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An intelligent support system for the analysis of power system transients Ibrahim, Awad Ibraik 2000

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AN INTELLIGENT SUPPORT SYSTEM FOR THE ANALYSIS OF POWER SYSTEM TRANSIENTS by AWAD IBRAIK IBRAHIM B.A.Sc. Garyouns University, Benghazi, Libya, 1989 M.A.Sc. University of Waterloo, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUBREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA September 2000 © Awad Ibraik Ibrahim, 2000  In  presenting this  degree  at the  thesis  in  University of  partial  fulfilment  of  of  department  this or  thesis for by  his  or  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  representatives.  an advanced  Library shall make  it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada  DE-6 (2788)  Abstract Electromagnetic transients programs such as E M T P are extensively used for simulating fast transient effects in electric power systems. However, these programs are not easy to use for the following two reasons:  1. A l l of them require a high level of technical expertise to apply them properly.  2. Most of them are not user friendly.  This project proposes an intelligent system to support simulations with E M T P and similar programs. The work is composed of three parts; the first part presents the development of a prototype intelligent support system, the second part introduces the knowledge base for switching surge studies, and the third part describes the development of a new line model for the representation of short transmission lines and cables.  The intelligent support system is composed of three stages. First, the support system selects a base case from a case database, to be modified to meet the user's requirement. Second, the expert system checks the syntax and validity of the new case data. Finally, the E M T P solution is checked to see whether the chosen models are appropriate for the frequencies contained in the solution, for the degree of imbalance, and for other criteria. If they are not appropriate, better models will be recommended to the user.  The knowledge base for switching surge studies solves the problem of selecting the proper models for representing power system components in the EMTP. It helps in checking the validity of the data used to represent the simulated transient phenomena, and gives some suggestions to the user to correct his case data before simulation. It also helps in the evaluation of the results, using  ii  the knowledge of the phenomena being simulated. From this knowledge base, the idea of developing a new line model for short lines and cables evolved as one of the practical rules that is recommended for the proposed intelligent support system.  The new E M T P transmission line model for the representation of short overhead lines and cables will overcome the limitation of using a time step size not larger than the travel time. The error analysis for the short and open-circuit responses shows that the new line model has a filtering effect for higher frequencies. In a comparison with actual field test measurements, it is shown that the new line model is suitable for a reasonable representation of short overhead transmission lines and cables.  iii  Abstract  11  List of Figures  v i i i  List of Tables  x i i i  Acknowledgment  X I V  1 Introduction  1  1.1 Overview  1  1.2 Thesis Objectives  6  1.3 Thesis Outline 2  7  Intelligent Support System  9  2.1 Introduction  9  2.2 The Need for Using an Expert System Approach  11  2.3 Expert Systems-Background  13  2.3.1 Expert System Components  14  2.3.1.1 Knowledge Base  14  2.3.1.2 Inference Engine  16  2.3.1.3 User Interface  16  2.3.2 Applications of Expert Systems to Power Systems  16  2.3.3 Integration of Expert Systems with Power Simulation Programs  18  2.4 System Structure 2.4.1  24  The Case Database  26  2.4.2 Data Validation  27  2.4.3 Results Evaluation  27  2.5 Implementation  28  2.6 A n Energization Case Study  30  2.6.1 Case Data Selection  30  2.6.2 Data Input and Validation  32 iv  2.6.2.1 The Data Input Form  32  2.6.3 Rule-Based Data Validation System  34  2.7 Results Evaluation  36  2.7.1 Characteristic Parameters  37  2.7.2 Step Size Variations  37  2.7.3 Fuzzy Logic Analysis  38  2.8 Summary  43  3 Switching Surge Transients  44  3.1 Introduction  44  3.2 Switching Surge Transients-Background  45  3.2.1  Summary of Different Classes of Overvoltages  45  3.2.2 Source and Characteristic of Switching Overvoltages  46  3.2.3 Parameters Influencing Switching Overvoltages  47  3.2.4 Switching Overvoltages in Closing and Reclosing Operations  50  3.2.5 Definitions  51  3.3 Switching Surge During Energization  53  3.3.1 Network Configuration  53  3.3.1.1 Feeding Network  53  3.3.1.2 Shunt Reactor  54  3.3.1.3 Transmission Line  55  3.3.1.4 Circuit Breaker  55  3.4 Modelling Suggestions  56  3.4.1 Step Size  56  3.4.2 Transmission Line Models  59  3.4.2.1 The Constant Parameter Line Model  59  3.4.2.2 The Frequency Dependent Line Model  61  3.4.2.3 Comparison Between the Two Line Models  66  v  3.4.2.4 The Single-Phase Energization Case Study  69  3.4.3 Shunt Compensation  75  3.4.4 Trapped Charges  79  3.4.5 Feeding Network  8 1  3.4.6 Closing Resistors  8  2  3.4.7 Line Length  8  5  3.4.8 Closing Angle and Pole Span  8  8  3.4.9 Statistical Switching  8  8  3.4.10 Derived Practical Rules from the Knowledge Base  89  3.5 Summary  91  4 Transmission Line Model  93  4.1 Introduction  93  4.2 Transmission Line Models-Background  94  4.2.1 The 7i-Circuit  95  4.2.2 The Constant Parameter Line Model  96  4.2.3 The Frequency Dependent Line Model  96  4.3 Transmission Line Model For Long Lines  96  4.4 The New Line Model For Short Lines  97  4.5 Interpolation Error Analysis  100  4.6 The Lossy Line Model  106  4.7 Case Studies  106  4.7.1 Transmission Line Energization  106  4.7.2 Power Electronics Case Study  110  4.8 Summary  116  5 Conclusions and Future Work  117  5.1 Overview  117  vi  5.2 Conclusions  1 1  8  5.2.1 The Prototype Intelligent Support System  118  5.2.2 Switching Surge Overvoltages  119  5.2.3 New Transmission Line Model  119  5.3 Recommendations for Future Work  119  Bibliography  121  A The Case Database  131  B  152  EMTP Connec Subroutine for the New Line Model  C Interpolation Error Analysis  160  D  173  Input & Output Data Files for EMTP  vii  List of Figures 2.1  Expert system components  15  2.2  Structure of transient simulation support system  25  2.3  The hierarchy of case database  29  2.4  System configuration for a single-phase switching case study  31  2.5  The data set of load energization case study  32  2.6 Input data form for load energization case study (R in , L in mH, and C in )  33  2.7 The support system running the EMTP  36  2.8  2.9 2.10  Characteristic parameters and case study comparison for step size of 50 s (solid) and 100 s (dashed)  38  The maximum voltage amplitude of the first peak  39  The time of zero crossing  40  2.11 Output voltage waveform comparison  40  2.12 Reasoning process  42  3.1  Evaluation of overvoltage factors dependent on type of operation and system [ 1 ] . . . . 