 32 40 48 56 TIME (MILLISECONDS) 5 L 2 A - G N D F A U L T AT WSN E N D . 64 72 80 88 2 C Y . "0 OHMS 96 1986100 3j Fig. 18(a). Williston phase-fault protection waveforms WSN 50LN/IOD 32 40 48 56 TIME (MILLISECONDS) H 0 9 0 0 2 : 5 L 2 A - G N D F A U L T AT WSN E N D . 2 C Y . 0 OHMS Fig. 18(b). Williston ground-fault protection waveforms Fig. 18. Protection waveforms for case H09002 96 19861003] 20 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 20 0 -20 WSN PHASE FAULT DIRECT TRIP WSN GROUND FAULT DIRECT TRIP WSN PHASE FAULT PERMISSIVE TRIP WSN GROUND FAULT PERMISSIVE TRIP WSN PHASE FAULT REVERSE BLOCKING WSN GROUND FAULT REVERSE BLOCKING 109 8 16 24 64 72 80 32 40 48 56 TIME (MILLISECONDS) L.3 H 0 9 0 0 2 : 5 L 2 A-GND FAULT AT WSN E N D . 2 C Y . 0 OHMS 96 19861003j Fig. 18(c). Williston phase- and ground-fault direct, permissive, and blocking sig-nals 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 WSN DIRECT LOCAL TRIP WSN LOCAL FORWARD PERMISSIVE WSN NO REVERSE BLOCKING WSN COMBINED PERMISSIVE TRIP LT 8 16 24 64 72 80 88 96 32 40 48 56 TIME (MILLISECONDS) i_ 4 H 0 9 0 0 2 : 5 L 2 A-GND FAULT AT WSN E N D . 2 C Y . 0 OHMS igaeioosj Fig. 18(d). Williston local reverse blocking and direct- and permissive-trip signals 20 • 110 GMS 50L -20 • 20- GMS 21L1 -20 • 20 - GMS 21L2 -20 -20 • GMS 21L3 U 5 l_ 6 -20 • 20 • 0 • -20-20 -0 --20-GMS 21LX O-SWITCHING OUTPUT GMS 21LX INSERT DELAY OUTPUT 8 16 24 64 72 80 32 40 48 56 TIME (MILLISECONDS) H 0 9 0 0 2 : 5 L 2 R - G N D F R U L T RT WSN E N D . 2 C Y . 0 OHMS Fig. 18(e). G . M . Shrum phase-fault protection waveforms GMS 50LN/IOD 88 96 19861003J 16 64 72 80 32 40 48 56 'T IME (MILLISECONDS) H 0 9 0 0 2 : 5 L 2 R - G N D • F R U L T RT WSN E N D . 2 C Y . 0 OHMS Fig. 18(0- G . M . Shrum ground-fault protection waveforms 88 96 19861003j. I l l 20 -20 20 -20 20 -20 20 -20 20 -20 GMS PHASE FPULT DIRECT TRIP GMS GROUND FAULT DIRECT TRIP GMS PHASE FRULT PERMISSIVE TRIP GMS GROUND FAULT PERMISSIVE TRIP GMS PHASE FAULT REVERSE BLOCKING GMS GROUND FAULT REVERSE BLOCKING 96 0 8 16 24 32 40 48 56 64 72 80 88 TIME (MILLISECONDS) H 0 9 0 0 2 : 5 L 2 R-GND FAULT RT WSN END. 2 C Y . 0 OHMS igseioosj 18(g). G . M . Shrum phase- and ground-fault direct, permissive, and blocking GMS DIRECT LOCAL TRIP signals 40 -20 -20 GMS LOCAL FORWARD PERMISSIVE 40 20 -20 GMS NO REVERSE BLOCKING GMS COMBINED PERMISSIVE TRIP 64 72 80 32 40 48 56 TIME (MILLISECONDS) 5 L 2 A-GND FAULT AT WSN END. 2 C Y . 0 OHMS 88 96 0 8 . H 0 9 0 0 2 : DL^ H-b U tH I HI VO L U  ^ LT . U S 19861003j 18(h). G . M . Shrum local reverse blocking and direct- and permissive-trip sig-nals 1 1 2 40 20 -20 WSN PERMISSIVE TRIP TRANSMIT GMS PERMISSIVE TRIP TRANSMIT 40 20 0 -20 40 20 0 -20 WSN REPEAT- IF-NO-BLOCK GMS REPEAT- IF -NO-BLOCK 40 20 0 -20 40 20 0 -20 40 20 0 -20 40 20 0 -20 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) H 0 9 0 0 2 : 5 L 2 fl-GND F A U L T AT WSN E N D . 2 C Y . 0 OHMS lgseiposj - Fig. 18(i). Permissive trip and repeat-if-no-block waveforms WSN CIRCUIT BREAKER TRIP GMS CIRCUIT BREAKER TRIP WSN TRANSFER TRIP TRANSMIT GMS TRANSFER TRIP TRANSMIT 8 16 24 32 40 48 56 - 64 72 80 88 96 TIME (MILLISECONDS) H 0 9 0 0 2 : 5 L 2 A - G N D . F A U L T AT WSN E N D . 2 C Y . 0 OHMS sraioosj Fig. 18(j). Transfer trip and Williston circuit breaker trip waveforms 113 reversal in fault direction, thereby inhibiting a local forward permissive condi-tion at Williston. This demonstrates the importance of the memory blocking feature of the Peace River protection. Referring to fig. 18(e), the G . M . Shrum 21LX fault-detecting relay can be seen to operate 3 ms after the fault. The 21L2 overreaching distance relay can be seen to have some tendency to overreach prior to the insertion of a pickup delay under the control of the 21LX insert delay control output. The G . M . Shrum ground-fault protection waveforms are shown in fig. 18(f). Forward directional element 32F is initially high due to load current, and remains high until the reversal in apparent fault direction after clearing at the Williston end of 5L2. Both low-set ground-fault relay 50LN/IOL and ground-permissive relay 50LN/IOH pick up on fault Current. The combination of 50LN/IOH and 32F establishes a ground-fault permissive signal prior to clearing at Williston, when the combination of 50LN/IOL and 32R establishes a ground-reverse blocking signal. These can be seen on fig. 18(g). Figure 18(h) shows the combined permissive signal (resulting from the ground-fault permissive signal) which, as a consequence of the no reverse blocking signal, establishes a local forward permissive condition at G . M . Shrum. (It is this situation which the Williston blocking memory is needed to protect against.) The local forward permissive condition is suspended by the reversal of apparent fault direction due to the Williston-end clearing. Figure 18(i) shows the G . M . Shrum permissive trip transmit signal which results from the local forward permissive condition. No corresponding condition exists at Williston (due to the reverse blocking memory) so that no trip 114 condition results, as can be seen in fig. 18(j). e. Case H09011 Case H09011 is for an internal 5L1 A C phase-to-phase fault at the Williston line end. The full power-system model was used. The fault was applied at 7.04 ms, corresponding to a point-on-wave angle of 143° between the faulted-phase voltages. Fault resistance is ignored. Only one set of waveforms is given for this simulation, fig. 19, which shows the characteristic timing behaviour of the phase-fault protection for a close-up fault. Note that 21L2 is the first of the SD-2H units to pick up at 13 ms after the fault, since it has the largest reach. Next to pick up is 21L1, at 16 ms after the fault. Of greatest interest here is 21L3, which picks up at 21 ms after the fault due to the offset static characteristic caused by the load angle compensator on this unit. The operation of 21L3 has been delayed by the shifted transient characteristic for reverse faults, which prevents the relay from seeing reverse faults until after decay of the memory polarizing voltage. This is exactly analogous to the expanded transient characteristic described in the closure to Hayden et al. (1971), which gives memory polarized relays extended reach for a short interval after a fault, allowing their use on series compensated lines. 115 WSN 50L l_ 3 H 0 9 0 1 1 : 5L 32 40 48 " 56 64 TIME (MILL I SECONDS) A-C FAULT AT WSN LINE END 72 80 88 96 0 OHMS 198604IO_j Fig. 19. Williston phase-fault protection waveforms for case H09011 2. Effect of System Truncat ion on Protection Response a. Case HI 1002 Case H I 1002 is a repeat of case H09012 except that the reduced power system model is used. The 5L1 voltage and current waveforms for this case, along with the corresponding waveforms for case H09012 for comparison, are shown in fig. 20(a-d). 500 0 -500 500 NV:VTlN.n (KIL0V0LTS) 116 NV:VT1N.B (KILOVOLTS) 8 16 24 32 40 48 56 64 72 80 TIME (MILLISECONDS) L . i HI 1002 : I N T E R N A L 5L1 A - B F A U L T (KDY S . 0 OHMS) Fig. 20(a). G . M . Shrum-end waveforms for H I 1002 5 0 0 ' NV:VTlS . f l (KILOVOLTS) 96 1986041 l j L 2 0 8 16 24 32 . 40 48 56 64 72 80 88 96 TIME (MILLISECONDS) HI 1002:. I N T E R N A L 5L1 A - B F A U L T (KDY S . 0 OHMS) isaeonij Fig. 20(b). Williston-end waveforms for H i 1002 Fig. 20. 5L1 waveforms for cases H11002 and H09012 NV:VT1N.R (KILGVOLTS) NV-.VT1N.B (KILOVOLTS) NV:VT1N.C (KILOVOLTS) BC:GMS. .B:5L1N.B (KILOflMPS) BC:GMS. ,C:5L1N.C (KILOHMPS) 0 B 16 24 32 40 48 56 64 72 80 88 96 • TIME (MILLISECONDS) H 0 9 0 1 2 : 5L1 R-B FRULT RT KOY SOUTH. 0 OHMS i98604 Fig. 20(c). G . M . Shrum-end waveforms for H09012 NV:VTIS.R (KILOVOLTS) NV:VT1S.B (KILOVOLTS) NV:VT1S.C (KILOVOLTS) BC:WSN. . f l :5L !S . f l (KILOHMPS) BC:WSN. . B : 5 L I S . B (KILOHMPS) BC:WSN. C :5L1S.C (KILOHMPS) 0 8 16 24 32 40 48 56 64 72 80 88 96 TIME (MILL I SECONDS) H 0 9 0 1 2 : 5L1 R-B FRULT RT KDY SOUTH. 0 OHMS 198604 Fig. 20(d). Williston-end waveforms for H09012 118 The upper three traces in each of these figures are the phase A , B, and C voltages (top to bottom), while the lower three traces are the phase currents (in the same order). Figs. 20(a) and (c) show the G . M . Shrum waveforms, while figs. 20(b) and (d) show the Williston waveforms. Comparison of the G . M . Shrum waveforms for H I 1002 in fig. 20(a) with the corresponding waveforms for H09012 in fig. 20(c) shows a distinct oscillation in the H11002 waveforms (at a frequency of approximately 600 Hz) which is absent in the H09012 waveforms. The amplitude of this oscillation is partic-ularly severe in the voltage waveforms. Comparison of the Williston waveforms of figs. 20(b) and (d) clearly shows this same difference. The distinctive oscillation is caused by reflection of fault-induced travelling waves from the power-frequency equivalent source at Williston. These reflections are incorrectly severe since the transmission lines of the actual system have been replaced by a series R L branch, which provides an impedance discontinuity which increases with frequency, behaving like a "brick wall" for high frequencies. Ordinarily, high frequency oscillations such as occur in the waveforms for case H I 1002 would be expected to cause delays in relay operation (Johns and Aggarwal, 1977). The delays would in this case be unrealistic (since the high frequency oscillation itself is unrealistic). The filters used in the 5L1 protection simulated here prevent the delays from occurring however. The values of Q for these filters were selected to ensure that the relays would operate correctly for the reduced-system model, in spite of the extreme high-frequency transient component. As a consequence, little difference was found in the operation of the protection for case H I 1002 as compared with case H09012. 119 This would not necessarily be the case with other power systems and protection however; the filtering for the SD-2H phase-fault relays is particularly heavy due to the problem with low-frequency series capacitor transients. Where only low-pass filters are used (rather than the bandpass filters used in the SD-2H), problems may be encountered with the low-frequency reflection transients characteristic of the actual system (as is the problem with the TEPCO system: Okamura et al., 1980; Kudo et al., 1985). Low-pass filtering which is effective for the artificially-high-frequency reflection transients of a truncated power system model may be inadequate for the lower-frequency transients characteristic of the actual system. Since the frequency and amplitude of reflection transients depend upon the termination details of the faulted line, the only general statement which can be made is that caution is required in modelling: it is safer to represent too much of the system than too little. Comparisons between the protection behaviour with the full and truncated power system models were also made for a 5L1 phase-to-phase fault at Williston line-end and a 5L1 S L G fault on the north side of Kennedy series capacitor station. No significant differences were noted in these cases either in the protec-tion responses or in the 5L1 waveforms. The reason for the 5L1 waveform similarity in the case of the Williston line-end phase-to-phase fault is probably due to the effective severing of the faulted phases of 5L1 from the system behind Williston (by the fault), so that the extent of that modelling is irrelevant. For the S L G fault at Kennedy, the reason for the similarity was probably the high ground-fault resistance, which reduced the magnitude of fault-induced trans-ients as compared with the power-frequency voltages and currents. This was not pursued further since the lack of frequency dependence for ground mode propagation would result in incorrectly-low damping of the high frequencies, that the apparent differences between the 5L1 waveforms for the full and truncated models would be greater than is actually the case. The lack of frequency-dependent modelling is not a significant concern for phase faults. C H A P T E R VI I . C O N C L U S I O N A. DIFFICULTY OF CREATING POWER SYSTEM AND RELAY MODELS Power system models for simulation of transient conditions can be time-consuming to prepare, due particularly to the difficulty of assembling the necessary data. This data is much more extensive than that required for the more-conventional fault, power-flow, and stability simulations. Fortunately it is becoming relatively common to do lightning and switching-surge studies using digital simulation, so that some system models may already be available. Where this is the case, a great deal of effort can be saved in setting up the transmission system, although some modelling improvement may be required in the immediate study area. The operating conditions will likely have to be adjusted in any case, so that considerable effort can still be required. Altering system operating conditions can be tedious, since many (if not all) Thevenin equivalents will require some adjustment, at least of the voltage. The fault levels must then be matched to conventional fault study results, and the pre-fault power flows must be matched to power-flow program results, so that several man-days can easily be required. The major problem generally lies with the preparation and testing of any required multi-bus Thevenin equivalents. This can take as much as one or two man-days even for a two-bus equivalent. The need for multi-bus equivalents decreases where the system is largely radial—the usual situation for major new generation, where extensive studies are most likely to be required. Since new transmission line models are always prepared from raw data, it is reasonable to allow at least half a man-day for each set of coupled lines 121 122 required. Where transient-event simulations are being conducted for the first time, the task of compiling the necessary data can be enormous. Once this has been done, however, the resulting system model can be updated from year to year along with the usual fault-study, power-flow, and stability models. The advan-tages of "base case" data files are as great here as for the more-conventional simulations. The author prepared the full-system B.C. Hydro model used for the sim-ulations of chapter V I by piecing together transmission from separate switching-study data cases, adding or deleting transmission lines as required to obtain the system representation for the desired study year, and then preparing the necessary Thevenin equivalents. (Detailed comments appear in the data listings in appendix A.) Relay models can also be time-consuming to prepare. Fortunately, howev-er, relays tend to be of standard types, and are more "shareable" between utilities than power system models. Ideally, manufacturers would provide suitable FORTRAN-callable models for their relays, at least for the newer designs. It is more likely, however, that the necessary models will have to come from utilities and universities. The advantages of developing models of specific relays using a good relay test facility (capable of determining relay response to transient events) cannot be over-estimated. The best modelling always results from "closing the loop", where the performance of the model is compared with that of a representative relay under identical conditions. In most cases, however, models will have to be 123 developed with no possibility of exact comparison with a representative relay. (This was the case for the models used for the simulations of chapter VI.) Models developed without test facilities can still provide a reliable indication of the performance of the protection as a whole. A robust protection scheme cannot be sensitive to the behavioural subtleties of the relays used. Protection schemes are generally designed in terms of functional requirements for the relays. Such requirements as operating principle, setting range, speed, and, in a general way, relative insensitivity to expected transients, can be specified without going into the details of relay design. If the model relay meets the necessary functional requirements, the overall protection performance should be substantially the same as with the actual relay. In the initial stages of protection planning the functional requirements of the relays will not, in any case, be completely known (it being the point of the simulations to determine what they must be). In this case, functional modelling is entirely appropriate. Models for generic relay types (such as the overcurrent and directional element models used in this project) are relatively fast to develop, taking of the order of one or two man-weeks, or even less if they are built up of subroutines already developed for other models. Models for specific relays (such as the SD-2H model used in this project) generally take much longer, one or two man-months being a reasonable estimate even with extensive use of subroutines devel-oped for other models. Naturally, the more comprehensive the model library becomes, the faster new models can be developed. 124 B. COST OF POWER SYSTEM AND PROTECTION SIMULATION One of the advantages of N L R techniques is that the total number of simulations required is kept to a minimum. This is an important advantage, since the digital simulation of large systems is relatively expensive. Power system simulations using the University of British Columbia version of the E M T P (with dimensions increased from the general-use version) and the large power-system model took about 37 s of C P U time on the U B C Amdahl 5860 (with FPU) running M T S . Similar simulations using the smaller power-sys-tem model took about 12 s of C P U time, or 33% of the large system time. The TRP simulation of the protection system took about 30 s of C P U time, or 80% of the large system simulation time. Comparable runs on a V A X 780 running V M S showed times about 20 times greater.! As dimensioned for the simulations of chapter VI , the TRP takes approx-imately 0.6 MByte of virtual memory. This is when compiled using the I B M compiler, which assigns all variables as static in storage. Compilers which assign subroutine local variables as dynamic will use less memory. Certain aspects of the TRP are now known to be less efficient than they could be, so that the C P U times for TRP execution can be considered conservative. Nevertheless, as a general guideline, the cost of a protection sim-ulation can be considered to be approximately the same as the cost of a (well-modelled) power-system simulation. tSubsequent testing at B .C. Hydro showed that the C P U requirements for sim-ulations of the full power system model and the 5L1 protection were comparable with requirements for typical transient stability simulations. 125 C. SUMMARY OF FINDINGS The findings of this research, and the conclusions which may be drawn from them, are as follow: 1. Numerical logic replacement (NLR) is a practical method of determining the tendency of a complex protection system to misoperate for simulated faults. The operating tendencies of individual relays (as reflected in their pseudo-outputs) are propagated through the protection scheme logic to the circuit-breaker trip signal. Misoperating tendency is thus visible from a single waveform. The information which can be extracted from a single simulation is greatly increased. 2. The simulation of complex, multi-relay protection schemes on digital computers is both feasible and (for a moderate number of individual simulations) practical. The practicality is significantly improved by using N L R , since impending protection insecurity can be seen directly from the circuit-breaker trip waveforms (see discussion of case HI0006 in chapter VI). The number of simulations needed to ensure protec-tion security and dependability is thus significantly smaller than when the scheme logic is represented directly using Boolean logic. For the same reason, significantly greater confidence can be placed in the conclusions drawn from a series of simulations. 3. Protection simulation is essential to ensuring protection security. It is essential to ensuring dependability with heavily-filtered memory-polarized mho relays when the expanded reach of the transient mho circle is to be relied upon. 126 4. Simulation cost and memory requirements are moderate. Combined simulations of the power system and the protection for one transmi-ssion line require comparable C P U time to a transient stability simula-tion. As dimensioned for the simulations described in chapter VI , the protection simulator (TRP) requires less than one megabyte of virtual memory. 5. Simulated protection behaviour was found to agree generally with the known behaviour of the actual scheme, indicating that "semi-specific" modelling! for the principal fault-detecting relays and generic modelling for the remaining relays can produce satisfactory results for protection application studies. This was found to be true in spite of certain known differences between the models and the actual relay hardware, suggesting that practical protection schemes are not strongly sensitive to the subtleties of individual relay behaviour. (This does not imply, however, that relays for industrial simulations need not be modelled as carefully as is practical.) Where it is possible to compare the performance of the actual relays (using a relay test facility, for example) with the performance of the models under identical conditions, this should be done. This comparison would have been especially valuable for determining the memory and IZ-V input filter Q values for the SD-2H relays simulated for this research. These values could not be adequately t A s was used for the SD-2H, for example, where only certain portions of the relay (input filters, special output logic, etc.) were modelled directly from the actual hardware. The remaining portions of the relay (e.g. the comparator) made use of generic models. 127 determined by test simulations using the model alone. 6. Careless truncation of the power system during modelling can result in gross errors in the transient components of the simulated voltages and currents applied to the protection. The extent to which this will produce errors in the protection simulations depends on factors such as fault location, relay location, and the sharpness of relay input filters. 7. "Sequential" simulation may be successfully employed for fault applica-tion studies. (The "simultaneous" technique must be used to model feedback loops within the sequential simulation.) "Sequential" simula-tion may be used for studies of external fault application and clearing, provided that realistic clearing times have been pre-determined and included in the power system simulations (i.e. the simulations are performed in two steps). 8. Generic models of uncomplicated relays can often be developed in one or two man-weeks. This time can be reduced by making use of a library of basic relay functions (single-input amplitude comparator, memory/filter circuit, etc.). One or two man-months can be required to develop models for the specialized portions of more sophisticated, specific relays (e.g. the SD-2H), even when a library of basic relay functions is available. 9. Finite sensitivity for current inputs can be modelled by using over-current relays operating "gate" elements in the current input circuit. For models of specific relays, the sensitivity could be more-efficiently 128 included directly in the model, preferably as an adjustable parameter. D. DIRECTIONS FOR FUTURE WORK a. Numerical Logic Replacement Further work is needed to determine the best N L R implementation of devices, such as timers, which use the output of other relays as input. There is a danger in this situation that a near start-up of the controlled-device (e.g. the timer) will not be indicated in the device output. For example, if a delayed-pickup timer were specified with a pickup delay of zero, it would be completely transparent in the logic flow. If the output did not reflect the level of the N L R input, a near operation (which could be significant to decision reli-ability) might not be visible in the output. While this specific case of a timer with zero delays is improbable, substantially-similar situations may occur in practice. These situations must be identified and resolved by developing appropriate N L R implementations for controlled devices. (Although the timer implementation used herein is believed to be satisfactory, there is not yet sufficient experience with it to be completely confident.) A second area of concern is hysteresis, which tends to obscure the amount by which a relay has operated (crossed its decision threshold). This may not be a serious practical problem; it may, however, be a chronic limitation of N L R , as remains to be established. 129 b. Better Data for Use in Simulations Standard methods are needed for describing the transient behaviour of instrument transformers completely enough, to allow suitable modelling. The adoption of standard models may be required. The model parameters could then become standard device specifications. Related to the need for better instrument transformer data is the need for better burden data. This is a more difficult task, since real burdens are completely installation-dependent. Field measurements, and sensitivity studies with various degrees of modelling detail, are required in this area. c. Proven Relay Models With the superb facilities which now exist for relay testing, it is possible to develop proven, FORTRAN-callable models for popular relays. The devel-opment of such models would be of tremendous service to the industry. With wide distribution the development cost could be spread over many users. Ideally, digital models of new relays would be provided by the manufac-turers, a task simplified by the fact that almost inevitably some digital modelling will be carried out prior to the construction of a hardware prototype anyway (Muller, 1980; Chamia and Hillstrom, 1983; Engler et al., 1985). As more commercial digital relays appear on the scene, the provision of digital "models" will become simpler, and, one hopes, standard practice. Meanwhile, however, many older relay designs are in use for which models will be required. 130 d. Sensitivity Analysis for Modelling Detail Careful analysis is required of the effects of various degrees of modelling detail on relay input waveforms, and on the response of standard relay designs. Although some analysis has been already done by various researchers, there remains a need for the coordination of further research and a summary of the results. E. CONTRIBUTIONS OF THIS RESEARCH There are three principal contributions of this research: 1. Numerical logic replacement (NLR) has been shown to be a practical method for significantly increasing the information available from individual protection simulations, thus permitting a reduction in the total number of simulations required to establish protection security and dependability. 2. The simulation of comprehensive protection schemes on a digital computer has been shown to be feasible, and computation requirements for individual simulations have been shown to be moderate. 3. A digital protection simulator has been developed which is suitable for use in industrial protection simulations. LIST OF REFERENCES Aggarwal, R .K. ; and A . T . Johns. "Digital simulation techniques for testing line protection relays during 3-phase autoreclosure", Developments in Power System Protection, IEE Conference Publication No. 185, 1980, pp. 250-4. Batho, J .L . ; J .E . Hardy; and N . Tolmunen. "Series capacitor installations in the B.C. Hydro 500 K V system", IEEE Trans, on PAS, Vol. PAS-96, No. 6, November/December 1977, pp. 1767-76. Bornard, P.; P. Erhard; and M . Pavard. " M O R G A T : A digital simulator for E H V relaying scheme tests", Proc. of the Eighth Power Systems Computation Conference, Helsinki, 19-24 August 1984, Butterworths, London, pp. 1147-54. Brandwajn, V . ; and H.W. Dommel. "Simulation of turbine generators in electromagnetic transients programs", Electrical Power and Energy Systems, Vol. 1, No. 2, July 1979, pp. 118-24. Brandwajn, V.; H.W. Dommel; and I.I. Dommel. "Matrix representation of three-phase N-winding transformers for steady-state and transient studies", IEEE Trans, on PAS, Vol . PAS-101, No. 6, June 1982, pp. 1369-78. . Breingan, W.D.; M . M . Chen; and T.F. Gallen. "The laboratory investigation of a digital system for the protection of transmission lines", IEEE Trans, on PAS, Vol . PAS-98, No. 2, March/April 1979, pp. 350-67. Burk, B . J . ; and P. Hindle. Relaying the B.C. Hydro Cheekye-Dunsmuir 500 KV Transmission System. Paper presented to the Canadian Electrical Association Power System Protection Subsection, 1984 Spring Meeting, Toronto, Ontario, March 1984. Chamia, M . ; and S. Liberman. "Ultra-high speed relay for E H V / U H V transmission lines—development, design, and application", IEEE Trans, on PAS, Vol. PAS-97, No. 6, November/December 1978, pp. 2104-16. Chamia, M . "Transient behaviour of instrument transformers and associated high-speed distance and directional comparison protection", Elektra, No. 72, October 1980, pp. 115-39. Chamia, Michel; and Birger Hillstrbm. "Modern simulation techniques in the protective relaying field", ASEA Journal, Vol. 56, No. 3, 1983, pp. 28-33. t h CIGRE Group 34. General Discussion, Proc. of the 27 Session, Vol . II, CIGRE, 1978. 131 132 CIGRE Group 34. General Discussion, Proc. of the 28 Session, Vol . II, CIGRE, 1980. CIGRE Working Group 34-06. Dynamic Test Procedures for Static Line Protection. Paper 34-08, 2 8 t h Session of CIGRE, 1980. CIGRE Working Group 36-05. "Harmonics, characteristic parameters, methods of study, estimates of existing values in the network", Elektra, No. 77, 1984, pp. 35-54. Coish, R.G.; J . N . Roik; W . H . Lehn; and G.W. Swift. "Minicomputer-based performance evaluation of protective relays", Developments in Power System Protection, IEE Conference Publication No. 185, 1980, pp. 264-8. Crossley, P.A.; and P.G. McLaren. "Distance protection based on travelling waves", IEEE Trans, on PAS, Vol. PAS-102, No. 9, September 1983, pp. 2871-83. Dommel, Hermann W. "Digital computer solution of electromagnetic trans-ients in single- and multiphase networks", IEEE Trans, on PAS, Vol. PAS-88, No. 4, Apri l 1969, pp. 388-99. Douglass, D.A. "Current transformer accuracy with asymmetric and high frequency fault currents", IEEE Trans, on PAS, Vol. PAS-100, No. 3, March 1981, pp. 1006-12. Ellis, H . M . ; J .E . Hardy; A . L . Blythe, and J .W. Skooglund. "Dynamic stability of the Peace River transmission system", IEEE Trans, on PAS, Vol . PAS-85, June 1966, pp. 586-600. Reprinted in Stability of Large Electric Power Systems, Richard T. Byerly and Edward W. Kimbark, eds. I E E E Press, 1974, pp. 261-75. Engelhardt, Kar l . Personal communication with the author regarding the testing of the relays for B.C. Hydro's Peace River system. September 1985. Engler, F. ; O.E. Lanz; M . Hanggli; and G. Bacchini. "Transient signals and their processing in an ultra high-speed directional relay for E H V / U H V transmission line protection", IEEE Trans, on PAS, Vol. PAS-104, No. 6, June 1985, pp. 1463-73. Esztergalyos, J . ; M.T . Yee; M . Chamia; S. Liberman. The Development and Operation of an Ultra High Speed Relaying System for EHV Transmission Lines. Paper 34-04, 2 7 t f t Session of CIGRE, 1978. Germay, N . ; S. Mastero; and J . Vroman. Review of Ferro-resonance Phenomena in High-voltage Power System and Presentation of a Voltage Transformer Model for Predetermining Them. Paper 33-18, 25 Session of CIGRE, 1974. 133 Girgis, Adly A . ; and R. Grover Brown. " A quantitative study on [sic] fault-induced noise signals", Proc. of IEEE International Conference on Electrical Energy, 13-15 April 1981, Oklahoma City, Oklahoma, U S A (IEEE, N . Y . , 1981), pp. 57-65. "Modelling of fault-induced noise signals for computer relaying applications", IEEE Trans, on PAS, Vol. PAS-102, No. 9, September 1983, pp. 2834-41. Hayden, S.R.; K . H . Engelhardt; J . Crockett; and W.P. Duggan. "Relaying the B.C. Hydro 500 K V system", IEEE Trans, on PAS, Vol . PAS-90, No. 3, May/June 1971, pp. 1190-1200. Horowitz S.H. Special Report for Group 34 (Protection). Paper 34-00, 2 8 t h Session of CIGRE, 1980. Humpage, W.D.; K . P . Wong; M . H . Al-Dabbagh; and E.S. Mukhtar. "Dynamic simulation of high-speed protection", Proc. IEE, Vol. 121, No. 6,> June 1974, pp. 474-80. Humpage, W. Derek; K . J . Cormick; and M . H . Al-Dabbagh. "Computer sim-ulation of high-speed protection", Developments in Power System Protection, IEE, 1975, pp. 384-91. Humpage, W.D.; and K . P . Wong. "Influence of capacitor-voltage-transform-ers on the dynamic response of distance protection", Trans, of Institution of Engineers, Aust., Vol. EE14 (Electrical Engineering), No. 2, 1978, pp. 59-63. "Some aspects of the dynamic response of distance protection", Trans, of Institution of Engineers, Aust., Vol. E E 15 (Electrical Engineering), No. 2, 1979, pp. 122-9. I E E E Power System Relaying Committee. "Fault induced wave distortion of interest to relay engineers", IEEE Trans, on PAS, Vol. PAS-104, No. 12, December 1985, pp. 3574-84. Jackson, L . "Feeder protection: distance systems", Power System Protection, Vol. 2 (Systems and Models), Ch. 9, Electricity Council, Ed. Peter Peregrinus Ltd. , Stevenage, U . K . , 1981. Johns, A.T. ; and R .K . Aggarwal. "Digital simulation of faulted e.h.v. transmission lines with particular reference to very-high-speed protection", Proc. IEE, Vol . 123, No. 4, Apri l 1976, pp. 353-9. "Performance of high-speed distance relays with particular reference to travelling-wave effects", Proc. IEE, Vol . 124, No. 7, July 1977, pp. 639-46. Discussion published in Proc. IEE, Vol . 125, No. 8, August 1978, pp. 761-5. 134 Klebanowski, A . ; A . Magdziarz; Z. Zagen; J . Zydanowicz; J . Klusek; and W. Winkler. Dynamic properties of differential and phase-comparison protection. Paper 34-05, 28 Session of CIGRE, 1980. Krishnamoorthy, T.S.; and M . Venugopal. "New mathematical model for current transformers", Proc. IEE, Vol. 121, No. 8, August 1974, pp. 826-8. Kudo, Hiroyuki; Atsumi Watenabe; Kazuo Seo; Yoshifumi Ohura; and Kunio Matsuzawa. "Development of new distance relays to cope with natural frequency transients in U H V / E H V transmission systems", IEEE Trans, on PAS, Vol. PAS-104, No. 12, December 1985, pp. 3518-23. Lionetto, P.F.; G. Santagostino; I. Heller; and M . Souillard. "Transient network analyzer and high-speed static relays: an interesting applica-tion to assess transient relay performance", Developments in Power System Protection, IEE Conference Publication No. 185, 1980, pp. 245-50. Mansour, Y . ; T .G . Martinich; and J .E . Drakos. " B . C . Hydro series capa-citor bank staged fault test", IEEE Trans, on PAS, Vol . PAS-102, No. 7, July 1983, pp. 1960-9. Marsman, H . G . Tests for the Evaluation of the Performance of Distance Protection. Paper 34-01, 2 8 t h Session of CIGRE, 1980. Morched, A.S. ; and V. Brandwajn. "Transmission network equivalents for electromagnetic transients studies", IEEE Trans, on PAS, Vol. PAS-102, No. 9, September 1983, pp. 2984-94. Morched, Atef S. Identification of Load Behaviour at High Frequency using Signal Processing, Memorandum to Dr. P. Kundur (File 202.113.41), Ontario Hydro. 30 May 1985. Muller, P. Network Model as a Testing Device for Protection Systems Able to Simulate Various Types of Operating and Fault Conditions. Paper 34-02, 2 8 t h Session of CIGRE, 1980. Nakra, H .L . ; and T . H . Barton. "Three-phase transformer transients", IEEE Trans, on PAS, Vol . PAS-93, No. 6, November/December 1974, pp. 1810-19. Nicol, Tom, Ed. UBC Matrix, University of British Columbia Computing Centre, Vancouver, March 1982. Okamura, M . ; F . Andow; I. Mitani; Y . Okita; and M . Masui. "Development of new relays with significantly improved performance against badly distorted transient waveforms", IEEE Trans, on PAS, Vol. PAS-99, No. 4, July/August 1980, pp. 1426-36. 135 Peng, Z.; M.S . L i ; C Y . Wu; T.C. Cheng; and T.S. Ning. " A dynamic state space model of a M H O distance relay", IEEE Trans, on PAS, Vol. PAS-104, No. 12, December 1985, pp. 3558-64. Redfern, M . A . ; M . M . Elkateb; and E.P. Walker. " A n investigation into the effects of travelling wave phenomena on the performance of a distance relay", Developments in Power System Protection, IEE Conference Publication No. 185, 1980, pp. 269-73. Rowbottom, F.; and C R . Gillies. " A digital model of a current transformer-distance relay combination", Trans, of Institution of Engineers, Aust., Vol. EE12 (Electrical Engineering), 1976, pp. 8-14. Souillard, M . Protection of E.H.V. Long-distance Transmission Lines—Distance Measurement and Directional Functions. Special Case of Series Condenser Compensated Lines. Paper 34-09, 27^ Session of CIGRE, 1978. Swift, G.W. "The spectra of fault-induced transients", IEEE Trans, on PAS, Vol. PAS-98, No. 3, May/June 1979, pp. 940-7. Thorp, J.S.; A . G . Phadke; S.H. Horowitz; and J .E . Beehler. "Limits to impedance relaying", IEEE Trans, on PAS, Vol. PAS-98, No. 1, January/February 1979, pp. 246-60. Warrington, A .R. van C. "Reactance Relays Negligibly Affected by Arc Impedance", Electrical World, 19 September 1931, pp. 502-5. Warrington, A.R. van C. Protective Relays: Their Theory and Practice, Vol. 1, Chapman and Hall , London. Second Edition, 1968. Westinghouse Electric Corporation. Electrical Transmission and Distribution Reference Book, Westinghouse Electric Corporation, East Pittsburg, Pennsylvania. Fourth Edition, 1964. SlG-lH Positive Sequence Restrained Ground Overcurrent Relay, Publication No. I.L. H41-1107, Westinghouse Electric Corporation, March 1968. Westinghouse Canada Inc. Instructions for Type SD-1H, SD-2H, SDX-1H, and LAC-1H Relays, Publication No. I .L. H41-1302E, Westinghouse Canada Inc., Hamilton, Ontario. July 1979. Williams, A . ; and R .H . J . Warren. "Method of using data from computer simulations to test protection equipment", Proc. IEE, Vol. 131, Pt. C, No. 7, November 1984, pp. 349-56. Wong, K . P . ; and W.D. Humpage. "Capacitor-voltage-transformer modelling and response evaluations", Trans, of Institution of Engineers, Aust., Vol. EE14 (Electrical Engineering), No. 2, 1978, pp. 48-52. 136 Wright, A . ; and D.J . Rhodes. "Protective-equipment analysis using a digital computer", Proc. IEE, Vol . 121, No. 9, September 1974, pp. 1001-6. Zadeh, L . A . "Fuzzy sets", Information and Control, Vol . 8, 1965, pp. 338-53. A P P E N D I X A P O W E R S Y S T E M M O D E L A. B.C. HYDRO 500 KV SYSTEM Two power system models were used for the simulations. The "full sys-tem" model includes the bulk of the 500 kV transmission; one-line diagrams can be found in figs. 4 and 21(a-c). (A list of the station abbreviations is given in table 3.) The second, "reduced system" model consists only of the G . M . Shrum to Williston transmission (fig. 4), and uses a Thevenin equivalent for the system south of Williston. The reduced system model was used to investigate the effects of system truncation on simulation results. Transmission line models for the Peace transmission are distributed-parameter models with discrete transposition, and full mutual coupling between phases and parallel lines. Line constants are treated as constant with respect to frequency, and have been computed at 60 Hz (for proper steady-state results). The constant parameter assumption can be expected to result in damping below actual levels for ground-mode propagation. No significant errors are to be expected for aerial propagation modes. Transmission lines away from the immediate study area are modelled either as continuously-transposed distributed-parameter lines, or using coupled pi-sections. Mutual coupling has been ignored between the parallel lines connecting the B.C. Hydro system at Ingledow substation and the "equivalent" representation for the Bonneville Power Administration system at Custer and Monroe. 137 138 Fig. 21(b). Transmission system south from Kelly Lake and east to Nicola. Fig. 21. One-line diagrams for B . C . Hydro power system, as modelled. 139 Fig. 21. (c) Transmission system from Mica and Revelstoke to Nicola. The E M T P distributed-parameter line model uses linear interpolation between "past-history" values from the opposite end of the line as a part of the . solution process. This causes some interpolation error. In setting up this sim-ulation, the lengths of transmission lines in the immediate study area were adjusted slightly so that interpolation would be small, and approximately equal for both aerial and ground modes. This resulted in 5L1, 5L2, and 5L3 being 140 T A B L E 3 List of Abbreviations for Station Names Abbreviation Station Name A C K Ashton Creek Substation C H P Chapmans Series Capacitor Station C K Y Cheekye Substation C R K Creekside Series Capacitor Station C U S Custer station (Bonneville Power Administration) G L N Glenannan Substation G M S G . M . Shrum Generating Station ING Ingledow Substation K D Y Kennedy Series Capacitor Station K L Y Kelly Lake Substation M C A Mica Generating Station M D N Meridian Substation M L S McLeese Series Capacitor Station M O N Monroe station (Bonneville Power Administration) M S A Malaspina Substation NIC Nicola Substation P C N Peace Canyon Generating Station R E V Revelstoke Generating Station S E L Selkirk Substation S K A Skeena Substation T K W Telkwa Substation W S N Williston Substation modelled as 170 miles in length (about 1% low). The interpolation also limits the minimum length of distributed-parameter line representations; the transit time for the fastest mode must be at least as great as one time step for the study. Thus the length of 5L4 has been increased by about 5 km (40%), and the length of one section of 5L30 from Cheekye to Malaspina has been increased by about 0.3 km (3%). Loads, subtransmission level portions of the system, and parts of the 141 system remote from the immediate area of study (such as the Vancouver Island system, and the Bonneville Power Administration system in the United States of America) were replaced by three-phase Thevenin equivalents. These equivalents were computed at 60 Hz. In most cases, the equivalent was connected to only a single bus, so that buses were not coupled through the equivalents. This is common practice for industrial switching-surge simulations. In the case of Kelly Lake and Williston, however, single-bus equivalents were inadequate, since there would be no allowance for 230 kV transmission (not represented in detail) between the two buses (see fig. 22). A two-bus (six phase) Thevenin equivalent was used in this case. The voltages at Williston and Kelly Lake thus reflected the contribution of flows on the 230 kV transmission to the fault current. (Mutual coupling between the 230 kV and 500 kV transmission systems was not accounted for in the equivalent.) The use of equivalents is discussed in chapter IV. 1. Series Capacitors A l l series capacitor installations are for 50% compensation of the line in which they are installed, with the single exception of Creekside. Protective gaps are installed at all series capacitor installations to bypass currents of dangerously high magnitudes (Batho et al., 1977; Mansour et al., 1983). These gaps have been modelled only at Kennedy (for 5L1, 5L2, and 5L3), since for faults considered herein, gap flashing can occur only for these lines. For all other lines with series compensation, only the effective series capacitance is modelled (i.e. gap flashing is suppressed). Figure 23 shows the detailed model for the series capacitor banks in 5L1, 142 W S N T 230 kV system transmission configuration W 1 . KLY W S N two single-bus Thevenin equivalents ignores coupling through 230 kV transmission KLY W S N single two-bus Thevenin equivalent accounts for coupling through 230 kV t ransmiss ion KLY Fig. 22. Derivation of two-bus Thevenin equivalent for Williston and Kelly Lake 143 10 K V 3.20 '^JILn 2 mn 0-169n I W v 1.89 mfl 190.89 K V O.Oin 7.54 mA 0.044 mho - A / V \ rrm [( 2.45 I 1.89 m(1 190.89 KV 3 2 A 10 KV 0189/* 2 mfl nTYTL 0.044 mho 7.54 mfl 0.010 -)|- -nrm. Fig. 23. Series capacitor detail for 5L1 and 5L2 5L2, and 5L3. The main protective gap setting of 190.89 kV shown is for 5L1 and 5L2; the correct setting for 5L3 is 192.42 kV. 2. Shunt Reactors Shunt reactors are single-phase units connected in grounded-wye, except where single-pole reclosing is employed. The standard reactance value is 2040J2 per bank. Shunt reactors are installed on the associated line, rather than the bus. This distinction was made in the power system model only for 5L1 and 5L2, since for 5L1 the line current must include reactor current, and for 5L2 the reactors must be cleared when the line is cleared. For all other lines, no distinction between bus and Une end is required. 144 3. Generator Equiva lents Generators are modelled as E " behind X ^ ' , as for conventional (steady-state) fault studies. No attempt has been made to account for generation detail (governors, exciters, etc.). Time constants R / L ^ ' associated with generation are not known, but a standard value used in B.C. Hydro specifications is 0.1 s. The resistive component of generator Thevenin equivalent impedances has thus been computed to obtain a 0.1 s time constant. Braking resistance at G . M . Shrum has not been included in the power system model. 4. System Operat ing Condi t ions Operating conditions for the study correspond to heavy load conditions for Peace River generation. The resultant loading on the line under study (5L1) is 1200 M V A at a power factor of 95% (as measured at the G . M . Shrum end). The generator internal voltages E " were computed to produce power flows consistent with power flow program results for the operating condition selected. 5. Der ivat ion of Two-bus Thevenin Equivalent at Wi l l i s ton and K e l l y Lake The desired Thevenin equivalent is six-phase, and is described by the matrix equation: E" - V" = [Z] I where E" is the vector of Thevenin internal (open-circuit) phase voltages at Williston and Kelly Lake 145 \? is the vector of phase voltages observed at the external buses at Williston and Kelly Lake [ Z ] is the Thevenin impedance matrix, and T is the vector of phase currents flowing into the external buses from the equivalent. Vectors E, V \ and T are all six-element vectors, and matrix [Z] is 6X6. The six columns of [ Z ] can be computed from the results of six S L G fault solutions (one for each of the three phases at each of the two buses, see fig. 22) from a conventional (steady-state) fault analysis program. A phase " j " S L G fault produces a fault current I j and a corresponding voltage vector V" ^ . The Thevenin internal voltage E is one per unit pure positive sequence at both buses for conventional fault analysis programs. The elements of [ Z ] can then be computed from = ( E ± - V , ) / I r The Thevenin internal voltage 1! to be used for the equivalent is then computed from E = [ z ] I + V" where T is the vector of phase currents out of the equivalent under pre-fault conditions, and \7 is the vector of pre-fault voltages at Williston and Kelly Lake buses. 146 6. Derivation of Equivalent South of Williston The equivalent south of Williston is a simple three-phase single-bus Thevenin equivalent. The impedance matrix for this equivalent was obtained from fault study results for an S L G fault at Williston. The elements of the matrix were computed from the (power-frequency) positive- and zero-sequence impedances of the equivalenced network, as seen from Williston. The Thevenin internal voltage E* was computed as for the Williston/Kelly Lake equivalent, from the steady-state voltage and current at Williston. 7. Simulation Step Size and Duration The size of the time-step for the study was 65 us. The maximum theoretical study bandwidth would thus be =7.7 kHz (based on the Nyquist requirement of two samples per cycle of the highest frequency). The modelling used (e.g. assumption of frequency-independent line parameters, lack of special transformer models) does not produce accurate results over this range, however. Lack of frequency-dependent line models is the most serious cause of inaccuracies. For single line to ground faults, in particular, damping at frequencies above 60 Hz is unrealistically low, so that high-frequency effects decay much more slowly than would actually be the case. Similarly, damping at frequencies below 60 Hz is unrealistically high, so that low-frequency effects decay more rapidly than would actually be the case. Since the relay filtering greatly reduces the impact of the high and low frequencies on relay operation, however, protection performance should not be seriously affected by the use of constant-parameter modelling. Total duration of the simulation was 4.0 cycles, which was sufficient to allow the protection to operate in all but one case (for which the simulation time was extended to 6.3 cycles). 8 . Listings of Full- and Equivalent-case Data for E M T P Listings of the E M T P data for the full and reduced (equivalent south of Williston) power system models are provided in figs. 24 and 25, respectively. L i s t i n g of SH09012 at 10:46:00 on APR 12. 19S6 for CCId-BRWG Page 1 1 H09012: 5L1 A-B FAULT AT KDV SOUTH, 0 OHMS 2 60. 60. 3 3 4 63.10417-666.66667-3 - 1 0 1 00 C65.10417-666.66667-3 - 1 0 1 00 C D 6 7 c C C Complied: 19860410 Source: H09003 -INTERNAL-FAULT 8 9 10 c c c DL f a u l t on KOYISA--KOY1SB Fault resistance: 0 Ohms ' i i 12 13 c c c Point-oh-wave: 143.13 degrees of KOYIS Vab -Fault Instant: 3.7805 msec 14 14.8 18 c KOY1SAFAULT1 0.001 1 KDY1SBFAULT2 0.001 16 17 18 c c • e 19860307: GMS reactors moved from bus to SL1 and 5L2 19 20 21 c c c Peace River simulation. F u l l 1984 500KV B.C. Hydro network from Jack Sawada of B.C. Hydro, supplemented by Peace transmission li n e s extracted from a case from Brent Hughes of B.C. Hydro. 22 23 24 c c c ( A i l data applies to 1984 system, and was obtained 13 Sept. 1985.) North Coast transmission Is o r i g i n a l data. Thevenin equivalent sources for GMS, PCN, WSN, REV, ACK. NIC, MCA, 28 26 27 c c c MSA, GLN, TKW, SKA, MON, ING, SEL, CKY, and KLY were obtained from SLG f a u l t study r e s u l t s from B.C. Hydro. 38 39 30 c c c Study step s i z e Is 65 microseconds. g i v i n g a study bandwidth of about 5 KHz. Study simulation time is 67 milliseconds, corresponding to four power-frequency cycles. There are 256 31 33 33 c c c time points/cycle. Transmlsalon-1Ine lengths for Peace River transmission have 34 38 36 c c c been adjusted to produce equal past-history Interpolation requirements for both p o s i t i v e and zero sequence, so as to minimize errors caused by linear interpolation within program. 37 38 39 c c c Peace River e l e c t r i c a l network follows: 40 41 43 c c c GMS Thevenin source: (GMS-E Is GMS Internal voltage node) GMS X/R r a t i o Is based on B.C. Hydro standard CT s p e c i f i c a t i o n 43 44 45 c •Viewing for 6 . i second time constant (-> X/R"37.6999) . Thus ZS has 2.65% R added. GMS-EAGMS..A .5756 21.700 46 47 48 2GMS-EBGHS..B -S.227 .5756 21.700 3GMS-EC0MS.,C -S.227 -5.227 .5756 21.700 C 49 SO 91 C GMS shunt reactors (2 unlts--one each 5L1 and SL2) VT1N.A 5.0 2040. VT1N.B VT1N.A S3 S3 54 VtiN.C VfIN.* VT2N.A VT1N.A VT2N.B VT1N.A 55 VT2N.C VTiN.A 1 2 . . . 3 4 . . . . . ....5 6 7 . . .8. . . 9 0 1 2 . Fig. 24. Listing of E M T P data for full power system model oo L i s t i n g Of SH09012 »t 10:46:00 on APR 12. 1986 for CCId-BRWG Page 2 96 C 57 C Si. i CT is from GMS to SL IN 58 C 5LI CVT I S at VTIN . 59 C 60 "C North end sli c l o s i n g r e s i s t o r s and sw i t e n - i s o i a t i n g impedances 61 C Also used for current measurement 62 GMS..A5L1N.A 0.01 ... .1 63 GMS.-B5LIN.BOMS..A5L1N A i 64 GMS..CSLIN.CGMS..ASLIN.A 1 65 CB1N1ACB1N2AGMS..A5L1N.A 6 6 C B 1 N 1 B C B 1N2BGMS . . A5L iN! A 67 CB1N1CCB1N2CGMS..A5L1N.A 68 CSINtAVTIN.A 400. " 6 9 C B iN10VT IN! BCB IN IAVTIN.A 70 CBINtCVTtN.CCBINIAVTIN.A 71 GMS..A5L2N.AGMS..ASLIN.A 7 2 G M S . . B5L2N. 8GMS. .A5L1N A 73 GMS..C5L2N.CGMS..A5L1N.A 74 C82N1ACB2N2AGMS..A5L1N.A 7 8 C B 2 N 1 B C B 2 N 2 B G M S . . A5L iN .A 76 CB2N1CCB2N2CGMS..A5L1N.A 77 CB2N1AVT2N.ACBINIAVTIN.A " 7 8 C B 2 N i B V T 2 N . BCB iNIAVT iN ! A 79 CB2N1CVT2N.CCBINIAVTIN.A 80 C ' S i C 5 L 1 ANO 5L2 from GMS to Junction with 813 from PCN 82 C Oata length-adjusted from Brent Hughe* case, lengths 83 C In miles. Untransposed l i n e model. ' 8 4 - 1 v t i N . C L i - i ! C 6 . 5877780. 3 16988E4 26 .'66 i 6 85 -2VT1N.BL1-1.6 0.0421433.681589E4 26.00 1 6 86 -3VT1N.AL1-1.A 0.0403283.781798E4 26.00 I 6 8 7 - 4 v f 2 N . C L 2 : 1 . C 6 0399274 .95 i823E4 26!66 1 6 88 -5VT2N.6L2-1.B O.0399230.43184BE4 26.00 1 6 89 -6VT2N.AL2-1.A 0.0400232.311847E4 26.00 1 6 9 0 6 . 4 1 8 7 9 E ! 00 - 6.516^ 60-6.24886E 66-6.29476E 66 91 0.37742E 00-0.39719E 00-0.12909E-01-0.16135E 00 0.54392E 00 0.57587E 00 92 0.42676E 00-0.27482E 00 0.49348E 00-0.51708E 00-0.37640E 00-0.28544E 00 9 3 6 . 4 2 6 7 6 E 66 6.27482E 66 6.49348E 00 6.51708E 66'6.37640E 66-6.28544E 66 94 0.37742E 00 0.39719E 00-0.12909E-01 0.16135E 00-0.B4392E 00 0.57587E 00 95 0.41B79E 00 0.51633E 00-0.S062SE 00-0.4S368E 00 0.24B86E 00-0.29476E 00 " 9 6 C 97 C PCN Thevenin source: 98 C (PCN-E i s PCN Internal vol tape node) " 9 9 C P C N x/R rat ib" i s based" oh 100 C allowing for O.I second time constant (-> X/R«37.6999) 101 C Thus 2S has 2.65X R added. 1 0 2 i P C N - E A P C N . " A 2 .496994 .130 103 2PCN-EBPCN.,B -24.92 2.496994.130 104 3PCN-ECPCN. .C -24.92 -24.92 2.496994.130 i o S c 106 C PCN shunt reactors (1 u n i t ) : 107 PCN.. A 5. 2040. i O B P C N . . B 5 . 2040" 109 PCN..C 5. 2040. H O C i i i C 5 L 4 from PCN to GMS 1 2. 3. . .4. .5. . . . .6 7 B 9 0 I 2. Fig. 24 (cont'd) L i s t i n g of SH09012 at 10:46:00 on APR 12. 1986 for CCId-BRWG P a g e 3 112 C Data length-adjusted from s o l i t a r y 5L3 data from Brent 1 1 3 C H u g h e s case , lengths in ml ies . Untransposed l i n e model. 114 C Line length Increase by 40% so travel time exceeds step 115 C s i z e . i " i s c 117 -1PCN. CGMS. C 0.3229627.S31188E4 12.03 1 3 118 -2PCN..BGMS..8 0.0489283.271806E4 12.03 1 3 1 1 9 - 3 P C N . . A G M S . . A 6 . 0 4 8 8 2 3 4 . 60 i847E4 i2.03 i 3 130 0.59747E 0O-0.707I1E OO-O.41230E 00 121 0.S3479E 00 0.20486E-12 0.81240E 00 122 "6.S9747E 00 6.70711E 66-6.41230E 66 123 C 124 C 5L3 from PCN. to June t Ion ..with ..5L.1. and 5L2. from GMS '125 ' C ' Data length-adjusted from Brent Hughes case , 126 C lengths In mi les . Untransposed l ine model. 127 -1PCN. .CL3-1 ,C 0.3229627.531188E4 26.00 1 3 i ' 3 8 - 2 P C N . . B L 3 - i ! B 6 . 6 4 8 9 2 8 3 27 ifl66E4 26.66 1 3 139 -3PCN. .AL3- I .A 0.0488234.601847E4 26.00 1 3 130 0.59747E 00-0.70711E O0-0.41230E 00 131 6.53479E 00 6.26486E-12 6.81240E 66 132 0.59747E 00 0.7071 IE 00-0.41230E 00 133 c ; 134 C 5L1, 5L3, arid BL3 from junct ion to f i r s t t r a n s p o s i t i o n p o i n t . 135 C Data length-adjusted from Brent Hughes case , lengths In 136 C m i l e s . Untransposed l ine model. 1 3 7 C f r a n s p b s i t i o n occurs •^••nSlntTinoi of th is l ine sec t ion 138 C for 5L3 139 -1L3-1 .AL3-3 .A 0.8582895.000891E4 33.34 1 9 i ' 4 0 - at 3 - i . C L 3 - 2'; C 6 . 6 s i 1497.861466E4 33 .24 i 9 141 -3L3-1 .BL3-3 .B 0.0435409.941654E4 33.34 1 9 143 -4L I - I .CL1 -3 .C 0.0372253.001799E4 33.24 1 9 1 4 3 - 5 L i - i . B l i - 2 . B 6 . 6 3 2 6 2 0 5 . 26I8I6E4 33. 34 i 9 144 -6L1- I .AL1-2 .A 0.0331215.861838E4 33.34 1 9 145 -7L3-1 .CL3-3 .C 0.0484333.46I848E4 33.24 1 9 1 4 6 - 8 L 3 - i . B L 3 - 3 8 6 0398229. 131848E4 33 . 24 i 9 147 -9L2-1 .AL3-3 .A 0.0398231.091847E4 33.24 1 9 148 0.32B43E 00-0.44379E 0O-0.38S42E 00-0.31701E 00-0.48316E 00 0.33343E 00 i ' 4 9 - 6 . 38674E 66-6. 34537E -6i-6. 28830E -01 150 0.39533E O0-0.37933E O0-0.35754E 00-0.41833E-01 0.70848E-01-0.11350E 00 151 0.7S290E 00 0.26841E-01 0.21073E-Oi 1 5 3 6 . 3 3 S 3 7 E CO-6.36233E 00-6.I0221E 00 6.273iIE 00 6.64467E 66-6.29908E 66 153 -0.46379E 00 0.46756E-01 0.4476OE-01 154 0.3S68SE O0-0.13903E 00 0.42073E 00 0.44855E 00 0.47026E-02 0.53196E 00 i S 5 6 . 5 6 B 6 0 E - 6 i - 6 . 3 5 2 3 6 E 66-6.27719E 66 156 0.3206 IE 00-0.15227E-01 0.45688E 00 0.39694E-01-0.19301E 00 0.13371E-01 157 0.55685E-03 0.64382E 00 0.43423E 00 1 5 8 6 . 3 5 8 4 8 E 66 6.16766E 66 6.43398E 66-6.41918E 66-6.I0699E 00-6.5344 IE 66 159 -0.11166E-01-0.4OO51E 00-0.17I83E 00 160 0.34970E 00 0.37OO1E 00-0.82757E-01-0.43325E 00 0.39258E 00 0.29025E 00 1 6 1 - 6 . 2 1 8 7 5 E - 0 2 O.SOISBE 66-0.36355E 00 163 0.30747E 00 0.39O77E 0O-O.24091E 00 0.13323E-01 0.84531E-OI 0.13409E 00 163 0.17366E-02-0.41258E 00 0.67345E 00 1 6 4 6 . 3 4 i 4 5 E 66 6 4S603E 0O-6.36662E 66 6 44814E 66-6.34472E 00-6.26097E 66 165 0.20493E-02 0.18335E 0O-O.33728E 00 166 C 1 6 7 C 5 L 1 and 5L2 from f i r s t transpbs i t ion point to KDY ser les 1 2 3 4 . . . . 5 6 .7 . .8 9 0 1 2. Fig. 24 (cont'd) L t•11ng Of SH09012 at 10:46:00 on APR 12. 1986 for CCId'BRWO Page 4 168 C capac i tor bank. Data 1ength-adjusted from Brant Hughes 169 170 171 C case , lengths In mites. C T ranspos i t ion occurs at sending end for a l t three l i n e s . -IL1-3.BKDY1NB O.S96I780.3O0988E4 26.00 1 6 173 173 174 -2L1-2.AKDY1NA 6.0505433.631589E4 26.66 1 6 -3L1-2.CKDY1NC 0.0486283.78I798E4 26.00 1 6 -4L2-2.6K0Y2N8 0.0482274.771823E4 26.00 1 6 178 176 177 -St i - i .AKOVJNA 6.0482230.26i84BE4 26.66 1 6 -6L2-2.CK0Y2NC 0.0484232.311847E4 26.00 1 6 0.41882E O0-0.S1607E 00-0.50617E 00 0.4S229E 00-0.25116E 00-0.29485E 00 178 179 180 6.37737E TO-6.39742E 66-6. 130641:'-6i-6. 15798E 66 6.S4457E 66 6.575B9E 0.42678E OO-0.27486E 00 0.49356E O0-0.51914E O0-O.37373E 00-0.28531E 0.42678E 00 0.27486E 00 0 49356E 00 0.S19I4E 00 0.37373E 00-0.28531E 00 00 00 181 183 183 0.37737E 00 0.39742E 00-0.13064E-01 0.15798E 00-0.64457E 00 0.57589E 0.41882E 00 0.51607E OO-O.B0617E 00-0.45229E 00 0.25116E 00-0.29485E C 00 00 184 18S 186 C 5L3 from f i r s t t r a n s p o s i t i o n point to KDY s e r i e s C capac i tor bank. Oata length-adjusted from Brent Hughes C case , lengths in mi les . 187 188 189 -113-2.BkDYSNB 0.3229627.531188E4 26.66 1 3 -2L3-2.AKDY3NA 0.0489283.271806E4 26.00 1 3 -313-2.CKDY3NC 0.0488234 601847E4 26.00 1 3 190 191 193 0.59747E OO-0.7071IE OO-O.4I230E 00 0.53479E 00 0.204S6E-12 0.8I240E 00 0.59747E 00 0.70711E 00-0.41230E 00 193 194 195 C C KDY s e r i e s capac i tor bank: C D e t a i l e d s e r i e s capac i tor model with p r o t e c t i v e gap 196 197 198 C modif ied from data from Brent Hughes C 6L1 Phase A: KDY INAKD 1N0A 1.89-3 199 200 201 KD1N0AKD1N2A 0.0020.18850 KO1N2AK01N1A 3.20001.89-3 KO1N3AKD1M.AKOYtNAKO1N0A 202 203 204 KO1N0AKD1M.A 0.01007.54-343960. KDIH.A 2.4504 KD 1M.AKDY1SAKD1N0AKD1M.A 205 206 207 KDIS3AK01M.AKDYINAKD1N0A KD1S2AKD1S1AKD1N2AKD1N1A KD 1S2AKDY t SAKD1N0AK01N2A 208 209 210 C SLI Phase B: KDY1NBK01NOBK0Y1NAKD1N0A KD1N0BKD1N2BKD1NOAKD1N2A 211 212 213 KD 1N2BkblNiBkb iN2A'kb'IN i A KD1N3BKD1M.BKDY1NAKb1N0A KD1N0BKD1M.BKD1NOAK01M.A 214 215 216 KD1M.B KD IH.A KOIH.BKDY1SBKDINOAKOIMA KO1S3BKD1M.BKDY1NAK01N0A 217 218 219 KO1S2BKDIS1BK01N2AKDIN 1A KO 1S2BKDY 1SBKD1N0AKD1N2A C 5L1 Phase C: 220 221 222 KOY1NCK0INOCKDYINAKD1N0A KO1N0CKD1N2CKDINOAKD1N2A KD1N2CKD1N1CKD1N2AKDIN 1A 223 KO1N3CKD1M.CKDYINAKD1N0A Fig. 24 (cont'd) L i s t i n g of 5H09012 at 10:46:00 on APR 12, 1986 f o r CC»d'8RWG Page 5 224 KD1NOCKO1M.CKO1NOAKO1M.A 225 226 227 K01M.C KD1M.A K01M.CK0Y1SCKD1NOAKD1M.A KO 1S3CKD1M. CKDY 1NAKD 1N0A 228 229 230 C KD1S2CKD1S1CKD1N2AKDIN 1A KO 1S2CKDY 1SCKD1N0AK01N2A 231 232 233 C 5L2 Phase A : K0Y2NAKD2NOAK0Y1NAK01N0A K02NOAKD2N2AKD INOAKO 1N2A 234 235 236 KD2N2AKD2N1AKO1N2AK0IN 1A KD2N3AKD2H.AKOY1NAK01N0A KD2NOAK02M.AK01N0AKD1M.A 237 238 239 KD2M.A K01M.A K02M.AK0Y2SAK01N0AKDIMA KD2S3AKD2M. AKOY 1NAK0 1N0A 240 24 1 242 C KD2S2AKD2S1AKD1N2AKDIN 1A K02S2AK0Y2SAKDINOAKO1N2A SL2 Phase 8: 243 244 245 K0Y2N8K02NOBK0Y1NAK01N0A KD2NO8KD2N2BK01N0AKD1N2A KD2N2BKD2N1BKD1N2AKDIN 1A 246 247 248 KD2N3BK02M. BKDY 1NAKD 1N0A K02NOBK02M.BKO1NOAKD1M.A KD2M.B K01M.A 249 260 251 K02M. 8KOY2S8K0 1 NOAKD 1M . A KD2S3BK02M. BKDY 1NAKD 1N0A KD2S2BK02SI8KDIN2AKDINIA 252 253 254 C K02S2BKDY2SBK0 tNOAKD 1N2A 5L2 Phase C: KDY2NCKD2N0CKDY1NAKD1N0A 256 256 257 KD2NOCKD2N2CKD1N0AKD1N2A KD2N2CKD2N1CKD1N2AK01N1A KD2N3CKD2M. CKDY 1NAKD1N0A 258 259 260 K02NOCKD2M,CKDINOAKO1M.A KD2M.C KD1M.A KD2M.CKOY2SCKDINOAKO1M.A 261 262 263 KD2S3CK02M.CKDY1NAKD1N0A KD2S2CKD2S1CK01N2AK0IN 1A KD2S2CKDY2SCKD1NOAKD1N2A 264 265 266 c c SL3 Phase A : K0Y3NAKD3NOAKDY 1NAK0 1N0A 267 268 269 KbiNbAkbsNiAkb iNoikoIN2A K03N2AKD3N1AKD1N2AKDIN 1A K03N3AK03M.AKDY1NAKD1N0A 270 271 272 KD3NOAKD3M.A 0.01007.54-343480. KD3M.A KD1M.A K03M.AKDY3SAK03NOAK03M.A 273 274 275 K03S3AKD3M.AKOY1NAKD1N0A KD3S2AKD3S1AKO1N2AKDIN 1A KD3S2AKDY3SAK0 1 NOAKD 1N2A 2*16*" 277 278 c 5L3 Phase 8: KDY3N8K03NOBKOY1NAKD1N0A KD3NOBK03N2BKDINOAKO1N2A 2 7 9 k b 3 N 2 B K 0 3 N iBKD 1N2AKD IN IA 1 2 3 4 5. • .6 7 8 9 0 1 2. Fig. 24 (cont'd) L i s t i n g of SH09012 at 10:46:00 on APR 15, 1986 for CCId»BRWG Page 6 280 KD3N38KD3M. BKDY 1KIAKD1N0A 281 KD3N06KD3M.BKD3NOAK03M.A 282 K03M.B KD1M.A 283 K03M. BK0Y3SBKD3NOAKD3M. A 284 KD3S3BKD3M.BKDY1NAKD1N0A 289 K03S2BK03S18KD1N2AK0INIA 286 KD3S2BKDY3SBKDINOAKD1N2A 287 C 5L3 Phase C: 288 KDY3NCKD3NOCKOYINAKD1N0A 289 K03N0CKD3N2CKDINOAKD1N2A 290 KD3N2CKD3N1CKD1N2AK0IN 1A 291 KD3N3CKD3H.CKDYINAKD1N0A 292 KD3NOCKD3M.CKD3NOAKD3H.A 293 KD3M.C KD1M.A 294 KD3M.CKDY3SCKD3NOAK03M.A 299 KD3S3CKD3M.CKOYINAKD1N0A 296 KD3S2CKD3S1CKD1N2AKD1N1A 297 KD3S2CKDY3SCK0INOAKD1N2A 288 C 299 C 5L1, SL2, and SL3 from KDY series capacitor bank to second 300 C transposition point. Data length adjusted from Brent Hughes 301 C case. Untransposed l i n e model. 302 -1KDY1SBL1-S.B 0.8623947.820893E4 26.00 1 9 303 -2KDY1SAL1-6.A 0.0484478.891S13E4 26.00 1 9 304 -3K0Y1SCL1-9.C 0.0433376.011709E4 26.00 1 9. 305 -4KDY2SBL2-9.B 0.0395271.18I803E4 26.00 1 9 306 -BKDY2SAL2-S.A 0.0331209.701 827E4 26.00 1 9 307 -6K0Y2SCL2-8.C 0.0324202.761 838E4 26.00 1 9 308 -7KOY3SBL3-S.B 0.0477228.791848E4 26.00 1 9 309 -8K0Y3SAL3-S.A 0.0390226.081 847E4 26.00 1 9 310 -9K0Y3SCL3-9.C 0.0385219.921 849E4 26.00 1 9 311 0.35665E 00-0.47I71E 00-0.42982E 00-0. 447I7E 00-0 35065E 00 0 23963E 00 312 -O.37O70E-O2 0.31I96E 00-0.13818E 00 313 0.31678E 00-0.39122E 00-0.23234E 00 0. 42209E-O2 0.1723SE 00-0.22650E 00 314 -0.415S2E-03-0.66235E 00 0.345I1E 00 319 0.34197E OO-0.3351SE 00 0.13433E-01 0. 42322E 00 0.40861E 0O-0.22I79E 00 316 0.B9792E-02 0.41813E 00-0.336S7E 00 317 0.34SI2E 00-0.13700E 00 0.39685E 00 0. 39533E 00-0.14213E 00 0 52I02E 00 318 0.37371E-O2 0.8SS72E-01 0.4431OE 00 319 0.32004E 00 0.14023E-01 0.45150E 00-0. 330B3E-01-0.32729E 00-0.58562E -01 320 -d.6'7696E-62-6.38795E 6o-0.6i489E 00 321 0.34294E 00 0.16435E 00 0.38142E 00-0. 43386E 00 0.32675E-02-0.51105E 00 322 -0.96139E-01 O.322O0E 00 0.37778E 00 iii 6.32544E 00 6.32838E 0 0 - 6 . i i 3 7 7 E - 6 l - 6 . 3I404E 00 0 49650E 00 0.32316E 00 324 0.BI130E 00-0.87018E-01-0.67666E-01 325 0.30399E 00 0.38167E 00-0.2452 IE 00 0. 34340E-01 0.12210E 00 0.17703E 00 326 -6.768B2E 66-6. SB044E-61-6. 66979E-61 327 0.34319E 00 0.46080E 00-0.43738E 00 0. 37312E OO-O.40668E 0O-0.2392OE 00 328 0.33910E 00 0.58969E-01 0.57106E-01 329 C 330 C SL1, 3L2, end BLJ from second transposition point tc last 5L3 331 C transposition point. 332 C Data length-adjusted from Brent Hughes case. Untransposed 333 C 1 1 ne mode 1. 334 C Transposition a f f e c t e d at sending end of sect ion for a l l tnree 335 C jInes. 1 2. . . 3 . . . . . . . . .4. . . . . . . . .5 6 7 8 9 0 1 2. Fig. 24 (cont'd) L i s t i n g of SH09012 at 10:46:00 on APR 12. 1986 for CCId'BRWG Page 7 336 -1L1-6 .AL1-6 .A 0.8623947.820893E4 33.24 1 9 337 338 339 - 2 L 1 - 5 . C L 1 - 6 . C - 3 L 1 - 5 . B L 1 - 6 . B -4L2 -5 .AL2 -6 .A 0.0484478.891S13E4 33.24 0.0433376.011705E4 33.24 0.0395271.18I803E4 33.24 1 9 1 9 1 9 340 341 343 - 5 L 2 - 6 . C L 2 - 6 . C -6L2-S .BL2-6 .B -7L3-5 .CL3-6 .C 0.0331209.701827E4 33.24 0.0324202.76I838E4 33.24 0.0477228.7S1848E4 33.24 1 9 1 9 1 9 343 344 345 -8L3 -5 .BL3 -6 .B -9L3-5 .AL3-6 .A 0.35665E 00-0 0.0390226.081B47E4 33.24 0.0385219.921849E4 33.24 47171E 0O-0.42982E 00-0.44717E 00-0 1 9 1 9 3506SE 00 0 23963E 00 346 347 348 -0.37070E-02 0 0.31678E 00-0 -0.41552E-O3-0 3I196E 00-0.138I8E 00 39I22E 0O-0.23234E 00 0 6623SE 00 0.3431 IE 00 42209E-02 0 17235E 00-0 22630E 00 349 350 351 0.34197E 00-0 0.S9792E-02 0 0.34512E 00-0 3351SE 00 0.13433E-01 0 41813E 00-0.336S7E 00 137O0E 00 0.39685E 00 0 42322E 00 0 39333E 00-0 4086 IE 14213E 00-0 00 0 22179E S2102E 00 00 332 353 354 0.37371E-02 0 0.320O4E 00 0 -0.67096E-02-0 B5572E-01 0.44310E 00 14023E-01 0.45150E 00-0 38795E 00-0.61489E 00 33083E-OI-0 32729E 00-0 S8562E -01 355 356 357 0.34294E 00 0 -0.96139E-01 0 0.32544E 00 0 1643SE 00 0.3B142E 00-0 32200E 00 0.37778E 00 32838E 00-0.11377E-01-0 43S86E 00 0 3I404E 00 0 3267SE 49650E -02-0 00 0 5110SE 32316E 00 00 358 359 360 0.51130E 00-0 0.30399E 00 0 -0.768B2E 00-0 87018E-01-0.67666E-01 3S167E 00-0.24521E 00 0 55044E-OI-0.66979E-01 34340E-01 0 12210E 00 0 17703E 00 361 363 363 0.34319E 00 0 0.35910E OO 0. C 46080E 00-0.43738E 00 0 S8969E-0! 0.67106E-01 373I2E 00-0 40668E 00-0 23920E 00 364 365 366 C 6L1. 6L2, and 5L3 from last 5L3 t r a n s p o s i t i o n point to WSN. C Data length adjusted from Brent Hughes case . Untransposed C l ine model. Lengths in mi les . 367 368 369 C Transposl -1L1-6.AVT1S.A -2L1-6 .CVT1S.C t l o n of 5L3 e f fec ted at sending end 0.8623947.820893E4 26.00 0.0484478.B91513E4 26.00 of t h i s s e c t i o n . 1 9 1 9 370 371 372 -3L1-6.BVT1S.B -4L2-6.AVT2S.A -5L2-6.CVT2S.C 0.0433376.011705E4 26.00 0.0393271.181803E4 26.00 0.0331209.701827E4 26.00 1 9 1 9 1 9 373 374 375 -6L2-6.BVT2S.B -7L3-6.AWSN..A -8L3-6.CWSN..C 0.0324202.761838E4 26.00 0.0477228.751848E4 26.00 0.0390226.081847E4 26.00 1 9 1 9 1 9 376 377 378 -9L3-6.BWSN..B 0.35665E 00-0. -0.37070E-02 0. 0.0385219.921 4717 IE 00-0.42982E 00-0. 31196E 00-0.13818E 00 849E4 26.00 44717E 00-0. 1 9 35065E 00 0. 23963E 00 379 380 381 6.3i678E 66-6. -0.41552E-03-0. 0.O4197E 00-0. 39122E 06-0.23234E 00 6.42209E-02 0. 