52  3.2 Network configuration for switching surge case study 3.3  Comparison between field test (solid) and constant parameter line model (dashed) in phase A  3.4  53  60  Comparison between field test (solid) and constant parameter line model (dashed) in phase B  60  viii  3.5 Comparison between field test (solid) and constant parameter line model (dashed) in phase C  61  3.6 Tower configuration of Jaguara-Taquaril line. A l l measurements in meters, earth resistivity = 100 m  63  3.7 Comparison between field test (solid) and frequency dependent line (dashed) in phase A 64 3.8 Comparison between field test (solid) and frequency dependent line (dashed) in phase B 64 3.9 Comparison between field test (solid) and frequency dependent line (dashed) in phase C 65 3.10 Comparison between frequency dependent line (solid) and constant parameter line (dashed) in phase A  67  3.11 Comparison between frequency dependent line (solid) and constant parameter line (dashed) in phase B  67  3.12 Comparison between frequency dependent line (solid) and constant parameter line (dashed) in phase C  68  3.13 Zero sequence current for Jaguara case study  68  3.14 Three phase currents for Jaguara case study  69  3.15 Comparison between frequency dependent line (solid) and constant line (dashed) for phase A  71  3.16 Comparison between frequency dependent line (solid) and constant line (dashed) for phase B and C  71  3.17 Zero sequence current and current in phase A  ix  72  3.18 Positive sequence inductance of the three-phase line  72  3.19 Positive sequence resistance of the three-phase line  73  3.20 Zero sequence inductance of the three-phase line  73  3.21 Zero sequence resistance of the tree-phase line  74  3.22 Overvoltages with shunt reactor (solid) and without shunt reactor (dashed) in phase A . 77 3.23 Overvoltages with shunt reactor (solid) and without shunt reactor (dashed) in phase B . 78 3.24 Overvoltages with shunt reactor (solid) and without shunt reactor (dashed) in phase C . 78 3.25 Effect of trapped charges on switching surge (1.0 p.u. on phase A)  80  3.26 Effect of trapped charges on switching surge (-1.0 p.u. on phase B)  80  3.27 Effect of trapped charges on switching surge (0.5 p.u. on phase C)  81  3.28 Overvoltages with closing resistors (solid) and without closing resistors (dashed) at phase A  83  3.29 Overvoltages with closing resistors (solid) and without closing resistors (dashed) at phase B  84  3.30 Overvoltages with closing resistors (solid) and without closing resistors (dashed) at phase C  84  3.31 The effect of line length on the overvoltages in phase A : original line (solid), shorter line (dashed)  86  3.32 The effect of line length on the overvoltages in phase B: original line (solid), shorter line (dashed)  87  3.33 The effect of line length on the overvoltages in phase C: original line (solid), shorter line  4.1  (dashed)  87  Lossless line model using Bergeron's method  98  4.2 Lossless transmission line model  100  4.3  The short-circuit ratio  104  4.4 The open-circuit ratio  104  4.5  105  The Current Im response in the time domain  4.6 The current Ik response in the time domain  105  4.7  Schematic of a lossy line model  106  4.8  Transmission line energization  108  4.9 The constant parameter model response  109  4.10 The new line model response  109  4.11 The 7t -circuit line model response  110  4.12 The power electronics case  113  4.13 The field test recording for the drive system  114  4.14 Simulation results for the new line model  114  4.15 Simulation results for the -circuit line model  115  4.16 Simulation results for the constant parameter model  115  A.l  133  Transposed transmission line  A.2 Untransposed transmission line  134  A.3 Reclosing of overhead lines with trapped charges  135  A.4 Capacitor bank De-energization  136  A.5 Capacitor switching with transformers  138  A.6 Three-phase cable switching  139  A.7 Cable switching with crossbonding  139  A.8 Transformer switching  141  A.9 Simple switching (single-phase)  142  A. 10 Simple switching (three-phase)  144  A . l 1 Single-line to-ground fault  147  A. 12 Fault analysis with frequency dependence  147  A. 13 Transient stability analysis  149  A. 14 Load rejection  150  A. 15 Ferro-resonance analysis  151  xii  List of Tables 2.1  Summary of E M T P models for transmission line and applications [54]  12  2.2 Conventional analysis programs and knowledge-based expert systems [32]  14  2.3 Results evaluation rules  41  3.1 Network parameters influencing the switching overvoltages [1]  49  3.2 Network steady-state nodal voltages with shunt compensation  76  3.3 Network steady-state nodal voltages without shunt compensation  76  3.4 Network steady-state nodal voltages with shunt compensation doubled  77  3.5 Network steady-state nodal voltages with 100% shunt compensation  77  3.6 Some derived rules from the knowledge base for switching surge transients  90  D . l Data input file for the switching surge case study  173  D.2 Output file for switching surge case study  174  D.3 The fd Data input file for Jaguara case study  175  D.4 Input data file for Jaguara case study using frequency dependent line model  176  D.5 Error analysis in time domain  177  xiii  Acknowledgment I would like to express my deepest gratitude to my thesis supervisors, Dr. Hermann Dommel and Dr. Takahide Niimura, whom I respect and admire tremendously, for their constant guidance and help throughout this work. Both their background and expertise in the areas of electromagnetic transients simulation and artificial intelligence not only made this work possible but also enriched my personal and professional life. Thank you both very much for your encouragement and support.  I further appreciate the cooperation and joint work with dear colleagues and friends, Daniel Lindenmeyer, whose suggestions for the improvement of the results evaluation process had been gladly accepted; Sebastian Henschel, whom I thank for his patience and encouragement during the development of the new line model; Antonio Carlos Siqueira de Lima, for providing the power electronics case study and field test results.  The financial assistance of the Natural Sciences and Engineering Research Council of Canada, and of B.C. Hydro & Power Authority, through funding provided for the N S E R C - B . C . Hydro Industrial Chair in Advanced Techniques for Electric Power Systems Analysis, Simulation and Control is gratefully acknowledged. The financial support of the Ministry of Education and Scientific Research of Libya, and the Canadian Bureau of International Education (CBIE) is also appreciated.  A warm and special thanks to all my friends and colleagues in the Power Group; their friendship through the past years have been a constant source of knowledge, enjoyment and energy. Thank you all and the best luck in your research. Thanks to all the Professors and staff in the Department  xiv  of Electrical and Computer Engineering who taught, guided and helped me constantly.  Finally, I would like to thank my wife Samira, my brother Ahmed, my lovely daughters Omama, Khadija and Safia, and my parents for their never-ending patience, encouragement and sensitive understanding. I am grateful for their love and support through the years.  XV  Chapter 1 Introduction 1.1 Overview The design of electric power systems requires a precise knowledge of the magnitude and duration of overvoltages that might occur and faults. Overvoltages appear due to lightning discharges, switching operations, and faults [55]. The insulation of transmission lines and terminal equipment, such as transformers and circuit breakers, must either be able to withstand the stresses imposed by these transient overvoltages, or surge arresters must be able to protect the equipment from them. To co-ordinate the insulation levels of equipment with the protective level of surge arresters is referred as "insulation coordination".  