66235E 00 0.34511E 00 33S1SE 00 0.13433E-01 0.42322E 00 0. 17235E 4086 IE 00-0. 00-0. 22650E 2217BE 00 00 382 383 384 6.59792E-62 6. 0.34S12E 00-0. 0.37371E-02 0. 41B13E 00-0.33657E 00 13700E 00 0.3968SE 00 0. 85S72E-01 0.44310E 00 39S33E 00-0. 14313E 00 0. S2 102E 00 383 386 387 6. 32004E 66 6. -0.67096E-02-0. 0.34294E 00 0. 14623E-61 6.43I50E 66-6. 3879SE 00-0.614B9E 00 1643SE 00 0.38142E 00-0. 33083E-01-0. 43586E 00 0. 32729E 32675E-00-0. 02-0. S8362E-S1105E 01 00 388 389 390 -0.96139E-01 0. 0.32544E 00 0. 0.51130E 00-0. 32200E 66 6.3777BE 66 32838E 00-0.11377E-01-0. 87018E-01-0.67666E-01 31404E 00 0. 49650E 00 0. 32316E 00 391 O.30399E 00 0. 38167E 00-0.2452IE 00 0. 34340E-01 0. 12210E 00 0. 17703E 00 Fig. 24 (cont'd) L i s t i n g of SH09012 at 10:46:00 on APR 12, 1986 for CCId'BRWG Page B 392 -0.76BB2E OO-0.55O44E-O1-0.66979E-O1 393 394 395 0.34319E 00 0.46O8OE OO-0.43738E 00 0.37312E OO-0.40668E 00-0.23920E 0.35910E 00 O.58969E-01 O.571O6E-01 C 00 396 397 398 C South end 5L1 c l o s i n g r e s i s t o r s and swl tch- Iso la t Ing impedances C Also used for current measurement VT 1S . ACS IS 1ACB IN 1AVT 1N . A 399 400 401 VT IS.BCBIS1BCB1N1AVT1N.A VTIS.CCB1S1CCBIN 1AVTIN.A CB1S2ACB1S1AGMS..A5LIN.A 402 403 404 CB1S2BCB1SIBGMS..A5L1N.A CB1S2CCB1S1CGHS..A5LIN.A WSN..A5L1S.AGMS..ASL1N.A 1 405 406 407 WSN..B5L1S.BGMS..ASL1N.A WSN..CSL1S.CGMS..ASL1N.A VT2S.ACB2S1ACB1N1AVT1N.A 1 408 409 410 VT2S.BCB3S1BC81N1AVT1N.A VT2S.CCB2S1CCB1N1AVT1N.A C82S2ACB2S1AGMS..A5L1N.A 411 412 413 CB2S2BCB2S1BGMS•.A5L1N.A CB2S2CC82S1CGMS..ASL1N.A WSN..A5L2S.AGMS..A5L1N.A 414 415 416 WSN..B5L2S.BGMS..A5L1N.A WSN..C5L2S.CGMS•.A5L1N.A C 417 418 419 C 5L1 CT is from WSN to 5L1S C 5LI CVT Is at VTIS C 420 421 422 C WSN shunt reactors (2 u n i t s ) : WSN..A 2.5 1020. W5N..B 2.5 1020. 423 424 425 WSN..C 2.5 1020. C C 5L11 and 5L12 from WSN to f i r s t t ranspos i t ion point 426 427 428 C Data length-adjusted from Brent Hughes case , lengths in C mi les . Untransposed 1 me model. -1WSN..AL11-1A 0.5887810.4B0989E4 69.37 1 6 429 430 431 -2WSN..CL11-1C 0.0413403.201639E4 69.37 1 6 -3WSN..BL11 - IB 0.0403287.B3I800E4 69.37 1 6 -4WSN..AL12-1A 0.0395264.40I833E4 69.37 1 6 432 433 434 - 5 W S N . . C L i i - i C d.b39S226.80i849E4 69.3? 1 6 -6WSN..BL12-1B 0.0400232.571847E4 69.37 t 6 0.42956E 00-0.55248E 00-O.S1383E 00 0.43O46E 00-0.20804E 00-0.28668E 00 435 436 437 6.38234E 6b-6.39i3SE 66 6.47696E-03-6.27482E 66 6.56687E 66 6.S7S96E 0.41140E 00-0.20348E 00 0.48559E 00-0.485I9E 00-0.45062E 00-0.29318E 0.41140E 00 0.20348E 00 0.485S9E 00 0.48S19E 00 0.4S062E 00-0.29319E 00 00 00 438 439 440 6.38234E 66 6.39t35E 66 0.47696E-03 6.274B2E O0-6.S6687E 66 6.57596E 0.429S6E 00 0.B524BE 00-0.513B3E O0-0.43O46E 00 O.20B04E 00-0.28668E C 00 00 441 442 443 C 5 L i i arid 5Li2 from f i r s t t r a n s p o s i t i o n point to MLS s e r i e s C capac i tor bank. Data length-adjusted from Brent Hughes C case , lengths in mi les . Untransposed l i n e mode). 444 445 446 C t r a n s p o s i t i o n e f fec ted at sending end of th is s e c t i o n . -1L11-1CMLS1NC 0.5887810.480989E4 33.24 1 6 -2L11-1BMLS1NB 0.0413403.201639E4 33.24 1. 6 447 -3Li i - iAMLSINA 0.0403287.83180OE4 33.24 1 6 1 3 3 .4 5 .6 7 B 9 0 1 2. Fig. 24 (cont'd) Cn Cn L1st (ng of SH09012 at 10:46:00 on APR 12. 1986 for CCId-BRWG Page 9 448 -4L12-1CMLS2NC 0.0395264.401833E4 33.24 1 6 449 490 451 -5LI2-1BMLSJN8 6 0395226 80I849E4 33.24 -6L12-1AMLS2NA 0.0400232.571847E4 33.24 0.42956E O0-O.55248E 00-0.51383E 00 0.43046E 00-0 1 6 1 6 20804E 00-0 28668E 00 452 453 454 6.38234E 6b-0.39i35E 66 6.47696E-03-627482E 66 6 0.4114OE 00-0.20348E 00 0.48559E 00-0.48S19E 00-0 0.41140E 00 0.20348E 00 0.48S59E 00 0.48519E 00 0 50087E 00 0 45062E 00-0 45062E 00-0 57S96E 29319E 29319E 00 00 00 455 456 457 0.38234E 00 0.39135E 00 0.47696E-03 0.27482E 00-0 0.42956E 00 0.55248E 00-0.51383E 0O-O.43046E 00 0 C 50087E 00 0 20804E 00-0 57S96E 2S668E 00 00 458 459 460 C MLS s e r i e s capac i tor bank MLS1NAMLS1SA 18518. MLS1N8MLS1SBMLS1NAMLSISA 461 462 463 MLS1NCMLS1SCMLS1NAMLSISA MLS2NAMLS2SAMLS1NAMLS1SA MLS2NBMLS2SBMLS1NAMLS1SA 464 465 466 MLS2NCMLS2SCMLS1NAMLS1SA C C 5L11 and 5L12 from MLS s e r i e s capac i tor bank to second 467 468 469 C t r a n s p o s i t i o n p o i n t . Data length-adjusted from Brent C Hughes case , lengths In mi les . Untransposed l i n e model -1MLS1SCL11-4C 0.5887810.4B0989E4 33.24 1 6 470 471 472 -2MLS1SBL11-4B 0. 04 13403 . 201639E4 33.24 -3MLS1SAL11-4A 0.0403287.831800E4 33.24 • -4MLS2SCL12-4C , 0.0395264.401833E4 33.24 1 6 1 6 . 1 6 473 474 475 -5MLS2SBL12-4B 0.0395226.801849E4 33.24 -6MLS2SAL12-4A 0.0400232.571847E4 33.24 0.42956E 00-0.85248E O0-0.51383E 00 0.43046E 00-0. 1 6 1 6 20804E 00-0. 28668E 00 476 477 478 6.38234E 66-6.39135E 66 6.47696E-63-6.27482E 66 6. 0.41140E OO-O.20348E 00 0.48559E O0-O.48519E 00-0 0.4II40E 00 0.2O348E 00 0.48559E 00 0.48519E 00 0. S0087E 00 0. 45062E 00-0 45062E 00-0. 57596E 29319E 29319E 00 00 00 479 480 481 0.38234E 00 0.39135E 00 0.47696E-03 0.27482E 00-0. 0.42956E 00 0.55248E 00-0.51383E 00-0.43046E 00 0. C 500B7E 00 0. 20804E 00-0. 57596E 28668E 00 00 482 483 484 C 6L11 and 6L12 from second t r a n s p o s i t i o n point to KLY. Data from C Brent Hughes case , lengths In mi les . Untransposed l ine model C Transpos i t ions e f fec ted at sending end of th is s e c t i o n . 485 486 487 - IL11-4BKLY..8 0.5887810.480989E4 69.37 -2L11-4AKLY..A 0.0413403.201639E4 69.37 -3L11-4CKLY..C 0.0403287.83180OE4 69.37 1 6 1 6 1 6 488 489 490 -4L12-4BKLY..8 6.0395264.46i833E4 69.37 -6L12-4AKLY..A 0.0395226.801849E4 69.37 -6L12-4CKLY..C 0.0400232.571847E4 69.37 1 6 1 6 1 6 491 492 493 6.42956E 66-6.S5248E 66-6.5i383E 66 6.43046E 66-6 0.38234E 00-0.39135E 00 0.47696E-O3-0.27482E 00 0. 0.4114OE O0-0.20348E 00 0.48S59E 0O-0.48519E 00-0. 20804E 00-0. 500S7E 00 0. 45062E 00-0. 28668E 57S96E 29319E 00 00 00 494 495 496 6.41 HOE 00 0.20348E 00 0.4BS59E 00 0.48519E 00 0.45062E 00-0. 0.38234E 00 0.39I35E OO 0.47696E-03 0.27482E OO-O.SO087E 00 0. 0.42956E 00 O.S5248E O0-0.51383E 00-0.43046E 00 0.20804E 00-0. 29319E 57596E 28668E 00 00 00 497 498 499 C end of Peace River system C C North Coast system fo l lows: 500 501 502 C Or ig ina l data C C WSN to GLN as untransposed d i s t r i b u t e d l ine model (5L61) 503 C (Lengths In Km) Fig. 24 (cont'd) L i s t i n g of SH090IS at 10:46:00 on APR 12. 1986 for CCId'BRWG Page 10 804 -1WSN .AL61-1A .197851.49633 216658.127 3 809 -2WSN. .CL6I-IC 2.28-2.364904 635558.127 3 806 -3WSN. .BL61-1B 2.28-2.293025 460658.127 3 907 S.98060E-01-7.07107E-01-4.11569E-01 808 S.33509E-01 5.60358E-I7 8.131S2E-01 809 S.9B060E-01 7.07107E-01-4.11569E-01 810 - 1L61- 1BL61-2BWSN..AL61-IA 811 -2L6I- IAL61-2A 812 -3L61- 1CL61-2C 513 -1L61- 2CGLN..CWSN..AL61-1A 814 -2L61- 2BGLN. B 515 -3L61- 2AGLN..A 816 C 817 C GLN Thevenin equivalent 518 C (GLN Internal voltage IS zero , so Thevenin impedance 519 C Is grounded) 520 51 GLN..A -228.6998596 107075.4375 821 52 GLN..B 114.4370880 -53488.20703 522 -228.6998596 107075.4375 823 53 GLN..C 114.4370880 -53488.20703 524 114.4370880 -53488.20703 526 -228.6998596 107075.4375 826 C 527 C GLN shunt reactors (1 u n i t ) 828 GLN. .A 2005.4 829 GLN. ,B 2005.4 530 GLN. .C 2003.4 531 C 632 C GLN to TKW as untransposed d i s t r i b u t e d l ine mode) (3L62) 533 C ( lengths In Km) 834 -1GLN. .CL62-1C ' .197851.49633 316643.847 3 535 -2GLN. .BL62-1B 2.28-2.364904 635543.847 3 636 -3GLN. .AL62-1A 2.28-2.295025 460643.847 3 537 S.98060E-01-7.07107E-01-4.11569E-01 838 S.33509E-01 5.60358E-17 8.I3152E-01 839 5.98060E-01 7.07107E-0I-4.11S69E-0I 540 -1L63- 1AL62-2AGLN..CL62-IC 541 -3L63- 1CL62-2C 542 -3L63- 1BL62-2B 543 -1L62- 3BTKW..BGLN..CL62-IC 544 -3L63- 2ATKW..A 549 -3L63- 2CTKW..C 546 C 547 c TKW thevehjh equivalent 848 c (TKW Internal voltage Is zero . so Thevenin Impedance 849 c Is grounded) 680 51 TKW..A 16666666.00 34.91661073 581 82 TKW..B -8333333.000 34.91661072 852 16666666.00 34.91661073 853 S3 TKW. .C -8333333.000 34.91661072 584 -8333333.000 34.91661073 555 16666666.00 34.91661072 556 C 657 C TKW to SKA as untransposed d i s t r i b u t e d l ine modal (5L63) 558 C ( lengths In Km) 659 -1TKW. .BL63-1B .197851.49633 316647.657 3 1 2 3. . . 4 5 . .6 7 8 9 0 1 2. Fig. 24 (cont'd) cn L i s t i n g of SH09012 at 10:46:00 on APR 12. 19B6 for CCId»BRWQ Page 1 1 960 -2TKW..AL63-1A 2.28-2.364904 635547.657 3 661 -3TKW..CL63-IC 2.28-2.295025 460647.657 3 562 8.9B060E-0I-7.07I07E-01-4.11569E-01 S63 9.33S09E-01 B.6035BE-17 8.13152E-01 564 5.98O6OE-01 7.07107E-01-4.11569E-01 566 -1L63-1CL63-2CTKW. BL63- IB 566 -2L63-1BL63-2B 567 -3L63-1AL63-2A 568 -1L63-2ASKA..ATKW. BL63-1B 569 -2L63-2CSKA..C 570 -3L63-2BSKA. B 571 C 972 C SKA Thevenin equivalent Impedance 573 C (SKA-E is SKA Internal voltage node) 974 1SKA-EASKA..A 7.9583165.03 979 2SKA-EBSKA..6 -2.742-36.33 7.9583165.03 976 3SKA-ECSKA..C -2.742-36.33 -2.743-36.33 7.9583165.03 977 C end of North Coast system 678 C 979 C K e l l y Lake south aystem--remaInder of B . C . Hydro network 880 C Data from Jack Sawada case. (CRK gap- f l ash ing removed) 581 C 582 C KLY Thevenin equivalent source 883 C (KLY-E Is Internal voltage node) 884 889 C WSN-KLY coupled Thevenin equivalent impedance 886 C (KLY-E IS KLY Internal voltage node, 887 C WSN-E is WSN Internal voltage node.) 888 S1VSN-EAWSN..A 11.70095158 217.7675171 889 . 52WSN-EBWSN..B -5.362372398 -70.73513794 890 11.70091248 217.7675171 891 53WSN-ECWSN..C -5.425845146 -70.72546387 892 -5.362503082 -70.73533630 893 11.70127869 217.7674408 894 54KLY-EAKLY..A 0.6675326228 26.30413818 898 -0.3888940811 -13.06832600 896 -0.3319950104 -13.07847474 897 8.224038124 132.3419342 898 5SKLY-EBKLY..B -0.3317694664 -13.07512856 898 0.6673421860 26.30416870 600 -0.3887786865 -13.06860542 601 -2.4 18684006 -10.85663509 602 8.223999023 132.3419495 603 S6kLY-ECkLY..C -0.3888553977 -13.06842995 604 -0.3320865631 -13.07566166 609 0.6679344177 26.30412292 666 -2.457177162 -16.84912014 607 -2.418750763 -10.85673428 608 8.223999023 132.3419189 609 610 C 611 C KLY resc tors (4 u n i t s ) 612 KLY. .A 1.25 510.0 613 KLY . .B 1.25 510.0 614 KLY. .C 1.25 510.0 ' 61B C 1 2 3 4 . . 5 .6 . . 7 . . . . . . . . .8 9 0 1 2 . Fig. 24 (cont'd) 00 L 1 a 11 ng of SH09012 at 10:46:00 on APR 12. 1986 for CCId- BRWG Page 12 616 C KLY to CRK s e r i e s capac i tor bank. Untransposed 1 me model (5L42) 617 618 619 -1KLY..BL42-2B 0.3153622.981174E4 -2KLY..AL42-2A 0.0405280.491802E4 -3KLY..CL42-2C 0.0404232. 181846E4 57 57 57 50 1 50 1 50 1 3 3 3 620 621 622 0.59717E O0-0.70711E 00-0.41249E 00 0.53551E O0-0.21620E-12 0.81222E 00 0.59717E 00 0.70711E OO-0.41249E 00 623 624 625 -1L42-2ACRK..A 0.3153622.981174E4 -2L42-2CCRK..C 0.0405280.491B02E4 -3L42-2BCRK. B 0.0404232. 181846E4 14 14 14 80 1 80 1 80 1 3 3 3 626 627 628 0.59717E O0-0.70711E O0-0.41249E 00 0.53551E OO-O.21620E-12 0.81222E 00 0.59717E 00 0.70711E 00-0.41249E 00 629 630 631 c < C CRK ser lea capac i tor bank CRK..ACRK.CA 26518. 632 633 634 CRK..BCRK.CBCRK..ACRK.CA CRK..CCRK.CCCRK..ACRK.CA C 635 636 637 C CRK s e r i e s capac i tor bank to CKY (5L42) -1CRK.CACKY..A 0.3153622.981174E4 -2CRK.CCCKY..C 0.0405280.491802E4 51 51 70 1 70 1 3 3 638 639 640 -3CRK.CBCKY. B 0.0404232.181846E4 0.S97I7E O0-0.70711E 00-0.41249E 00 0.S3S51E 00-0.21620E-12 0.81222E 00 51 70 1 3 641 642 643 0.59717E 00 0.70711E 00-0.4I249E 00 C C CKY to MSA (5L30) (untransposed l ine model) 644 64S 646 -1CKY..CL30-1C 0.3113623.421183E4 -2CKY..BL30-1B 0.0370284.26I803E4 -3CKY..AL30-1A 0.0369235.98I846E4 16 18 18 64 1 64 1 64 1 3 3 3 647 648 649 0.59666E O0-0.70711E OO-O.41260E 00 0.53664E 00-0.63310E-12 0 31211E 00 0.B9666E 00 0 7071 IE 00-0.41360E 00 650 651 652 -IL30-1AL30-2A 0.3112623.421183E4 -2L30-1CL30-2C 0.0370284.261803E4 -3L30-1BL30-2B 0.0369235.981846E4 12.02 1 12.02 1 12.02 1 3 3 3 653 654 655 0.59666E 00-0.7071 IE 00-0.41260E 00 0.53664E 00-0.63310E-12 0.B1211E 00 0.59666E 00 0.7071IE 00-0.4I260E 00 656 657 £58 -1L30-2BMSA. B 0.3112623.4211B3E4 -2L30-2AMSA..A 0.0370284.261803E4 -3L30-2CMSA..C 0.0369235.981846E4 18 18 18 90 1 90 1 90 1 3 3 3 659 660 661 6.59666E 00-6.7071 IE 00-0.41260E 66 0.53664E 00-0.63310E-12 0.81211E 00 0.S9666E 00 0.70711E O0-0.41260E 00 662 663 664 C C MSA Thevenin equivalent C (MSA-E la Internal voltage node) 665 666 667 1MSA-EAMSA. A 7.24 1783.442 2MSA-EBMSA..B -1.358-6.683 7 3MSA-ECMSA.,C -1.356-6.683 .241783 1.358-6 442 683 7 241783.442 668 669 670 C C MSA shunt reactors (1 un i t ) MSA. .A 5. 2040.0 • 67 1 MSA..B 5. 2040. . 2 . Fig. 24 (cont'd) C D L ts t (ng Of SH09012 at 10:46:00 on APR 12. 1986 for CCId'BRWG Page 13 672 MSA..C 5. 2040. 673 674 673 C C CKV to MDN (5L45) -1CKY..CMDN..C 0.3153622.981174E4 46.00 1 3 676 677 678 -2CKY..BMON..B 0.0405280.491802E4 46.00 1 -3CKY..AMDN..A 0.0404232.181846E4 46.00 1 0.59717E OO-0.70711E 00-6.41249E 00 3 3 679 680 681 O.S3551E 00-0.21620E-12 0.81222E OO 0.59717E 00 0.70711E 00-0.41249E 00 C 682 683 684 C MDN Thevenin source: C (MDN-E Is Internal vol tage node) IMON-EAMDN..A 2.558349.283 685 686 687 2MDN-EBMDN..8 .13333-2.742 2.558349. 3MDN-ECMDN..C .13333-2.742 .13333-2. C 283 742 2 558349. 283 688 689 690 C MDN to ING (SL44) - 1MDN..CING..C 0.3153622.981174E4 12.16 I -2MDN..BING. B 0.0405280.491802E4 12.16 1 3 3 691 692 693 -3MDN. ,A ING..A 6 0404232. 18 I846E4 12.16 i 0.59717E OO-0.70711E 00-0.41249E OO 0.S3551E 0O-0.2162OE-12 0.81222E 00 3 694 695 696 0.59717E 00 0.70711E OO-0.41249E 00 C C ING Thevenin equivalent source 697 698 699 C '<i'NO-i is internal vol tage node) 1tNG-EAING..A 5.350052.250 2ING-EBING..B -1.825-10.83 5.350052. 250 700 701 702 3ING-ECING..C -1.825-10.83 -1.825-10.83 5 C C KLY to CHP s e r i e s capac i tor bank 350052. 250 703 704 70S 1KLY . .BL41-2B 8.68 67.3146~4.B1 2KLY..AL41-2A 6.05 34.26-85.40 8.68 67 3KLY..CL41-2C 6.04 28.73-25.91 6.05 34 .31479.17 .26-85.40 8 68 67 .31464 91 706 707 708 1L41-2ACHP.3A 4.37 33.86233.87 2L41-2CCHP.3C 3.04 17.23-42.96 4.37 33 3L41-2BCHP.3B 3.04 14.45-13.04 3.04 17 .86241.04 .23-42.96 4 37 33 .86233 87 709 710 711 C C CHP s e r i e s capac i tor bank CHP.3ACHP.4A 19531. 712 713 714 CHP . 3BCHP . 4BCHP . 3ACY'P . 4 A CHP.3CCHP.4CCHP.3ACHP.4A C 715 716 717 C 5L4 1 from CHP s e r i e s capac i to r bank to junct ion 1CHP.4AL41-5A 4.37 33.86233.87 2*CHP.4CL41-5C 3.04 17.23-42.96 4.37 33 of SL81 .86241.04 718 719 720 3CHP.48L41-5B 3.04 14.4S-13.04 3.04 17 C C junct ion of 5L4 1 from CHP to ING (with p a r a l l e l .23-42.96 5L81) 4 37 33 .86233 87 721 722 723 1L8I-5C1NG..C 8.32 65.26465.64 2L81-5BINQ..8 5.91 33.97-84.16 8.32 65 3L81-5AING..A 5.80 28.59-23.64 6 91 33 .26480.29 .97-82.37 8 32 65 .26471 59 '724 728 726 4L4 i -SCiNG. ,C 5 88 23.93 -8.50 3.88 26 8.44 6S.47458.47 5L41-5BING..B 5.86 2 1 . 9 0 - 4 . 5 5 5.87 23 .40-15.72 .74 -6.73 S 5 89 30 88 26 .05-46 . 14-14 22 37 127 5 88 33.32-80.94 8.44 65 .47466.80 Fig. 24 (cont'd) o L i s t i n g of SHO9012 at 10:46:00 on APR 12, 1986 for CCId-BRWG Page 14 728 6L41-5AING..A 5 85 20.30 -3 33 3.86 21 76 -4 26 5 .87 23 55 -7 27 729 5 .87 27.94-24 05 3.88 33 32-82 66 B .44 65 47452 42 730 C 731 C SL81 from Junct ion with 5L41 to Junct ion with SL82 732 733 1L81-SAL81-3A 2L81-SCL81-3C 2 .88 .94 21.41152 11.15-27 69 7B 2.88 21 41157 32 734 3L81-5BL81-3B 1 94 9.38 -8 19 1 .94 1 1 15-27 78 2 .88 21 41152 69 733 C 736 C 5L82 from MDN to Junct ion with 5L81 737 1M0N..CL82-SC 8 22 61.18436 26 738 2MDN..BL82-5B 5 .54 31.84-79 37 8.22 61 18449 48 739 3M0N..AL82-5A S .53 26.80-23 40 5.54 31 84-79 37 a 22 61 18436 26, 740 1LB2-SAL82-3A 2 33 17.33123 61 741 742 2LB2-5CL82-3C 3L82-5BLB2-3B 1 1 .57 .57 9.02-22 7.59 -6 49 63 2.33 1 .57 17.33127 9.02-22 35 49 2 .33 17 33123 61 743 C 744 C 8L81 and 8L82 from. JunctIon to NIC 7.43 1L82-3AL82-2A 4 38 32.63232 71 746 2LB2-3CLB2-2C 2 95 16.98-42 27 4.38 32 63339 80 747 3L82-38LB2-2B 2 95 14.29-12 37 2. 95 16 98-42 17 4 .38 32 63232 99 748 4L81-3AL81-2A 2 .93 10.34 -2 10 2 .94 1.1 11 -3 08 2 .95 12 OB -6 64 749 4 38 32 63232 99 7 SO SL81-3CL81-2C 2 92 9.70 -1 26 2 .93 10 34 -I 66 2 94 11 11 -3 08 781 2 95 16.98-42 17 4.38 32 63239 80 7S2 6L8I-3BLB1-2B 2 92 9.15 -1 03 3.92 9 70 -1 26 2.93 10 34 -2 10 783 2 95 14.29-12 37 2.95 16 98-42.27 4 38 32 63232 71 784 1L82-2BN1C..B 6 SO 50.98363 62 788 2L82-2ANIC..A 4 61 26 54-66 05 6.50 SO 98374 68 756 3L82-2CN1C. C 4 61 22 34-19 32 4.61 26 54-6B 90 6 .90 50 98364.05 787 4L81-2BN1C..8 4 SB 16.16 -3 28 4.S9 17 36 -4 81 4 60 18 87-10 38 758 6 50 SO 98364 OS 789 BL81-2ANIC..A 4 57 15.16 -1 97 4.S8 16 16 -2 59 4 59 17 36 -4 81 760 4 61 26.54-63 90 6.30 30 98374 68 761 6L81-2CNIC. C 4 56 14.30 -1 61 4.87 13 16 -1 97 4 58 16 16 -3 28 762 4 61 22.34-19 32 4.61 26 54-66 05 6 50 50 98363 62 763 C 764 C NIC thevenin equivalent source 765 C (NIC-E is internal vol tage node) 766 1NIC-EANIC..A 47.02 426.18 767 2NIC-EBNIC..6 -22 99- 165. 1 47.02 426 18 768 SNiC-ECNIC. .C -22 99- i65. i -22.99- 165. 1 47.02 426 18 769 C 770 C NIC shunt reactors (3 un l ta ) 771 772 C (values repeated because of two p a r a l l e N I C . A 1. 408.30 1 branches) 773 NIC. .8 1. 408.30 774 NIC. .C 1. 408.30 775 C 776 C 5L87 NIC to KLY 777 C Data from Jack Sawada. Conttnuously- transposed d l s t r l b u t e d -778 779 C parameter l ine model, ( lengths -1N1C . .AKLY . . A 0.205 1.350 3.1400 in KM) 146.0 780 -2NIC. .BKLY. .B 0.028 0 .322 5.0850 146.0 781 -3N IC . .CKLY. .C 782 C 783 C 5L7I and SL72 from NIC to MCA 1 . 2 3 4 .5 6 7 8 9 0 I 2. Fig. 24 (cont'd) L i s t i n g of SH09012 st 10:46:00 on APR 12. 1986 for CCtd-BRWG Page 15 784 1NIC..BADL..8 8 06 63 22450.88 785 2NIC. .AAOL..A 5 72 32 91-81.91 8 06 63 22464 61 786 3NIC. .CADL. .C 5 72 27 70-23.96 5 72 32 91-81 71 8 06 63 22451 42 787 4NIC..BL71-5B 5 68 20 04 -4.06 5 69 21 53 -5 96 5 71 23 40-12 87 788 8 06 63 22451.42 789 5NIC..AL71-5A 5 67 18 79 -2.44 5 68 20 04 -3 21 5 69 21 53 -5 96 790 5 72 32 91-81.71 a 06 63 22464 61 791 6NIC..CL71-5C 5 65 17 73 -2.00 5 67 18 79 -2 44 5 68 20 04 -4 06 792 5 72 27 70-23.96 5 72 32 91-S1 91 8 06 63 22450 88 793 1A0L..AL72-2A 7 93 62 20443.61 794 2ADL. .CL72-2C 5 63 32 37-80.58 7 93 62 20457 12 795 GAOL..BL72-28 5 62 27 25-23.57 5 63 32 37-80 39 7 93 62 20444 14 796 4L71-5AL7I-2A 5 59 19 71 -4.00 5 60 21 18 -5 86 5 61 23 02-12 66 797 7 93 62 20444.14 798 5L71-5CL71-2C 5 57 18 49 -2.40 5 59 19 71 -3 16 5 60 21 18 -5 86 799 5 63 32 37-80.39 7 93 62 20457 12 eoo 6L71-5BL71-28 5 56 17 44 -1.97 5 57 18 49 -2 40 5 59 19 71 -4 00 801 5 62 27 25-23.57 S 63 32 37-80 58 7 93 62 20443 61 802 1L72-2CMCA..C 6 85 50.98363.62 803 2L72-2BMCA. .8 4 62 26 54-66.05 6 85 50 98374 68 804 3L72-2AHCA..A 4 61 22 34-19.32 4 62 26 S4-65 90 6 85 50 98364 OS 805 4L71-2CMCA..C 4 58 16 16 -3.28 4 59 17 36 -4 81 4 60 18 87-10 38 806 6 85 50 98364.05 807 5L71-2BMCA..8 4 57 15 16 -1.97 4 58 16 16 -2 59 4 59 17 36 -4 81 808 ' 4 62 26 54-65 90 6 85 50 98374 68 809 6L71-2AMCA..A 4 56 14 30 -1.61 4 57 IS 16 -1 97 4 58 16 16 -3 28 810 4 61 22 34-19.32 4 62 26 54-66.05 6 85 50 98363 62 811 C 812 C MCA Thevenin equivalent 813 C (MCA-E IS Internal voltage node) 814 1MCA-EAMCA..A 26.4 815 2MCA-EBMCA..8 -4.29 26.4 816 3MCA-ECMCA..C -4.29 4.29 26.4 817 C 818 C MCA shunt reactors (2 un l ts ) 819 MCA..A 1020. 1 820 MCA..8 1020.1 821 MCA . . C 1020.1 822 C 823 C NIC to ACK (5L76 and 5L79) 824 1NIC..BL76-2B 3 28 24 48171.09 825 2NIC..AL76-2A 2 2t 12 70-33.17 3 28 24. 48 177 02 826 3NIC..CL76-2C 2 20 10 68-10.05 2 21 12. 70-32 97 3 28 24 48171 66 827 4NiC. .BL?9-2B 2 19 8 12 -2 . 16 2 26 a. 80 -3 43 2 20 9 68 -8 23 828 3 28 24 48171.66 829 5NIC..AL79-2A 2 19 7 57 -1.25 2 19 a. 12 -1 73 2 20 8 80 -3 43 830 2 21 12 70-32.97 3 28 24 4817? 02 831 6NIC..CL79-2C 2 18 7 11 -1.00 2 19 7. 57 -1 25 2 19 8 12 -2 16 832 2 20 10 68-10.05 2 21 12. 70-33 17 3 28 24 48171 09 833 iL76-2CL76-IC 3 28 24 4817 1.09 834 2L76-2BL76-IB 2 21 12 70-33.17 3 28 24. 48177 02 835 3L76-2AL76-IA 2 20 10 68-10.05 2 21 12. 70-32 97 3 28 24 48171 66 836 4L79-2CL79-it 2 19 8 12 -2.16 2 20 8. 80 -3 43 2 20 9 68 -8 23 837 3 28 24 48171.66 838 5L79-2BL79-IB 2 19 7 57 - i . 2 5 2 19 8. 12 -1 73 2 20 8 80 -3 43 838 2 21 12 70-32.97 3 28 24. 4817? 02 I 2 3 4 5 6 7 8 9 0 1 2. Fig. 24 (cont'd) L i s t i n g Of SH09012 at 10:46:00 on APR 12. 1986 for CCId> SRWG Page 16 840 6L79-2AL79-1A 2. 18 7 .11 -1.00 2.19 7 . 5 7 - 1 25 2. 19 8.12 -2 16 841 842 843 1L76-1AACK..A 2L76-1CACK..C 2.20 10 S.28 24 2.21 12 .68- 10 .48171 .70-33 05 09 17 2.21 12.70-33 3.28 24.48177 17 02 3.28 24.48171 09 844 849 846 3L76-1BACK..8 4L79-1AACK..A 2.20 10 2.19 8 3.28 24 .68-10 . 12 -2 .48171 OS 16 66 2.21 12.70-32 2.20 8.80 -3 97 43 3.28 24.48171 2.20 9 . 6 a -8 6 6 23 847 848 849 5L79-1CACK..C 6L79-1BACK. B 2.19 7 2.21 12 2. 18 7 . 5 7 - 1 .70-32 .11 -1 25 97 00 2. 19 8.12 -1 3.28 24.48177 2. 19 7.57 -1 73 02 25 2.20 8 . 8 0 - 3 2. 19 8. 12 -2 43 16 890 861 852 2.20 10 C C ACK Thevenin equivalent .68-10 05 2.21 12.70-33 17 3.28 24.48171 09 853 854 853 C (ACK-E is Internal vol tage node) 1ACK-EAACK..A 62.25 328.27 2ACK-EBACK..B -29.78-111.8 62.25 328.27 856 837 858 3ACK-ECACK..C C C ACK shunt reactors (1 29.78-111.8 uni t) 29.78-111.8 62.25 328.27 859 860 861 C (repeat values because of two p a r a l l e l ACK..A 1. 2040.0 ACK..B 1. 2040.0 branches) 862 863 864 ACK. .C 1 C C ACK to REV (5L77 and 2040.0 5L75) 865 866 867 1ACK..AREV..A 2ACK..BREV. B SACK. .CREV. .C 6.58053. 4.71526. 4.70921. 751348 252-70 840-23 30 74 78 6.58053.750357 4.71526.2S2-71 86 61 6 .58053.751345 34 868 869 870 4ACK..AREV..A SACK. .BREV. .B 4.71122. 6 .58050. 4.67916. 524-40 752330 294 -3 77 67 41 4.70319.708-15 4.69217.783 -9 52 07 4.69217.764 -8 4.70319.734-21 58 24 871 872 873 6ACK. .CREV. .C 4 64814 4.66315. 4.62813. 275 -3 105 -3 392 -2 42 92 S3 6.58053.751343 4.67916.310 -5 4.71626.330-77 78 15 95 4.69317.803-10 6 .58053.751342 18 IS 874 875 876 C C REV Thevenin equivalent C (REV-E 1s Internal voltage node) 877 878 879 1REV-EAREV..A 1 2REV-EBREV..8 3REV-ECREV..C .67-243. 8.3-3-11 8.3-3-11 333 .42 .42 1 .67-343.333 8.3-3-11.42 1.67-243.333 880 881 882 C C 5L91 from ACK to SEL 1ACK. AL91-1A 6.42 47 .95334 93 883 884 889 2ACK..CL91-IC SACK..8L91-IB IL91-IBL91-2B 4.32 24 4.32 20 6.42 47 .86-65 .91-20 .95334 12 OS 99 6 . 4 2 47.94346 4.32 24.86-65. 43 12 6 . 4 2 47.93334 95 886 887 888 2L9 i - 1AL91-2A 3L91-1CL91-2C 1L91-2CSEL..C 4.32 24 4.32 20 6.42 47 .'86-65. 12 .91-20.05 .95334.95 6 . 4 2 47.94346. 4.32 24.86-65. 43 12 6 . 4 2 47.95334 95 889 890 891 2L91-2BSEL. .S 3L91-2ASEL..A C 4.32 24 4.32 20 .86-65 .91-20 12 OS 6 . 4 2 47.94346. 4.32 24.86-65. 43 12 6 . 4 2 47.95334 95 892 893 894 C SEL thevenin equiva lent : C (SEL-E Is internal voltage 1SEL-EASEL..A 2.008355. node) 442 895 2SEL-EBSEL. .B 8 .33-2-4. 083 2 .008355.442 1 2 . .3 5 6 ; 7 . 8 . . . . . . . .0 . . . 1 2 Fig. 24 (cont'd) CO L i s t i n g of SHO9012 at 10:46:00 on APR 12, 1966 for CCId-BRwG Page 17 696 3SEL- ECSEL. .C 8.33-2-4.083 8.33-2-4.083 2.008355 442 897 C 896 C SEL shunt reactors (1 un i t ) 899 SEL .A 2040.1 900 SEL .8 2040.1 901 SEL .C 2040.1 S02 C 903 C 5L98 NIC to SEL 904 c Oata from Jack Sawada, conttnuously- t ransposed d l s t r l b u t e d -90S c parameter l ine model ( lengths In KM7) 906 -1SEL .ANIC..A .2034 1.249 3.14 302. 907 -2SEL .BNIC. .B .0277 0.323 S.08 302. 908 -3SEL .CNIC. .C 909 C 910 C end of BC Hydro system 911 C 912 C BC Hydro In te r t le to Bonnev i l le Power Adminis t ra t ion f o l l o w s : 913 C 914 C ING to CUS (5L51 and 5L52) (untransposed l ine model) 91S C (twin c i r c u i t s , modelled uncoupled) 916 -IING. .ACUS..A 0.31 15627.61 1I80E4 22.50 1 3 917 -2ING. .BCUS..B 0.0370279.94180SE4 22.50 1 3 918 -SING. .CCUS. .C 6.036923i 23i846E4 22.50 i 3 919 0.59815E 00-0.707I1E 00-0.41217E 00 920 0.53332E 00-0.1335SE-08 0.812S4E 00 921 0.59815E 00 0.70711E OO-0.41217E 00 922 -1ING. .ACUS. .AING. .ACUS. .A 923 -2INQ. .BCUS..8 924 -SING. .ecus. .C 925 C 926 C CUSTER to MONROE (untransposed l ine model) 927 C (twin c i r c u i t s , mode l i e d uncoupled) 928 -1CUS. .AMON..A 0.2994687.901243E4 86.00 1 3 929 -2CUS. .BMON..B 0.0272263.OS1831E4 86.00 1 3 930 -3CUS. .CMON..C 0.0274254.461843E4 86.00 1 3 931 0.63026E 00-0.70711E 00-0.39035E 00 932 0.4S336E 00 0.66850E-05 0.83382E 00 933 0.63026E 00 0.707I1E 00-0.39035E 00 934 -ICUS. .AMON..ACUS..AMON..A 93S . -2CUS. .BMON..8 836 -3CUS. .CMON..C 937 c 938 c MON Thevenin equivalent source 939 6 (MON-E is in te rna l vol tags node) 940 1M0N- EAMON..A 2.030 52.13 941 2M0N- EBM0N..B 1.660 4.380 2.030 52.13 942 3M0N- ECMON..C i.660 4.380 1.660 4.380 2.030 52 13 943 C 944 C end of network 94S 946 FAULT1FAULT23.780583-31.OOOOOOOO 947 5L1N .ACB1N1A-1. 1.0 30.0 948 5L1N .BCBIN IB-1. 1.0 30.0 949 SL1N .CCBIN IC-1. 1.0 30.0 950 CBIN2AVTIN.A-I. 1.0 30.0 95 1 CB1N2BVT1N.B-1 1.6 30.0 1 2 3 4 5 6 7 8 9 0 1 2. Fig. 24 (cont'd) CD L i s t i n g of SH09012 at 10:46:00 on APR 12. 1986 for CCId-BRWG Page 18 952 CB1N2CVTIN.C-1. 1 .0 30 0 953 9L1S.ACB1S1A-1. 1 .0 30 0 954 5L1S.BCB1S16-1. 1.0 30 0 955 5LIS.CCB1SIC-I . 1 .0 30 0 956 CB1S2AVTIS.A-1. 1.0 30 0 957 CB1S2BVT1S.8-1. 1 .0 30 0 958 CB1S2CVTIS.C-1. 1.0 30 0 959 5L2N.ACB2N1A-1. 1 .0 30 0 960 5L2N.BCB2N1S-1. 1.0 30 0 961 5L2N.CCB2N1C-1. 1.0 30 0 962 CB2N2AVT2N.A-1. 1.0 30 0 963 CB2N2BVT2N.B*1. 1.0 30 0 964 CB2N2CVT2N.C-1. 1 .0 30 0 965 CB2S1ASL2S.A-1. 1.0 30 0 866 CB2S1B5L2S.B-1. 1 .0 30 0 967 CB2S1C5L2S.C-1. 1.0 30 0 968 CB2S2AVT2S.A-1. 1.0 30 0 869 CB2S2BVT2S.B-1. 1.0 30 0 970 CB2S2CVT2S.C-1. 1.0 30 0 971 KD1NOAKD1N1AO. .083 30.0 10000. 972 KD1N2AKD1N3A0. .083 30.0 190890. 973 KDY1SAKDIS1A0. .083 30.0 10000. 974 KD 1S2AKD1S3A0. .083 30.0 190890. 975 K01NOBK01N180. .083 30.0 10000. 976 KD1N2BKD1N3B0. .083 30.0 190890. 977 KDY1SBKDIS1B0. .083 30.0 10000. 978 K01S2BK01S3B0. .083 30.0 190890. 979 KD1N0CKD1N1C0. .083 30.0 10000. 980 KD1N2CKD1N3C0. .083 30.0 190890. 981 KDY1SCKOIS ICO. .083 30.0 10000. 982 KD1S2CKD1S3CO. .083 30.0 190890. 983 KD2NOAKD2N1AO. .083 30.0 10000. 984 KD2N2AK02N3AO. .083 30.0 190890. 989 KDY2SAKD2S1A0. .083 30.0 10000. 986 KD2S2AKD2S3AO. .083 30.0 190890. 987 K02NOBK02N1BO. .083 30.0 10000. 988 KD2N2BK02N3BO. .083 30.0 190890. 989 KDY2SBKD2S160. .083 30.0 10000. 990 K02S2BKD2S3BO. .083 30.0 190890. 991 K02NOCKD2N1CO. .083 30.0 10000. 992 KD2N2CK02N3CO. .083 30.0 190890. 993 K0Y2SCK02SICO. .083 30.0 10000. 994 K02S2CKD2S3CO. .083 30.0 190890. 993 KD3NOAKD3N1AO. .083 30.0 10000. 996 K03N2AK03N3AO. .083 30.0 192420. 997 KDY3SAKD3S1A0. .083 30.0 10000. 998 kb3SJAKD3S3i6. .083 30.0 192420. 999 K03N0BK03NIBO. .063 30.0 10000. 1000 KD3N2BK03N380. .083 30.0 192420. 1001 KDY3SBKD3S1B0. 083 30.0 10000. 1002 K03S2BK03S3B0. .083 30.0 192420. 1003 K03NOCK03N1CO. .083 30.0 10000. 1004 KD3N3CKD3N3CO. .083 30.0 192420. 1005 KDY3SCKD3S1C0. .083 30.0 10000. 1006 KD3S2CK03S3CO. .083 30.0 ' 192420. 1007 1 2 3 . . . . 4 5 6 . .7 8 9 0 1 2. Fig. 24 (cont'd) C3 L i s t i n g of SH09012 at 10:46:00 on APR 12. 1986 for CCIOBRWG Page 19 1008 14GMS-EA 0423767 790 60. 46.201000 -1 . 1 . 1009 14GMS-EB 0425767 790 60. -73.799000 - 1 . 1. 1010 14GMS-EC 0425767 790 60. 166.20100 - 1 . 1. 101 1 14PCN-EA 0425818 370 60. 49.345000 - 1 . 1. 1012 14PCN-E8 0425815 370 60. -70.655000 - 1 . 1. 1013 14PCN-EC 0425815 370 60. 169.34500 - 1 . 1. 1014 14KLY-EA 0396003 260 60. 2.3866000 - 1 . 1. 1018 14KLY-EB 0396003 260 60. -117.61340 - 1 . 1. 1016 14KLY-EC 0396003 260 60. 122.38660 - 1 . 1. 1017 14WSN-EA 0468378 670 60. - 1.351100 1 -1 . 1. 1018 14WSN-EB 0468376 670 60. -121.35110 -1 . 1 . 1019 14WSN-EC 0468378 670 60. 118.64890 - 1 . 1. 1020 14SKA-EA 0403532 450 60. 21.140000 - 1 . 1. 1021 14SKA-EB 0403532 450 60. -98 .860000 - 1 . 1. 1022 14SKA-EC 0403532 450 60. 14 1 .14000 - 1 . 1. 1023 14SEL-EA 0430136 720 60. 11.854000 - 1 . 1. 1024 14SEL-EB 0430136 720 60. - 108. 14600 - 1 . 1. 1028 14SEL-EC 0430136 720 60. 131.85400 -1 . 1 . 1026 14MCA-EA 0429803 690 60. 17.896000 - 1 . t. 1027 14MCA-EB 0429803 690 60. -102. 10400 -1 . 1 . 1028 14MCA-EC 0429803 690 60. 137.89600 - 1 . 1. 1029 14ING-EA 0400537 460 60. -18.018000 - 1 . 1. 1030 14ING-EB 0400537 460 60. -138.01800 -1 . 1 . 1031 14ING-EC 0400537 460 60. 101.98200 - 1 . 1. 1032 14MDN-EA 0413208 120 60. -12.505000 - 1 . 1. . 1033 14M0N-EB 0413208 120 60. -132.50500 -1 . 1. 1034 14MDN-EC 0413208 120 60. 107.49500 -1 . 1 . 1038 14MSA-EA 0448088 150 60. -8.8511000 - 1 . 1. 1036 14HSA-EB 0448088 150 60. -128.85110 - 1 . 1. 1037 14MSA-EC 0448088 150 60. 111.14890 - 1 . 1 . 1038 14ACK-EA 0318622 130 60. -21.693000 - 1 . 1. 1039 14ACK-EB 0318622 130 60. -141.69300 - 1 . 1 . 1040 I4ACK-EC 0318622 130 60. 98.307000 - 1 . 1. 1041 14NIC-EA 0450609 600 60. -19.416000 -1 . 1 . 1042 14NIC-EB 0450609 600 60. -139.41600 -1 . 1 . 1043 14NIC-EC 0450609 600 60. 100.58400 -t. 1. 1044 14REV-EA 0427298 100 60. 2.7086000 - 1 . 1. 1045 14REV-EB 0427298 too 60. -117.29140 -1 . 1 . 1046 14REV-EC 0427298 100 60. 122.70860 - 1 . 1. 1047 14M0N-EA 0452996 230 60. -35.425000 - 1. 1. 1048 MMbN-EB 0452996 250 60. -155.42500 -1 . 1. 1049 14M0N-EC 0452996 250 60. 84.575000 -1 . 1 . 1030 1 0 5 1 V T IN.AVT1N7BVT IN . CVT IS - AVT i S.BVTIS.C 1052 1083 1 0 3 4 E N D OF RUN 1 2 . .3. . . 4 8 . .6 7 B 9 0 1 2. Fig. 24 (cont'd) L 1st ing 1 Of SHI 1002 at 10:46:01 On APR 12. 1986 f o r CCId-BRWG HI 1002: INTERNAL 6LI A-B FAULT (KDY S. 0 OHMS) 2 60. 60. Page 1 2 3 4 65.10417-666.66667-3 - 1 0 1 00 C6S.10417-666.66667-3 - 1 0 1 00 C S 6 7 C C C Complied: 19860317 Source: H10006 -8 9 10 C C C INTERNAL-FAULT Equivalent aouth of WSN 11 12 13 C C C OL fau l t on KDY1SA-K0Y1SB Faul t r e s i s t a n c e : 0.0 Ohms 14 15 16 C C C Polnt-on-wave: 143.13 degrees of KDY1S Vab Fault Instant: 3.7806 msec 17 18 19 C KDY1SAFAULT1 0.001 1 KDY1SBFAULT2 0.001 20 21 22 C C C 19860307: GMS reactors moved from bus to 5L1 and 5L2 23 24 25 C C C Peace River s imula t ion . Ful l ' 1984 SOOKV B . C . Hydro network from Jack Sawada of B . C . Hydro, supplemented by Peace transmission l i n e s extracted from a case from Brent Hughes of B . C . Hydro. 26 27 28 c c c ( A H data appl ies to 1984 system, and waa obtained is Sept. igss. ) North Coast t ransmission ts o r i g i n a l data. Thevenin equivalent sources for GMS. PCN, WSN, REV, ACK, NIC, MCA, 29 30 31 c c c MSA, GLN, TKW, SKA, MDN, ING, SEL, CKY, and KLY were obtained from SLG fau l t study r e s u l t s from B . C . Hydro. 32 33 34 c c c Study step s i z e is 65 microseconds, g i v i n g a study bandwidth of about 5 KHz.' Study s imulat ion time Is 67 m i l l i s e c o n d s , corresponding to four power-frequency c y c l e s . There are 256 35 36 37 c c c time p o i n t s / c y c l e . ' Transmission-1Ine lengths for Peace River t ransmission have 38 39 40 c c c been adjusted to produce equal p a s t - h i s t o r y In terpolat ion requirements for both p o s i t i v e and zero sequence, so as to minimize e r ro rs csused by l inear In terpola t ion wi th in program. 41 42 43 c c c Peace River e l e c t r i c a l network fo l lows: 44 45 46 c c c GMS Thevenin source: (GMS-E IS GMS Internal vol tage node) GMS X/R r a t i o is based on B . C . Hydro standard CT s p e c i f i c a t i o n ii 48 49 c c al lowing for 6 . i second time constant (-> X /R»37 .6999 ) Thus ZS has 3.65% R added. GMS-EAGMS..A .5756 21.700 50 51 52 2GMS-E8GMS..B -5.227 .5756 21.700 3GMS-ECGMS..C -5.227 -5.227 .5756 21.700 C S3"" 54 55 C GMS shunt reactors (2 u n l t s - - o n e each SL1 and 5L2) VT1N.A 5.0 2040. VT IN. B VT IN. A 6 6 V T IN C V T IN". A 1 2 3 4 5 . .6 7 .8 . . . . . . . . .9 0 1 2 Fig. 25. Listing of E M T P data for reduced power system model D a t i n g of SHI1002 at 10:46:01 on APR 12, 1986 for CCId'BRWG Page 2 S7 VT2N.A VTIN.A 58 VT2N.B VTIN.A 59 VT2N.C VTIN.A 60 C 61 C 5L1 CT la from GMi to 5L1N 62 C 5L1 CVT IS at VT1N 63 C 64 C North end 5L1 c l o s i n g r e s i s t o r s and s w i t c h - I s o l a t i n g impedances 65 c Also used for current measurement 66 GMS..A5L1N.A 0.01 1 67 GMS..B5LIN.BGMS..A5LIN A 1 68 GMS..CSLIN.CGMS..ASLIN A 1 69 CBIN 1ACB1N2AGMS..A5LIN A 70 CBIN1BCB1N2BGMS. .ASL IN A 71 CB1N1CCB1N2CGMS. .ASL IN A 72 CBIN 1AVTIN.A 400. 73 CB1N1BVT1N.BCB1N1AVT1N A 74 CB1N1CVT1N.CCB1N1AVT1N A 75 GMS..ASL2N.AGMS..A5L1N A 76 GMS..B5L2N.BGMS..ASLIN A 77 GMS. .C5L2N.CGMS. .ASL IN A 78 CB2N1ACB2N2AGMS..ASLIN A 79 CB2N1BCB2N2BGMS..ASLIN A 80 81 CB2N1CCB2N2CGMS..A5LIN CB2N1AVT2N.ACBIN 1AVTIN A A 82 CB2N1BVT2N.BCB1N1AVT1N A 83 CB2N1CVT2N.CCB1N1AVT1N A 84 c 85 c 5L1 AND 5L2 from GMS to Junct ion with 5L3 from PCN 86 c Data length-adjusted from Brent Hughes case, lengths 87 c In mi les . Untransposed l ine mode). 88 - 1VT1N.CL1-1.C 0.5877780. 310988E4 26.00 1 6 89 -2VTIN.BL 1 - 1.8 0.0421433.6815B9E4 26.00 1 6 90 -3VT1N.AL1-1.A 0.0403283.781798E4 26.00 1 6 91 -4VT2N.CL2-1,C 0.0399274.9SI823E4 26.00 1 6 92 -SVT2N.BL2-1.B 0.0399230.431848E4 26.00 I 6 93 -6VT2N.AL2-1.A 0.0400232.311847E4 26.00 1 6 94 0.41879E OO-0.51633E 00- 0.50625E 00 0.45368E OO-0.24886E 00-0.29476E 00 95 0.37742E OO-0.39719E 00- 0.12909E-01-0.16135E 00 0.54392E 00 0.575B7E 00 96 0.42676E O0-0.27482E 00 0.49348E 00-O.SI708E OO-O.37640E O0-O.28S44E 00 97 0.42676E 00 0.27482E 00 0.49348E 00 O.S1708E 00 0.37640E 0O-0.28544E 00 98 0.37742E 00 0.39719E 00- 0.129O9E-01 0.1613SE OO-0.64392E 00 0.67S87E 00 99 0.41B79E 00 0.S1633E 00- 0.S062SE 00-0.45368E 00 0.24886E OO-0.29476E 00 100 c . 101 c PCN Thevenin source: 102 c (PCN-E Is PCN Internal voltage node) 103 c PCN x/R r a t i o is based oh B . C . Hydro standard CT s p e c i f i c a t i o n 104 c al lowing for 0.1 second time constant (-> X/R-37.6999) 105 c Thus 2S has 2.63% R added. 106 1PCN-EAPCN..A 2.496994.130 107 2PCN-EBPCN. B -24.92 2.496994.130 108 3PCN-ECPCN. .C -24.92 -24.92 2.496994 . 130 109 c 110 c PCN shunt reactors (1 u n l t ) : 111 PCN..A 5. 2040. 1 12 PCN..B 5. 2040. 1 2 3. . . . . . . . .4. 5. . . . . . . . .6 7 8 9 0 I 2. Fig. 25 (cont'd) C2 00 L i s t i n g of SH11002 at 10:46:01 on APR 12. 1986 for CCld'BRWG Page 3 113 PCN..C S. 2040. 1 14 115 116 C C 9L4 from PCN to GMS C Data length-adjusted from s o l i t a r y 5L3 data from Brent 117 118 119 C Hughes case , lengths in mi les , uhtrahspbsed l i n e model. C Line length increase by 40% so travel time exceeds step C s i z e . 120 121 122 C -1PCN..CGMS..C 0.3229627.531188E4 12.03 1 3 -2PCN..BGMS..B 0.0489283.271806E4 12.03 1 3 123 124 125 -3PCN..AGMS..A 0.0488234.601847E4 12.03 1 3 0.59747E O0-0.70711E 00-0.41230E 00 0.53479E 00 0.20486E-12 0.81240E 00 126 127 128 0.S9747E 00 0.70711E 00-0.41230E 00 C C 5L3 from PCN to JunctIon .wlth 6L1 and 5L2 from GMS 129 130 131 C Data length-adjusted from Brent Hughes case , C lengths In mi les . Untransposed l ine model. -1PCN. .CL3-1:C 0.3329627.531188E4 26.00 1 3 132 133 134 - 2 P C N . . B L 3 - i . B 6 0489283.27i806E4 26.00 1 3 -3PCN. .AL3-1.A 0.0488234.601847E4 26.00 1 3 0.59747E 00-0.70711E 00-0.41230E 00 135 136 137 O.S3479E 00 0.20486E-12 0.81240E 00 0.59747E 00 0.70711E OO-0.41230E 00 C 138 139 140 C 5L1, 5L2, and 5L3 from Junct ion to f i r s t t r a n s p o s i t i o n p o i n t : C Data length-adjuated from Brent Hughes esse , lengths in C mi les . Untransposed t ine model. 141 142 143 C Transpos i t ion occurs at sending end of th is l ine sec t ion C for 5L3 -IL3-1 AL3-3 A 0.8582899.000891E4 33.24 1 . 9 144 145 146 -2L3-1 .CL3-2 .C 0.0511497.861460E4 33.24 1 9 -3L3-1 BL3-2.B 0.0435409.941654E4 33.24 t 9 -4L1-1 .CL1-2 .C 0.0372253.001799E4 33.24 1 9 147 148 149 - S L i - i B L 1 - 2 . B 0.0326209.261816E4^ 33.24 i 9 -6L1-1 .AL1-2 .A 0.0331215.B61828E4 33.24 1 9 -7L2-1 .CL2-2 .C 0.0484232.461848E4 33.24 1 9 150 151 192 - B L J - i . B L 2 - 2 . B 6 6398229.i3i848E4 33.24 1 9 -9L2-1 .AL2-3 .A 0.0398231.09I847E4 33.24 1 9 0.32842E 00-0.44279E 00-0.38542E 00-0.31701E 00-0.483.16E 00 0.23342E 00 153 194 159 -0.38674E O0-0.34537E-01-0.38830E-01 0.29S33E O0-0.37922E O0-0.25754E 00-0.41833E-01 0.70848E-01-0.11350E 0.79290E 00 0.2684IE-OI 0.2I073E-0I 00 196 197 198 6.33557E 66-6.36222E 66-6. 1022 IE' 66 6. 2731 IE 66 6.S4407E 00-0 29908E -0.46379E 00 0.46756E-01 0.44760E-0I 0.35685E 00-0.13903E 00 0.42073E 00 0.44855E 00 0.47026E-02 0.53196E 00 00 199 160 161 O.568OOE-01-O.35236E 00-0.277I9E 00 0.32O61E 00-0.1S227E-01 0.45688E 00 0.29694E-01-O.19301E 00 0.13271E O.S568SE-02 0.642B2E 00 0.43423E 00 -01 162 163 164 6.3SS4BE 66 6. 107661 66 6.43398E 00-6.4 i9l8E 66-0.10699E 00-6.5344 it -0.11I66E-01-0.4005 IE 00-0.I7I83E 00 0.34970E 00 0.37O01E 00-0.82757E-01-0.43325E 00 0.39258E 00 0.29025E 00 00 169"" 166 167 -6.2iB7SE-62 6.3'6i58E 66-6.363S5E 66 0.30747E 00 0.39077E OO-O.24091E 00 0.13323E-01 0.84531E-01 0.13409E 0.17366E-02-0.4125BE 00 0.67345E 00 00 t68 0.34145E 00 0.45603E 00-0.36662E 00 0.44814E 00-0.34472E O0-0.26097E 00 1 2 3 4 5 6 7 8 9 . . . . 0 . . . 1 7 Fig. 25 (cont'd) CTl to L i s t i n g of SH11002 at 10:46:01 on APR 12. 1986 for CCId-BRWG Page 4 169 0.30493E-03 0.18335E 00-0.33728E 00 1 7 0 C 171 C 5L1 and SL2 from f i r s t t ranspos i t ion point to KDY s e r i e s 172 C capac i tor bank. Data length-adjusted from Brent Hughes 173 C case, lengths in m l ies . 174 C Transpos i t ion occurs at sending end for a l l three l i n e s . 175 - 1L.1-a.BKDY 1NB p. 596 1780. 300988E4 26.00 1 6 176 177 178 -2L 1-2. AKOY 1KIA 0 -3L1-2.CKDY1NC 0 -4L2-2.BKDY2NB 0 .0505433.631589E4 26.00 1 6 .0486283.781798E4 26.00 1 6 .0462274.771823E4 26.00 1 6 179 180 181 -5L2-2.AKDY2NA 0 -6L2-3.CK0Y3NC 0 0.4I882E O0-0.51607E 00-0. .0482230.261848E4 26.00 1 6 .0484232.31I847E4 26.00 1 6 506I7E 00 0.4S229E 00-0.25116E 00-0. 29485E 00 182 183 184 0.37737E 00-0.39742E 00-0. 0.42678E 00-0.27486E 00 0. 0.42678E 00 0.27486E 00 0. 13064E-01-0.15798E 00 0.54457E 49356E O0-0.51914E 0O-0.37373E 49356E 00 0.S1914E 00 0.37373E 00 0. 00-0. 00-0. 57589E 28531E 28531E 00 00 00 185 186 187 0.37737E 00 0.39742E 00-0. 0.41882E 00 0.516O7E 00-0. C 13064E-01 0.1579BE 00-0.54457E 50617E O0-0.4S229E 00 0.25116E 00 0. 00-0. S7589E 29485E 6b 00 188 189 180 C SL3 from f i r s t t r a n s p o s i t i o n point to KOY s e r i e s C capac i tor bank. Data length-adjusted from Brent C case , lengtha In m i l e s . Hughes 191 192 193 -1L3-2.BKDY3NB 0 -3L3-3.AKDY3NA 0 -3L3-3.CKDY3NC 0 .3229627.531 1BBE4 26.00 1 3 .0489283.271806E4 26.00 1 3 .0488234.601847E4 26.00 1 3 194 193 196 0.59747E O0-0.70711E 00-0. O.S3479E 00 0.20486E-12 0. 0.59747E 00 O.70711E 00-0. 4I230E 00 81240E 00 41230E 00 197 198 ' 199 C C KOY s e r i e s capac i tor C Deta i l ed s e r i e s capac bank: i t o r model with p r o t e c t i v e gap 200 201 202 C modif ied from data C 5L1 Phase A: KDY 1NAKD1N0A from Brent Hughes 1.89-3 303 204 305 KDINOAKO1N2A 0 K01N2AKD1N1A 3 K01N3AKD1M.AKDY1NAKD1N0A .0020.18850 .20001.89-3 306 307 208 KD1N0AKD1M.A 0 K01M.A KD1M.AKDYISAKD1NOAKDIMA .01007.54-343960. 2.4504 209 2 tO 211 KDISSAkbiM.AKOY1NAKOINOA KD 1S2AK0 IS 1AK01N2AK0 IN 1A KO1S2AK0YISAKOINOAKD1N2A 212 213 214 C fell Phase B: KOY1NBKD1NOBKOY1NAKD1NOA K01NOBK01N2BK01 NOAKD 1N2 A 215 216 217 KD1N2BKD1N1BKD1N2AKDIN 1A KO 1N3BKD1M. BKDY 1NAKD1N0A KO1N0BK01M.BKD1N0AKD1M.A 218 219 220 KD1M.B KD1M.A KD1M.BKDY1SBKDINOAKDIMA KD1S3BKD1M.BKDY1NAKD1N0A 2 2 1 K D i S28KD1 Si BKD 1N2AKD IN 1A 222 KD1S2BKDY1SBKDINOAKD1N2A 233 C 6L1 Phase C: 2 3 4 K D Y 1NCKD1N0CK0Y 1NAK0 1N0A 1 2 3 4. . 5 6 7 8 9 0 1 2. Fig. 25 (cont'd) L i s t i n g of SH11002 at 10:46:01 on APR 12, 1986 for CCId-BRWG Page 5 22S KD1N0CK01N2CKDINOAKD1N2A 2 2 6 K D 1N2CKD1N1CKD1N2AKD IN 1A 227 KD1N3CKD1M.CKDVINAKD1NOA 228 KDIN0CKDIM.CKD1NOAKD1M.A 2 2 8 K D I M . C K O IH. A 230 KD1M.CKOY1SCKDINOAKDIH.A 231 KD1S3CKD1H.CKDYINAKD1N0A " 2 3 2 K D 1S2CKD IS1CKD1N2AKD INI A 233 KD1S2CKDY1SCKDINOAKD1N2A 234 C 2 3 5 C 5 L 2 Phase A: 236 KDY2NAKO2NOAK0YINAKD1N0A 237 K02NOAK02N2AKDINOAKD1N2A ' 2 3 8 K 0 2 N 2 A K 0 2 N 1 A K D 1N2AK0 IN 1A 239 KD2N3AKD2H.AKOYINAKD1N0A 240 KD2NOAK02H.AK0INOAKD1M.A ' 2 4 1 K 0 2 H . A K 0 1 M . A 242 KD2H.AKOY2SAKDINOAKD1H.A 243 K02S3AKD2H.AKDYINAKD1N0A 2 4 4 K D 2 S 2 A k b 2 S 1AKD1N2AKD IN 1A 249 K02S2AKOY2SAK0INOAKD1N2A 246 C 6L2 Phase 6: ' 2 4 7 k b Y 2 N 8 k b 2 N 6 B k D Y INAKD INOA 248 KD2NOBKD2N2BKDINOAKD1N2A 249 K02N26KD2N18KD1N2AKDIN 1A 2 S O k b 2 N 3 B K D 2 H . BKDY 1NAKD INOA 291 KD2NOBKD2M.BKDINOAKD1M.A 292 KD2M.B K01H.A 2 9 3 K 0 2 M BKDY2SBKD INOAKD IMA 2S4 KD2S3BK02M.BKDYINAKD1N0A 299 KD2S2BKD2S1BKD1N2AKD1N1A 2 9 6 k b 2 S 2 B K b Y 2 S B K D INOAKD 1N2A 257 C 512 Phase C: 256 KOY2NCK02NOCKOYINAKDINOA 2 5 9k62NOCk62N2CkblNOAKblN2A 260 K02N2CKO2N1CK01N2AK01N1A 261 KD2N3CKD2H.CKDYINAKDINOA 2 6 3 K 0 2 N 6 C K 0 2 H . CKO INOAKD 1H. A 263 K02H.C K01M.A 264 KD2M.CKDY2SCK0INOAKD1M.A 2 6 5 k b 2 S 3 C k b 2 M . C K D Y INAKD INOA 266 K02S2CK03S1CK01N2AK01N1A 267 KD2S2CKDY2SCKD1NOAKD1N2A 2 6 8 C 269 C SL3 Phase A: 270 KDY3NAK03N0AK0YINAKDINOA 2 7 1 k b 3 N 6 A k b 3 N 2 A k 6 I N O A K D 1N2A 272 K03N2AKD3N1AKD1N2AKDIN 1A 273 KD3N3AKD3M.AKDYINAKDINOA 2 7 4 k b S N O A K D S M . A 6 . 0 1 0 0 7 . 5 4 - 3 4 3 4 8 0 276 KD3M.A KDIH.A 276 KD3H.AKDY3SAKD3N0AKD3H.A 2 7 7 K D 3 S 3 A K D 3 M ' . AKDY INAKD INOA 278 KD3S2AKD3S I AKD1N2AKDIN 1A 279 KD3S2AKDY3SAK0INOAKD1N2A 2 8 0 C S L 3 " "Phase'B': I 2 3 4 5 6 7 B 9 0 1 2 . Fig. 25 (cont'd) L1s 11ng Of SH11002 « t 10:46:01 on APR 12. 1986 for CCId-BRWQ Page 6 281 KDY3NBK03N08K0Y1NAK0INOA 282 283 284 K03NOBKD3N2BK0INOAKO1N2A KD3N2BK03N1BK01N2AK0IN 1A K03N3BKD3M.BKDY1NAK01N0A 285 286 287 KD3NOBKD3M.BK03NOAKD3M.A KD3M.B KOIM.'A KD3M.BK0Y3SBKD3NOAKD3M.A 288 289 290 KD3S3BKD3M.BKDYINAKDINOA KD3S2BKD3S1BK01N2AKDIN 1A K03S2BKDY3SBKDINOAKD tN2A 291 292 293 C 5L3 Phase C: K0Y3NCK03NOCKDY1NAK01N0A K03NOCK03N2CK0INOAKO1N2A 294 295 296 K03N2CK03N1 CKO 1N2AKD1N1A KD3N3CKD3M.CKDY1NAK0INOA KD3N0CKD3M. CKD3NOAKD3M . A 297 298 299 K03M.C KD1M.A KD3M.CKDY3SCK03NOAKD3M.A KD3S3CKD3M.CKDY1NAK0INOA 300 301 302 KD3S2CKD3S1CK01N2AKD1N1A KD3S2CKDY3SCKD INOAKD 1N2A C 303 304 305 C 5L1, 5L2. and 5L3 from KOY s e r i e s capac i tor bank to second C t r a n s p o s i t i o n p o i n t . Data length adjusted from Brent Hughes C case . Untransposed 1 Ine model . 306 307 308 -1KDY1SBL1-S.B 0.8623947.820893E4 26.00 1 9 -2KDYISALI-5.A 0.048447B.891513E4 26.00 1 9 -3K0Y1SCL1-5.C 0.0433376.011705E4 26.00 1 9 309 310 311 -4KDY2SBL2-B.B 0.0395271.181803E4 26.00 1 9 -5K0Y2SAL2-5.A 0.0331209.701827E4 26.00 1 9 -6K0Y2SCL2-5.C 0.0324202.761B38E4 26.00 1 9 312 313 314 -7KDY3SBL3-5.B 0.0477228.751B48E4 26.00 1 9 -8KDY3SAL3-5.A 0.0390226.081B47E4 26.00 1 9 . -9KDY3SCL3-B.C 0.0385219.921849E4 26.00 1 9 315 316 317 0.3S665E O0-0.47171E 0O-0.42962E 00-0 -0.37O70E-02 0.31196E O0-0.1381BE 00 0.31678E 00-0.39122E O0-0.23234E 00 0 447 17E 00-0.35065E 42209E-02 0.17235E 00 0.23963E 00-0 22650E 00 00 318 319 320 -0.415S2E-O3-O.66235E 00 0.34511E 00 0.34197E 00-0.339166 00 0.13433E-01 0 0.59792E-02 0.41813E 00-0.336S7E 00 42322E OO 0.40861E 00-0.22179E 00 321 322 323 6.345i2E 66-6.13766E 66 6.3968SE 66 6 0.3737IE-02 0.85572E-01 0.44310E 00 0.32OO4E 00 0.14023E-01 0.45150E 00-0 39533E 66-6.14213E 33083E-01-0.32729E 00 0.62t02E 00-0 58562E 00 -01 324 325 326 -6.67696E-62-6.38795E 60-6.61489E 66 0.34294E 00 0.1643SE 00 0.38142E 00-0 -0.96139E-01 0.32200E 00 0.37778E 00 435B6E 00 0.32676E- 02-0.5110SE 00 327 328 329 0.32544E 00 0.32838E 00-0.11377E-01-0 0.51130E 0O-0.B7018E-O1-0.67666E-01 0.30399E 00 0.3B167E 00-0.2452 IE 00 0 31404E 66 6.49650E 34340E-01 0.12210E 00 0.32316E 00 0.17703E 00 00 330 331 332 -0.76882E OO-O.55044E-01-0.66979E-O1 0.34319E 00 0.46080E O0-0.43738E 00 0 0.35910E 00 0.58969E-01 0.57106E-01 37312E OO-0.40668E OO-0.23920E 00 333 334 335 C C 5L1. 512, and 5L3 from second t r a n s p o s i t i o n point to last 5L3 C t r a n s p o s i t i o n po in t . 336 C beta length-adjusted from Brent Hughes case . Untransposed 7 Fig. 25 (cont'd) L i s t i n g Of SHI 1002 at 10:46:01 on APR 12. 1986 for CCId'BRWG Page 7 337 C 1Ina model. 338 339 340 C Transpos i t ion e f fec ted at sending end of s e c t i o n for a l l three C 1Inea. -1L1-S .AL1-6 .A 0.8623947.820B93E4 33.24 1 9 34 1 342 343 -2L1-6 .CL1-6 .C -3L1-5 .BLI -6 .B -4L2-5 .AL2-6 .A 0.0484478.891513E4 33.24 0.0433376.O11705E4 33.24 0.0395271.181B03E4 33.24 1 9 1 9 1 9 344 345 346 -5L2-5 .CL2-6 .C -6L2-5 .BL2-6 .B -7L3-5 .CL3-6 .C 0.0331209.701827E4 33.24 0.0324202.761838E4 33.24 0.0477228.751848E4 33.24 1 9 1 9 I 9 347 348 349 -8L3-S .BL3-6 .B -9L3-S .AL3-6 .A 0.35665E 00-0 0.0390226.081847E4 33.24 0.0385319.921849E4 33.24 4717IE 00-0.42982E 00-0.447I7E 00-0 1 9 1 9 35065E 00 0.23963E 00 350 351 352 -0.37070E-02 0 0.31678E 00-0 -0.41652E-03-0 31I96E 00-0.13818E 00 39122E 00-0.23234E 00 0.42209E-02 0 66235E 00 0.34511E 00 17235E OO-0.2265OE 00 353 354 355 0.34197E 00-0 0.59792E-02 0 0.34512E 00-0. 335I5E 00 0.13433E-01 0.42322E 00 0 41813E 00-0.33657E 00 13700E 00 0.3968SE 00 0.39S33E 00-0 40861E 14213E OO-0.22179E 00 0.521O2E 00 00 356 3S7 358 0.37371E-02 0. 0.32O04E 00 0 -0.67096E-02-0 85572E-01 0.44310E 00 14O23E-01 O.45150E 00-0.33083E-01-0 38795E 00-0.61489E 00 32729E OO-0.58562E -01 359 360 361 0.34294E 00 0 -0.96139E-01 0 0.32544E 00 0. 16435E 00 0.38142E 00-0.43586E 00 0 32200E 00 0.37778E 00 32838E 00-0.11377E-01-0.31404E 00 0 32675E 496SOE -02-0.51105E 00 0.323IEE 00 00 362 363 364 0.51130E 0O-0. 0.30399E 00 0. -0.76882E 00-0. 87018E-0I-0.67666E-01 38167E O0-0.24521E 00 0.34340E-01 0 55044E-01-0.66979E-01 12210E 00 0.17703E 00 365 366 367 0.34319E 00 0. 0.35910E 00 0. C 46080E 00-0.43738E 00 0.373I2E 00-0 58969E-01 0.57 106E-O1 40668E 00-0.23920E 00 368 369 370 C SL1, SL2. and SL3 from last 5L3 t r a n s p o s i t i o n point to WSN. C Data length adjusted from Brent Hughes case . Untransposed C l i n e model. Lengths In mi les . 371 372 373 C T ranspos i t ion of 513 e f fec ted at sending end -1L1-6.AVT1S.A 0.8623947.820893E4 26.00 -2L1-6.CVTIS.C 0.0484478.891513E4 26.00 of th is s e c t i o n . 1 9 1 9 374 375 376 -3L1-6.BVT1S.B -4L2-6.AVT2S.A -5L2-6.CVT2S.C 0.0433376.01170SE4 26.00 0.0395271.181803E4 26.00 0.0331209.701827E4 26.00 1 9 1 9 • t 9 37? 378 379 -6L2-6 .Bvt2S.B -7L3-6.AWSN..A -8L3-6.CWSN. C 0.0324202.761838E4 26.00 0.0477228.751848E4 26.00 0.0390226.081847E4 26.00 1 9 1 9 1 9 380 381 382 -9L3-6.BWSN..6 0.3S665E 00-0. -0.37070E-02 0. 6.6385219.92i849E4 26.66 47171E 0O-O.42982E 00-0.447I7E 00-0. 31196E 00-0.13B18E 00 1 9 3506SE 00 0.23963E 00 383 384 385 6.3i678E 66-6. -0.4I552E-03-0. 0.34197E 00-0. 39i22E 60-6.23234E 66 6.42209E-62 6. 6623SE 00 0.34S11E 00 33515E 00 0.13433E-01 0.42322E 00 0. 17235E 4086 IE 00-0 22650E 00-0 22179E 00 00 386 387 3BB 0.B9792E-02 0. 0.34512E 00-0. 0.37371E-02 0. 41813E 0O-O.33657E 00 13700E 00 0.39685E 00 0.39533E 00-0. 85572E-01 0.44310E 00 14213E 00 O.S2102E 00 389 390 391 6.32664E 66 6. -0.67096E-02-0. 0.34294E 00 0. I4623E-61 0.45I50E 66-6.33083E-01-0. 38795E 00-0.61489E 00 16435E 00 0.3B142E OO-0.43S86E 00 0. 32729E 32675E-00-0 58S62E 02-0.51105E -01 00 392 -6.96i39E-6i 6. 32200E 00 0.37778E 00 Fig. 25 (cont'd) CO L i s t i n g of SHI 1002 at 10:46:01 on APR 12. 1986 for CCId-BRWG Page 8 393 0.32544E 00 0.32838E 00- 0. 1 1377E-01-0.3I404E 00 0.49650E 00 0.32316E 00 394 0.S1130E 0O-O.87O18E-OI- 0.67666E-01 396 0.30399E 00 0.38I67E 00- 0.24521E 00 0.34340E-01 0.12210E 00 0.17703E 00 396 -0.76882E O0-0.55044E-01- 0.66979E-01 397 0.34319E 00 0.46080E 00- 0.43738E 00 0.37312E OO-0.40668E 00-0.23920E 66 398 0.35910E 00 0.58969E-01 0.57106E-01 399 C 400 C South end 5L1 c l o s i n g r e s i s t o r s and sw1tch-1 sol atIng Impedances 401 C A lso used for current measurement 402 VTIS.ACB1S1AC8IN1AVT1N A 403 VTIS.BCBISIBCBtNIAVTtN A 404 VTIS.CCBIS1CCBIN 1AVTIN A 405 CB1S2ACB1S1AGMS..A5L1N A 406 CB1S2BCB1S1BGMS..ASLIN A 407 CB1S2CCB1S1CGMS..A5L1N A 408 WSN..ASL1S.AGMS..A5L1N A t 409 WSN..BSL1S.BGMS..A5L1N A 1 410 WSN..C5LIS.CGMS..A5L1N A i 411 VT2S.ACB2S1ACBINIAVTIN A 412 VT2S.BCB2S1BCBINIAVTIN A 413 VT2S.CCB2S1CCBIN 1AVTIN A 414 CB2S2ACB2S1AGMS. .ASL IN A 415 CB2S2BCB2S1BGMS..ASL1N A 416 CB2S2CCB2S1CGMS..ASLIN A 417 WSN. .A5L2S.AGMS. .A5L IN A 418 WSN..B5L3S.BGMS..A5LIN. A 419 WSN..C5L2S.CGMS..ASLIN. A 420 C 421 C 8L1 CT Is from WSN to 5L1S 422 C BL1 CVT la at VT1S 423 C 424 C WSN Thevenin source: 426 C (WSN-E Is WSN Internal voltage node) 426 1WSN-EAWSN. . A 3.724443. 127 427 2WSN-EBWSN..8 -.19332.3852 3.724443.127 428 3WSN-ECWSN. C -.19332.3852 -.19332.3852 3.724443 . 127 429 C 430 C WSN shunt reactors (2 u n i t s ) : 431 WSN..A 2.5 1020. 432 WSN. B 2.5 1020. 433 WSN..C 2.5 1020. 434 C 435 C end of network 436 437 FAULT IFAULT23.780583-31 .00000000 438 5L1N.ACB1N1A-1. 1 .0 30.0 439 5LIN.BCBIN IB-1. i .6 30.0 440 5LIN.CCB1N1C-1. 1 .0 30.0 441 CB1N2AVTIN.A-1. 1 .0 30.0 442 CBiN2BVf1N.B-1. i .0 30.0 443 CB1N2CVT1N.C-1. 1 .0 30.0 444 5LIS.ACB1S1A-1. 1 .0 30.0 445 S L I S . B C B I S i B - i . i .0 30.0 446 5L1S.CCB1S1C-1. 1 .0 30.0 447 CB1S2AVTIS.A-1. 1 .0 30.0 448 CB1S2BVT1S.B-1. 1 .0 30.0 1 2 3 4 S 6. 7 8 9 0 1 2 . Fig., 25 (cont'd) L i s t i n g of SH11002 at 10:46 01 on APR 12. 1986 for CCId-BRWG Page 9 449 CB1S2CVTIS.C-1 1.0 30.0 4SO 431 452 SL2N.ACB2N1A-1 SL2N.BCB2N1B-1 5L2N.CC82N1C-1 1 .0 1 .0 1 .0 30.0 30.0 30.0 433 434 453 CB2N2AVT2N.A-1 C82N2BVT2N.B-1 CB2N2CVT2N.C-1 1 .0 1.0 1 .0 30.0 30.0 30.0 456 457 458 CB2S1A5L2S.A-1 CB2S1B5L2S.B-1 CB2S1C5L2S.C-I 1 .0 1 .0 1 .0 30.0 30.0 30.0 459 460 461 CB2S2AVT2S.A-1 CB2S2BVT2S.B-1 CB2S2CVT2S.C-1 1 .0 1 .0 1 .0 30.0 30.0 30.0 462 463 464 KD1NOAKDIN1A0. K01N2AKD1N3AO. KOY1SAKO1S1AO. .083 .083 .083 30.0 30.0 30.0 10000. 190890. 10OO0. 465 466 467 K01S2AKD1S3A0. KD1NOBKD1N180. KD 1N2BK0 1N3B0. .083 .083 .083 30.0 30.0 30.0 190890. 10000. 190890. 468 469 470 KDY1SBKD1S180. K01S2BK01S3BO. KO1N0CKD1N1C0. .083 .083 .083 30.0 30.0 30.0 10000. 190890. 10000. 471 472 473 KO 1N2CKD 1N3C0. KDY1SCKD1S1C0. KD1S2CKD1S3C0. .083 .083 .083 30.0 30.0 30.0 190890. 10000. 190890. 474 475 476 KD2NOAKD2N1AO. K02N2AKD2N3A0. KOY2SAKD2S1AO. .083 .083 .083 30.0 30.0 30.0 10000. 190890. 10000. 477 478 479 K02S2AK02S3AO. KD2NOBKD2N180. KD2N2BK02N3BO. .083 .083 .083 30.0 30.0 30.0 190890. 10000. 190B90. 480 481 482 KDY2SBK02S1BO. KD2S2BK02S3BO. K02NOCK02N1CO. .083 .083 .083 30.0 30.0 30.0 10000. 190890. 10000. 483 484 485 K02N2CK02N3CO. KDY2SCKD2SICO. KD2S2CKD2S3CO. .083 .083 .083 30.0 30.0 30.0 190890. 10000. 190890. 486 487 488 KD3NOAKD3N1AO. KD3N2AK03N3AO. KOY3SAK03S1A0. .083 .083 .083 30.0 30.0 30.0 10000. 192420. 10000. 489 490 491 K03S2AKD3S3AO. KD3NOBKD3N1BO. KD3N2BKD3N3BO. .083 .083 .083 30.0 30.0 30.0 192420. 10000. 192420. 492 493 494 KDY3S6K03S180. KD3S2BK03S3BO. K03NOCK03N1CO. .083 .083 .083 30.0 30.0 30.0 10000. 192420. 10000. 495 496 497 K03N2CKD3N3CO. KDY3SCKD3S1C0. KD3S2CKD3S3C0. .083 .083 .083 30.0 30.0 30.0 192420. 10000. 192420. 498 499 800 14GMS-EA 042576? 14GMS-EB 0425767 790 790 60. 60. 46.201000 -73.799000 1 . 1 . 1 . 1. 801 802 803 i4GMS-EC 0425767 14PCN-EA 0425818 14PCN-EB 042S81S 790 370 370 60. 60. 60. 166.20100 49 . 34S0O0 -70.655000 , i . i . i . 1. 304 14PCN-EC 0425815 370 60. 169.34500 i . i . 2 Fig. 25 (cont'd) L i s t i n g of SHII002 at 10:46:01 on APR 12. 1966 for CCId'BRwG Page 10 508 . 14WSN-EA 0470553.000 60. - 4.730900 - 1 . 1. 506 UWSN-EBT 64705531666 60. -124.73690 - i . 1 507 I4WSN-EC 0470553.000 60. 115.26910 -1 . 1. 508 509 VT IN.AVTIN.BVTIN.CVT i s . A V t i S . B V f i S . C 810 511 812 END OF RUN 1 2 3 4. 5 6 7 8 9 O 1 2 Fig. 25 (cont'd) APPENDIX B PROTECTION MODEL A. TRP PROTECTION SIMULATION The operation of the protection for the B.C. Hydro Peace River transmi-ssion line 5L1 has been described in chapter V . Figure 26 shows a listing of the TRP commands which simulate this protection. The Williston phase-fault protection is simulated first (lines 5-112) followed by the Williston ground-fault protection (lines 113-210). The G . M . Shrum relays are simulated next: the phase-fault protection first (lines 214-332), followed by the ground-fault protection (lines 333-430). Finally the Williston and G . M . Shrum signals are combined in the permissive trip block according to the permissive- and transfer-trip logic (lines 431-447). B. USER FUNCTION DESCRIPTIONS This section describes the special TRP user functions which were written to allow modelling of the 5L1 protection. 1. AND The A N D function is performed as an N L R operation (see chapter III). The output is thus the algebraic minimum of the inputs. Only two inputs are available for this implementation, although more could have been provided.! The A N D function is implemented as an alias of the TRP internal function M I N I M U M . tThis presents only a minor annoyance in practice, since multiple two-input A N D functions can easily be cascaded to get a multiple-input A N D function. 177 L t 8t1ng of 1 IWSNCBP COMM at 12:41:07 on O C T 4, 1986 for C C I d - B R W G SIMULATION F O R SL1 PROTECTION (19860927) Papa 1 1.5 2 3 C O M M COMM COMM N E W PERMISSIVE TRIP BLOCK WSN-END PROTECTION 4 5 6 COMM COMM COMPUTE COMPUTE DELTA VOLTAGES C V : W V A B - S U B T R A C T ( N V : V T 1 S . A , N V : V T 1 S . B ) 7 S 9 COMPUTE COMPUTE COMM CV: WVBCi•SUEif PACT(NV: V T i5 . B , N V : V T i S.C ) CV:WVCA"SUBTRACT(NV: V T 1S . C , N V : V T 1S . A ) COMPUTE OELTA CURRENTS 10 1 1 12 COMPUTE COMPUTE COMPUTE 'CV:'wiAB»SUBfRACf (BcYwSN. .A:5L i S . A , B C : WSN. . B : 5 L 1 S . B ) C V:WIBC-SUBTRACT ( B C : W S N . . B : 5 L 1 S . B , B C :WSN . , C:5L1S . C ) C V . W I C A " S U B T R A C T ( B C : W S N . . C : 5 L 1 S . C , B C : W S N . , A : 5 L 1 S . A ) 13 14 15 COMM COMM COMM PHASE-FAULT RELAYS 21LX FILTER-SWITCHINO RELAY IE 17 18 COMPUTE CV:21LX-SDX1H(CV:WVAB,CV:WVBC,CV:WVCA.360E3,22.5E3,.33..33) PLOT HOLD Y-RANGE*(19,9', -19.9) Y-UNITS- -PLOT Y - L A B E L " " W S N 21LX Q-SWITCHING OUTPUT" TRACE (2 ) - C V :21LX(0) -19 20 21 PLOT V -OISPLAY COMM LABEL-'WSN 21LX INSERT DELAY OUTPUT" TRACE(1) -CV :21LX(1) -RANGE - C V:21LX (0 ) ; C V:21LX(1) 21L1 ZONE 1 (UNDERREACHING) DISTANCE RELAY 22 23 COMPUTE DISPLAY ' C V : 2 a i ' A B-SD2H ( C V:WVAB i ) , 3 5 . 4 , 8 5 , i6. i , B . 40E-3 , 82 . 5 , RANGE-CV:21L1AB .33)' 25 26 27 DISPLAY COMPUTE DELETE RANGE-CV:21L1BC CV:TMPO -0R (CV:21L1AB ,CV:21L1BC) ENTRY-CV:21L1AB:CV:21L1BC 28 29 30 COMPUTE C V : 2 1 L 1 C A»S02H ( C V :WVCA,C V:WICA , C V : 2 1 L X(o) , C V:21LX(1 ) , 3 5 . 4 , 8 3 ,10.1 . 5 ,40E - 3 . 8 2 . 5 . DISPLAY RANGE»CV:21L1CA COMPUTE C V:21L1 " O R ( C V:21L1CA , C V:TMPO) .33) 31 32 33 DELETE DISPLAY PLOT Y -ENTRY-CV:21L1CA;CV:TMP0 RANGE-CV:21L1 LABEL-'WSN 21L1" TRACE(S )-CV :21L1 -34 35 36 COMM COMPUTE DELETE 21L2 ZONE 2 (OVERREACHING) DISTANCE RELAY C V:21L2AB-S02H ( C V:WVAB , C V:WIAB , C V:21LX ( O ) , C V:21LX(1) .1 2 3 , 85 .10 .1.S.40E-3.82 . 5 , . ENTRY-CV : WVAB 33) 37 38 39 DISPLAY COMPUTE DELETE RANGE«CV:21L2AB C V:21L2BC-S02H ( C V:WVBC , C V:WIBC , C V:21LX ( O ) , C V:21LX(1 ) ,123 , 6 5 , 1 0 , 1 , 5 ,40E - 3 , 8 2 .S.. ENTRY-CV: WVBC 33) 40 41 42 DISPLAY COMPUTE DELETE 'R'ANGE'"CV:2iL'2BC C V :TMPO - O R ( C V:21L2AB , C V:21L2BC) ENTRY -CV:21L2A8 ;CV:21L2BC 43 44 43 COMPUT1 CV: 2' i LicA- S02HTC V : W V C A . Ci V: W iC A , C:V12! 1LX (Ci), C V : 21UX'(1), 123 ,85 , 10. 1,5.40E -3.82 . 5 , . DISPLAY RANGE-CV:21L2CA COMPUTE C V : 2 1L2 - 0 R ( C V : 2 1L2CA , C V :TMPO) 33) 46 47 48 DELETE DISPLAY PLOT Y -ENTRY"CV:21L2CA;CV:TMPO;CV:WVCA;CV:WICA:CV:WIBC:CV:WIAB RANGE-CV:21L2 LABEL*"WSN 21L2" TRACE(4)"CV :21L2 -49 SO 51 COMM COMM COMPUTE 21L3 26NI 3 ( S E V E R S E BLOCkiNG) DiSfANCE RELAY NEGATE CURRENTS--21L3 C T I S REVERSE LOOKING C V : I A-NEGATE ( B C:WSN. .A:SL1S .A ) 52 53 54 COMPUTE COMPUTE COMM C V : I B - N E G i t E ( B C : W S N . . B : 5 L i S . B ) C V : 1 C " N E G A T E ( B C : W S N . , C : S L 1 S . C ) LOAD ANGLE COMPENSATOR 5S COMPUTE C V : L ACA-'LACTCV:t A,33.7?) Fig. 26. Listing of TRP data for 5L1 protection simulations L i s t i n g of IWSNCBP at 12:41:07 on OCT 4, 1986 for CCId-BRWG P a g e 5 6 C.P.MPyiE Cy.:LACB-5 7 58 5 9 COMPUTE C V : L A C C - L A C ( C V : I C . 3 3 . 7 7 ) COMPUTE CV:VA»ADD(NV:VTIS.A,CV:LACA) COMPUTE C V : V B " A D O ( N V : V T 1 S . B , C V : L A C B j 60 61 62 COMPUTE C V : V C - A D D ( N V : v t I S . C . C V : L A C C ) DELETE ENTRY - C V :LACA;C V :LACB;C V :LACC COMPUTE C V : V A B - S U B T R A C T ( C V : V A . C V : V B ) 6 3 64 65 COMPUTE C V : V B C ' S U B T R A c f ( C V : V B . C V : V C ) COMPUTE CV:VCA-SUBTRACT(CV:VC ,CV:VA) DELETE ENTRY-CV :VA ;CV:VB;CV:VC 6 6 6 7 68 COMPUT1 CV : IAB-SUBT R A C T ( C V : I A , C V : I B ) COMPUTE CV: IBC-SUBTRACT(CV: IB.CV:IC) COMPUTE CV:ICA-SUBTRACT(CV:IC,CV:IA) 6 9 70 71 OELETE ENTRY-CV: IA;CV: IB : C V : IC COMM FILTER DROPOUT DELAY COMPUTE CV:FILTERX-TIMER(CV :21IX (0 ) .0 .60E-3) 72 73 74 DISPLAY RANGE"CV:FILTERX COMPUTE C V : 2 1 L 3 A B - S D 2 H ( C V : V A B . C V : I A B . C V : F I L T E R X . C V : 2 1 L X ( 1 ) , 1 6 0 . 7 , 8 7 OELETE ENTRY-CV:VAB;CV:IAB 1 , 10 , 1 . 3 , 0 . 8 2 5 , 3 3 ) 75 76 77 OISPLAY RANGE-CV:21L3AB COMPUTE CV:21L3BC-S02H(CV: V B C C V : IBC . CV : FI LTERX , CV : 2 1 LX( 1 ) . 160.7,87 DELETE ENTRY-CV:VBC;CV:IBC 1 . 10, 1 . 5 , 0 , 8 2 5 , 3 3 ) 78 7 9 ' 80 DISPLAY RANGE-CV:21L3BC COMPUTE CV:TMP0-0R(CV:21L3AB,CV:21L3BC) DELETE ENTRY-CV:21L3AB;CV:21L3BC 81 82 83 COMPUTE C V : 2 rL3CA - s 6 2 H ( c V : V C A , C V : I C A , C V : F I L T E R X , C V : 2 i LX(1 ) . 160-7 , 8 7 DELETE ENTRY-CV:VCA;CV:ICA;CV:FILTERX;CV :21LX DISPLAY RANGE-CV:21L3CA 1 , 10, 1 , 5 . 0 . 8 2 5 . 33)' 84 85 86 COMPUTE C V : 2 iL3-0R(CV:2 iL3CA,CV:f'MPO) DELETE ENTRY-CV:21L3CA;CV:TMP0 DISPLAY RANGE-CV:21L3 87 88 6 9 p'LOT Y-LABEL- "WSN 2 1 L 3 " f RAC'E'(3)'"CV : 2 i L 3 -COMM COMM DISTANCE SUPERVISION CURRENT RELAYS 9 0 91 COMM COMPUTE CV:50LA-OVERCURRENT.IT(BC:WSN..A:5L1S.A,268,1, .33) 9 3 94 95 COMPUTE C V : 5 b L C » 6 v E R C U R R E N f . i f ( B C : W S N . . C : 5 L 1 S . C , 2 6 8 , i , . 3 3 ) DISPLAY RANGE-CV:50LA;CV:50LB;CV:50LC COMM " O R • TO GET DISTANCE SUPERVISION OUTPUT 96 97 98 COMPUT£ CV:fHPo-eft(CV:50LA,CV:SbLB) COMPUTE CV : 5 O L - 0 R (CV:5OLC , C V :TMPO) OELETE ENTRY-CV:TMPO;CV:50LA;CV:50LB:CV:50LC 99 100 101 OI SPLAY RANGE-CV: SOL' PLOT Y-LABEL-"WSN SOL" TRACE(6)-CV:SOL RELEASE COMM 102 103 104 COMM "AND" tb GET PHASE-FAULf blRECT TRIP COMPUTE CV:PFDT-AND(CV:21L1,CV:50L) DELETE ENTRY-CV:21L1 105 106 107 COMM "AND* t'O GET PHASE-FAULf PERMiSSIVE TRIP COMPUTE CV:PFPT-AND(CV:21L2,CV:50L) DELETE ENTRY-CV:21L2 108 109 1 10 d i s p i a y rahge-cv:pf 'dt ;CV:PFPf COMM " A N D " TO GET PHASE REVERSE BLOCKING COMPUTE C V : P R B - A N D ( C V : 2 1 L 3 , C V : 5 0 L ) 1 1 1 DELETE ENTRY-CV : 2 i L 3 ; C V : 5'6't 2. Fig. 26 (cont'd) L i s t ! n g of IWSNCBP at 12:41:07 on OCT 4 , 1986 for CCId-BRWG Page 3 112 DISPLAY RANGE-CV:PRB 1 13 1 14 1 15 COMM COMM GROUND-FAULT RELAYS COMM COMPUTE 3 * ZERO-SEOUENCE VOLTAGE 1 16 1 17 1 18 COMPUTE CV:TMPO"ADO(NV:VT i 5.A,NV:VT1S. B) COMPUTE CV:TMP1-ADD(CV:TMPO,NV:VT1S.C) COMM FILTER 3V0 FOR INPUT TO DIRECTIONAL ELEMENTS 1 19 120 12 1 COMPUTE CV:3V'6-FiLTER<CV:tMPi, 1> OELETE ENTRY-CV:TMP0;NV:VT1S.A;NV:VT1S.B;NV:VT1S.C;CV:TMP1 COMPUTE CV:PSFILTER-PS-FILTER.A(BC:WSN. .A:5L1S.A,BC:WSN. .B:5L1S.B,BC:WSN. .C:5L1S.C) 122 123 124 DELETE ENTRY-BC:WSN..A:5L1S.A;BC:WSN..B:5L1S.B;BC:WSN..C:5L1S.C COMM FILTER 310 FOR INPUT TO DIRECTIONAL ELEMENTS AND 50LN / I0 . . . COMPUTE CV:3I0-FILTER(CV:PSFILTER(1) ,1) 125 126 127 COMM USE INSTANTANEOUS OVERCURRENT ELEMENT FOR FINITE SENSITIVITY COMM (NO HYSTERESIS WANTED HERE) COMPUTE CV:GATE-OVERCURRENT.IT(CV:3I0,50) 128 129 130 COMM GATE 310 COMPUTE CV:G3I0-GATE(CV:310,CV:GATE) COMPUTE CV:32R-DIRECTI0NAL(CV:G3IO,CV:3VO.-89.5,96, .33) 131 132 133 COMM NEGATE GATED 310 FOR FORWARD ELEMENT COMPUTE CV:NG3I0-NEGATE(CV:G3I0) COMPUTE CV:32F-0IRECTI0NAL(CV:NG3I0.CV:3V0.-89.5,85, .33) 134 135 136 DELETE 'ENTRY-CV:NG310:CV:3V0;CV:G3l6:CV:GATE PLOT HOLD Y-RANGE-( -19 .9 ,19 .9) Y-UNITS- -PLOT Y-LABEL-"WSN 32F" TRACE(2)-CV:32F -137 13B 139 PLOT Y-LABEL-"WSN 32R" TRACE(i)-CV:32R -DISPLAY RANQE-CV:32F;CV:32R COMM 140 14 1 142 COMM GROUND INVERSE-TIME OVERCURRENT ELEMENT COMPUTE CV:5OLN1S-0VERCURRENT.IT(CV:PSFILTER(1),200,1000,.33) PLOT Y-LABEL-"WSN 50LN1S" TRACE(3)-CV:50LN1S -143 144 145 DISPLAY RANGE-CV:50LN1S COMM COMM "AND" TO GET DIRECTIONAL GROUND OVERCURRENT OUTPUT 146 147 148 COMPUT E CV:DGOC-AND(CV:32F,CV:50LN i S) DISPLAY RANGE-CV:DGOC DELETE ENTRY-CV:50LN1S 149 150 151 COMM COMM INSTANTANEOUS GROUND OVER-CURRENT RELAY COMPUTE CV:RESTRAIN-C0PY(CV:PSFILTER,0.2) 152 1S3 1S4 COMPUTE CV:SbLNibb-dvERCURRENt.R(CV:310,CV:RESTRAIN,'466,630,.33) PLOT Y-LABEL-"WSN 50LN/I0D" TRACE(6)-CV:50LNIOD -COMPUTE CV:50LNI0H-0VERCURRENT.R(CV:310,CV:RESTRAIN,300,630,.33) 155 156 157 COMPUTE CV:S'OlNiOL*&"vi^ 166,630, .33) PLOT Y-LABEL-"WSN 30LN/I0L" TRACE(4)-CV:50LNI0L -PLOT Y-LABEL--WSN 50LN/I0H" TRACE(5)-CV:50LNIDH RELEASE 158 159 160 DiSPLAY RANGE-CV:SOLNIOD;CV:SOLNiOH:CV:SOLNiO'L DELETE ENTRY-CV:PSFILTER;CV:RESTRAIN;CV:310 COMM 16 i C O M M ' • ' b ' R ' ' " ' ' ' f O ' ' ' G ' E ' ' f ' ' ' c " b M P L E t ' E 162 COMPUTE CV:GFDT-0R(CV:5OLNI0D.CV:DG0C) 163 DISPLAY RANGE-CV:GFDT 1 6 4 P L O T HOLD Y-RANGE - ( - 19 . 9. 19 . 9) Y -UNitS- -165 PLOT Y-LABEL-"WSN GROUND FAULT DIRECT TRIP" TRACE(5)-CV:GFOT -166 PLOT Y-LABEL-"WSN PHASE FAULT DIRECT TRIP" TRACE(6)"CV:PFDT -1 6 7 D E L E T E ENtRYiCv':'5'6LNibb:CV:OGOC 1 . . . . . . . . .2 . 3 . . . . .4 5 6 7 8 9 0 1 2. Fig. 26 (cont'd) 1 I 3 t I n g of IWSNCBP at 12:41:07 On OCT 4, 1986 for CCId-BRWG Page 4 168 COMM "AND" TO GET GROUND FAULT PERMISSIVE TRIP' 169 170 171 COMPUTE CV:GFPT-AND(CV:50LNI OH,CV:32F j PLOT Y-LABEL-"WSN GROUND FAULT PERMISSIVE TRIP" TRACE(3)-CV:GFPT -PLOT Y-LABEL-"WSN PHASE FAULT PERMISSIVE TRIP" TRACE(4)-CV:PFPT -172 173 174 DELETE ENTRY"CV:5OLNI0H:CV:32F COMM "AND" TO GET GROUND REVERSE BLOCKING COMPUTE CV:GRB-AND(CV:S0LN10L,CV:32R) 175 176 177 'PLOT Y-LABEL- "WSN GROUND FAULT REVERSE BLOCKING" TRACE ( i ) "CV: GR8 -PLOT Y-LABEL-"WSN PHASE FAULT REVERSE BLOCKING" TRACE(2)-CV:PRB PLOT RELEASE 178 179 180 DISPLAY RANGE"CV:GFPT;CV:GRB DELETE ENTRY-CV:50LNI0L;CV:32R COMM 18 1 182 183 COMM "OR" PHASE AND GROUND DIRECT TRIP TO GET DIRECT LOCAL TRIP COMPUTE CV:WSNDLT-OR(CV:PFDT,CV:GFDT) DISPLAY RANGE-CV:WSNDLT 184 185 186 DELETE ENTRY-CV:PFDT;CV:GFDT COMM "OR" PHASE AND GROUND PERMISSIVE TRIP TO GET COMM COMBINED PERMISSIVE TRIP 187 188 189 COMPUTE CV: CPT "OR (CV : PFPT , CV : GF'p'f ) DISPLAY RANGE-CV:CPT DELETE ENTRY-CV:PFPT;CV:GFPT 190 191 192 COMM "OR" PHASE AND GROUND REVERSE BLOCKING TO GET REVERSE COMM BLOCKING COMPUTE CV:RB-OR(CV:GRB,CV:PRB) 193 194 195 OISPLAY RANGE-CV:RB DELETE ENTRY-CV:GRB;CV:PRB COMM USE DROP-OUT DELAY AND INVERSION TO GET "NO-REVERSE-BLOCKING" 196 197 198 COMPUTE CV:fMP-fiM'ER(cV:'R'B.6. iOOE-S)' DELETE ENTRY-CV:RB COMPUTE CV:WSNNRB-NOT(CV:TMP) 199 200 201 DISPLAY RANGE-CV:WSNNR8 DELETE ENTRY-CV:TMP COMM "AND" COMBINED PERMISSIVE TRIP AND NO-REVERSE BLOCKING TO GET 202 203 204 COMM LOCAL FORWARD PERMISSIVE COMPUTE CV:WSNLFP-AND(CV:CPT,CV:WSNNRB) PLOT TRACES/PAGE-4 HOLD Y-RANGE•(- 19.9,19.9) Y-UNITS- -205 206 207 PLOT Y-LABEL-"WSN COMBINED PERMl'SSiVE TRIP" f RACE( 1 ) • C V : CPt -PLOT Y-LABEL-"WSN NO REVERSE BLOCKING" TRACE(2)-CV:WSNNRB -PLOT Y-LABEL-"WSN LOCAL FORWARD PERMISSIVE" TRACE(3)-CV:WSNLFP -208 209 210 PLOT Y - L ' A B E L - ' W S ' N ' DIRECf LOCAL TRIP" TRACE (4 )-CV : WSNDLT RELEASE DELETE ENTRY-CV:CPT DISPLAY RANGE-CV:WSNLFP 21 1 212 213 COMM COMM GMS-END PROTECTION COMM 214 214 214 2 4 COMM COMPUTE DELTA VOLTAGES COMPUTE CV:GVAB-SUBTRACT(NV:VT1N.A.NV:VT1N.B) COMPUTE CV:GVBC«SUBTRACT(NV:VT1N.B.NV:VT1N.C) 214 2 14 215 6 8 COMPUTE CV:GVCA"SUBTRACT(NV:VT iN.C,NV:VT iN.A) COMM COMPUTE DELTA CURRENTS COMPUTE CV:GIAB"SUBTRACT(BC:GMS..A:5L1N.A,BC:GMS..B:5L1N.B) 215 215 233 2 4 COMPUTE C'v':GiBC"S'UBf'RACf (BC:GMS. . B : 5L i N. B , BC : GMS . .C:SL1N.C) COMPUTE CV:GICA"SUBTRACT(BC:GMS..C:5L1N.C,BC:GMS..A:5L1N.A) COMM 234 COMM PHASE-FAULT RELAYS . . . 1 2 . Fig. 26 (cont'd) L1s 11ng Of IWSNCBP at 12:41:07 on OCT 4, 1986 for CCId-BRWG Page 5 233 COMM 21LX FILTER-SWITCHING RELAY 236 237 238 COMPUTE' CV:2iLX'SOX1H"<CV:GVAB.CV:GVBC.CV:GVCA.360E3.22. 5E3. .33. .33)' PLOT HOLD Y-RANGE-(19.9 , -19.9) Y-UNITS- -PLOT Y-LABEL-"GMS 21LX Q-SWITCHING OUTPUT * TRACE(2)-CV:21LX(0) -239 240 24 1 PLOT Y-LABEL-"GMS 21LX INSERT DELAY OUTPUT" fRACE(i!)-CV:2iLX(1) -01 SPLAY RANGE-CV:21LX(0);CV:21LX(1) COMM 21L1 ZONE 1 (UNDERREACHING) DISTANCE RELAY 242 243 COMPUTE CV:2iLiAB-SD2H(CV:GVA8,CV:GIA8.C i ) . 3 5 . 4 , 8 5 . 1 0 , i , 5 . 4 0 E - 3 . 8 2 . 5 DISPLAY RANGE-CV:21L1AB .33) 245 246 247 DISPLAY RANGE-CV:21L1BC COMPUTE CV:TMPO-0R(CV:21L1AB,CV:21L1BC) DELETE ENTRY-CV:21L1AB;CV:21L1BC 248 249 250 COMPUTE CV: 2 i t iC*»s6'2H'(CV: GVCA, CV: GICA. CV: 2 iCtfo), CV: 2 it'x( 1)', 3Si. 4 ,85i, 10, i . 5i, '40E-3,82 . 5. DISPLAY RANGE-CV:21L1CA COMPUTE CV:21L1-0R(CV:21L1CA,CV:TMPO) .33) 251 252 253 DELETE ENTRY-CV:21L1CA;CV:TMP0 DISPLAY RANGE-CV:21L1 PLOT Y-LABEL-"GMS 21L1" TRACE(5)-CV:21L1 -254 255 256 COMM S iL2 ZONE 2 (OVERREACHING) DlSfANCE RELAY COMPUTE CV:21L2AB-SD2H(CV:GVAB,CV:GIAB,CV:21LX(0) ,CV:21LX(1) ,123,85,10,1 ,5 ,40E-3,82.5 , . DELETE ENTRY-CV:GVAB 33) 257 258 259 DISPLAY RANGE-CV:21L2AB COMPUTE CV:21L2BC-SD2H(CV:GVBC,CV:GIBC,CV:21LX(0) ,CV:21LX(1) ,123,85,10.1 ,5 ,40E-3,82.5 , . DELETE ENTRY-CV:GVBC 33) 260 26 1 262 DISPLAY RANGE-CV:21L2BC COMPUTE CV:TMPO-OR(CV:21L2AB,CV:21L2BC) DELETE ENTRY-CV:21L2AB;CV:21L2BC 263 264 265 COMPUTE CV:2iL2CA-SD'2H'rc'V:GVCA 1 )', 123.85, 10, i , 5 , 40E-3 , 82 . 5 , . DISPLAY RANGE-CV:21L2CA COMPUTE CV:21L2-0R(CV:21L2CA,CV:TMPO) 33) 266 267 268 DELETE ENTRY-CV:2iL2CA;CV:fMPO;CV:GVCA;CV:GIAB; C V : GIBC;CV:GICA DISPLAY RANGE-CV:21L2 PLOT Y-LABEL-"GMS 21L2" TRACE(4)-CV:21L2 -269 270 271 COMM 21L'3 ZONE 3 '(REVERSE Bt'OCMNG)' DI STANCE RELAY COMM NEGATE CURRENTS--21L3 CT IS REVERSE LOOKING COMPUTE CV:IA-NEGATE(BC:GMS..A:5L1N.A) 272 273 274 COMPUTE CV':IB-NEGAtE(BC:GMS. . B : 5L 1N.B ) COMPUTE CV:IC-NEGATE(BC:GMS..C:5L1N.C) COMM LOAD ANGLE COMPENSATOR 275 276 . 277 COMPUTE' CV':LACA-LAC(CV: iA ,33 .77) COMPUTE CV:LACB-LAC(CV:IB.33.77) COMPUTE CV:LACC-LAC(CV:IC.33.77) 278 279 280 'COMPUTE' CV: VA-ADb(NV : VT i'SI. A , CV : LACA )' COMPUTE CV:VB-ADD(NV:VT1N.B.CV:LACB) COMPUTE CV:VC-ADD(NV:VT1N.C,CV:LACC) 281 282 283 DELETE ENTRY-CV:LACA;CV:LACB;CV:LACC COMPUTE CV:VAB»SUBTRACT(CV:VA,CV:VB) COMPUTE CV:VBC-SUBTRACT(CV:VB,CV:VC) 284 283 286 'COMPUTE' CV: VC'A-S'UatRACtTc'V: VC. CV : VA )' DELETE ENTRY-CV:VA:CV:VB;CV:VC COMPUTE CV:IAB-SUBTRACT(CV:IA,CV:IB) 287 288 289 COMPUTE CV: i B C-SUBfRACtrcV: IB'.CV: IC) COMPUTE CV:ICA-SUBTRACT(CV:IC.CV:IA) DELETE ENTRY-CV:IA;CV:IB;CV:IC 290 COMM FILTER' bROPuUt DELAY . . . 1 2 Fig. 26 (cont'd) L 1 s 11ng Of IWSNCBP at 12:41-.:07 on OCT 4, 1986 for CC1d"BRWG Page 6 291 COMPUTE CV:FILTERX-TIMER(CV:21LX(0),0,60E-3) 292 293 294 OISPLAY RANGE-CV:FILTERX COMPUTE CV:21L3AB-SD2H(CV:VAB.CV:IAB,CV:FILTERX.CV:21LX(1) ,160.7,87. DELETE ENTRY-CV:VAB; CV:IAB 1 ,10 ,1 ,5 ,0 ,82 .5 . 