The most practical and effective way currently to study the different types of transient overvoltages, their effects and the design of adequate insulation levels is through simulations with  1  Chapter 1. Introduction  2  computer programs. The most widely known of these programs is the Electromagnetic Transients Program (EMTP) [5]. The EMTP is a combination of mathematical models and solution techniques representing the different components of the electrical network and their interpolations. The E M T P represents each component through equivalent resistances and history current sources obtained from mathematical models. Finally, the whole electrical systems is solved using numerical methods to solve the resulting simultaneous equations. The EMTP is well tested, powerful, and flexible. However, one drawback of the EMTP is its unfriendly user interface, which limits the effectiveness and usability of the program. There are also multiple choices of models of network elements now offered in the EMTP, and users must choose the proper models that best suit the specific study. For example, a transmission line would be represented accurately enough by a n -circuit for sub-synchronous resonance studies, while a transient recovery voltage study requires a distributed parameter model.  Many efforts have been made to improve the user interface of the E M T P during the last few years. A n Integrated Engineering Simulation Environment (IESE) [22] [23] [24] was proposed to solve the user interface problem with the EMTP, in which a graphic oriented interface is integrated with a modular engineering database.  A data modularization concept, which was incorporated into the alternative transient program (ATP) version of the E M T P [25], has been used in [26] to simplify the data input. A supporting subroutine called "Data Base Module" allows the user to create component modules that will be used later as library modules.  Chapter 1. Introduction  3  A new approach was presented in [27] and [75] to use M A T L A B [28] for the development of a new EMTP. The benefits of the M A T L A B environment, such as toolboxes and the graphic user interface (GUI), will then be available to the EMTP. However, the execution time of M A T L A B programs is much longer than that of the original EMTP, because M A T L A B uses an interpreter rather than a compiler at the present time.  A T P D R A W [29] was developed as a mouse-driven preprocessor for the A T P version, where the user can build up a circuit by choosing components from menus. For the DCG/EPRI version of the E M T P , a graphical user interface is being developed by Ontario Hydro, Canada. The Manitoba H V D C Research Center has developed a graphical user interface for the E M T D C [76]. The Power Research Group at the University of British Columbia also has developed a graphical user interface for the U B C version of the E M T P (MicroTran) [16] and for the Real Time Power System Simulator (OVNI) [77].  Although the ease of data entry may be solved by the above mentioned techniques, such as graphic displays and data modularization, the difficulty of proper modeling of power systems remains basically unchanged. Also, data validation and data sanity checks have not yet been fully implemented in the EMTP.  The problem of selecting the proper models of power system elements is not as easy as it may appear. Each model has its unique features such as frequency range, time step, maximum time, and the type of phenomena being studied. The selection of the proper model is usually made based on engineering experience and judgment, which often is not available to many of  Chapter 1. Introduction  4  the users. For example, the selection of the n -circuit line model depends on length (I) of the line as well as on the frequency range of the transient phenomena if) as shown in the following equations [79]:  / < 10^000  /<  f  f  or  or  o v e r  h  e a c  l lines,  underground cables  (1.1)  (1.2)  (For/= 60 Hz, / < 167 km for overhead lines, / < 50 km for cables). These approximate rules are derived from frequency domain comparisons of the open and short-circuit behavior of the 7t -circuit (nominal 7t) and the exact solution (exact equivalent 7t). Furthermore, the issue of data validation requires all of the analyst's knowledge about the reasonableness of the data and the frequency range over which the model is valid. Also, the results evaluation of the E M T P is not simple, because the answers are different for different types of studies. Results evaluation depends on the model used, the extent of the system represented, and other factors.  To use the E M T P properly, it is best to have an experienced user to oversee the initial stages of the E M T P learning curve. However, a beginning user does not always have a supervisor who is familiar with the procedures of E M T P simulation and the phenomena to be simulated. There are various E M T P applications to power system transient studies in the literature, but the expertise is normally personalized and not stored as electronically accessible information.  Chapter 1. Introduction  5  A l l the factors of power system transients simulations using the E M T P imply that an intelligent support system approach could be effective in dealing with the above mentioned problems. The main advantage of this approach is its ability to deal with knowledge in an easily accessible form. This was the motivation for adopting the intelligent support systems approach to power system transients simulations.  This thesis presents an intelligent system to support simulations with E M T P and similar programs. The work is composed of three parts: the first part presents the development of a prototype intelligent support system, the second part introduces the knowledge base for switching surge studies, and the third part describes the development of a new line model for the representation of short overhead transmission lines and underground cables. The intelligent support system works in three stages. First, the support system selects a base case from a case database, to be modified to meet the user's requirement. Second, the expert system checks the syntax and validity of the new case data. Finally, the E M T P solution is checked to see whether the chosen models are appropriate for the frequencies contained in the solution, for the degree of imbalance, and for other criteria. If they are not appropriate, better models will be recommended to the user.  For the knowledge base, switching surge transients have been chosen as an example. The knowledge base will solve the problem of selecting the proper model for representing power system components in the E M T P according to problem specifications. It will help in checking the validity of the data used to represent the simulated transient phenomena, and will give  Chapter 1. Introduction  0  some suggestions to the user to correct his case data before the simulation. It will also help in the evaluation of the results of the E M T P simulation, using the knowledge of the phenomena being simulated. From this knowledge base, the idea of developing a new line model for short lines and cables evolved as one of the practical rules that is recommended for the proposed intelligent support system. The new E M T P transmission line model for the representation of short overhead lines and underground cables will overcome the limitation of having to use a time step size not larger than the shortest travel time. The error analysis for the short-circuit and open-circuit responses shows that the new line model has a filtering effect for higher frequencies. In a comparison with actual field test measurements, it could be shown that the new line model is suitable for a reasonable representation of short overhead transmission lines and underground cables.  1.2 Thesis Objectives 1.  