33) 295 295 297 DISPLAY RANGE-CV:21L3AB COMPUTE CV:21L3BC-SD2H(CV:VBC.CV:IBC,CV:FILTERX.CV:21LX(1) ,160.7,87. OELETE ENTRY"CV:VBC; CV:IBC 1 ,10 .1 ,5 ,0 ,82 .5 , 33) 29B 299 300 DISPLAY RANGE-CV:21L3BC COMPUTE CV:TMP0-0R(CV:21L3A8,CV:21L3BC) OELETE ENTRY-CV:21L3AB;CV:21L38C 301 302 303 COMPUTE CV:2iL3CA-SD2H(CV: VCA ,CV: ICA ,CV : F 'Kf ERX , CV : 2 iLX( i j , 160.7.87 . OELETE ENTRY-CV:VCA;CV:ICA:CV:FILTERX;CV:21LX DISPLAY RANGE-CV:21L3CA 1 ,10 .1 ,5 ,0 ,82 .5 , 33) 304 305 306 COMPUTE CV:2iL3»6R(CV:21L3CA.CV:TMPO) DELETE ENTRY-CV:21L3CA;CV:TMP0 DISPLAY RANGE-CV:21L3 307 308 309 PLOT Y-LABEL*"GMS 21L3" TRACE(3)-CV:2 i L3 -COMM COMM DISTANCE SUPERVISION CURRENT RELAYS 310 311 312 COMM COMPUTE CV:50LA-0VERCURRENT.IT(BC:GMS..A:5L1N.A.268.1, .33) COMPUTE CV:5OLB"0VERCURRENT.IT(BC:GMS..B:5L1N.B,268,1..33) 313 314 315 COMPUTE 'CV:56LC*bVE'RCURRENt. I f(B'c': GMS . . C : 5L IN. C ,'268 , i , .33) OISPLAY RANGE-CV;SOLA;CV:50LB:CV:SOLC COMM "OR" TO GET OISTANCE SUPERVISION OUTPUT 316 317 318 COMPUTE C"v:f Mi°d*6& (Tv°:SOL*.CV: 50LB)' COMPUTE CV:SOL-OR(CV:SOLC,CV:TMPO) OELETE ENTRY-CV:TMPO;CV:SOLA;CV:SOLB;CV:50LC 319 320 321 OISPLAY RANGE-CV:50L PLOT Y-LABEL-"GMS SOL" TRACE(6)-CV:50L RELEASE COMM 322 323 324 COMM "AND" TO GET PHASE-FAULT DIRECT TRIP COMPUTE CV:PFDT-AN0(CV:21L1,CV:S0L) DELETE ENTRY-CV:21L1 325 326 327 COMM "AND" TO GET PHASE-FAULT PERMISSIVE TRIP COMPUTE CV:PFPT-AND(CV:21L2,CV:SOL) DELETE ENTRY-CV:21L2 328 329 330 d i s p l a y r a h g e - c v : p f d t ; C V : P F P f COMM "ANO" TO GET PHASE REVERSE BLOCKING COMPUTE CV:PRB-AND(CV:21L3,CV:SOL) 331 332 333 DELETE ENfftV-CV:2''L3;CV:5'6L DISPLAY RANGE-CV:PRB COMM 334 335 336 c'OMtf GR'bufab-f*A'ULt R'ETAY'S COMM : COMPUTE 3 • ZERO-SEQUENCE VOLTAGE COMPUTE CV:TMPO-A00(NV:VT1N.A,NV:VT1N.B) 337 338 339 COMPUTE C V: f MP 1"ADD(CV:TMPO.NV: VT IN.ft') COMM 'FILTER 3V0 FOR INPUT TO DIRECTIONAL ELEMENTS COMPUTE CV:3V0-FILTER(CV:TMP1,1) 340 341 DELE'tE ENTRY-CV: fM'P'6; NV : Vt IN . A ;NV : VT iKl'.B ;NV : Vf i"N . C'; CV : T'M'P i COMPUTE CV:PSFILTER-PS-FILTER.A(BC:GMS. .A:5L1N.A ,BC:GMS. .B:5L1N.B,BC :GMS..C:5L1N.C) 343 344 345 COMM FILTER '310 FOR INPUT TO 01RECtIONAL ELEMENTS AND 50LN7I0. . . COMPUTE CV:3I0-FILTER(CV:PSFILTER(1) ,1) COMM USE INSTANTANEOUS OVERCURRENT ELEMENT FOR FINITE SENSITIVITY 346 COMM (NO HYSfERESiS 'WANTEb HE'R'8) . . . 1 2 . Fig. 26 (cont'd) L1st Ing of IWSNCBP at 12:41:07 on OCT 4, 1986 for CCId-BRWG Page 7 347 COMPUTE CV:GATE-OVERCURRENT.IT(CV:3IO,50) 348 349 350 COMM GATE 310 COMPUTE CV:G3I0-GATE(CV:310,CV:GATE) COMPUTE CV:32R-DIRECTIONAL(CV:G3IO,CV:3VO,-89.5,96,.33) 351 355 353 COMM NEGATE GATED 310 FOR FORWARD ELEMENT COMPUTE CV:NG3I0-NEGATE(CV:G3I0) COMPUTE CV:32F-0IRECTI0NAL(CV:NG3IO,CV:3VO,-89.5,85, .33) 354 355 35S DELETE ENTRV-CV:NG3I0:CV:3VO;CV:G3IO:CV:GATE DISPLAY RANGE"CV:32F;CV:32R PLOT HOLD Y-RANGE-( -19.9 ,19.9) Y-UNITS- -357 358 359 PLOT Y-LABEL" "GMS 32F" f RACE t 2 )'-CV : 32F -PLOT Y-LABEL-"GMS 32R" TRACE(1)-CV:32R -COMM 360 361 362 COMM GROUND INVERSE-TIME OVERCURRENT ELEMENT COMPUTE CV:50LN1S-0VERCURRENT.IT(CV:PSFILTER(1),200.1000,.33) OISPLAY RANGE"CV:S0LN1S 363 364 365 PLOT Y-LABEL* "GMS SOLN'iS" f R"ACE*3)«CV:SdXHIS -COMM COMM "AND" TO GET DIRECTIONAL GROUND OVERCURRENT OUTPUT 366 367 368 COMPUTE CV:DGOC-ANDfCV:32F,CV:50LNiS) DISPLAY RANGE"CV:DGOC DELETE ENTRY-CV:50LN1S 369 370 371 COMM COMM INSTANTANEOUS GROUND OVER-CURRENT RELAY COMPUTE CV:RESTRAIN-C0PY(CV:PSFILTER,0.2) 372 373 374 'COMPUTE 'c'v':5b'LNibb'0v'ERCU'RRENf . R(CV : 310, CV: RE'STR'A IN, 1400,630, .33) PLOT Y-LABEL-"GMS 50LN/IOD" TRACE(6)-CV:5OLNI0D -COMPUTE CV:5OLNI0H-0VERCURRENT.R(CV:310,CV:RESTRAIN,300,630,.33) 375 376 377 COMPUTE C'v':5'6LNib'L-b'v'ER'Cu'RRE'N '63.636. .33)' 01 SPLAY RANGE-CV:50LNI0D:CV:50LNI0H;CV:50LNI0L PLOT Y-LABEL-"GMS 5OLN/I0L" TRACE(4) -CV:50LNI0L -378 379 380 PLOT Y-LABEL-"GMS SOLN/ibH" fRACE(5)-CV:56LNiOH RELEASE DELETE ENTRY-CV:PSFILTER:CV:RESTRAIN;CV:310 COMM 381 382 383 COMM "OR" TO GET COMPLETE GROUND FAULT DIRECT TRIP OUTPUT COMPUTE CV:GFDT-OR(CV:50LNIOD,CV:DGOC) OISPLAY RANGE-CV:GFDT 384 385 386 DELETE ENTRY-CV:5OLNI0D;CV:DG0C COMM "AND" TO GET GROUND FAULT PERMISSIVE TRIP COMPUTE CV:GFPT-ANO(CV:50LNIOH,CV:32F) 387 388 389 DELETE ENTRY-CV:SOLNiOH;CV:32F COMM "AND" TO GET GROUND REVERSE BLOCKING COMPUTE CV: GRB-ANO(CV: 50LNIOL , CV-.32R) 390 391 392 Di SPLAY RANGE-CV : G'FPT; CV: S'RB DELETE ENTRY-CV:50LNI0L;CV:32R PLOT HOLD Y-RANGE-( -19.9 ,19.9) Y-UNITS- -393 394 395 PLOT Y-LABEL- "GMS GROUND FAULT blRECf TRIP* f RACE (5)'-CV :SFDT -PLOT Y-LABEL-"GMS PHASE FAULT DIRECT TRIP" TRACE(6)-CV:PFOT -PLOT Y-LABEL-"GMS GROUND FAULT PERMISSIVE TRIP" TRACE(3)-CV:GFPT -396 397 398 PLOT' Y-LABEL-"GMS PHASE FAULT PERMISSiVE TRIP" f'R'ACE(4)'-CV:PFPt -PLOT Y-LABEL-"GMS GROUND FAULT REVERSE BLOCKING" TRACE(1)-CV:GRB -PLOT Y-LABEL-"GMS PHASE FAULT REVERSE BLOCKING" TRACE(2)-CV:PRB 399 400 401 PLOT' RELEASE' COMM COMM "OR" PHASE AND GROUND DIRECT TRIP TO GET DIRECT LOCAL TRIP 402 COMPUTt CV:GMSbLf-OR(CV:PFDT,CV:GFbf) Fig. 26 (cont'd) L1s 11 ng of IWSNCBP at 12:41:07 on OCT 4, 1986 for CCId-BRWG Page 8 403 OISPLAY RANGE-CV :GM5DLT 404 405 40S OELETE ENTRY-CV.PFDT;CV:GFDT COMM "OR" PHASE AND GROUND PERMISSIVE TRIP TO GET COMM COMBINED PERMISSIVE TRIP 407 408 409 COMPUTE CV: CPf-OR"<CV: PFPT , CV : GFPT j OISPLAY RANGE-CV:CPT DELETE ENTRY-CV:PFPT;CV:GFPT 4 tO 4 1 1 4 12 COMM "OR" PHASE AND GROUND REVERSE BLOCKING TO GET REVERSE COMM BLOCKING COMPUTE CV:RB-OR(CV:GRB,CV:PRB) 4 13 4 14 4 15 DISPLAY RANGE-CV:RB DELETE ENTRY-CV:GRB:CV:PRB COMM USE DROP-OUT DELAY AND INVERSION TO GET "NO-REVERSE-BLOCKING" 416 4 17 4 18 COMPUTE' c'v':fMP-f IMERi CV : RB ,0 , i 6 0 E - 3> DELETE ENTRY-CV:RB COMPUTE CV:GMSNRB-NOT(CV:TMP) 4 19 420 421 DISPLAY RANGE-CV:GMSNRB DELETE ENTRY-CV:TMP COMM "AND" PERMISSIVE ENABLE AND NO-REVERSE BLOCKING TO GET 422 423 424 COMM LOCAL FORWARO PERMISSIVE COMPUTE CV:GMSLFP-AND(CV:CPT.CV:GMSNRB) PLOT TRACES/PAGE-4 HOLD Y - R A N G E - ( - 1 9 . 9 , 1 9 . 9 ) Y - U N I T S - -425 426 427 PLOT Y - L A B E L - "GMS COMBINED PERMISSIVE TRIP" f RACE"( i )'-CV: CPT -PLOT Y -LABEL-"GMS NO REVERSE BLOCKING" TRACE(2)-CV:GMSNRB -PLOT Y-LABEL-"GMS LOCAL FORWARO PERMISSIVE" TRACE(3)-CV:GMSLFP -428 429 430 PLOT Y-L'A'BEL'»"GMS DIRECT LOCAL TRIP- TRACE(4)-cv:GMSOLT "RELEASE DELETE ENTRY-CV:CPT OISPLAY RANGE-CV:GMSLFP 431 432 433 COMM COMM COMBINE W S N AND GMS SIGNALS IN PERMISSIVE TRIP BLOCK COMM 434 435 436 COMPUTE CV: PERM-'PERMi SSI VE'( CV : WSNLFP , CV: WSNDLt, CV : WSNNRB , CV : GMSLFP .CV : GMSbLf , CV : GMSNRB ) DISPLAY RANGE-CV:PERM(O);CV:PERM(1);CV:PERM(2);CV:PERM(3);CV:PERM(4);CV:PERM(5) DISPLAY RANGE-CV:PERM(6);CV:PERM!7) 437 438 439 PLOT HOLD fRA'CEs7PAGE-4 Y -RANGE • ( - 19. 9, 19. 9>' Y -UN l tS ' - -PLOT Y - L A B E L - " W S N PERMISSIVE TRIP TRANSMIT" TRACE(4)-CV:PERM(2) -PLOT Y - L A B E L - ' G M S PERMISSIVE TRIP TRANSMIT" TRACE(3j-CV:PERM(3) -440 44 1 442 'PLOT Y - L A B E L - " W S ' N ' R E P E A T - I F - N O - B LOCK" tR''ACE('2)-C'v':PE'RM'(4) -PLOT Y - L A B E L - " G M S REPEAT- I F -NO - B L O C K " TRACE(1)-CV:PERM(5) RELEASE PLOT HOLD T R A C E S / P A G E - 4 Y - R A N G E - ( - 1 9 . 9 , 1 9 . 9 ) Y - U N I T S - -443 444 445 'PLOT Y - L ' A 6 E L - " W S N T R A N S F E ' S TRIP f RANSMlf " f RACE ($1 -CV : PE"R'M'('6) -PLOT Y - L A B E L - " G M S TRANSFER TRIP TRANSMIT" TRACE(1)«CV:PERM(1) -PLOT Y - L A B E L - " G M S CIRCUIT BREAKER TRIP" TRACE(3)-CV:PERM(7) -'446 447 PLOT Y - L ' A ' B E ' L ' " W S N CIRCUIT BREAKER TRIP" TRACE (4 )-CV : PERM( 6) RELEASE STOP Fig. 26 (cont'd) CO 186 The form of the function invocation in the TRP is: C O M P U T E odsg=AND(idsg-l , idsg-2) where odsg is the designator for the A N D result, idsg-1 is the designator for one input, and idsg-2 is the designator for the second input. 2. D I R E C T I O N A L The DIRECTIONAL function provides a model of a directional element based on a block-average phase comparator, with a transactor input to provide the adjustment for maximum torque angle (MTA). The M T A may be specified between 0 and about -89.5° (angles approaching -90° can cause numerical overflow during computation). For situations where the M T A is positive, so that the current leads the voltage, the current input must be negated. The negative of the actual M T A is then specified. The form of the function invocation in the TRP is: C O M P U T E odsg=DIRECTIONALddsg,Vdsg,MTA,opzone, rhys t ,ga in) where odsg is the designator for the output. This is a TRP waveform vector. 187 Element 0 is the relay (phase comparator) output. Element 1 is the output of the transactor, which is one of the phase comparator inputs (the other being the voltage). Idsg is the designator for the input current. Vdsg is the designator for the input voltage. M T A is the designator for the maximum torque angle (angle of current for maximum relay operating tendency, using the voltage as reference), in degrees. The default value of the M T A is -45° . o p z o n e is the angular zone (in degrees) for which the relay will pick up, viz. the relay will operate if the angle of the current is M T A ± o p z o n e with respect to the voltage. rhyst is the ratio of hysteresis to the full relay output range. Hysteresis here refers to the amount by which the comparator trip threshold exceeds the comparator reset threshold. Note that the hysteresis results in a "reset ratio" (ratio of input for reset to input for trip) of less than one for instantaneous (non-integrating) comparators. For integrating comparators, such as is used for this model, the reset ratio can be unity in spite of hysteresis, so that the effects of hysteresis may not be evident from steady-state testing. For the integrating comparator used here a value for rhyst of 1/3 results in trip and reset thresholds equally spaced between the relay output limits. This is usually the best arrangement for the prevention of chattering due to noise. The default value is zero, for no hysteresis. 188 gain is the integrator gain for the phase comparator. The default value is the maximum gain for correct operation under steady-state conditions (computed internally). 3. F I L T E R The F I L T E R function simulates the operation of a simple R L C filter. The form of the function invocation in the TRP is: C O M P U T E odsg=FILTER(idsg, Q, FO) where odsg is the designator for the filter output, idsg is the designator for the filter input. Q is the filter quality factor (circuit Q). FO is the frequency to which the filter is tuned, in Hertz (default value is power frequency) 4. L A C The L A C function simulates the Westinghouse Canada L A C - 1 H load angle compensator used with the SD-2H reverse-reaching (zone 3) element 21L3. The form of the function invocation in the TRP is: C O M P U T E odsg=LAC(idsg,setting,Q,FO) 189 where odsg is the designator for the L A C output voltage. idsg is the designator for the L A C input current. setting is the L A C impedance setting (circuit gain at resonance). Q is the L A C quality factor (circuit Q) at resonance (default 0.5). FO is the L A C resonance frequency, in Hertz (default value is power fre-quency). 5. N O T The NOT function is performed as an N L R operation. The output is thus the algebraic negation of the input. This function is implemented as an alias of the TRP internal function N E G A T E . The form of the function invocation in the TRP is: C O M P U T E odsg=NOT(idsg) where odsg is the designator for the output, idsg is the designator for the input. 190 6. OR The OR function is performed as an N L R operation. The result is thus the algebraic maximum of the inputs. As for the A N D function, this implementation permits only two inputs, although more could have been provid-ed, t The function is implemented as an alias of the TRP internal function M A X I M U M . The form of the function invocation in the TRP is: C O M P U T E odsg=OR(idsg-l,idsg-2) where odsg is the designator for the OR output. idsg-1 is the designator for one input. idsg-2 is the designator for the second input. 7. OVERCURRENT.IT The O V E R C U R R E N T . I T function simulates an inverse-time overcurrent relay. The nominal relay operating time (in seconds) is given by t = 0.661 TMS /U-1 ) where i is the R M S input current as a multiple of the relay setting and TMS is the time-multiplier setting (with a minimum value of one). (The curve tMultiple two-input OR functions can easily be cascaded to produce a multiple-input OR function. 191 represented by this equation corresponds to the time-overcurrent curve supplied by relay manufacturers.) In use, the value of T M S would be selected to best approximate the time-overcurrent curve for the relay being modelled. The O V E R C U R R E N T . I T function may also be used to simulate an instantaneous overcurrent relay by specifying a T M S value of one, which gives the highest possible speed for correct operation under steady-state conditions. The form of the function invocation in the TRP is: C O M P U T E odsg=OVERCURRENT.IT(idsg,set t ing,TMS,rhyst) where odsg is the designator for the output. idsg is the designator for the input current. setting is the relay pickup setting. T M S is the relay time multiplier setting (default is one) rhyst is the ratio of hysteresis to the full relay output range, as for the D I R E C T I O N A L function. The default value is zero, for no hysteresis. 8. O V E R C U R R E N T . R The O V E R C U R R E N T . R function simulates a restrained instantaneous over-current relay. The relay operates when the difference between the average operating and restraining currents exceeds the setting. This model is used with the positive-sequence filter model PS-FILTER. A 192 and the R L C filter model F I L T E R to simulate the operation of a Westinghouse Canada type S1G-1H positive-sequence-restrained ground overcurrent relay. The S1G-1H design is different from that of the model used here. The S1G-1H uses a phase-shifting network, three-phase bridge rectifier, and RC filter network to obtain a DC level proportional to the positive sequence restraint. This level is augmented by the setting; the combination forms a bias which offsets the rectified zero-sequence operating current. The offset zero-sequence quantity is then applied to an instantaneous level detector, which operates when the offset zero-sequence quantity exceeds a threshold. More information can be found in the manufacturer's instruction manual (Westinghouse, 1968). Details of the model are given in part C, section 10 of this appendix. Differences between the operating details are bound to result in small differences in the transient behaviour. The form of the function invocation in the TRP is: C O M P U T E o d s g = O V E R C U R R E N T . R ( i d s g - o , i d s g - r , s e t t i n g , m a x a r , r h y s t ) where o d s g is the designator for the output. i d s g - o is the designator for the operating current. i d s g - r is the designator for the restraining current. s e t t i n g is the difference between the R M S values of the operating and restraining currents which barely causes the relay to pick up. 193 maxar is the maximum R M S amplitude for the restraining quantity. This value determines the relay gain. For correct operation, the value must be larger than the maximum possible R M S restraining current under steady-state conditions. rhyst is the ratio of hysteresis to the full relay output range, as described for the DIRECTIONAL function. The default value is zero, for no hysteresis. 9. P E R M I S S I V E The P E R M I S S I V E function simulates the permissive- (and transfer-) trip logic for the Peace River protection. The modelling used requires the transfer-and permissive-trip signals to be low ("off" state) before the start of the simula-tion. A l l logical operations are performed as N L R operations. The operations involved are shown in figs. 11, 12, and 13. The form of the function invocation in the T R P is: C O M P U T E od = PERMISSIVE(lfpa,dlta,nrba,lfpb,dltb,nrbb,pd,pudl,ddl,pud2 )dd2) where od is the designator for the output, which is a TRP waveform vector. Elements 0 and 1 are the transfer-trip signals for ends A and B, respectively. Elements 2 and 3 are the permissive-trip transmit sig-nals for ends A and B , respectively. Elements 4 and 5 are the repeat-if-no-block signals for ends A and B, respectively. Elements 6 194 and 7 are the circuit-breaker trip signals for ends A and B, respec-tively. l f p a and l f p b are the local forward permissive signals for ends A and B, respectively. d l t a and d l t b are the direct local trip signals for ends A and B, respec-tively. n r b a and n r b b are the no-reverse-blocking signals for ends A and B, respectively. p d is the propagation delay of the communications channels. The delay is the same for both transfer- and permissive-trip channels. The default value is 9 ms. p u d l and d d l are the pickup and dropout delays, respectively, for the first (start) repeat-if-no-block timer. The defaults are 55 and 100 ms, respectively. pud2 and dd2 are the pickup and dropout delays, respectively, for the second (stop) repeat-if-no-block timer. The defaults are 45 and 20 ms, respectively. 10. P S - F I L T E R . A The P S - F I L T E R . A function simulates the positive sequence filter used in 50LN, which is shown in the Westinghouse T & D Book (Westinghouse, 1964, fig. 31h, pg. 374). Residual current output (3I n) is also available from this 195 filter. The form of the function invocation in the TRP is: C O M P U T E odsg=PS-FILTER.A(dsg-IA,dsg-IB,dsg-I c) where odsg is the designator for the output. This is a TRP waveform vector, for which element 0 is the positive-sequence filter output, and element 1 is the residual current (3 IQ) output. dsg-I^, dsg-Ig, and dsg-Ip are the designators of the three phase currents in phase-sequence order. 11. S D X 1 H The S D X 1 H function is a model of the Westinghouse Canada fault-detecting relay SDX-1H. The form of the function invocation in the T R P is: C O M P U T E odsg=SDXlH(dsg-VA,dsg-VB,dsg-V c,uvset,nsset,uvrh,nsrh,nsfq) where odsg is the designator for the output, which is a TRP waveform vector. Element 0 is the signal for controlling the SD-2H filter Q. Element 1 is the signal for controlling the insertion of the pickup delay in 21L1 and 21L2. Element 2 is the output of the undervoltage relay internal to the SDX-1H. Element 3 is the output of the negative sequence relay internal to the SDX-1H. (The TRP also creates and automatically deletes a fifth element, which is used for temporary storage.) dsg-V^, dsg-Vg, and dsg-V^, are the designators for the three phase vol-tages in phase sequence order. uvset is the setting for the undervoltage relay. nsset is the setting for the negative-sequence relay. uvrh and nsrh are the hysteresis ratios (as for the DIRECTIONAL func-tion) for the undervoltage and negative-sequence relays, respectively. The default values are zero, for no hysteresis. nsfq is the circuit Q of the memory portion of the negative sequence filter. The default value is one. 12. S D 2 H The SD2H function is a model of the Westinghouse Canada type SD-2H memory-polarized mho relay. Note that whereas the actual relay uses a block-instantaneous (diode ring modulator) phase comparator, this model uses a block-average phase comparator. Some difference in the transient behaviour can thus be expected. The form of the function invocation in the TRP is: C O M P U T E odsg=SD2H(idV,idI,idS,idD,zc,azc,qh,qI,qm,dIy,gam,rh,gf,fX)) 197 where odsg is the designator for the output, which is a TRP waveform vector. Element 0 is the relay output. Element 1 is the phase-comparator output without the additional pickup delay. Element 2 is the IZ-V input to the phase comparator. Element 3 is the polarizing voltage (memory output) input to the phase comparator. i d V is the designator for the input voltage. i d l is the designator for the input current. idS is the designator for the filter-switching control input. idD is the designator for the pickup-delay-insertion control input. zc is the magnitude of the impedance setting in ohms. azc is the angle of the impedance setting in degrees. q h is the high-Q value for the IZ-V input filter. q l is the low-Q value for the IZ-V input filter. q m is the value of the memory Q. d l y is the pickup delay inserted when the pickup-delay-insertion control input is positive. gam is the phase difference (in degrees) which the phase comparator will accept as phase coincidence. The default value is 90° , which 198 produces the usual circular mho characteristic. r h is the ratio of hysteresis to the full relay output range, as described for the D I R E C T I O N A L function. The default value is zero, for no hysteresis. ft) is the frequency to which the input circuitry is tuned, in Hertz. The default value is the power system frequency. 13. T I M E R The TIMER function simulates the operation of a delayed-pickup/delayed-dropout timer. The output is compatible with N L R . The form of the function invocation in the TRP is: C O M P U T E odsg=TIMER(idsgC,pudly,dodly,ic) where odsg is the designator for the output. idsgC is the designator for the timer control input. The timer begins timing the pickup delay when this signal goes high, and begins timing the dropout delay when it goes low. The timer resets immediately (i.e. the timing cycle aborts) if the control signal returns low before the timer picks up, or returns high before the timer drops out. p u d l y is the pickup delay in seconds (default zero). 199 dodly is the dropout delay in seconds (default zero). ic is the timer initial condition. Any positive value causes the timer to be initialized to a high state; a negative value causes the timer to be initialized to a low state, which is the default. A value of zero is illegal. C. RELAY MODELLING DETAILS This section gives details of the relay modelling which forms the basis for the TRP user functions described in the previous section. A l l models are written as self-contained, stand-alone F O R T R A N subroutines. As the relay modelling was secondary to the main thrust of this research, certain details have been left out where the complexity of the derivation was not justified by the importance of the details. 1. Assumptions The following assumptions and comments apply to the relay modelling for this project: In all cases, relay sensitivity is assumed to be essentially infinite—that is, the input quantities are not required to exceed thresh-old values before the relay will operate (apart from any thresholds intrinsic to the relaying function, such as the input current trip sett-ing for an overcurrent relay, for example). The time base of the input data is to have a constant step size. 200 Wherever possible, generic relay models are employed. Al l models are self-contained. Inputs and outputs are considered to be fully bufferred—source impedances are assumed to be zero, load impedances are assumed to be infinite. A l l input and output loading effects have therefore either been incorporated into the models, or ignored. A l l relays use an output compatible with N L R . Figure 2 shows a hardware-equivalent method of obtaining this output for a static relay. 2. Model Initialization Each model is initialized as the first step when it is invoked. A l l models are assumed to be initially in steady state. The first two time-steps of input quantities are assumed t to come from a steady-state cosine function at power frequency of the form i n p u t ( t ) = m a g n i t u d e ' c o s (ojgt + a n g l e ) where m a g n i t u d e and a n g l e are obtained in the following manner: Assume: = m a g n i t u d e « c o s ( w s t 1 + a n g l e ) t i n use, the first two steps of the input quantities must occur before any power system disturbance. This is generally convenient when doing digital power system simulations using, for example, the B P A E M T P . In the event that the first two steps do not correspond to a pure power-frequency sinusoid, there will be some error in initialization, causing a transient response in the relay model at the start of the simulation. 201 f 9 = m a g n i t u d e ' c o s ( c j s t 2 + a n g l e ) Expanding the cosine terms and expressing the equations in matrix form: C O S WgtjL c o s c u s t 2 s i n " e . ^ s i n u s t 2 where a = m a g n i t u d e • c o s ( a n g l e ) b = - m a g n i t u d e • s i n ( a n g l e ) Now solving for a and b a = ( t 1 s i n w s t 2 - f 2 s i n " g t ^ ) / d e t b = ( f 2 c o s u Q t 1 - f 1 c o s w g t 2 ) / d e t where d e t = c o s t^gt-j^ s i n " s t 2 - c o s ^ s t 2 s i n ^ g ^ It is now possible to solve for m a g n i t u d e and a n g l e , since b - = - t a n ( a n g l e ) a ( a 2 + b 2 ) 1 / 2 = m a g n i t u d e 202 3. Accounting for Finite Sensitivity There are several methods which can be used to account for finite relay sensitivity where this is an important factor in the operation of the protection scheme. One method is to A N D the output of the "infinite" sensitivity relay with the output of an instantaneous low-set element (current or voltage, as appropriate) which picks up at the sensitivity limit. Typically one low-set element would be used for each input with a significant input sensitivity. One disadvantage of this scheme is that extra simulation is involved for the low-set elements and the A N D combination. A more serious disadvantage is that the technique can lead to apparent misoperation due to the reset time of the prin-cipal relay (since it can pick up on inputs below the sensitivity limit). A second method of accounting for finite sensitivity is to use low-set elements as just described to "gate" the input to the principal relay. The objective here is to produce a non-zero output from the gate (equal to the input) only when the low-set element has picked up. This is similar to conventional practice with electromagnetic directional overcurrent relays, where torque is produced in the principal (overcurrent) element only when the modulating (direc-tional) element has picked up. While additional simulation (for the low-set elements and the gate) is also required with this method, there is no longer a problem with pickup or reset delays caused by input below the sensitivity thresh-old. A third method of accounting for finite sensitivity is by incorporating the sensitivity-limiting detail directly into the relay model. This is clearly the most accurate of the three methods, but is applicable only for models of specific relays, and where schematic diagrams and component details are available. Due 203 to the high cost of software development, the advantages of this method will seldom be sufficient to justify its use for applications studies. A fourth method of accounting for the effects of finite sensitivity is to treat the input sensitivity as a hard threshold—the instantaneous value of the input quantity is considered to be zero unless it exceeds the specified threshold. Values exceeding the threshold will either be left unchanged (similar to the second method), or be reduced by the threshold level (probably the more realistic choice for semiconductor relays). A n expression which produces the latter effect is x' = max(x-t,0) + min(x+t,0) where t is the threshold (> 0), x is the input quantity, and X ' is the input quantity modified for finite sensitivity. The fourth method probably offers the best compromise between realism and efficiency. 4. Solving State Equations using Central Differences The general form of the state equations is Dy = Ay + Bu + Cu 204 where y is the vector of state variables, y is the time-derivative of y , u is the vector of inputs, U is the time-derivative of u , and A , B , C, and D are matricies. Writing this as a central difference equation: y k _ y k - 1 y k + y k ~ 1 u k + U k _ 1 u k - u k _ 1 D ( - ) = A ( - ) + B( ) + C ( ) At 2 2 At Collecting the y terms on the left and all other terms on the right and solving for y k gives: - k = Eyk 1 + F u k - G u k 1 /here 2D . 2D E = ( — - A ) ( — + A ) At At 2D , 2C F = ( - A ) _ 1 ( — + B) At At 2D . 2C G = (— - A ) _ 1 ( — - B) At At 205 5 . Directional Element Modelling The directional element is implemented using the block-average phase comparator model and the transactor model (see sections 6 and 7, following). The phase comparator inputs are sA = I Z S B = V where the impedance Z is selected to get the required maximum torque angle (MTA). Input Sg is the voltage input to the directional element. Input is obtained from the output of the transactor model. The transactor input is the current input to the directional element. The transactor is set to provide mimic impedance Z . The M T A is the difference between the angle of the current and the angle of the voltage when S A and Sg are in phase. Thus MTA = arg(I) - arg(V) = a r g ( I ) - a r g ( l Z ) = a r g ( I ) - (arg ( I ) + a r g ( Z ) ) = - arg ( Z ) where a r g ( l ) is the angle of I , etc. The M T A is thus controlled by the transactor mimic impedance, and may range from zero to nearly -90°. (The latter limit must be excluded so that numerical difficulties do not arise as a consequence of extremely small values of R in the transactor model.) 206 6 . Transactor Mode l l ing a. Circuit The transactor is modelled as a parallel combination of the magnetizing inductance and a load resistance (fig. 27). The output is taken as the current in the resistance. Where the voltage across the resistance is required, the out-put current can be multiplied by a factor equal to R. b. Derivation of the differential equations The differential equations describing the transactor circuit are: VR " R iout = L [ L Lin = i o u t + i L where the variables are identified in fig. 27. Eliminating v R , and expressing i L in terms of and i Q u ^ : R i . = L ( i . - i J out i n out In standard form (section 4) this becomes Dy = A y + B u + C u where y = ^ u t u = im. D = L 207 'in 1 L 'R Z= 1 1 J _ + R jwL Fig. 27. Transactor equivalent circuit A = - R B = 0 C = L c. Equations as programmed The differential equation derived earlier is programmed using central diff-erences, as described in section 4. The transition equation is, in standard form, y k = E y k _ 1 + F u k - G u k ~ 1 and the matricies E , F , and G are 2L , 2L E = ( +1 ) - 1 ( - 1 ) AtR AtR 2L , 2L F = ( AtR AtR G = F 208 d. Initialization Initial values are required for and i o u f By assumption, lin{t) = * in c o s ^ s t + e i n ) where I . and 6. are found as described in section 2. i n i n The phasor I ^ may be found from the phasor I ^ n by current-divider action: I O U T = R T J ^ Z I I N Thus H : i n i O U t ( t ) = I O U T C O s ( w S t + 9 o u t ) where *OUT = l H l * in 8 Q u t = arg(H) + 8^ The initial values can now be computed directly. 7. B l o c k - a v e r a g e P h a s e C o m p a r a t o r M o d e l a. Circuit The block-average phase comparator is modelled as a polarity coincidence circuit (performing a Boolean N O R ) , the output of which is offset by a setting-dependent bias and integrated between two output limits. 209 b. Equations as programmed The coincidence circuit is modelled with the following logic: I F ( ( S 1 ( I ) . G T . O . . A N D . S 2 ( I ) . G T . O . ) . O R . ( S I ( I ) . L T . O . . A N D . S 2 ( I ) . L T . O . ) ) THEN I N P U T = ( 1.-bias) E L S E INPUT=-bias END I F The use of the . G T . and . L T . rather than . GE . and . L E . ensures that the comparator will not produce an output if either input is zero. The value bias is the bias current for the integrator, used to determine the phase angle spread (between the two inputs) for which the comparator will produce an output (this is the comparator "setting"). The value of bias may be computed from bias = 1 - 7/I8O where 7 (in degrees) is the phase angle spread (between inputs) for which the comparator must produce an output (the phase angle spread corresponding to an "in-phase" comparison). The integration is performed using trapezoidal integration At output(k) = output(k-l) + gain*(input(k)+input(k- 1 ) ) • — 210 where gain is the integrator gain, and At is the time step. The value of output is constrained to lie within preset limits. c. Initialization Initial values are required for both input signals and the integrator output voltage. The input signals are described by 'S]_(t) = A 1cos(co st + f31) = A 1cos a S 2 ( t ) = A 2 cos ( < J st + 02) = A 2 cos(a+5a) where 5a = @2~^1' ^ e v a ^ u e s °^ ^ 2 , ^ 1 ' a n ( ^ ^2 a r e 0 D t a i n e c * a s described in section 2. The integrator output voltage can be found by computing the amount by which the output has integrated away from one of the output voltage limits. Since the initial conditions are taken from a steady-state condition, the comparator must initially be stable in either a high or low state. Which of these states the comparator is in can be determined from the phase difference between the steady-state values of the two input signals, and will determine which of the two voltage limits the integrator is working from. From knowledge of the comparator state, it is also possible to determine the instant at which the integrator will leave the limit and enter the linear region (first instant of polarity non-coincidence for comparator in high state, first instant of polarity coincidence for comparator in low state). This is the approach which will be used to derive initializing equations for 211 the integrator output. Since the phase comparator is symmetrical with respect to the two inputs, for convenience designate S ^ and S£ such that 5 a > 0. (The case for 6 a = 0 is trivial, since the comparator would then be constantly at the high l i m i t F max } -The inputs to the phase comparator now have the appearance shown in fig. 28, where the shaded regions indicate the zones of phase coincidence, a x is the value of a at which the phase coincidence terminates, and a y is the value of a at which the phase coincidence begins. Note that the integrator input will be 1 .+ b i a s from a y to and b i a s from a x to a^+ir. The integrator will accumulate if the average input is positive, viz. ( 1 - b i a s ) ( a x - a y ) - b i a s ( a y+7r-a x ) > 0 so that, collecting terms and solving for b i a s b i a s < ( a x - a y ) / 7 r But ( a x ~ a y ) = 7r -6a , so the phase comparator output will be true when b i a s < 1 - da/ir and so b i a s = 1 - s e t t i n g / 7 r where the setting is the maximum value of phase difference, in radians, for 212 which coincidence is detected. Now in the case where 6a < s e t t i n g , the comparator will be in the "true" state, and the integrator output at a.Q (the initial value of a) will be (taking advantage of the half-cycle symmetry) for a ^ a _ ^ a y 0 x o u t p u t ( a Q ) = F m a x + g a i n { b i a s ( 7 r - a y - a x ) + ( a 0 - a y ) ( 1 - b i a s ) }/CJ S for a ^drSa +u x 0 y o u t p u t ( a Q ) = - g a i n « b i a s ( a n - a x ) / c j s while in the case where 6 a > s e t t i n g , the comparator will be in the "false" 213 state, and the integrator output at a n will be for ay<a0<ax output(aQ) = F m i n + gain( 1-bias) ( a Q - a y ) / c o s for ax<a0<ay+7r output(aQ) = F m i n + gain{(1-bias)(a x~a y) - bias(a Q -a x )}/w s where F „ . is the minimum integrator output limit, and F is the maximum min ° r ' max 7T 7T 7T integrator output limit. Note that for - AQ - ~2> a y = ~~2 an(^ o. — -5- 5 a. x 2 8. Fi l ter /Memory C i r cu i t Model l ing The memory and R L C Filter circuits are identical, and so use the same model. There are essentially two possible configurations of the circuit: series RLC with voltage drive, and parallel R L C with current drive. Two other equiv-alent configurations can be obtained by converting the voltage source to a Norton equivalent source, and the current source to a Thevenin equivalent source. The series R L C with voltage drive and parallel R L C with current drive configurations produce identical equations. Only the series R L C configuration will , therefore, be described here. 214 a. Circuit The filter consists of a series combination of R, L , and C, with a voltage drive (fig. 29). The output may be either i or v r = k « R i , where 0 < k ^ 1. The gain at resonance <(J=CJ0) will be R " 1 in the first case, and k in the second case. In both cases, output = g a i r i ' R i b. Derivation of the state equations The differential equations describing the filter circuit are V = L i + v c + R i i = C v c where the variables are identified in fig. 29. Let q= circuit gain, o= output, u = input=v, and y 2 = state variable = V Q -The circuit Q is Q = C O Q L / R where C J 0 is the resonance frequency, given by a>0 = ( L C ) _ 1 / 2 (For the current driven parallel R L C configuration, using U=i, Y2=i\J> an(* Q = C J 0 C R will produce results identical to the following.) It follows that • VR Fig. 29. Series R L C filter equivalent circuit L = R Q / C J Q C = ( C J 0 2 L ) " 1 = ( C J Q R Q ) " 1 Substituting into the differential equations u = o + y + | 9"o ' g o _ J _ i Letting y ^ = o / g be the normalized output Q • u = — * i + * i + y 2 1 Y l = 7 ?2 In standard form (section 4) these become Dy = A y + B u + C u where 216 D = A = B = Q 6 J 0 — 0 1 -1 1 1 0 ^ o Q -1 0 C = U c. Equations as programmed The differential equations derived earlier are programmed using central differences, as described in section 4. The transition equation is, in standard form, y k = Ey k 1 + Fu k - Gu k 1 where the matricies E, F, and G are E = d e t -1 -1 1 + — C 2 ^1 2Q C , 1 + QC, c 2 ^1 F = d e t c l Q 217 G = - F where co 0 A t 1 1 d e t = 1 + + — C^Q C* d. Initialization Initialization will be at power frequency (CJ=CJ s). Initial values are required for the input, the output, and the state variable. The derivations which follow are for the generalized state equations, and so produce identical results for both series and parallel R L C configurations. The input is described by u ( t Q ) = U C O S ( < J s t o + 0 u ) where U and 8^ are found as described in section 2. The phasor equations may be found from the state equations: U = j u s Y i ; ^ + Y L + Y 2 Let S i=a) s /a) 0 , and using the second equation to substitute for Y 2 in the first: U = Y , ( j f i Q + 1 + — ) 1 jn 218 which implies (1-fi 2)Q+jfi U Now using the second state equation Q Q (l-fi 2)Q+jfl U 9. Inverse-Time Overcurrent Model The inverse-time overcurrent model is essentially a single-input amplitude comparator, and may be used as such with an appropriate input quantity and setting. The nominal operating time (in seconds) is given by where TMS is the time multiplier setting, with a minimum value of one, and i is the RMS input current as a multiple of setting. The curve described by this equation corresponds to the time-overcurrent curves provided by manufacturers for their relays. The value of TMS is selected to match, as closely as possible, the curve of the model to the curve of the actual relay. With TMS = 1 the model operates at maximum speed, and can be used to simulate "instantaneous" elements (e.g. overcurrent, overvoltage, etc.). TMS t = 0.661 (i-1) 219 a. Circuit The comparator design on which this model is based consists of a full-wave rectifier, the output of which is offset by a setting-dependent bias and integrated between two output limits. The comparator thus operates on the average value of the input quantity. For the inverse-time overcurrent relay,, the input is the current being monitored. b. Equations as programmed The output is computed from trapezoidal integration of | i ( t ) | - bias: At output(k) = outp u t ( k - 1 ) + g a i n ( | i ( k ) | + | i ( k - 1 ) | - 2 ' b i a s ) • — where gain is the integrator gain, and At is the time step. The value of gain is the maximum comparator gain (see subsection (d) following) divided by the value of T M S . Operating speed is thus inversely proportional to T M S , and is highest for T M S = 1. The value of output is constrained to lie within two range limits. c. Initialization Initial values are required for the input signal and the integrator output voltage. The input signal is described by s(t) = A cos(u.t + 6) where the values of A and 6 are obtained as described in section 2. The approach used to derive initializing equations for the integrator output is similar to that used for the block-average phase comparator. From knowledge 220 of the comparator state, it is possible to determine the instant at which the integrator will leave the limit and enter the linear region. This will occur at the first instant at which the bias exceeds the rectified input if the comparator is in the high state, and the first instant at which the rectified input exceeds the bias if the comparator is in the low state. Define an angle a such that a = C J t + 6 and s (t) = A cos a. The integrand has the appearance shown in fig. 30, where a = cjgt + 0 a n = value of a at which integrand becomes negative a = value of a at which integrand becomes positive. IT I Note that a and a both satisfy n p |A cos a n| = |A cos a p| = bias. If COS a.Q > 0 where is the initial value of a, normalized such that 7 - a 0 < 37> then the equations are 221 Fig. 30. Input waveforms for amplitude comparator derivations A|cos = |A|cos = bias so = arccos a' = -a P n bias and let = < X Q . Otherwise so A|cos a^* = |A|cos ap* = -bias bias a'' - K + arccos = n + a' I A | bias a" = it - arccos = it - a' P IAI n and let = = a . Q + 7 r . In the case where the relay is in the trip state: 222 A| > /2 setting = £«bias. If a' < a' < £ then n 0 Z ga in output = F m a x + {|A|(sin - sin a^) - bias(ag-a^)} s otherwise gain output = F m a x + {|A|(2 + sin - sin o^) - bias (rr+aQ-a^) } s In the case where the relay is in the reset state: | A | < /2 setting = -j-bias. If dp < O Q < then ga in output = F m i n + {|A|(sin CIQ - sin a') - bias(aQ-a')} s otherwise gain output = F m i n + {|A|(2 + sin - sin a') - bias (it+a^-a')} d. Computation of maximum comparator gain The maximum value of comparator gain is limited by the ripple in the comparator output. The ripple will be a maximum for a steady-state input just below setting. The maximum gain will be just large enough so that the comparator nearly operates for maximum ripple. Assuming symmetry between the trip and reset thresholds (the usual case), the peak integrator ripple at setting will be at <XQ for the reset-state equations derived in the previous section, so that 223 For an input equal to the setting ga in peak output = F m i n + { |A|(sin - s i n a')- bias(a^-a')} "s bias a' = -a' = -arccos P n 2 = -arccos — 7T so the peak output is _ gain F . + 0.2105(2/2 setting). mm , , 3 s The maximum gain will produce a peak output just equal to the thresh-old. For a threshold of Frp, the maximum gain is (F - F . ) ] . 6 7 9 co T _ m i n _ setting 10. Positive-Sequence-Restrained Overcurrent Relay The positive-sequence-restrained overcurrent relay is essentially a double-input amplitude comparator. The relay operates when the average value of the operate input exceeds the average value of the restrain input by an amount greater than the setting. 224 a. Circuit The comparator design on which this model is based consists of two full-wave rectifiers, one for each input, the outputs of which are connected so that the restrain input will oppose the operate input. This difference output is offset by a setting-dependent bias and integrated between two output limits. The comparator thus operates on the difference between the average operate and restrain quantities. b. Equations as programmed The output is computed from trapezoidal integration of \ W t ) l - l i r e s t { t ) \ ~ b i a s where i Q p is the operate current i - ^ - i . is the restrain current rest bias is the setting control current. Hence A t output (k) = output (k-1) + g a i n — • 2 ( | i o p ( k ) | - | i r e s t ( k ) | + | i o p ( k - l ) | - | i r e s t ( k - l ) | - 2 - b i a s ) where g a i n is the integrator gain, and A t is the time step. The value gain is computed in generally the same manner as was described for the maximum gain for the inverse-time overcurrent model. The gain is computed to ensure that the maximum measurement ripple for an input 225 just below setting will not quite cause comparator operation. For this dual-input comparator, the peak ripple is dependent on the maximum possible value of the restraining input under no-fault conditions. The details of the gain calculation are too involved to be included here. The value of output is constrained to lie within two range limits. c. Initialization Initial values are required for the input signals and the integrator output voltage. The input signals are described by: i o p ( t ) = f o P c o s ( o s t + eop) i r e s t ^ " Jrast cos(« st + 6 ^ ) where the values of I . 6 5 , and d^^^. are obtained as described in op' rest' op' rest section 2. Initialization of the integrator output is by "silent simulation", rather than by direct computation as with the other comparators. With silent simulation, a simulation is performed for which intermediate values of the simulation variables are discarded, and only the final values are retained (see chapter IV). Although a brute force technique, it is an effective (although not necessarily the least expensive) method of initializing highly nonlinear networks. The technique is reli-able here as long as the comparator output reaches one of the output limits during the one cycle which is used for initialization. 226 1 1 . Permissive-Trip Model The permissive-trip model contains both the permissive trip logic (figs. 11 and 12) and the repeat-if-no-block (RINB) logic (fig. 13). It is clear from fig. 11 that the model involves a feedback loop for P T T X g (which is delayed by the channel propagation time before being fed back). Because of the feedback, the permissive-trip model uses the simultaneous approach (i.e. simulate the entire subsystem for each time step) internally, even though the simulation as a whole uses the sequential simulation approach (i.e. simulate the complete response of one model before proceeding to another).! The permissive-trip model is an example of how logic feedback can be handled in the sequential approach. The simultaneous approach requires single-step models of the permissive-trip and RINB logic to be used. The logic of the permissive-trip sub-block (fig. 12) is straight-forward. The RINB sub-block (fig. 13) is more complex, since the timer model $ includes its own feedback loop within the internal SR flipflop. The two levels of feedback cause no special difficulty, however, since, except for some temporary storage, each sub-block is self-contained. 1 2 . Positive-Sequence Filter Modelling The filter modelled here is that used in the Westinghouse S1G-1H positive-sequence-restrained overcurrent relay. This filter is shown in the Westinghouse T & D Book (Westinghouse, 1964, fig. 31h, pg. 374). It has the advantage for this application of providing both positive-sequence and residual current outputs. tSee chapter IV for a discussion of these two approaches. + The timer model is a single-step version of the timer model described in section 18. 227 a. Circuit Figure 31(a) shows the circuit for the positive-sequence filter, while fig. 31(b) shows the equivalent circuit (the transactor having been replaced by its magnetizing inductance and a current source). b. Derivation of the state equations The differential equation describing the circuit is (writing the equation for the principal loop) v +L (1 — v ) + f R ( ^ - i )+lR(Zo ) = 0 o m c r j p R R b e where i a , i ^ , and i c are the phase currents, and the remaining variables are as noted in fig. 31. Collecting terms in V Q L R — v +v (1+—) = L ( L - L ) + R ( i where R l R l R L m = — The gain of the filter is to be one, which places a constraint on the values of R and R^. As a phasor expression the differential equation is R R R j ^ — V + V (1+—) = j — ( I h - I „ ) + R ( I ~ I n ) . V 3 R 1 ° R L V 3 b c a 0 (b) Equivalent circuit Fig. 31. Positive-sequence filter equivalent circuit. Solving for V The gain is thus 2 R R 1 ( R 2 1 + 2 R R 1 + | R 2 ) 1 / 2 ' For the gain to be unity, ( 2 R R 1 ) 2 = R 2 + 2 R R X + | R 2 which can be solved for R ^ to get R 1 6 1 R N = { l + ( — R 2 - - ) 1 / 2 } 1 ( 4 R 2 - 1 ) 3 3 which is real and positive for R > 1 / 2 . In standard form (section 4) the differential equation • • Dy = A y + B u + C u where R R , 21. R , + R + j — 1 V 3 230 R A = - ( 1 + — ) B C = . [ R 0 0 - R ] D = m R, c. Equations as programmed The differential equation derived earlier is programmed using central diff-erences, as described in section 4. The transition equation is, in standard form, r k = E y k 1 + F u k - Gu k - 1 where the matricies E , F , and G are 2L At JQ-u -R - R E = 2 L . m At +R +R F = 2 L . m 2 L . At At - R 2L m At +R L+R G = 2 L . - R m 2 L . m R At At 2 L . m At +R,+R 231 d. Initialization Initial conditions are required for the phase currents i a , i ^ , and i c , the residual current 3 1 Q , and the positive-sequence output voltage v . The phase currents can be found from i _ ( t ) = I. cos(a)_t + 0 ) , a. a, o a i b ( t ) = I b cos (a>st + 0 b ) , and i c ( t ) = I c cos(co st + c9c), where I , I . , I . 0 , 6., and 6 are found as described in section 2. a' b c a b c The residual current is just the sum of the three phase currents. The output voltage may be found by writing the phasor expression found earlier for V Q in terms of I A , I g , and 1^, only, to get RR V = - • — ( I + e 3 1 2 0 O I v + e - j l 2 0 ° I ) o 3 R a b c Rj+R+j — so that ^ v (t) = 3 ( 1 cos(cj ot + 0 +6) + I. cos (co_t + 0 . + 1 2 0 ° + 6) o a s a b S b + I cos(o_t+0 - 1 2 O ° + 0) ) C S C where R 6 = -arctan (— .) i/3 ( R j + R ) 232 13. Westinghouse SD-2H Modelling The phase-fault distance relays are Westinghouse Canada type SD-2H units, which are block-instantaneous memory-polarized mho relays. The ZI-V input is tuned to reduce susceptibility to high-frequency voltage-derived transients and low-frequency transients associated with series capacitors. The Q of the circuit is kept low under normal conditions to prevent the memory action of the tuned circuit from excessively delaying relay operation. The delay is most severe for faults barely within the relay reach. Under fault-conditions the ZI-V circuit is switched to a high-Q configuration by fault-detecting relay 21LX (Westinghouse Canada type SDX-1H). Relay 21LX also inserts a pickup delay of 35-45 ms into the output of the SD-2H units for 21L1 and 21L2 (provided they have not already operated). The purpose of the delay is to prevent relay misoperation due to transients asso-ciated with fault clearing or switching of the input filter. A "load angle compensator" (Westinghouse Canada LAC-1H) is used to modify the voltages applied to 21L3. The modified voltages ensure coordination under transient conditions between reverse blocking relay 21L3 at one terminal and the overreaching relay 21L2 at the opposite terminal (see chapter 2). A complete description of the SD-2H and S D X - 1 H relays is given in the manufacturer's instruction manual I .L. H41-1302E (Westinghouse Canada, 1979). The phase comparator used in this model is not block-instantaneous; it is the block-average phase comparator described in section 7. The transient behaviour of the model can be expected to be somewhat different than that of the actual relay. 233 a. SD-2H input circuits A somewhat simplified schematic of the SD-2H input circuits is shown in fig. 32(a). The polarizing voltage is obtained from a series R L C memory circuit, and so can be modelled using the general memory/filter model of section 8. The input circuit for the IZ-V voltage is essentially a double-tuned circuit with a switchable Q, as can be seen from the simplified equivalent circuit of fig. 32(b). The Q of the circuit can be increased by closing the contact across resistor in the series resonant circuit. The reach and line angle of the relay are set by the parallel combination of (transactor magnetizing inductance) and R^, which together form impedance Zy If the parallel combination of the current source (transactor) and is replaced by an equivalent Thevenin network (at CJ =co ), it is clear that the net forcing voltage is I Z ^ - V , so that the replica impedance Z^ — Zy For proper operation of the relay, it is essential that the output voltage be in phase with the input voltage regardless of • the position of the contacts. The transfer function at co=co_ can be shown to be s ( R s R r X s X p > + 3< R l X p + X s R l + X p R s > where R s R 2 + | z c | c o s ez X s X p X L / ( 1 " X L 1 Y C > 1 "1 * - l (b) equivalent circuit for IZ-V input Fig. 32. SD-2H input circuits. 235 This transfer function must be real for V and V to be in phase. One o condition which yields a real transfer function is R s R r x s x P = °' which, however, cannot hold for the two values of R G corresponding to the two contact positions. The only other possible solution is if Xp tends to infinity and X s = 0, so that R l V = ± V ° ( * l + R s > Thus L 1 and C . must be resonant at ui = C J , L I C I = <V2 as must L +L_ and C_ c z z ( L C + L 2 ) C 2 = a>-s* where C O S L C = | z c | s i n eZc It is now possible to find L ^ , C ^ , R ^ , and given C ^ , L 2 , | Z ^ | , and Br, . The latter two values are settings, and so are known. It remains to C find values for R ^ , R 2 , C ^ , and L 2 . The quality factor (Q) at resonance may be used to specify the degree of filter "sharpness" required. The Q at resonance may be determined. from the ratio of the total energy stored to the average power loss. The energy stored is the sum of the energies in L 3 , L 2 > C 2 , L ^ , and Cy The energy stored in and is constant and equal to 1 where V r is the peak value of the voltage across C , , which at resonance 1 (CO=CJ0) is R 1 I T , so that the energy stored in C . and L , is ^ c i ( ¥ i 2 ' J where I is the peak value of the current through L _ . The energy in C 2 is zero, and the energy in L 2 is a maximum, at the peak of i . The energy stored in C_ and L _ at the instant of I , is thus b 2 & l L 2 IT f 2 The energy stored in at this same instant is 2 L 3 X L 3 where R T C J Q L T ^ i T = I - 1 cos(-arctan - ) « I T L3 R 3 + j c o 0 L 3 R 3 2 Thus the total stored energy (which is constant) is K C . R ' + L . + L . I — 12 cos 2 (-arctan ) } • £ 1 1 2 3 R 3 + j c j 0 L 3 R 3 L 2 The average power dissipation at resonance is equal to the sum of the powers dissipated in R ^ , R 2 , and R 3 - The average power dissipated in R ^ and R 2 is 2 3 7 The average power dissipated in is 3 where ] C J 0 L 3  K 3 R 3 +]o ;oL3 L 2 The total power dissipated is thus . " 0 L - 5 •i(R +R +R | ;— 1 2 ) • I 2 1 2 3 R 3 + j c o 0 L 3 L 2 The circuit Q (under steady-state conditions at CO=CJ 0) is thus Q = Wo C 1 R 1 + L 2 + L 3 ' R 1 + R 2 + R 3 ' where *3 = R o i j 3 | 2 3 R 3 + j c u 0 L 3 R~ CJnL-L ' = L - | 3 1 2 cos 2 (arctan -4 ) R 3 + j c o 0 L 3 R 3 With the contacts closed, the Q is high and equal to C 1 R 2 + L 2 + L 3 -Q H = " o R l + R 3 ' 238 2 is selected to ensure that C^R^ + L 2 > 0. Rearranging the above expression for so that C 1 R 1 + L 2 = ( R 1 + R 3 ' > ^ " L 3 »I > -f--Now set L 2 = C ^ R ^ 2 , thus ensuring that both L 2 and are positive, with L 2 = i { ( R 1 + R 3 ' ) ^ - L 3 ' } , and C . = 1 R 2 ! The value of R 2 can be found from the ratio of high and low values of Q: OH . R i + R 2 + R 3 ' Q L R l + R 3 " Solving for R 2 : R , = (R n +R ' ) (— - 1 ) 2 1 3 Q L A l l circuit values are now known. b. Derivation of the state equations The state and input variables are where the variables are as shown in fig. 32. The state equations are R 3 H = — ( l _ 1 L _ 1 i ) L 3 L 3 L 2 L 3 V 1 . 3 " V L 2 = V + V C 2 + Vl^ + v o c 2 - c 2 = H2 v 1 ° L 2 R 1 L l 1 O Arranging in the standard form (section 4) Dy = Ay + Bu and noting that 240 the matricies A , B , and D are D = 0 - L . 0 0 0 1 0 0 0 0 0 0 R 3 L 3 0 0 C, 0 0 A = B = 0 0 0 - 1 0 0 0 0 - C J C Q , - t o S Q 3 0 ' S « 3 R, 1 0 1 0 0 0 0 1 0 0 0 1 - v 1 0 1 0 0 0 c. Equations as programmed The differential equations are programmed using central differences, as described in section 4. The transition equation is, in standard form, y k = Ey k~ 1 + Fu k - Gu k~ 1 241 where the matricies E, F, and G are 2 2 E = (— D - A)- 1 ( — D + A) At At 2 F = (— D - A)" 1 B At G = -F The above equation is solved using the University of B. C. Computing Centre routine SLIMP (Nicol, 1982), which uses Gaussian elimination with an iterative improvement algorithm, t To use S L I M P , it is necessary (for efficiency) to rearrange the standard form equation into k k- 1 k k-1 Hy K = HEy K 1 + HFu - HGu ' 2 where H = (— D - A) . At The right-hand side of the equation is compiled at each time step, and S L I M P is used to find the solution to Hy k = x k where x k is the right-hand side at step k. tThis improvement may not have been required—it was used because it was available and provided some protection in the event the matrix was ill-conditioned, at little increase in overall computation time. 242 d. Initialization Initial values are required for the input voltage and current, and for all state variables. The expressions for the input voltage and current are v ( t Q ) = V cos ( t o st o + 0 v ) i ( t Q ) = I cos ( c j st 0 + c ? I ) where V , I , dy, and 6j are obtained as described in section 2. The analysis for the state variable initial conditions is simplified by using a Thevenin equivalent source network. The current source and parallel combina-tion of R^ and can be converted to a Thevenin equivalent with open-circuit voltage E = Z^I , where I is the phasor input current, and impedance w 2 L 2 R +jco L R 2 Zr = 5 3 3 S 3 3 = R +jw L Now let Z l - 1 1 — + +jco c C and 1 J S 1 S I 1 Z t o t = W V ^ s V — - 7 -3 " s C 2 The total driving voltage is now I Z ^ - V and the output voltage, by voltage divider action, is v = — ± - ( i z r - v ) O n C ^tot The phasor expressions for the other state variables are: V Z I T = ° — = i ( i z r - v ) 1 ^ S L 1 ^ S L l Z t o t 243 ( I Z - V ) h = " 2 z t o t h2 1 V = ^ - = ( I Z - - V ) C 2 j c s C 2 j c J s C 2 Z t o t and finally, since the voltage across L ~ is ) Z ~ , V L 3 Z I , = = - { ( Z + Z , ) l + V } J S 3 J S 3 t o t where Z 2 = V ^ s V " 1 ^ S C 2 The values y(tQ) are found by using the derived phasor expressions for to get y i ( t Q ) = i/2 | Y ± | c o s ( c j s t o + 0 i ) where 9 . = arg(Y. ). I ^ i e. SD-2H output stage The output stage of the SD-2H includes the circuitry for the insertion of a pickup delay, as controlled by the S D X - 1 H fault-detecting relay. The delay is inserted only if the SD-2H output is not already high at the time the insert-delay control input goes high. The circuitry which is used in the model to provide the delay insertion feature is shown in fig. 33. The control logic, consisting of two inverters and an A N D gate, enables or disables the A N D gate which bypasses the delay 244 delay Fig. 33. SD-2H output circuit (as modelled) timer!, according to the state of the insert-delay control input. The feedback in the control circuit disables the control input in the event the SD-2H unit has already picked up. The logic feedback loop in the control circuit leads in the program to a F O R T R A N DO loop enclosing the control logic. The reason for the loop is that initially the value being fed back (the output) is unknown, and so must be assumed. A first iteration will propagate the effect of the assumption through the model. At the end of the first iteration the output (feedback) value will correspond to the assumed input (feedback) value. If the output value is the same as was initially assumed, no further iterations are required. If the output value is different than was initially assumed, one final iteration will be required. If the simulated logic is stable, the final iteration must produce no change in tThe timer element is the same as for the timer model described in section 18. 245 the output feedback signal. A l l logic is performed using N L R . 14. Model l ing for Westinghouse S D X - 1 H Fault-detecting Relay The fault-detecting relay 21LX is a Westinghouse Canada type S D X - 1 H unit, which is a combination negative sequence/undervoltage relay. Timer units are used in the output stage to control the switching of the input filters for 21L1, 21L2, and 21L3, and the pickup delays for 21L1 and 21L2. A simplified diagram of this unit is shown in fig. 34. In the actual device, the undervoltage unit is a three-phase device; three single phase elements are used in the model for simplicity. (The difference did not appear to cause any adverse effects.) The purpose of the undervoltage unit is to ensure contin-ued operation of the SDX-1H relay for three-phase faults. The negative sequence device consists of a negative sequence filter and an overvoltage element. This is the principal fault-detecting element, and operates at fault inception for all fault types. The filter-switching output stage consists of an SR flipflop which is set upon operation of either the negative sequence or undervoltage device. The flipflop receives a reset pulse every 90-120 ms (modelled as 100 ms) from a unijunction relaxation oscillator. The filter switching (SWQ) output is driven from the normal ("Q") output of the flipflop. The same output drives the SET input of a second SR flipflop through a 30-40 ms (modelled as 35 ms) delayed-pickup timer. Thus 35 ms after the SWQ output goes high, the second flipflop receives a SET impulse, turning on the INSDLY insert delay output to cause the insertion of a pickup delay in 246 N E G A T I V E S E Q U E N C E R E L A Y U N D E R V O L T A G E E L E M E N T S T I M E R S (m6ec) R E L A X A T I O N O S C I L L A T O R Fig. 34. SDX-1H general layout 21L1 and 21L2. The second flipflop is reset 20-60 ms (modelled as 25 ms) after reset of the first flipflop. The reset input of the second flipflop is driven through a delayed-pickup timer from the inverted ("Q") output of the first flipflop. A complete description of this relay is given in the manufacturer's instruc-tion manual I.L. H41-1302E (Westinghouse Canada, 1979). The SR flipflop and delayed pickup timer models are described in section 18 for the delayed-pickup/delayed-dropout timer model. The relaxation oscillator provides feedback around the first flipflop, so that the two models must be treated using the simultaneous approach within a F O R T R A N DO loop. The 247 composite model forms a timed-reset latch. The SR flipflop portion of the latch is a single-step version of the flipflop described in section 18. The relaxation oscillator is based on a standard unijunction relaxation oscillator. The oscillator can be turned on and off with an input signal. The model produces a high output for one time step at the first step after the oscillation period has elapsed, and repeats at equal intervals thereafter. When the oscillator is turned off, the output is equal to the input switching waveform. (This is for increased usefulness of the model with NLR.) An input of exactly zero is taken as a positive input if the oscillator is already on, or a negative input if the oscillator is off. The timing state of the oscillator is reset when the oscillator is turned off. 15. Undervoltage Relay The undervoltage relay model is implemented using the inverse-time over-current model as a single-input amplitude comparator. The overcurrent model is set for "instantaneous" operation by setting T M S = 1. The voltage being mon-itored is applied directly as the input to the "overcurrent" model, the output of which is negated (NLR inversion) to produce a "b" contact output. 16. Negative-sequence Relay The negative-sequence relay model is implemented using the inverse-time overcurrent relay model as a single-input amplitude comparator. The overcurrent model is set for "instantaneous" operation by setting T M S = 1. The output from a negative sequence filter is applied directly as the input of the "over-current" model. 