Developing an intelligent support system to support practicing engineers and engineering students who are not familiar with EMTP simulations [52] [70] [71] [74]. This expert system will be composed of three parts. First, the expert system selects a base case data from a case database, to be modified later to meet the user's own goal. After that, the expert system checks the validity of the modified case data. Finally, the E M T P solution is verified for the user's specific data case.  2. Developing a knowledge base, with switching surge overvoltages used as an example. From this knowledge base, we can derive some practical rules for switching surge tran-  Chapter 1. Introduction  '  sients. These practical rules will be used in the proposed E M T P intelligent system. The objective of this part of the thesis is to give the simple and approximate rules for the support system. These rules will provide the beginning EMTP users and practicing engineers with a simple scheme based on the experience of EMTP uses. 3. Developing a new E M T P line model for the representation of short overhead transmission lines and cables [64] [72] [73]. It overcomes the limitation of having to use a time step size not larger than the shortest travel time. This modelling approach is proposed by one of the practical rules for the intelligent support system.  1.3 Thesis Outline Due to the diversity of the topics handled in this thesis (e.g. expert systems, switching overvoltages, transmission line models, etc.) it was decided not to include one literature review chapter of all the topics by itself. Rather, literature reviews will be included with each chapter for the relevant topics.  Chapter Two describes the development of an intelligent support system to help engineers and students in the proper use of the EMTP.  Chapter Three presents the development of a knowledge base for switching surge overvoltages. A typical study for switching transient overvoltages is also introduced.  Chapter Four presents a new EMTP line model for the representation of short transmission lines and cables.  Chapter 1. Introduction  8  Chapter Five gives the conclusions derived from this work, and suggests recommendations for future work in this area.  Chapter 2 Intelligent Support System  2.1 Introduction The electromagnetic transient program (EMTP) [5] is a general-purpose computer program for simulating fast transient effects in electric power systems.  The E M T P is a widely used  program for transient analysis, in industry as well as in universities. There are several versions available. The program features an extremely wide variety of modeling capabilities, encompassing electromagnetic and electromechanical transients ranging in duration from microseconds to seconds.  The E M T P is reasonably well tested, powerful, and flexible for various types of transient studies. However, the main drawback of the E M T P is the difficulty of building a proper representation of the power system to be studied. A high level of expertise is required for the  9  Chapter 2. Intelligent Support System  10  analysis of transient phenomena in power systems. The users are assumed to have a basic knowledge of the phenomena to be simulated, and at the same time they are required to have a certain familiarity with the input data format of the EMTP. In this situation, it is best to have an experienced E M T P user to overlook the initial stages of the E M T P learning curve. However, it is not always possible for the beginning user to have a supervisor who is familiar with both the procedures of EMTP simulation and the phenomena to be simulated.  Many efforts have been made to improve the use of the E M T P during the past few years. Although the ease of using the program may be improved by different techniques, such as graphic display [22] [29] and data modularization [26], the difficulty of proper modeling of the power system being studied remains basically unchanged. Also, possible user support in data validation and results evaluation has not yet been fully investigated in the E M T P simulation environment.  This chapter describes the development of an intelligent support system to help engineers and students in the proper use of the E M T P [52] [70] [71] [74] and similar programs, such as E M T D C and ATP. This chapter is composed of eight sections. The next section introduces an overview of expert systems and their applications in power systems. Section 3 explains the need for expert system approaches. Section 4 introduces the structure of the proposed intelligent support system. Section 5 presents the implementation of a prototype support system. Section 6 describes a simple energization case study as a base case example. Section 7 introduces case study results evaluation, and section 8 summarizes the conclusions and  Chapter 2. Intelligent Support System  11  comments about the proposed intelligent system.  2.2 The Need for Using an Expert System Approach Unfortunately, the problem of selecting the proper models of power system is not as simple as it may appear. Each model has its unique features such as frequency range, time step, maximum time, and the type of phenomena being studied. For example, hysteresis effects may be important in ferresonance but unimportant in inrush current studies. The selection of the proper model is usually made based on engineering experience and judgment, which often is not available to many of the users. As an example, Table 2.1 shows the different models available for transmission lines, and the recommended applications for each model.  Furthermore, the issue of data validation requires all of the analyst's knowledge about the reasonableness of the data and the frequency range over which the model is valid. For example, the n -circuit type of transmission line model is only valid for lower frequencies from 0 to 200 Hz for a line length of 50 km. There are many other model limitations as well, e.g., voltages should not be higher than 1.2 p.u. i f transformer saturation is ignored. Also, the results evaluation of the E M T P is not simple, because answers are different for different types of studies. Results evaluation depends on the model used, the extent of the system represented, and other factors.  A l l the characteristics of power system transients simulations using the E M T P suggest that an intelligent support system approach could be capable in dealing with the above designated issues. The most significant benefit of an intelligent support system approach is its capability  Chapter 2. Intelligent Support System  12  to deal with knowledge in an easily accessible form. This will make the experience and analysis of power system transients simulations using the EMTP available for all users.  Table 2.1: Summary of E M T P models for transmission line and applications [54]  Model  Best Fit For  A) Frequency Independent Line Positive sequence R-L  lumped parameter  Best for parametric studies, power frequency or low phenomena, or where exact data is unavailable  frequency  Unswitched line, unbalanced conditions, load flow, initial conditions for balanced systems, and remote source equivalent.  representation, and positive and  zero sequence lumped parameter R - L representation - C a n be used for switched lines, although not recommended.  7i-section representation  - Data similar to Transient Network A n a l y z e r ( T N A ) data. Distributed parameter transposed line model  Distributed  parameter  untransposed  line model ( K . C . Lee's model)  General purpose studies, switched lines, lightning and high frequency studies, and where typical and line-specific data is available. Untransposed lines, high grounding resistivity and unbalanced circuits, general purpose studies, modal analysis, and traveling wave analysis.  B) Frequency Dependent Line  When frequency dependence is important, for switching surge studies, and those studies dealing with transient system resonances in excess of I kHz.  