248 a. Circuit The circuit used for the negative-sequence filter is shown in fig. 35. This circuit is essentially a memory circuit driven by V . , the output of which is v ^ g . The output of the filter is v l m IB vmB = V 1 B " K B b. Derivation of equations The filter is implemented using the memory model, the output of which is scaled and combined with 2v/-~-The steady-state output of the filter can be found from the phasor equations. By voltage-divider action, R V = V V 1 B 1 AB R+j ( c o c L - - ) Since | X c | - | X L | = / 3 R, S CJ C 1 - co s L = \/3R and 1+J / 3 a 2  V 1 B = ^ VAB ~2~ VAB where a = e ^ 1 2 0 o The v-^ output voltage is thus 249 Fig. 35. Negative-sequence filter equivalent circuit -ia 2(V A+a 2V B+aV c) = -|a 2V 2 The voltage v ^ m is internally scaled by a factor of § to obtain the filter output, which is thus -a 2V 2 c. Equations as programmed The memory circuit must be operated off resonance to obtain the correct relationship between X„ and X T . Both the resonance frequency and the Q of the memory are required. The Q is specified as a parameter. To find an expression for the resonance frequency u>0, start with the 250 equations for memory Q a ) 0 L 1 Q = R a>0CR where C J 0 = ( L C ) " 1 / 2 Substituting this expression into the relation between X^, and X ^ gives Q ( — - - £ ) = / 3 which rearranges to cog - 2. - = 0 Q s which can be solved to get 2Q Q 2 s 17. Load Angle Compensator Mode l l ing a. Circuit The Load Angle Compensator (LAC) is essentially a series-tuned transactor, as can be seen from the equivalent circuit in fig. 36 (where the transactor has been replaced by a current source and its magnetizing inductance). The output is the voltage across the load resistance. The circuit Q, the gain g , and the resonance frequency co 0 are all spec-ified as parameters. The values of the circuit constants R, L , and C are computed from the specified parameters as follows. The circuit Q at cj=k>0 is given by 251 Fig. 36. Load angle compensator equivalent circuit 1 C J 0 L Q = = C J 0 C R R where C J 0 = ( L C ) - ^ 2 . The gain of the circuit at C J = C J 0 can be found by replacing the current source and magnetizing inductance with a Thevenin equiv-alent at co=co 0. The open-circuit voltage at co=a)0 is then equal to V, so that V = j c o 0 L I . The gain is thus |V| 9 - — - " o L Solving for L L = q/a)0. Substituting for L in the inductive expression for Q and solving for R gives R = g / Q -Substituting for R in the capacitive expression for Q and solving for C gives C = (co 0 g) " 1 252 b. Derivation of state equations The differential equations describing the L A C are LiL = ( i - i L ) R + v c where the variables are identified in fig. 36. In standard form (section 4) Dy = Ay + Bu + Cu where y = U = 1 D = A = B = C 0 0 L 0 - T 1 -R 1 R C = U The output is 253 v = ( i - i L ) R = (u-y 2)R c. Equations as programmed The differential equations are programmed using central differences, as described in section 4. The transition equation is, in standard form, y k = Ey k 1 + Fu k - Gu k 1 where E = d e t 4'LC 2RC + -1 A t 2 A t 4C A t 2L A t 4L At 2RC 4LC - 1 + A t A t 2 B = d e t G = -F 1 +-2RC A t 4LC 2RC where d e t = + + 1 A t 2 A t 254 The output is - y ^ ) R d. Initialization Initial values are required for the input current and the state variables v_ and i . The input current is given by C L i i ( t Q ) = I cos(cj st Q + 0 ) where is the initial time, and I and 6 are found as described in section 2. The phasor equations for the state variables may be found from the state equations j c o s C V c = I - I L j c o s L I L = ( I " I L ) R + V c Substituting the first equation for in the second equation and solving for I L gives 1 + jco_RC I. = § I L 1 - C J 2 L C + J C J _ R C Substituting now for I L in the first equation and solving for gives jco L V _ = § I L 1 - w * L C + j w _ R C Thus the initial magnetizing current is i L ( t 0 ) = lh C O S ( c s t o + 6 9 + 0 L ) where #L = arctan(C J S R C) - arctan( ) and the initial capacitor voltage is v c ( t 0 ) = v c c o s ( c s t 0 + e + e c ) where I | 1 -to | L C + j c o s R C | 0„ = 90° - arctan( 18. Delayed-pickup/delayed-dropout timer a. Circuit The delayed-pickup/delayed-dropout timer model consists of a delayed-pickup timer driving the SET input of a SR flipflop, and a delayed-dropout timer driving the RESET input, as shown in fig. 37(a). The timer output is taken from the normal ("Q") output of the flipflop. b. Delayed-pickup and delayed-dropout timers The delayed-pickup and delayed-dropout timers are almost identical, the only difference being the input polarity for which delayed operation occurs. A diagram of a circuit which is approximately equivalent to the delayed-pickup element is shown in fig. 37(b). The following description will apply to this start input (a) Delayed pickup/delayed dropout timer unit start input set-(b) Delayed pickup timer detail Fig. 37. Delayed-pickup/delayed-dropout timer. element, with the understanding that the delayed-dropout element is similar. The delayed-pickup element begins timing when the input goes positive. Timing continues as long as the input remains positive, the output gradually 257 becoming less negative over the timing interval. A t the end of the time delay, the output is positive and is assigned a value equal to the input (as an enhancement for use with NLR) . When the input becomes negative the timer is immediately reset, the out-put being set to a fixed negative level. (The input must remain positive for the entire delay interval before the output will become high.) The effect of a zero input value depends on the last non-zero input value. If that value was negative, the timer continues in a reset condition; if it was positive, the timer continues in a timing (or set) condition. c. SR flipflop The SR flipflop model is based on the classical cross-coupled NOR gate circuit, shown in the right-hand portion of fig. 38. The input section includes logic to force the S input to be dominant, thereby overcoming the indeterminacy which is characteristic of the basic SR flipflop when both inputs are high. The feedback inherent in the flipflop requires the use of simultaneous modelling. A l l logic is implemented using N L R operations. The (single-step) logic is embedded within a F O R T R A N DO loop, which iterates to a stable feedback condition (assuming one exists) within two iterations. 258 R r 3 > 0^  Q V. Fig. 38. SR flipflop logic, with S-input dominance A P P E N D I X C T R A N S I E N T R E S P O N S E P R O C E S S O R A. INTRODUCTION The Transient Response Processor (TRP) is a comprehensive package of software (written in A N S F O R T R A N 77) for the manipulation and display of waveforms. Operation may be either interactive or "batch". The TRP maintains an internal data area containing the waveforms, and has commands for adding data, deleting data, and saving the entire data area into external (mass-storage) files. A command is provided for plotting waveforms from the data area with minimum effort. Input to the T R P and output from the TRP may be directed from/to any file or device (within operating system limitations). Waveforms held by the TRP may be used as input to TRP-intrinsic or user-supplied functions, the output being added to the TRP data area as new waveforms. This feature permits the TRP to function as a special-purpose simulator. B. SUMMARY OF OPERATION When the TRP is started, the internal data area is empty. The G E T command is used to read in data from external files. This data may then be PLOTted, D I S P L A Y e d , or manipulated via the C O M P U T E command. Data may be added to or deleted from the data area as required. The resulting data area may be S A V E d in T R P format at any point during TRP operation for use at a future time. Execution of the TRP is terminated with the S T O P command. 259 260 C. STRUCTURE OF THE DATA The data in the data area is organized into one or more c a s e s . Each case has a distinct case title (which may be changed by the S E T command). Each case has its own associated time base. Within each case, the data is further organized into e n t r i e s . Each entry has a d e s i g n a t o r , which must be unique within the associated case. Each entry is a vector of one or more e l e m e n t s (waveforms), and has a d a t a t y p e asso-ciated with it. The data type determines both the exact form of the designator and the default "units" (e.g. "Volts") used when plotting. The data type may also determine how the entry can be used in certain f u n c t i o n s of the C O M P U T E command. The general form of a designator is c a s e : d a t a - t y p e : n a m e ( e l e m e n t ) where c a s e is a non-negative integer case number d a t a - t y p e is an alphanumeric data type code n a m e is either a single or paired (i.e. n a m e l : n a m e 2 ) character-string identifier e l e m e n t is a non-negative integer identifying a specific waveform ( e l e m e n t ) of the e n t r y . Only the d a t a - t y p e and n a m e must be specified (except where d a t a - t y p e is "TIME" , indicating the time base, in which case neither n a m e nor e l e m e n t may be specified). If c a s e is not specified it defaults to case 1. If e l e m e n t is 261 not specified, it defaults to element 0. Case numbers are not necessarily preserved, and may change when data is saved or deleted. When data is added from an external file, the distinction between cases is preserved, but the case numbers become sequential to the cases already in the data area, starting at 1. (Case 0 is somewhat special—it need never exist, it must be explicitly created since it is never created from an external file, and it may be deleted without causing other cases to be renumbered.) Valid data types are currently: C V - Computed Value, generally arising from the use of the C O M P U T E command N V - Node Voltage, generally a phase-to-ground voltage within the power system B V - Branch Voltage, either a phase-to-phase voltage or a voltage across some power system component BC - Branch Current, generally the current flowing through some power system component T I M E - time base for the case in question. For data types B V and BC, the name component of the designator must be a name pair of the form name 1: name2. Whether the name is simple or compound (name pair), it must be unique within one case for any given data type. The permissible number of characters 262 is installation dependent. Characters which serve as delimiters (i.e. blank, colon, semicolon, apostrophe, quote, equal sign, left and right parentheses, comma, and slash) should normally be avoided, since these characters usually require the use of delimiting quotes. The preferred set of characters consists of the alpha-numerics, period, number sign ("#"), hyphen, underscore, ampersand, asterisk, and at sign (••©"). D. COMMANDS Leading blanks on command lines are ignored. Commands may be abbreviated to any unambiguous short form. Commands are followed by one or more keyword parameters, separated from the command and other parameters by one or more blanks. Keyword parameters may have values as appropriate. Where values have embedded blanks, the entire value must be enclosed in apostrophes or quotes. Embedded apostrophes within an apostrophe-delimited string must be doubled (also applies to quotes). The general form of a command is C O M M A N D p a r i = value 1 par2 where p a r i is assigned value value 1 par2 takes no value. Some commands permit the use of designator lists, which are comprised of two or more designators separated by semicolons. 263 1. B A T C H The B A T C H command indicates that operation is to be non-interactive. The TRP is set to abort on recognition of any error condition (ABEND-CODE = 5). Command echoing is turned on. This command takes no parameters. Example: B A T C H 2. C O M M E N T The C O M M E N T command provides a means of inserting comments into the TRP input. It has no effect on TRP operation. The C O M M E N T command takes no parameters per se, but may be followed by any text. Example: C O M M E N T this is the comment text 3. C O M P U T E The C O M P U T E command provides a means of manipulating existing wave-forms and adding the result to the data area as a new waveform. This is by far the most powerful and flexible command, since it permits the user to invoke intrinsic TRP functions and optional user-created functions to create a custom waveform processor, or a custom simulator. Because each C O M P U T E operation is stand-alone, any feedback loops in simulated systems must be incorporated entirely within a single C O M P U T E 264 function. The C O M P U T E command takes a single keyword, which is the designator of the new entry to be generated. The "value" taken by this keyword is the name of the function to be invoked, immediately followed by a list of parameters to be "passed" to the function. The parameters are enclosed in parentheses. No blanks may appear between the function name and the parameter list. If any of the parameters in the list (e.g. a name) has blanks in it, the entire keyword value (i.e. function name followed by parameter list) must be enclosed in apostrophes or quotes. A list of intrinsic functions available through the C O M P U T E command is given in a later section. Example: C O M P U T E C V : S U M = ADD(CV:A,CV:B) produces a new waveform of data type " C V " , named " S U M " , which is the addition (function ADD) of existing waveforms " C V : A " and " C V : B " . 4. D E L E T E The D E L E T E command provides a means of deleting data from the data area. The command takes three forms: D E L E T E A L L - this form deletes all data in the data area, and resets the TRP to the startup condition. D E L E T E C A S E = case-number 265 - this form deletes case case-number. D E L E T E E N T R Y = designator-l ist - this form deletes entries associated with the designators in designator-list. The individual designators in a "designator list" are delimited from one another by semi-colons (e.g. C V : O N E ; C V : T W O ; C V : T H R E E ) . Deletions do not actually occur until more data is added to the data area, or until the data is saved into an external file. Where an entire case is deleted, subsequent (higher numbered) cases will be renumbered down during the data compaction stage which follows deletion (that is, when the data associated with the case is actually removed). A warning is issued when this occurs. Subsequent references to case numbers must take this renumbering into account. (The single exception is case 0, which may be deleted without resulting in case renumbering.) Example: D E L E T E E N T R Y = C V : O N E ; C V : T W O ; C V : T H R E E 5. D I S P L A Y The D I S P L A Y command permits the display of information from the data area. The specified information is written to the user terminal or TRP output file/device. Available items are: C A S E = case-number - the title and entry names associated with case case-number are 266 displayed on the user output device. R A N G E = designator-l ist - the maximum and minimum values are displayed for each of the waveforms specified in the designator list designator-list. If more than one designator is given in the list, the overall maximum and minimum are also displayed. VALUES(start,stop,step) = designator - the values from the selected waveform are displayed on the user output device, starting with the point specified by start and ending with the point specified by stop, with points being displayed at steps of every step points ( F O R T R A N DO loop format). The numbers start, stop, and step represent integer (ordinal) positions within the waveform. For example, VALUES(23,46,2) would indicate the 23rd through 46th points, in steps of 2. The start and step values default to one, and the stop value defaults to the last point in the waveform. AVERAGE(start ,stop) = designator - the average value of the waveform, or the portion thereof starting at start and ending at stop, is displayed on the user output device. The start value defaults to one and the stop value defaults to the last point in the waveform. RMS(start,stop) = designator - the R M S value of the waveform, or the portion thereof starting at 267 start and ending at stop, is displayed on the user output device. The start value defaults to one and the stop value defaults to the last point in the waveform. HARMONICS(start-time,base-freq, start-freq) = designator - the ten harmonics of a portion of the specified waveform starting at start-time, using a base frequency of base-freq, and starting with the harmonic at start-freq, are displayed on the user output terminal. The total extent of the waveform used for the harmonic analysis is one period of the base frequency, which defaults to the power system frequency. The start time and start frequency both default to zero. Example: D I S P L A Y R A N G E = C V : O N E ; C V : T W O ; C V : T H R E E 6. G E T The GET command adds data from an external file to the data area. Two file formats are currently available: E M T P = study-identifier - The external file from which EMTP-written data is to be read must have a name starting with a "P", to which the study-identifier string has been appended. Since consecutive transient runs may be included in a single E M T P output ("plot") file, the file is kept open after the GET to permit the consecutive runs to be accessed through consecutive GETs with the same study identifier. The file is released 268 only if R E L E A S E is included after the E M T P keyword parameter, or an end-of-file condition is detected. TRP=study-identifier - The external file from which the TRP-written data is to be read will have a name starting with a "D" , to which the study-identifier string has been appended. This file must have been written by the TRP S A V E command. The study identifier string is appended to an alphabetic character to form a file name (as indicated above), which of course must conform to rules (as to length, for example) appropriate to the host operating system. Thus the study identifier string selected must be chosen to ensure that the ultimate file name will conform to these rules; The use of the study identifier string with a use-dependent prefix to form file names permits all files associated with a given simulation to be quickly located and identified. Example: GET E M T P = H09002 R E L E A S E which causes the EMTP-written file PH09002 to be accessed for a single simulation result (case) and then released. 269 7. P A U S E The P A U S E command halts operation of the TRP and executes a F O R T R A N P A U S E . The effect and usefulness of this command depends on the host operating system. For the command to be useful, the operating system requires the capability to restart halted programs. This command takes no parameters. Example: P A U S E 8. P L O T The PLOT command plots waveforms from the data area, from 1 to 6 traces ("channels") per page. Only the number of the trace position ("channel") to be used and the designator of the waveform to be plotted need be specified. Defaults are used for the other parameters to ensure acceptable plots. This provides complete freedom from plotting details, and maximizes ease of use. A full complement of control keywords are available to allow the plot details to be specified where this is preferable. The available P L O T keywords are: H O L D - This keyword causes the plot page being generated to be held for a sequence of P L O T commands (between which other commands may be used). The plot page must subsequently be explicitly released for plotting, using the R E L E A S E keyword. The default action where H O L D has not been specified is to release the plot page after the 270 single P L O T command has been completed. R E L E A S E - This keyword releases a plot page which has been explicitly held with the use of the H O L D keyword. T R A C E S / P A G E = n - This keyword specifies the number of plot traces which are to be formatted on a single page. The number n may range from one to six, inclusive. The default value, where this keyword is not specified, is six. T I T L E = str ing (or) * (or) #n - This keyword specifies the title to be used for the plot. The s t r ing is any character string (limited to characters available for the ultimate plotting device), enclosed in quotes or apostrophes where blanks are used. The use of the asterisk character * specifies that the default title is to be used. The default title is the title of the case corresponding to the first plotted waveform. The use of the sequence #n, where n is the case number, spe-cifies that the title for case n is to be used as the plot title. The plot title used where this keyword has not been specified is either the default title mentioned above, or the global plot title established with the TRP SET command (if one has been set). The plot title may be up to 50 characters long. Longer titles will be truncated on the plot. 271 X - L A B E L = s t r i n g (or) Y - L A B E L = s t r i n g - These keywords specify the text to be used as labels for the axes. Since there are up to six Y axes, one label may be specified for each trace. Where the label strings contain embedded blanks, the strings must be enclosed in quotes or apostrophes. The default labels are the designators of the plotted waveforms. The labels may be up to 50 characters long; longer labels are truncated on the plot. X-UNITS = s t r i n g (or) Y-UNITS = s t r i n g - These keywords specify the units to be used for the axes. Only fundamental units (e.g. Volts, Amps, seconds) should be specified, since the correct prefix (e.g. kilo, milli) will be prefixed automatically as part of the plot scaling procedure. The default value for the units depends on the data type. The C V data type uses the string UNITS, since the actual unit is often arbitrary. Voltage data types (BV, N V ) use the string VOLTS, while the current data type B C uses the string AMPS. A null string (one or more blanks immediately to the right of the equal sign) may be specified, but this suppresses the scaling prefix also (since there is nothing to prefix to), and so should be used cautiously. The units string may be up to 10 characters long; longer strings will be truncated on the plot. X - S C A L E = s c a l e - f a c t o r (or) Y - S C A L E = s c a l e - f a c t o r - These keywords specify scaling factors to be applied to the data 272 prior to plotting. Thus a waveform which, for example, had been computed in volts, can be plotted in per unit. The default values of s c a l e - f a c t o r are one. X - R A N G E = ( l i m i t - l , I i m i t - 2 ) (or) Y - R A N G E = ( l i m i t - l , l i m i t - 2 ) - These keywords specify the limits of the scales on the corresponding axes. The default action is to use the maximum and minimum data values, obtained by scanning the data. However the values are determined, the actual values used on the axes are rounded up according to internally-programmed rules which assure "nice" labels and steps between divisions. The two limits need not be specified in any particular order, since they will be ordered internally. T R A C E ( t r a c e - n u m b e r ) = y - d s g / x - d s g - This is the only keyword required for a plot. The traces on the plot page are numbered consecutively starting at one, located at the bottom of the page. The trace designated by t r a c e - n u m b e r is generated with data from y - d s g as the y-coordinate, and data from x - d s g as the x-coordinate. If x - d s g is not specified, the default action is to use the time base, which is the usual, requirement. More than one waveform may be included in a single trace. This feature, called o v e r l a y i n g , establishes the labels, units, and axis scaling from the first waveform. This should be kept in mind when determining the order of overlaying. S Y M B O L S / T R A C E = n 273 - This keyword is of use during overlaying. The only assured means of distinguishing between overlays is by means of symbols which are included in the waveforms during plotting. (Where the plotting device has colour capability, the TRP P L O T routines also distinguish between overlays by using different colours.) The number of such symbols used is determined by n. The default value used when this parameter is not specified is generated by subtracting one from the overlay number. Thus the first overlay has no identifying symbol, the second has one, etc. The symbols used are determined by the plotter interface routines used. The basic design of the PLOT command is such that all plot-formatting parameters for the various y axes are reset between P L O T command lines, even when the plot is being held. To permit the same y axis parameters to be used for more than one trace (and one overlay of that trace), a plot command may be continued by putting a hyphen at the end of the line to be continued, as the last non-blank character. Note that all plot-formatting parameters must be spec-ified before the associated T R A C E parameter is issued, so that ordinarily it is best to specify the T R A C E parameters last. Note also that all plot-formatting parameters which determine the plot page layout (such as the title and number of traces per page) or the x-axis details (such as the x-a.xis label) must be spec-ified before the first T R A C E parameter. This is because a trace is produced as the last step after executing a PLOT command, before reading the next TRP input line, even when a P L O T command is being continued. Example: 274 P L O T T R A C E S / P A G E = 2 TRACE(1) = N V : W S N . A TRACE(2)=NV:WSN.B 9. S A V E The S A V E command saves the present contents of the data area into an external file. Only one S A V E format is currently available: TRP = s t u d y - i d e n t i f i e r The s t u d y - i d e n t i f i e r string, described under the TRP command GET, is appended to the character " D " to form the name of the external file. Together, S A V E and GET using TRP format form a pair; the actual external file name is important only so far as the host operating system restrictions on legal file names affect the choice of s t u d y - i d e n t i f i e r (as described under GET). Within the TRP, only study identifiers are used. Example: S A V E TRP = H09002 10. S E T The SET command sets global parameters for TRP operation. These parameters remain in effect only during a single TRP run—there is no memory between runs. Parameters available are: A B E N D - C O D E = n - This parameter determines the value of TRP-generated "return codes" which will cause the TRP run to abort automatically. This 275 feature is useful when the TRP is executing a prepared set of instructions; for truly interactive use the user is in full control. Internal "return code" values greater than or equal to n cause the TRP to abort. C A S E - T I T L E (case-number) = s t r ing (or) #n - This parameter permits the case title to be set for case case-number. If the string to be used for the title includes blanks, the string must be delimited by apostrophes or quotes. The title can be duplicated from another case by using form #n, where n is the number of the case from which the title is to be copied. (Clearly, this precludes the use of a title string beginning with the character "#" unless the entire string is delimited by apostrophes or quotes.) P L O T - T I T L E = str ing (or) * (or) #n - This parameter permits the default plot title to be set. The specif-ics of use are the same as for the T I T L E parameter of the PLOT command. F R E Q U E N C Y - B A S E = frequency - This parameter sets the TRP internal record of the power system frequency. The default value (at TRP startup) is 60 Hz. E C H O = O N (or) O F F (or) b lank - This parameter controls echoing of T R P input lines. This feature is useful when the TRP is used in batch mode, or when the input commands are coming from an input file. If the keyword value is 276 null (one or more blanks following the equal sign), rather than O N or OFF, the E C H O state is toggled (OFF to ON, or O N to OFF). INPUT = study-identifier (or) * - This parameter directs the TRP to take its input from another source. If study-identifier is given, the source is an external file with a name formed by prefixing the character "I" to study-identifier. The same considerations apply as were given under the GET command regarding choice of study identifiers. If an asterisk is specified rather than a study identifier, the input will be taken from the user input device, which is the input source assigned at TRP startup. O U T P U T = study-identifier (or) * - This parameter directs the TRP to send its output to another destination. If study-identifier is given, the destination is an external file with a name formed by prefixing the character "O" to study-identifier. The same considerations apply as were given under the GET command regarding choice of study identifiers. If an asterisk is specified rather than a study identifier, the output will be sent to the user output device, which is the output destination assigned at TRP startup. M E S S A G E S = study-identifier (or) * - This parameter directs the TRP to send its informational, warning, and error messages to another destination. If study-identifier is given, the destination is an external file with a name formed by 277 prefixing the character " M " to study-identifier. The same considera-tions apply as were given under the GET command regarding choice of study identifiers. If an asterisk is specified rather than a study identifier, the messages will be sent to the user output device, which is the message destination assigned at TRP startup. Example: SET F R E Q U E N C Y - B A S E = 50 A B E N D - C O D E = 5 11. S T O P The STOP command stops TRP execution and returns control to the host operating system using F O R T R A N STOP n, where n is selected by the TRP to indicate a "return code" established by the TRP to flag the detection of errors. Return code values are 4 for warnings, 8 for errors which permit the TRP to continue execution, and 16 for errors which are fatal to continued TRP operation (the TRP will always abort in this latter case, sometimes gracelessly). Where the value n is accessible by the host operating system, this feature can be used to facilitate conditional execution of operating system commands in a macro or batch mode (where the operating system offers this feature). Example: STOP 278 E. TRP INTERNAL FUNCTIONS The TRP internal functions, accessed through the C O M P U T E command, provide a basic set of waveform operations. The total set of available functions may be extended by adding user functions, as described in the next section. A l l trailing scalar parameters for which default values are given may be omitted. Parameters may not be omitted between specified parameters; if one parameter is omitted, all following parameters must also be omitted. The available internal functions are A D D , B A S E , B L O C K , C O P Y , COSINE, G A T E , I N T E G R A T E , M A X I M U M , M I N I M U M , N E G A T E , S U B T R A C T , and Z E R O - S E Q U E N C E , and are described following. 1. A D D The A D D function adds two waveforms point by point; the sum is multiplied by an optional scaling factor. The form of the TRP function invocation is: C O M P U T E o d s g = A D D ( i d s g - l , i d s g - 2 , s c l f c t ) where o d s g is the designator for the A D D result, i d s g - 1 is the designator for one input, i d s g - 2 is the designator for the second input, s c l f c t is the factor by which the sum is to be scaled to produce the 279 output waveform. The default value is one. 2. B A S E The B A S E function generates a time base for a specified case; this feature is useful when the TRP is used to generate waveforms directly. The time base produced has a constant step size. The form of the TRP function invocation is: C O M P U T E odsg=BASE(stepsize,#-steps) where odsg is the designator for the time base result, of the form n :TIME, where n is the case number, stepsize is the size of the time steps, in seconds, and #-steps is the number of time steps to be generated. 3. B L O C K The B L O C K function "blocks" the path from the input through to the out-put if the control input is greater than zero. This is approximately equivalent to a normally-closed switch, except that the output is zero in the "blocked" (open) state. The B L O C K function is the converse to the G A T E function. The form of the TRP function invocation is: C O M P U T E odsg=BLOCK(idsg,idsg-C) 280 where odsg is the designator of the output waveform, idsg is the designator of the waveform to be controlled, and idsg-C is the designator of the controlling waveform. 4. C O P Y The C O P Y function permits a scaled copy of a waveform to be produced. C O P Y . is helpful when accounting for CT and V T ratios in protection simulations where actual CT and V T models are not used. The form of the TRP function invocation is: C O M P U T E odsg=COPY(idsg,sc!fct) where odsg is the designator of the output waveform, idsg is the designator of the input waveform, and sclfct is the scaling factor applied during the copy. The default value is one. 281 5. C O S I N E The COSINE function permits the generation of a pure cosine waveform of specified amplitude, phase, and frequency. The form of the TRP function invocation is: C O M P U T E odsg=COSINE(case,magn,phase,freq) where odsg is the designator of the output waveform, case is the number of the case from which the time base is to be used to generate the cosine (usually the same as the case to which odsg belongs). magn is the magnitude of the resulting cosine. The default value is one. phase is the phase angle of the resulting cosine, in degrees. The default value is zero. freq is the frequency of the resulting cosine, in Hertz. The default value is the power system frequency. 6. G A T E The G A T E function "gates" the input to the output if the control input is greater than zero. This is approximately equivalent to a normally-open switch, except that the output is zero in the "ungated" (open) state. The G A T E function is the converse to the B L O C K function. 282 The form of the TRP function invocation is: C O M P U T E o d s g = G A T E ( i d s g , i d s g - C ) where o d s g is the designator of the output waveform, i d s g is the designator of the waveform to be controlled, and i d s g - C is the designator of the controlling waveform. 7. I N T E G R A T E The I N T E G R A T E function produces a running integral of the input wave-form, starting from a specified initial condition at the first point. A gain can also be specified, permitting the output to be scaled. The numerical technique used is trapezoidal integration. The form of the TRP function invocation is: C O M P U T E o d s g = I N T E G R A T E ( i d s g , g a i n , i c ) where o d s g is the designator of the output waveform, i d s g is the designator of the input waveform, g a i n is the gain (scale factor) to be used for the integration. The default 283 value is one. i c is the initial condition to be used at the start of integration. The default value is zero. 8. M A X I M U M The M A X I M U M function produces a result which is the point-by-point maximum of two input waveforms. If desired, an index can be produced which gives a measure of the amount by which the resultant waveform differs from the first of the two specified input waveforms. This index is the R M S diff-erence between the first waveform and the result. The form of the TRP function invocation is: C O M P U T E o d s g = M A X I M U M ( i d s g - l , i d s g - 2 , c i n d e x ) where odsg is the designator of the output waveform, i d s g - 1 is the designator of one input waveform, i d s g - 2 is the designator of the second input waveform, and c i n d e x is a value for controlling the computation of the R M S index. If c i n d e x is positive the index is computed and displayed. The default value of c i n d e x is negative, for no index. 