J. Marti m o d e l  Can be used for transposed or untransposed lines constant transformation matrix)  L . Marti m o d e l  Can  (assumed  be used for untransposed lines and cables (transformation  matrix frequency dependent) Corona Model  Can  be used for transposed or untransposed lines with corona  effects (assumed constant transformation matrix)  Chapter 2. Intelligent Support System  13  2.3 Expert Systems-Background Expert systems are a sub-field of artificial intelligence (Al) methods. Artificial intelligence is the branch of computer science that studies how computers can be used to simulate and duplicate functions of the human brain. The name "expert system" is used interchangeably with the term "knowledge-based system". A n expert system is a computer program which embodies human knowledge and understanding in a way which imitates a human expert who can solve specific types of problems. Such programs can be used by non-experts to improve their problem solving abilities or by experts to provide consistent and perhaps, faster approaches to the application of knowledge [30].  Expert systems have been successfully applied to a variety of areas. These include diagnosis, planning, intelligent tutoring, monitoring, control, and scheduling [31]. Also, the expert system has the ability to deal with knowledge in a symbolic form. This makes it easier to incorporate knowledge which is only present as human expertise in heuristic form.  Moreover, the expert system approach can handle real world data which involves uncertain, missing, and inaccurate data.  The expert system approach is more effective than conventional analysis techniques in dealing with problems where judgment and experience are needed. The differences between knowledge-based expert systems and conventional analysis programs outlined in [32] are summarized in Table 2.2.  Chapter 2. Intelligent Support System  14  Table 2.2:Conventional analysis programs and knowledge-based expert systems [32]  Conventional Analysis Programs  Knowledge-Based Expert Systems  Stated equations which can be proven. If  Usually based on rules of thumb that are  correct numerical data is provided, a correct  generally reliable and cannot be reduced to  answer will result.  formulae or numbers.  Provides answers only  Can explain its logic and reasoning  Needs all data called for to operate  Can function with incomplete data  Often programmed in isolation from domain  Development team includes domain experts  experts and users  and users  May  be  extremely  difficult  to  examine  imbedded knowledge  2.3.1  Provides  capability  to  easily  examine  knowledge base  Expert System Components  The expert system has three components, as shown in Figure 2.1 [33]. These components are as follows:  2.3.1.1  Knowledge Base  A knowledge base is a collection of data, rules, inference, and procedures organized into frames, scripts, rules and other formats. It contains everything necessary to understand, formulate and solve the problem [33].  Also, it includes two basic elements: facts such as problem situations, and special heuristics or If-Then rules that direct the use of knowledge to solve the problem. The heuristics express the  Chapter 2. Intelligent Support System  15  informal judgment knowledge of the application area. The information in the knowledge base is incorporated into a computer program by a process called knowledge representation.  Generally, the knowledge base is written in a natural language for ease of development by inexperienced computer programmers [33].  Figure 2.1 Expert system components  Chapter 2. Intelligent Support System  2.3.1.2  16  Inference Engine  The inference engine is the brain or the thinking part of the expert system. It is a computer program which processes the knowledge contained in the knowledge base. It contains methods to reason with information in the knowledge base and to arrive at conclusions. The inference engine responds to user input and to changes that occur in the knowledge base [33].  2.3.1.3  User Interface  The user interface is the facility which accommodates communication between the user and the computer. In some cases this communication may be by line command or through menus. It is through this facility that the inexperienced user can be trained in the use of the knowledge contained in the knowledge base [33].  2.3.2 Applications of Expert Systems to Power Systems Interest in the application of expert systems to power systems is growing strongly. There is a need for expert systems in response to the inherent difficulties that are associated with the daily operation and future planning of very large and complex power systems.  For example, power system disturbances which may lead to system collapse are relatively fast, and the time available to decide and take corrective action is very limited. As human beings are incapable of judging and correcting situations within a very short time, based on a large amount of incomplete information, it is strongly hoped that expert systems will be able to fill the gap between human capability and power system complexity.  In recent years, many power systems applications of expert systems have been implemented  Chapter 2. Intelligent Support System  17  successfully [34][35][36][37]. They can be classified as follows: Monitoring: The monitoring category heads the development of expert systems in power system. Fault diagnosis and alarm processing are the dominant applications in the monitoring category. The fault diagnosis area includes fault detection, location of the faulty section, and prediction of the behavior of the system in the emergency state. Alarm processing usually includes the real time monitoring of sequential events and the detection of malfunctioning of protective devices.  Control: The control area applications include the normal, emergency, and restorative states. Control of the normal state depends heavily on state estimation, load forecasting, system stability and voltage and V A R control. The control of emergency state includes corrective actions against voltage collapse and countermeasures for maintaining system security. The restorative state deals with system restoration of transmission lines and switching operations in substations.  Planning: Operational planning includes system structure planning, generation scheduling, reactive power scheduling, system stabilization, and security assessment.  Education & Training: According to a recent survey [38], many applications of expert systems are used for training simulators for various tasks. These training simulators are used by operators and students.  System Analysis: System analysis applications include system model validation, load flow  Chapter 2. Intelligent Support System  18  analysis, and voltage instability studies.  2.3.3 Integration of Expert Systems with Power Simulation Programs A n expert system can be integrated with conventional power simulation programs, to combine the ability and strength of both environments. The conventional power simulation program can efficiently solve the defined problem, while the expert system is much better at handling heuristic knowledge. The integration of the expert system with power simulation programs will overcome the difficulty of incomplete simulation knowledge.  This approach will be used in the proposed research project, to integrate a prototype expert system with the E M T P . This approach is new and only a few papers can be found on it [3 9] [40]. These two papers present a prototype expert system which was incorporated with a power converter simulation program to reduce the design time and costs. The knowledgebased system imitates an experienced designer's approach in choosing the proper topology and component values to satisfy the design specifications. The converter responses are calculated with the converter simulation program to verify the design, using the knowledgebased system. If there is any violation in design specifications, the knowledge-based system will modify the design parameters and continue the design procedure until all specifications are met. The knowledge-based system also prepares the SPICE-like input file for the converter simulation program.  Chapter 2. Intelligent Support System  2.3.4  19  Tools and Shells of Expert Systems  Most of the knowledge-based systems are created using expert system shells, because they are easy to use when compared with programming languages. Each shell is suitable for a specific domain. A comprehensive list of different shells and languages used in power systems applications is presented in [34] [41]. Special artificial intelligence (Al) languages such as LISP and P R O L O G were frequently used [42]. These A l languages are different from conventional programming languages as they provide effective possibilities to handle symbolic information and data structures that change dynamically during run time. However, these A l language tools are limited to their machines and high-end workstations. Also, they often have difficulties in interfaces with other software systems.  Conventional programming languages such as C, F O R T R A N , and Pascal can also be used to develop expert systems. These conventional programming language shells are faster, more flexible, easy to interface with other software systems and widely available as compared with traditional A l languages tools [42]. However, they require skillful programmers and a great deal of effort to work with them.  There are some popular expert system shells such as E X S Y S , INSIGHT 2+, and T I M M , which are written in C, Pascal, or F O R T R A N [42]. The remarkable advances in the area of developing expert system shells has provided very sophisticated shells which reduce the need to use A l or conventional programming languages.  Chapter 2. Intelligent Support System  20  2.3.5 A Survey of Expert System Tools In this section several expert system tools are reviewed [44] [45] [46] [47] [48] [49][50]. The goal of this survey is to assess the functionality and performance of the expert system tools and to gain insight into their advantages and disadvantages.  1. C Language Integrated Production System (CLIPS) CLIPS [44] was developed by N A S A at the Lyndon B. Johnson Space Center. It was designed to overcome a number of difficulties that N A S A had experienced using LISP-based tools. CLIPS is written in C to support the goals of high portability, low cost, and ease of integration with external systems.  CLIPS uses rules as its primary knowledge representation approach and its inference is based on a forward-chaining control strategy only. The source code of CLIPS is provided, to allow the developer to modify it to meet his desired application. CLIPS has some disadvantages, such as its lack of support for backward-chaining, and it does not support a graphics tool kit for building end-user interfaces.  The Fuzzy CLIPS is now available as an extended version of the CLIPS rule-base shell for representing and manipulating fuzzy facts and rules [45].  2. Automated Reasoning Tool for Information Management (ART-IM)  A R T [46] [47] [48] was introduced in 1985 by Inference Corporation as a LISP-based expert system tool targeted to L I S P machines. A R T - I M is the company's current version  Chapter 2. Intelligent Support System  2  1  implemented in C. It uses N A S A ' CLIPS as a base and has several enhancements added, including a frame system, an object oriented programming capability, and a graphic development environment called the A R T - I M Studio.  3.  Level 5  A backward-chaining expert system tool was introduced by Level Five Research in 1984. Level 5 [46] [47][48] is written in Pascal and it supports backward-chaining, an English-like rule language, and certainty factors. Level 5 does not provide a frame system and its ability to emulate forward-chaining is limited to simple problems. Level 5 supports several windows, dialogue boxes, and a debug menu on Macintosh However, it has several drawbacks, such as the absence of a graphic tool kit for building user interface applications.  4. VAX OPS5/OPS83 Official Production System Version 5 (OPS5) [46] [47] [48] [49] was developed at Carnegie Mellon University. It has influenced the development of a number of expert system tools, including A R T and CLIPS. It is written in Bliss (DEC's system implementation language) and executes only on D E C hardware. Also, it can be interfaced with a number of DEC-supported languages. V A X OPS5 has fast execution times and it can support the development and delivery of large expert systems. However, it is characterized by forward-chaining and it does not support backward-chaining. There is a PC version called OPS83 that is used to build up an expert system for a voltage control application [3 4] [3 9].  Chapter 2. Intelligent Support System  5.  22  Knowledge Engineering System (KES)  KES [46][47][48] was introduced by Software A & E in 1982. The early versions of KES were implemented in LISP, but it was ported to C in recent versions. K E S provides forwardchaining rules, backward-chaining rules, and a frame system for knowledge representation. KES also handles uncertainty using certainty factors as a measure of belief in a value.  The K E S development environment for U N I X systems supports a graphical development interface based on X Windows, however it does not provide an editor. Also, K E S does not support a graphic tool kit for user interface applications. 6.  COMDALE/X  C O M D A L E / X [50] is an expert system shell which provides a highly effective, efficient and easy to use environment for the development and delivery of expert system applications. C O M D A L E / X has many built-in features and advantages that make development of an expert system easier and straightforward. These advantages include:  1. A customized windowed user interface and a hypertext facility including graphical presentations.  2. Simultaneous backward and forward chaining capabilities.  3. It includes debugging features (watch variables and rule tracing).  4. Excellent meta-knowledge capabilities, such as customized questions and explanations,  Chapter 2. Intelligent Support System  23  hypertext documents, forms, and graphics.  5. Technical support is provided by Comdale Technologies (Canada) Inc. to the users of C O M D A L E / X . Also, the Department of Mining and Mineral Processing of U B C has offered a course in expert systems applications using C O M D A L E / X , and good feedback and consultations are provided.  These mentioned advantages make C O M D A L E / X the best choice among the surveyed expert system shells, especially for its technical support and consultation at U B C . This is why C O M D A L E / X is used for the current prototype support system. The principal components of a COMDALE/X expert system are:  1. The Knowledge Base: The knowledge base can handle all types of information that humans use to make decisions in a particular domain. The knowledge base therefore contains:  2. Objects that represent factual information.  3. Classes which are the structural relationships of the facts in hierarchical classification.  4. Rules which are the complex relationships formulated between facts.  5. Procedures that are used to dictate the application of rules and the manipulation of classes and rules.  Chapter 2. Intelligent Support System  24  C O M D A L E / X compiles a knowledge base when it is loaded for use. Maintaining and consulting a knowledge base requires loading of the system only once. Objects, classes, rules, and procedures are incrementally compiled as they are modified.  