284 9. M I N I M U M The M I N I M U M function produces a result which is the point-by-point min-imum of two input waveforms. If desired, an index can be produced which gives a measure of the amount by which the resultant waveform differs from the first of the two specified input waveforms. This index is the RMS diff-erence between the first waveform and the result. The form of the TRP function invocation is: C O M P U T E o d s g = M I N I M U M ( i d s g - l , i d s g - 2 , c i n d e x ) where o d s g is the designator of the output waveform, i d s g - 1 is the designator of one input waveform, i d s g - 2 is the designator of the second input waveform, c i n d e x is a value for controlling the computation of the R M S index. If c i n d e x is positive the index is computed and displayed. The default value of c i n d e x is negative, for no index. 10. N E G A T E The N E G A T E function provides a simple algebraic negation of the input waveform. The form of the function invocation in the T R P is: 285 C O M P U T E odsg=NEGATE ( idsg) where odsg is the designator for the output, idsg is the designator for the input. 11. S U B T R A C T The S U B T R A C T function subtracts one waveform from another point by point; the difference is multiplied by an optional scaling factor. The form of the TRP function invocation is: C O M P U T E odsg=SUBTRACT( idsg- l , idsg-2 ,scl fct) where odsg is the designator for the result, idsg-1 is the designator for one input, idsg-2 is the designator for the second input, sclfct is the factor by which the difference is to be scaled to produce the output waveform. The default value is one. 286 12. Z E R O - S E Q U E N C E The Z E R O - S E Q U E N C E function computes the zero-sequence component of three input waveforms. The result has meaning only where the input wave-forms are the three phase Components of a single three-phase quantity (e.g. voltage). The form of the TRP function invocation is: C O M P U T E odsg= ZERO-SEQUENCE ( idsg -A , idsg -B , idsg -C) where odsg is the designator for the zero-sequence output waveform, idsg -A is the designator for the phase A component, idsg-B is the designator for the phase B component, and idsg -C is the designator for the phase C component of the input quantity. F. PREPARING AND INTERFACING TRP USER FUNCTIONS TRP user functions are best prepared by first writing a self-contained FORTRAN-callable subroutine which takes as parameters all required settings and input values, and returns as parameters the necessary vector outputs. The length of the input and output vectors is equal to the number of time steps, which is available as a parameter from the TRP interface routine. The TRP interface skeleton T R P U F X , listed in fig. 39, provides a L i s t i n g of TRPUFX.F77 at 01:16:25 on MAY 9, 1986 for CCId'BRWG Pago 1 1 SUBROUTINE TRPUFX(RESULT, NELMNT. NDATA, DATA, MDATA. 2 3 4 C 1 PARMS. NPARMS. I TYPE. ISTART. I END. NAMES. 2 NENTRY, COOES. KEYS. NCODES. SETVLU, LABORT) • • • FORTRAN 77 • • • S 6 7 c c c Purpose prototype user funct ion 6 9 10 c Q • • • Constant parameters: INTEGER SIDATE, DPARMS 11 12 13 c c CHARACTER*!*) SBNAME 14 15 16 c c c • • » • *« - -change SIOATE to date of rout ine c rea t ion • - -change SBNAME to name of subroutine * - -change DPARMS to number of designators required • 17 18 16 c c PARAMETER (SIDATE•19660210.SBNAME•'TRPUFX'.DPARMS-1) 20 21 22 c c c DPARMS: SBNAME: SIDATE: number of designator parameters requi red rout ine name SI form of date of last change to th is rou t ine . 23 24 25 c c ' c • • * General var tab les: 26 27 28 INTEGER 1 2 SDATE, NDATA, NELMNT, MDATA. NPARMS. INDX(DPARMS), ICASE(OPARMS). DTYPE(DPARMS), NVPEL. IELMNT (DPARMS ) , ITVPEI • ) . NCODES. ISTART(M, IEND(« 29 30 31 3 ), IBASE(OPARMS). NENTRY. CODES!*). OSTARTIDPARMS), 4 DENO(DPARMS) REAL DATA(•) , RESULT(») , SETVLU(') 32 33 34 c LOGICAL LABORT CHARACTER*(•) PARMS(*),NAMES< 2 . • ) . K E Y S ! •) 35 36 37 c c c CODES: DATA: OENO: L i s t of data type codes ( input) Data for database ( Input/output) l i s t of ending pointers to data In database 38 39 40 c c c OSTART: DTYPE: IBASE: l i s t of s t a r t i n g po inters to data In database L i s t of type codes for en t r i es L i s t of Ind lc les for bases for en t r i es 41 42 43 c c c ICASE: 1ELMNT: I END: L i s t of case numbers for en t r ies L i s t of elements for en t r i es L i s t of ending locat ions for database en t r i es (Input) 44 45 46 c c c INDX: I START: I TYPE: L i s t of i n d i c l e s for en t r i es L i s t of s t a r t i n g locat ions for database en t r i es (Input) L i s t of data types for database en t r i es ( input) 47-46 49 c c c KEYS: LABORT: MDATA: L i s t of data type keys ( input) true If rout ine aborts (output) Maximum number of locat ions In database (Input) 50 51 52 c c c NAMES: NCODES: NDATA: L i s t of names for database en t r ies ( input ) Number of data type codes ( input) Number of data values In database ( Input/output) S3 54 55 c c c NELMNT: NENTRY: NPARMS: Number of elements being created (output) Number of e n t r i e s In database (Input) Number of parameters being passed (Input) 66 c NVPEL: Number of data values per element 1 2. . .3 4 . .5 . 6 7 8 9 O 1 2. Fig. 39. Listing of skeleton T R P U F X 00 L i s t i n g of TRPUFX.F77 at 01:16:25 on MAY 9. 19B6 for CCId-BRWG Page 2 57 C PARMS: L i s t of parameters being passed (Input) 5B C RESULT: Result of computation (output) 59 C SDATE: Sat non-2ero If rout ine date has already been passed 60 C to NVDATE. 61 C SETVLU: var ious TRP set t ings (Input) 62 C 63 C • • • External rout ines: 64 C 65 INTEGER NVDATE 66 C 67 C ERRMSG: sends er ror message to user 6B c NVDATE: Version dat ing rou t ine . F i r s t parameter is SI 69 c date, second is "vers ion group" number of th is 70 c subprogram. 71 c TRCBAK: keeps subroutine traceback l i s t 72 c UFAUX: a u x i l i a r y rout ine for user funct ions to: 73 c - get po inters etc for parameter designators 74 c - check that data have matching time bases 75 c - ensure that database has enough room for data 76 c 77 c 78 c • • t 79 c 80 c INTEGER 81 c REAL 82 c DOUBLE PRECISION 83 c COMPLEX • 4 c LOGICAL 85 c CHARACTER 86 c 87 c 88 c • • • 89 c 90 c 91 c 92 c INTEGER 93 c REAL 94 c OOUBLE PRECISION 99 c COMPLEX 96 c LOGICAL 9? c EXTERNAL 98 c 99 c 100 c • • » 101 c 102 DATA SDATE / O / 103 SAVE SDATE 104 c 105 c Pass rout ine date to NVDATE If not done a l ready. 106 IF (SDATE .EQ. 6) SOATE - NVDATE(S1 DATE,3 V 107 CALL TRCBAK(SBNAME,1) 108 c 109 c • • • 110 c * • 4 --change value of NELMNT to number of • 111 c • • » waveforms which w i l l resu l t from • 112 c « * • funct ion * 1 2 3 4 5 6 7 8 9 0 1 2. Fig. 39 (cont'd) OO 00 L i s t mg Of TRPUFX.F77 »t 01:16:25 on MAY 9. 1986 for CCId-BRWG Page 3 113 C constant : t 14 115 1 16 C C NELMNT • 1 117 1 IB 119 c check for requi red number of parameters LABORT • NPARMS .LT. DPARMS IF (LABORT) THEN 120 121 132 c c • • * c • • • --change error message to r e f l e c t • 133 134 135 c •** number of en t r i es required CALL £RRMSG(SBNAME, 'Exac t ly 0 parameters are r e q u i r e d ' , 1 a.l • 136 137 138 c • * • c c GO TO IS "ABORT" 139 130 131 c GO TO 1000 END IF 133 133 134 c get po in ters and make standard checks CALL UFAUXlINDX. ICASE. DTYPE. DSTART. DEND. IELMNT. IBASE, 1 NVPEL, LABORT, NOATA. DATA, MDATA, PARMS, DPARMS, 133 136 137 c 2 I START, I END, 1 TYPE, NAMES. NENTRY, CODES. KEYS. 3 NCODES. NELMNT) GO TO Is "ABORT" 138 139 140 c c • • • IF (LABORT) GO TO iOOO 141 143 143 c ••• c c ••• 144 145 146 10 DO 10 i • 6. NVPEL - 1 RESULTd • 1) • 0.0 CONTINUE 147 148 149 c c 1000 CALL TRCBAKf/ ' , - 1 ) 150 151 RETURN END Fig. 39 (cont'd) 290 relatively simple method of interfacing the stand-alone subroutine just described with the TRP. The second stage in the interfacing process is to modify the T R P U F X skeleton as required to get the required interface subroutine. The modification procedure, which will be described now, can be most easily followed by referring to the T R P U F X skeleton in fig. 39 and an example interface routine U F T I M R (for the delayed-pickup/delayed-dropout timer model described in appendix B) listed in fig. 40. The first step is to change the subroutine name to something unique and more-or-less descriptive (TRPUFX lines 1 and 17; U F T I M R lines 14001 and 14016). (The parameter S B N A M E at T R P U F X line 17 and U F T I M R line 14016 is used to maintain a "traceback" list within the TRP in case of errors.) It is wise to use " U F " as the first two characters of interface routine names to prevent conflict with other names, and to allow them to be easily identified as interface routines. It is also helpful at this step to enter a description of the purpose of the function ( T R P U F X line 6; U F T I M R line 14006). The next step is to set the last-modification date for the routine as parameter SID A T E (TRPUFX line 17; U F T I M R line 14016). This date is used to maintain a dynamic "version date" within the TRP, which reflects the TRP version represented by the subroutines actually invoked. This date is kept in S A V E files and is printed at TRP termination. The parameter D P A R M S ( T R P U F X line 17; U F T I M R line 14016) should now be changed to reflect the number of designator parameters required by the ultimate function. This information is used for storage allocation within the interface routine. The example timer model requires only one designator (for the timer start/stop control input). L i s t i n g of TRPUF1.F77(14001,15000) at 01:16:27 on MAY 9, 1986 for CCId-BRWG '• Page T 14001 SUBROUTINE UFTIMR(RESULT, NELMNT, NDATA, DATA, MOATA, 14002 1 PARMS. NPARMS. ITYPE. ISTART, IENO, NAMES, 14003 2 NENTRY. COOES. KEYS. NCODES. SETVLU. LABORT) 14004 C • • • FORTRAN 77 • • • 14005 C 14006 C Purpose : tImer model 14007 C 14008 C • • • Constant parameters: 14009 C 14010 INTEGER SIDATE, DPARMS 1401 1 CHARACTER* (•) SBNAME 14012 c 14013 c • » » - -change SIDATE to date of rout ine c rea t ion • » • • » • • • • • 14014 c * • • 14015 c * • * 1 - -change DPARMS to number of designators required 14016 PARAMETER ( SIOATE-19860227,SBNAME•'UFTIMR',DPARMS"1) 14017 c 14018 c 14019 c DPARMS: number of designator parameters requi red 14020 c SBNAME: rout ine name 14021 c SIDATE : SI form of date of last change to th is rout ine . 14022 c 14023 c General v a r i a b l e s : 14024 c 14025 INTEGER SDATE, NDATA, NELMNT, MDATA, NPARMS, INDX(DPARMS), 14026 1 ICASE(DPARMS), DTYPE(DPARMS). NVPEL, 14027 2 IELMNT(DPARMS), ITYPE( ' ) . NCODES. ISTART(•). IENO(* 14028 3 ), IBASE(DPARMS) , NENTRY. CODES!,*), OST ART (DPARMS) , 14029 4 DENDtDPARMSj 14030 REAL DATA!* ) , RESULT(•) , SETVLU(>) 14031 LOGICAL LABORT 14032 CHARACTER* (•) PARMS(*), NAMES! 2, • / . KEYSCI 14033 c 14034 c COOES: L i s t of data type codes (Input) 14036 c DATA: Data for database ( input /output ) 14036 c DENO: l i s t of ending pointers to data In database 14037 c DSTART: l i s t of s t a r t i n g po in ters to data In database 14038 c OTYPE: L i s t of type codes for en t r i es 14039 c IBASE: L i s t of Indlciea for bases for e n t r i e s 14040 c ICASE: L i s t of case numbers for en t r i es 14041 c 1E LMNT: L i s t of elements for e n t r i e s 14042 c I END: L i s t of ending locat ions for database en t r ies (Input) 14043 c INDX: L i s t of Indlciea for en t r i es 14044 c ISTART: L i s t of s t a r t i n g ideat ions for database en t r ies ( input) 14048 c • ITYPE: L i s t of data types for database en t r i es (Input) 14046 c KEYS: L i s t of data type keys ( input) 14047 c LABORf: true i f rout ine aborts (output) 14048 c MDATA: Maximum number of loca t ions In database (Input) 14049 c NAMES: L is t of names for database en t r i es (Input) 14050 c NCODES: Number of data type codes ( input) 14051 c NOATA: Number of data values In databaae ( Input/output) 14052 c NELMNT: Number of elements being created (output) 14053 c NENTRY: Number of en t r i es in database ( input) 14054 c NPARMS: Number of parameters being passed (Input) 14055 c NVPEL: Number of data values per element 14056 c PARMS: L i s t of parameters being passed ( input) 1 2. 3 4 5. 6. 7 .8. . 9 0 1 2. Fig. 40. Listing of example interface routine U F T I M R L i s t i n g of TRPUFI.F77(14001.15000) et Ot:16:27 on MAY 9. 1986 for CCld'BRWG Page 2 140S7 C RESULT: Result of computation (output) 14058 C SDATE: Set non- iero If rout ine date haa already been passed 140S9 C to NVOATE. 14060 C SETVLU: var ious TRP se t t ings (Input) 14061 c 14062 c • • • External rou t ines : 14063 c 14064 INTEGER NVOATE 1406S c 14066 c ERRMSG: sends er ror message to user 1406 7 c NVDATE: Version dat ing rout ine . F i r s t parameter 1s SI 14068 c date, second la "version group* number of th is 14069 c subprogram. 14070 c TRCBAk: keeps subroutine traceback l i s t 14071 c UFAUX: a u x i l i a r y rout ine for user funct ions to: 14072 c - get po inters etc for parameter designators 14073 c - check that data have matching time bases 14074 c - ensure that database has enough room for data 1407S c 14076 c 14077 c 14079 c 14079 REAL IC. PUDLY. UOOIY, VLIM 14060 LOGICAL LREAL 14081 c 14082 c D0DLV: drop-out delay 14083 c IC: i n i t i a l cond i t ion for timer (high If (C > 0) 14084 c LREAL: true If s t r i n g Is real number 14085 c PUDLY: pickup delay 14086 c VLIM: l im i t for output range 14087 c 14088 c • * * End of user va r iab les • • • • • * • » * * • • * • • • ' • • * • * • • • • • • • * • • • • • • * 14089 c 14090 c 14091 c 14092 c INTPNB: t r i e s to Interpret s t r i n g as real number 14093 c TIMER: simulates delayed pickup/dropout timer 14094 c 14098 c 14096 c 14097' DATA SDATE /6/ 14098 SAVE SDATE 14099 c 14100 c Pasis rout ine date to NVOATE i f hot done a l ready. 14 101 IF (SDATE .EQ. 0) SOATE • NVOATE(SIDATE,3) 14102 CALL TRCBAK(SBNAME, 1) 14 163 c 14104 c constant : 14 105 c • *« 14106 c » » • --change value of NELMNT to number of 14 107 c «• • waveforms which w i l l resu l t from 14 108 c •«» 14109 c s p e c i f y brie extra element for temporary storage 14 1 10 NELMNT • 2 14111 c «• • 14 112 c 1 2 3 4 5 6 7 8 9 O 1 2. Fig. 40 (cont'd) to C O to L l e t l n g of TRPUF 1 . F77( 14001 , 150OO) at 01:16:27 on MAY 9~, 1986 for CCId-BRWG Page 3 14113 C check for required number of parameters 14 1 14 LABORT • NPARMS . LT. OPARMS 14115 IF (LABORT) THEN 14 1 16 C 141 17 C • * • - -change error message to r e f l e c t 14 1 18 C number of en t r ies requi red 14119 CALL ERRMSG(SBNAME, 'At least 1 parameter Is r e q u i r e d ' , 14120 i 2) 14121 C 14122 C GO TO IS "ABORT" 14123 GO TO 1 0 14124 END IF 14125 C 14126 C get po in ters and make standard checks 14127 CALL UFAUXIINDX, ICASE, DTYPE , DSTART, DEND. IELMNT, IBASE, 14128 1 NVPEL, LABORT, NDATA, DATA, MOATA, PARMS, DPARMS, 14129 2 ISTART, I END. I TYPE, NAMES. NENTRY, CODES. KEYS. 14130 3 NCODES, NELMNT) 14131 C GO TO IS "ABORT" 14132 IF (LABORT) GO TO 1 0 14133 C 14134 C 14135 c constants : 14136 VLIM • 10.0 14137 c 14138 c d e f a u i t s : 14139 IC • -VLIM 14140 PUDLY - 0 . 0 14141 bOOLY -6.6 14142 IF (NPARMS .GE. 2) THEN 14143 CALL INTPNB(PUDLY, PARMSI2), LREAL) 14144 LABORT • .NOT. LREAL OR. PUDLY .LT. 0.0 14 145 IF (LABORT) THEN 14146 CALL ERRMSG(SBNAME, 'Bad value for pickup d e l a y ' , 2) 14147 ELSE IF (NPARMS .GE. 3) THEN 14148 CALL INTPN8(000LY. PARMSO), LREAL) 14149 LABORT • .NOT. LREAL .OR. DOOLY .LT . 0.0 14150 IF (LABORT) THEN 14151 CALL ERRMSQ(SBNAME. 'Bad value for dropout d e l a y ' , 14152 1 2) 14153 ELSE IF (NPARMS .GE. *] THEN 14154 CALL INTPNB!IC. PARMS(4). LREAL) 14155 LABORT • .NOT. LREAL .OR. IC .LT. 0.0 14186 IF (LABORt) CALL ERRMSGfSBNAME, 'Bad value for I C 14157 1 . 2) 14158 END IF 14 159 END IF 14160 ENO IF 14161 C GO TO la ABORT 14162 IF (LABORT) GO TO 1 0 14163 c 14164 c 14 1 6 3 c 14166 c 14167 CALL TIMER(RESULT,RESULT(NVPEL*1),OATA(DSTART(I)),0ATA(1STA 14168 JRT(IBASE(1))).NVPEL. PUDLY, DODLY. IC, VLIM) 1 2 3 4 5 . .6 . .7 8. . 9. 0 1 . . . . . . . . .2. Fig. 40 (cont'd) L t ft 11 ng of 14169 TRPUF1,F77(14001,15000) B t 01:16:27 on MAY 9, 1986 for CCId-BRWG Page 4 14170 C 14171 C remove extra element now to free storage 14172 10 NELMNT • 1 14 1 7 3 N D A T A "• NO AT A - NVPEL 14174 CALL TRCBAKC -I) 14t75 RETURN 1 4 1 7 6 E N D I 2. 3. . 4 5. • .6. . .7 , , , 8 9 O 1 2. Fig. 40 (cont'd) £ 295 The next step is to define any user variables or external routines which will be required within the interface routine ( T R P U F X lines 78-100; U F T I M R lines 14077-14095). (The function INTPNB at U F T I M R line 14092 is a stock TRP function which is useful when decoding constant parameters.) The next step is to specify the number of elements needed in the output vector, via N E L M N T ( T R P U F X line 114; U F T I M R line 14110). In the example routine U F T I M R , the number of elements has been set high by one, in order to force the TRP to get extra storage for temporary use. This storage has been released again at lines 14172-3. Only the highest numbered contiguous elements can be released, so these are the ones to use for temporary storage (element 2 in the example). It is now necessary to change the error message produced when insufficient parameters have been given ( T R P U F X line 124; U F T I M R line 14119). Ordinarily only designators are required parameters, the others taking default values when not specified. The next step is to specify the instructions to recover any scalar parameters (the routine U F A U X at T R P U F X line 133 automatically handles des-ignators, which are always specified as the first parameters in the function parameter list), between T R P U F lines 140-1. This is done as shown for the U F T I M R example routine at lines 14134-64. Finally, the code to compute the function must be added, replacing the dummy lines 144-6 in T R P U F X . This generally consists of a call to the self-contained subroutine prepared earlier, perhaps with some preparatory computa-tions. For the U F T I M R example routine, only a call was required (at lines 296 14167-8). The output waveforms are interfaced to the two elements stored sequentially in R E S U L T . The number of values (time steps) in each element is available from N V P E L . This is used here both for specifying the length of the input and output vectors, and for computing the offset of the second (and subsequent) elements in R E S U L T . (Full advantage is taken here of the superior and now-standard "pass-by-location" method of parameter reference in F O R T R A N 77 parameter lists.) The input waveforms are taken directly from the data area D A T A , using starting locations in DSTART. The time base (where required) for each input waveform is accessed by using the corresponding element of I B A S E to address the data area through the indexing vector ISTART, as shown at U F T I M R lines 14167-8. The significance of the entries in the T I M E R parameter list is: R E S U L T : output waveform in element 0, R E S U L T ( N V P E L + 1 ) : temporary storage in element 1, DATA(DSTART(1)): input waveform for timer on/off control, DATA(ISTART(IBASE(1))): time base for case corresponding to input wave-form, N V P E L : number of time steps per waveform, equal to the number of values per element, P U D L Y : timer pickup delay, D O D L Y : timer dropout delay, 297 IC: initial condition for timer on/off status, and V L I M : output-range limit for timer. The third and final stage in the interfacing process is to include the func-tion name in the routine which calls the interface routine from the TRP. A special TRP routine, T R P U F N , has been prepared for this purpose. The initial form of this routine has no subroutine calls; the calls are added as user func-tions are added. A "mature" form of this routine, developed for the user func-tions described in appendix B, is listed in fig. 41. The function name taken from the C O M P U T E command is contained in F N C T N (e.g. line 5084). The name in F N C T N is tested against valid function names in an extended IF-ELSEIF instruction. The form of the entries can be seen from lines 5150-4, for example, which provide the call to the subroutine U F T I M R described earlier. The function list in T R P U F N is scanned before the list of TRP internal functions, so that user-functions may replace internal func-tions of the same name. G. TRP FILE PREFIXES A l l files used by the TRP have names beginning with a TRP-specified prefix which depends on the use to which the file is put. The remainder of the file name consists of a "study identifier" string specified in TRP commands. The file prefix is assigned according the the list in table 4. L i s t i n g of TRPUF1.F77(5001.6000) at 01:16:25 on MAY 9, 1986 for CCId'BRWG Pago" T 5001 SUBROUTINE TRPUFNfLNFND, RESULT, NELMNT, NDATA, DATA, 5002 1 MDATA. PARMS. NPARMS. ITYPE, ISTART. I END. 5003 2 NAMES. NENTRY. CODES, KEYS, NCODES. SETVLU. 5004 3 LABORT, FNCTN) 5005 C • • • FORTRAN 77 • • • 5006 C 5007 C Purpose Recognizes user funct ion name, and c a l l s 5008 C appropr iate rout ine 50O9 C 5010 C • • • Constant parameters: 5011 C 5012 INTEGER SIDATE 5013 CHARACTER* (•) SBNAME 5014 PARAMETER (SIDATE-19860326.SBNAMETRPUFN'j 5015 C 5016 C SBNAME: rout ine name 5017 c SIDATE: SI form of date of last change to th is rout ine . 5018 c 5019 c • • • General v a r i a b l e s : 5020 c 5021 INTEGER SOATE, NDATA, NELMNT, MDATA, NPARMS. CODES, NCODES, 5022 1 ITYPE(*) . ISTART(• ). I E N D ( « ) . NENTRY 5023 REAL DATA! • j , SETVLU(*), RESULT*•) 5024 LOGICAL LABORT, LNFND 5025 CHARACTER* (•) FNCTN, PARMS('), K E Y S ! * ) . NAMES(2,*) 5026 c 5027 c COOES: Data type codes (Input) 5028 c DATA : Data for database ( Input/output) 5029 C FNCTN: Funct ion name ( input) 5030 c IENO: L i s t of ending locat ions for database en t r ies ( l / o ) 5031 c ISTART: L i s t of s t a r t i n g locat ions for database en t r ies ( l / o ) 5032 c ITYPE: L i s t of data types for database en t r i es ( input /output ) 5033 c KEYS: Data type keys (Input) 5034 c LABORT: true If funct ion c a l l has aborted (output) 6035 c LNFNO: true If funct ion name has not been i d e n t i f i e d 5036 c 1n th is rout ine (output) 5037 c MDATA: Maximum number of locat ions In database (Input) 5036 c NAMES: Name l i s t for database en t r ies ( input) 5039 c NCODES: Number of data type codes (Input) 5040 c NDATA: Number of data values In database ( Input/output) 504 1 c NELMNT: Number of elements in funct ion 6u tput ( i /o ) 5042 c NENTRY: Number of e n t r i e s In database ( Input/output) 6043 c NPARMS: Number of parameters found in funct ion parm. l i s t 5044 c ( input) 5045 c PARMS: Parameters from funct ion designator (Input) 5046 c RESULT: resu l t from funct ion (output) 504* c SOATE: Set non-zero If rout ine date has already been passed 5048 c to NVOATE. 5049 c SETVLU: var ious se t t ings for TRP (Input) 5050 c 8051 c • • • External routInes: 9052 c 5053 INTEGER NVDATE 5054 c 5055 c ERRMSG: sends er ror message to user 5056 c NVOATE : Version dat ing rout ine . F i r s t parameter is SI 1 .2. .3 4 .5. . 6. . . 7. 8 9 0 1 .2 . Fig. 41. Listing of example of completed routine T R P U F N to CD CO L i s t i n g of TRPUF1. F 77 (5001.6000) at 01:16:25 on MAY 9, 1986 for CCId-BRWG ' Page 2 5057 C date , second Is "vers ion group" number of th is 5058 C subprogram. 5059 C TRCBAK: keeps subroutine traceback l i s t 5060 C TRPBLK: blocks f i r s t waveform by second, point by point 5061 C TRPCAR: converts po lar representat ion back to Car tes ian form. 5062 C TRPQAT: gates f i r s t waveform by second, point by point 5063 C TRPLVL: s h i f t s level of waveform by constant amount, point by 5064 C point 5065 C TRPPLR: converts two waveforms Into polar representa t ion , f i r s t 5066 C Is taken as X, second as Y, resu l t Is two-element 5067 C vec tor , with f i r s t element being r a d i u s , second angle . 5068 C base has no meaning. • * « * 5069 C UFNEG: negates s p e c i f i e d entry . 6070 c UFOCR: res t ra ined overcurrent re lay 5071 c UFPSFA: p o s i t i v e sequence f i l t e r , type A 5072 c UFPTA: permissive t r i p b lock , type A 6073 c UFTIMR: delayed pickup/dropout timer 5074 c 5075 DATA SOATE /O/ 5076 SAVE SOATE 6077 5078 c Pass rout ine date to NVOATE if not done a l ready. 5079 IF (SOATE .EQ. 6) SOATE • NVOAT E(SIDATE,2) 5080 CALL TRCBAKfSBNAME, 1) 5081 c 5082 c Ident i fy funct ion and c a l l appropr iate rout ine 6083 LNFND • .FALSE. 5084 IF (FNCTN .EQ. 'DELAY') THEN 5085 C delay u n l t - - u s e s "pass by l o c a t i o n * 5086 CALL TRPUF7(DATA(ISTART(NENTRY)), NELMNT. NDATA, DATA, 5087 1 MDATA, PARMS. NPARMS. ITYPE, ISTART, I END, NAMES. 5088 2 NENTRY, CODES. KEYS, NCODES, SETVLU. LABORT) 5089 ELSE IF (FNCTN .EQ. 'GATE') THEN 8090 c gate f i r s t waveform by second--uses 'pass by loca t ion" 6091 CALL TRPGAT(OATA(1STARTiNENTRY)). NELMNT, NDATA. OATA, 5092 1 MDATA, PARMS, NPARMS. ITYPE. I START, IEND. NAMES. 5093 2 NENTRY, CODES, KEYS. NCODES. SETVLU, LABORT) 5094 ELSE IF (FNCTN .EO. 'BLOCK') THEN 5095 c block f i r s t waveform by second--u«es "pass by locat ion" 5096 CALL TRPBLK(DATA(I START(NENTRY)), NELMNT. NDATA, DATA, 5097 1 MDATA, PARMS, NPARMS. I TYPE. 1START, IEND, NAMES. 5098 2 NENTRY. CODES. KEYS, NCODES. SETVLU. LABORT) 5099 c ELSE IF (FNCTN .EQ. 'LEVEL-SHIFT') THEN S10O c s h i f t s level of waveform by constant amount—uses "pass by 5101 c l oca t ion" 5102 c CALL TRPLVL(DATA(ISTART(NENTRY)), NELMNT. NDATA, DATA, 5103 c i MDATA. PARMS, NPARMS, ITYPE, ISTART. IEND, NAMES, 5104 c 2 NENTRY, CODES. KEYS, NCODES, SETVLU. LABORT) 5105 c ELSE IF (FNCTN .EQ. 'POLAR') THEN 5106 c converts two waveforms Into polar representa t ion . F i r s t 5107 c is taken as X. second as Y, resu l t is two-element vector , 5108 c f i r s t Is rad ius , second Is angle - -uses "pass by loca t ion" 6 109 c CALL YRPPLR(DATA(I START(NENTRY) ) , NELMNT, NDATA, DATA. 5110 C 1 MOATA. PARMS. NPARMS, ITYPE, J START, IEND. NAMES, 5111 c 2 NENTRY. CODES. KEYS, NCODES, SETVLU, LABORT) 51 12 c ELSE IF (FNCTN .EO. 'CARTES I AN') THEN 1 2 3 4 5 6 7 8 9 O 1 2. Fig. 41 (cont'd) to C O C D D a t i n g Of TRPUF 1 . F77( 5001,6000) at 01:16:25 on MAY 9. 1986 for CCId'BRWG Pago 3 6113 C converts p o l a r representat ion R a c k Into Car tes ian form. F i r s t S i 1 4 C e l e m e n t Is X, second is Y ( resu l t is two-element v e c t o r ) . 5115 C For Input, f i r s t element is rad ius , second Is angle 5116 C Uses "pass by loca t ion" S 1 1 7 C C A L L TRPCARi DATA ( 1 START( NENTRY ) ), NELMNT, NDATA, DATA. 5118 C 1 MDATA, PARMS, NPARMS, I TYPE, ISTART, IENO, NAMES. 5119 C 2 NENTRY, CODES, KEYS, NCOOES, SETVLU, LABORT) S l i d E L S E IF (FNCTN . EQ i 'OVERCURRENT.R') THEN 5121 C r e s t r a i n e d over -current r e l a y - u s e s "pass by loca t ion" 5122 CALL UFOCR(0ATA( ISTART( NENTRY ) ), NELMNT, NDATA, DATA, 5 1 2 3 1 M D A T A . PARMS, NPARMS, I TYPE , ISTART, IEND, NAMES. 5124 2 NENTRY, CODES, KEYS. NCODES. SETVLU. LABORT) 8125 ELSE IF (FNCTN .EQ. 'NEGATE' .OR FNCTN .EQ. 'NOT') THEN 5126 C negate s p e c i f i e d e n t r y - u s e s "pass by loca t ion" 5127 CALL UFNEG(DATA(ISTART(NENTRY)), NELMNT. NDATA, DATA, 6128 1 MDATA, PARMS. NPARMS, I TYPE, I START, IEND, NAMES. 5 1 2 9 2 N E N T R Y , COOES, KEYS. NCOOES, SETVLU, LABORT) 5130 ELSE IF (FNCTN .EQ. 'OVERCURRENT.IT') THEN 5131 C Inverse time over -current r e l a y - u s e s "pass by loca t ion" 5 1 3 2 C A L L TRPUM )) , NELMNT .NDATA i DAT 5133 1 MDATA. PARMS. NPARMS, I TYPE, ISTART. IENO, NAMES. 5134 2 NENTRY, CODES, KEYS, NCODES, SETVLU, LABORT) 8 1 3 5 E L S E IF (FNCTN .EQ. ' PS-FILTER . A ' ) THEN 5136 C p o s i t i v e sequence f i l t e r type A- -uses "pass by loca t ion" 5137 CALL UFPSFA(OATA(ISTART(NENTRY)), NELMNT, NDATA, DATA, 5 1 3 8 i M O A T A , ' PARMS', NPARMS, '"Tf YPE'V'" i"STARtV"'l'EKrD'."' NAMES, 5139 2 NENTRY, CODES, KEYS, NCOOES, SETVLU, LABORT) 5140 ELSE IF (FNCTN .EQ. 'S02H') THEN B)4j ' C W e s t inghouse 5D-2H re l ay- -uses "pass by loca t ion" B142 CALL UFS02H(DATA(I START(NENTRY)), NELMNT, NDATA. DATA, 5143 1 MDATA, PARMS, NPARMS, 1 TYPE, ISTART, IEND, NAMES. 5 1 4 4 2 N E N T R Y , CODES. KEYS. NCODES. SETVLU. LABORT) 5145 ELSE IF (FNCTN .EO. 'SDX1H') THEN 5146 C Westinghouse SDX-1H r e l a y - u s e s "pass by loca t ion" ' 5 1 4 7 C A L L UFSDXHtOAT Af I ST ART ( NENTRVT) ,' NELMNT . NDATAT "DATA".' 5148 1 MDATA, PARMS, NPARMS. I TYPE, ISTART. IEND, NAMES, 5149 2 NENTRY, CODES, KEYS. NCODES, SETVLU, LABORT) S i 6 0 E L S E IF (FNCTN . EQ!'"' ft MER T 'THEN 5151 C delayed pickup/dropout t imet—uses "pasa by locat ion" BI52 CALL UFTIMR(DATA(I START(NENTRY)), NELMNT, NDATA, DATA, 5 1 5 3 i M D A T A , PARMS .NPARMS , 1 TYPE, I START, IENO. NAMES. S1S4 2 NENTRY, COOES, KEYS, NCODES, SETVLU, LABORT) 8155 ELSE IF (FNCTN .EQ. 'UNDERVOLTAGE') THEN 5 1 5 6 C ' u h d e r v o l t a g e r e l a y - u s e s "pass by locat ion" 5157 CALL TRPUF2(DATA(ISTART(NENTRY)), NELMNT, NDATA, DATA, 5158 1 MDATA, PARMS. NPARMS. 1 TYPE, I START, IEND, NAMES, SI 5 9 ' 2 N E N T R Y . CODES, KEYS. NCODES. SETVLU, LABORT i 8160 ELSE IF (FNCTN .EQ. 'OVERVOLTAGE.NS') THEN 5161 C negative sequence r e l a y - u s e s "pass by l o c a t i o n ' 3 1 6 2 C A L L tRPUF3(DATA(lSfART(NE^ 5163 1 MDATA, PARMS, NPARMS, I TYPE, ISTART, IEND, NAMES, 8164 2 NENTRY, CODES, KEYS, NCOOES, SETVLU, LABORT) 8 1 6 8 C ' E L S E IF (FNCTN :EQ . 'USER-4 THEN 5166 C user * 4 - -uses "pass by l o c a t i o n * 5167 C CALL TRPUF4(DATA(I START(NENTRY)), NELMNT, NDATA, DATA, 5 1 6 8 C i M D A T A , PARMS .NPARMS . 1 TYPE , ISTARt, IEND, NAMES, .1 , . 2 . 3 4 9 6 7 8 9 0 1 2. Fig. 41 (cont'd) CO o o L 1stIng of TRPUF1.F7715001,6000) St 01:16:25 On MAY 9, 1986 for CCId-BRWG Page 4 5169 C 2 NENTRY, COOES, KEYS, NCODES, SETVLU, LABORT) 5170 5171 5172 C ELSE IF (FNCTN .EQ. 'POLARI ZED-MHO.B') THEN p o l a r i z e d mho (type B) r e l a y - - u s e s "pass by loca t ion" CALL TRPUF5(0ATA(ISTART(NENTRY)), NELMNT, NOATA, OATA, 5173 5174 5175 1 MDATA, PARMS. NPARMS. ITYPE, I START. lENO, NAMES. 2 NENTRY. CODES. KEYS. NCODES. SETVLU, LABORT) ELSE IF (FNCTN .Eq . 'LAC ' ) THEN 5176 5177 5176 C C - load angle compensator ( s e r i e s tuned t ransactor ) uses "pass by locat ion" CALL UFLAC(DATA( I START (NENTRY )) , NELMNT, NDATA, DATA, 5179 5160 5181 1 MDATA, PARMS. NPARMS, ITYPE. ISTART, IENO, NAMES, 2 NENTRY, CODES. KEYS. NCODES. SETVLU, LABORT) ELSE IF (FNCTN . E q . 'MEMORY' .OR. FNCTN .EQ. 'F ILTER') THEN 5182 5183 5184 C memory or RLC f i l t e r — u s e s "pass by loca t ion" CALL TRPUF6(DATA(ISTART(NENTRY)), NELMNT. NDATA, OATA. 1 MDATA, PARMS. NPARMS, ITYPE, ISTART, IEND, NAMES. 5185 5186 5187 C 2 NENTRY. CODES. KEYS, NCODES. SETVLU, LABORT) ELSE IF (FNCTN .EQ. 'DIRECTIONAL') THEN d i r e c t i o n a l element--uses "pass by loca t ion" 5168 5189 5190 CALL fRPUF9(DATA(I START(NENTRY)), NELMNT, NDATA, OATA, 1 MOATA. PARMS. NPARMS, ITYPE, ISTART, IEND, NAMES, 2 NENTRY, CODES, KEYS. NCOOES, SETVLU, LABORT) 5191 8192 5193 C ELSE IF (FNCTN .EQ. 'PERMISSIVE') THEN permissive t r i p block type A- -uses "pass by loca t ion" CALL UFPTA(DATA(ISTART(NENTRY)), NELMNT, NDATA, OATA, 5194 5195 5196 1 MDATA, PARMS. NPARMS, ITYPE, I START, IEND, NAMES, 2 NENTRY, CODES, KEYS. NCOOES, SETVLU, LABORT) ELSE 5197 5198 6198.5 C C func t ion name not recogn!zed--not user funct ion LNFND • .TRUE. LABORT not assigned s ince no c a l l s were made, ao: t! 6198.7 6199 6200 C LABORT • .FALSE. END IF 5201 6202 8203 10 CALL fRCBAK(' ' , - 1) RETURN END 1 2 3 4 5 6 . .7 . . . . 8 . . . . . . . 9 . . . . . . . .0 . . . 1 2 . Fig. 41 (cont'd) 302 T A B L E 4 Prefix List for TRP Files Prefix File Use I command input file (SET INPUT = . . .) O output log file (SET O U T P U T = . . .) M messages file (SET M E S S A G E S = . . .) P EMTP-generated data file (GET E M T P = . . ,) D TRP-format S A V E file (SAVE/GET T R P = . . .) H. TRP DESIGN LIMITS The design limits for the TRP are shown in table 5. Installation limits apply on the memory allocated to the TRP and on lengths of names, number of cases, etc., which will determine the actual practical limits. T A B L E 5 T R P Design Limits Limit Maximum number of cases Maximum number of data types Maximum number of elements per waveform vector Maximum number of base types Maximum length of P L O T U N I T S string (characters) Maximum length of PLOT L A B E L S string (characters) Maximum length of PLOT T I T L E string (characters) Value 2148 8999 100 1000 10 50 50 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0097377/manifest

Comment

Related Items