The Inference Engine: The inference engine processes the knowledge to make decisions. The User Interface: It provides the window to observe and communicate with C O M D A L E / X during the development and use of an expert system application. The Utilities: They facilitate various approaches to represent and display information as well as provide security of the knowledge base. The Hypertext Facility: It has been produced so that the system designers can easily create documents for on-line reference for use with expert system applications. To facilitate this ease of use, the hypertext format consists of constructing a text within a text editor and saving the file as an ASCII format file.  2.4 System Structure The proposed structure of the intelligent support system for E M T P simulation is shown in Figure 2.2. The support system's operation can be divided into three stages: case data selection, data validation, and results evaluation.  25  Chapter 2. Intelligent Support System  -Part  Case Database  1  Start General Idea  1 Input Case Setting  mn Case] data base  i—i  Search for Closest Data Base Case  pt 2 ar  Data Validation  Modify Case Data  Rule Base  Verify Case Data  <  H  Guidance  No Is Case Data Valid? Yes  Results Evaluation Output  EMTP Simulation  1  -Part 3 Guidance  Results Evaluation  End  Figure 2.2 Structure of transient simulation support system  Chapter 2. Intelligent Support System  26  Experienced users of E M T P have an advantage over beginners because they can choose a previously successful data set which is similar to a given simulation case. The experts can also tell what values of diverse parameters will be appropriate for the simulation. When the simulation results are obtained, they can often immediately recognize i f the simulation is successful or not by the output of waveform, due mainly to their capacity of roughly estimating the expected output. This support system imitates such actions of a transient analysis expert.  2.4.1  The Case Database  A database that contains a collection of various power transient study cases is the most fundamental part of the proposed support system. The case-related information have been collected from E M T P experts, technical papers, and manuals, and compiled into a hypertextbased database. The case database engine locates the case data set that is closest to the system configuration and type of study of the user's base case by an interaction with the user. In many cases, inexperienced users may have a vaguely defined goal for the simulation, but through the interactive search, the system can be narrowed down to a specific case. The interactive search can also draw the context information of the target study, which will be valuable in the later stages of the support process. The hypertext data cases are classified in such a way that the user can reach a relevant data case easily through the search menus.  The selection of a particular case data by the user initiates the support system to retrieve the data set necessary for running the E M T P simulation. Since this is only a base data which  Chapter 2. Intelligent Support System  27  resembles the user's case, the data is copied to a user file, in which the user can modify the data to meet the requirements of the specific case to be studied.  2.4.2  Data Validation  In the second stage, the support system checks the structure and the validity of the new case data that the user modified for his or her specific purposes. The support system will give the user some guidelines and explanations to correct suspicious data. Also, some hints about the system representation are provided. Such a checking procedure examines the reasonableness of the power system parameters, the frequency range over which the selected models are valid, the discrete time step, the overall length of simulation, and other factors [53][54].  From the experts' knowledge of different models of power system elements, such as transmission lines, and the phenomena being studied, certain rules have been compiled for the support system and are applied to verify the validity of the case data. If the support system finds that the modified case data is valid, it will activate E M T P to simulate this case. If not, the modification-validation procedure will be repeated until a proper case data set is obtained.  2.4.3 Results Evaluation After the E M T P engine numerically solves the simulation case, the results verification step is executed, where the E M T P solution is checked whether it is reasonable. The most important tool for verifying the E M T P case results is the basic knowledge of the phenomena to be simulated. Such knowledge can be found in field test results [7][8][53][54], technical papers [1][2][3], textbooks [13][17][55] [56], and E M T P experts. The support system will propose a  Chapter 2. Intelligent Support System  28  list of possible corrections to the users so that they can improve their case data.  In the results evaluation process, the E M T P output waveforms are examined in the time domain. One of the potential evaluation processes is to compare the obtained results with that of the base case, because the base case is known to produce a reasonable result. If the modification is relatively minor, for example, with a slight variation of parameters, the simulation results will be reasonably similar to that of the base case. However, i f the modification is extensive and there are some drastic changes in configuration, the support system no longer assumes that the results will be satisfactory. Models used in the simulation case may not be valid for the new study.  When two output curves are compared, however, it is usually not easy to simply say that they are similar or not. In real life, the truth lies rather between these statements. The application of fuzzy logic allows defining such statements mathematically by mapping them into a certain range of parameters, which can then be used to measure the degree of similarity.  2.5 Implementation To test the feasibility of the proposed system, a prototype case-based expert system has been implemented to support E M T P simulation. The E M T P support system currently has the case database shown in Figure 2.3. This case database is presented in more detail in Appendix A .  29  Chapter 2. Intelligent Support System  [Menu]  [Sub-Menu]  Power System  Switching Transient  Transient Studies  [Case Data] Overhead Line. Energization  Simple Switching (Single-Phase) Simple Switching (Three-Phase) Energization of Transposed Transmission Line Energization of Untransposed Transmission Line  Overhead Line Re- Energization with Trapped Charges . Capacitor Switching  .Capacitor Bank De-nergization Capacitor Bank Energization  Underground Cable Energization  . Three-Phase Cables Three-Phase Cables with Crossbonding  Transformer and Shunt Reactor Energization  - Transformer & Shunt Reactor Energization Ferroresonance Analysis  -  —Fault Analysis.  Load Energization  _ Interruption of Small Inductive Currents _ Single Line-to-Ground Fault of an Overhead Line Single Line-to-Ground Fault of a Cable _Transient Stability Analysis for Three-Phase Short Circuit _Load Rejection -  —Resonance-  .Linear Resonance at Power Frequency Linear Resonance at Harmonics  Figure 2.3 The hierarchy of case database  Chapter 2. Intelligent Support System  30  The MicroTran version of EMTP, developed at U B C [10], is used to run transient simulation cases [7][17][53][54]. The transient program exchanges data with the support system through an input case data file and result files. The expert system shell C O M D A L E / X [50] is used to build up the knowledge base of the prototype support system.  This prototype support system is installed on a PC with Pentium Pro 200 MHz-Class C P U running Windows N T with 32MB of main memory. This intelligent support system provides a case data library that can help users to build up their case data quickly and properly. Then, the rule-based system validates the data that was modified by the users to meet their simulation requirement.  Suspicious case data will be rejected, and the users will be prompted to correct the parameter values and models. The simulation results are examined by the waveform comparison for particular features.  In the following section a sample case study from [53] is used to show the performance of the proposed support system.  2.6 An Energization Case Study 2.6.1 Case Data Selection A single-phase load energization transient study from [53] is used for demonstration purposes in this section. The system configuration is shown in Figure 2.4.  Chapter 2. Intelligent Support System  SRC  Busl  31  Busl2  Busl3  Figure 2.4 System configuration for a single-phase switching case study Figure 2.4 represents the energization of a single-phase R - L - C load bank from a voltage source behind a Thevenin equivalent impedance through a transmission line modeled by a n circuit.  This case data is located in the case database of the proposed intelligent support system under the switching transients category. The case data, when selected, is displayed to the user with some relevant information. The information is organized so that the user can look at the system configuration and a short description in a single frame. If the user wants more information about the case, he or she can simply jump to a detailed description by a point-and-click operation of a mouse on the hypertext data. The data file of this case study with its description is shown in Figure 2.5.  32  Chapter 2. Intelligent Support System  Index  Start  i  E-Browse g.Browse  Busl  SRC  Bus 12  Back  PrevDoc  3  Print..  Exjt  Help  Bus 13  u  V cosat  |0  Userl - Notepad Ble Edit Search belp  Sample Case Data [SA1 ] S w i t c h i n g T r a n s i e n t s Case-1 C C Case i d e n t i f i c a t i o n c a r d An E n e r g i z a t i o n Case Study w i t h more d e t a i l e d s o u r c e model C C Time c a r d 5Q.E-6 50.E-3 C C Lumped RLC b r a n c h SRC BUS1 6.0  Figure 2.5 The data set of load energization case study 2.6.2  Data Input and Validation  2.6.2.1  The Data Input Form  After the user chooses to modify this case data, a form that contains some information about this case data will come up as shown in Figure 2.6. These data are contained in instance objects for each component model used to represent the target power system. Each object has specific attributes and each attribute has a default value. Different instance objects are assembled under class objects that represent various case data sets. For example:  Chapter 2. Intelligent Support System  33  Class:Load Energization Through Transmission Line Case  Object: n -Circuit Line Model  Attributes: Resistance, Inductance, Capacitance, and Nodes.  Data validation rules are also classified by objects for efficient application and maintenance.  WELCOME  TO EMTP SUPPORT  SYSTEM  SWITCHING T R A N S I E N T S : CASE-1 Enter t h e f r e q u e n c y r a n g e of y o u r s t u d y in Hz: length o f y o u r t r a n s m i s s i o n line in k m : T i m e S t e p S i z e [s]  T R A N S M I S S I O N LINE: Resistance  SOURCE:  Resistance 22.61  24.000  50.0E-6  S i m u l a t i o n T i m e [s]  |o.050 I I n d u c t a n c e Inductance  C l o s i n g T i m e [sj  0.00100 I  V o l t a g e [VJ  Phase Angle  [56J  |500.00 |  hg.71 I  J2.000 I  Capacitance  Capacitance  O p e n i n g T i m e [s]  19999.00 I  Frequency  0.050  ffl  Io.OOb]  lo.tMO I  Nodes  Node  Nodes  Inductance  |Bus1-Busl2  IbusU  Bus12-Busl3  [6£]  Node  |sRC  Figure 2.6 Input data form for load energization case study (R in Q , L in mH, and C in \xF)  Chapter 2. Intelligent Support System  34  2.6.3 Rule-Based Data Validation System After the user modifies the case data and clicks on the D O N E button, the rule-based system will initiate the validation process for this case data. For this simple switching case data, approximately 20 rules were applied to perform the data validation on different objects. The diagnostics from these rules will tell the users about possible inconsistencies of data, so they can correct the case data. Some of these rules are explained as related to their models (objects) as follows:  1. Frequency range & transmission line length rule  The validity of the % -circuit line model depends on length (I) of the line as well as on the frequency range of the transient phenomena (f), as shown in equation (1.1).  "If the frequency range of this load energization study isf, then the length of the transmission line should not exceed ^ 1_0_CJ00 ^ j£  i  Qr overneac  n " nes  2. The step size rule  The step size is related to the maximum frequency through the Nyquist frequency. The step size rules will be discussed in more detail in Chapter 3.  "If the maximum frequency in your system is f , max  1  „  then use a simulation step size of  Chapter 2. Intelligent Support System  3.  35  Transmission line model rules  In the following cases, the parameters or models are considered incorrect, and the users are instructed to check the parameters.  i) "If the line model parameters (L and C) are equal to zero, then this is not a line model".  ii) "If the characteristic impedance of the transmission line z = J(R + j(£)L) / (;'co C) « JL^C is greater than 1000 Q or less than 200 Q , then the surge impedance of the line is incorrect if it is an overhead line ".  Hi) "If the wave speed c = 1 /(VlC) of the line is greater than 300, 000 km/s or less than 250, 000 km/s then the wave speed of the line is incorrect".  The other rules will perform similar sanity checking for the other objects of the case data instance, and the rule-based system will guide the user to select the proper values for each object attribute. Then, the support system will save these values to a file to be converted later to an EMTP format.  When the user is finished with this case data, the support system will activate the EMTP to run this case data as shown in Figure 2.7.  36  Chapter 2. Intelligent Support System  "z Command Prompt - mt208 userl.dat  = Case T i t l e :  MT u2.08-32 = = ^ = = = =  =  =  =  =  =  =  =  =  Energization of an RL load with more detailed source model  Estimated Time: Elapsed Time:  00:00:01 00:00:01  Nodes: Branches:  Press ESC to stop program  Figure 2.7 The support system running the EMTP  2.7 Results Evaluation This section describes a new method to evaluate the results of E M T P simulations. This method provides a quick check for E M T P results based on parameter variations. In this section, the step size is selected to explain this methodology. This is because the selection of the step size is very important for the accuracy of EMTP simulation results. The step size must be sufficiently small to maintain accuracy and it should be as large as possible in order to provide high simulation efficiency.  Chapter 2. Intelligent Support System  37  Other parameters such as the load variations were considered in [71] for our results evaluation process. These variations have been applied to the load elements (R, L, and C) in order to see how these elements can affect the output voltage waveform.  2.7.1 Characteristic Parameters We selected some features as an example, to evaluate the output waveform of the modified case. More practical features for switching surge studies are discussed in Chapter 3. The two parameters chosen for this particular case study are the maximum voltage amplitude of the first peak (V ), max  (T ). zero  and the time at which it crosses the zero voltage axis for the first time  Figure 2.8 shows a typical energization output waveform and the characteristic  parameters that are used to evaluate the results. The overall simulation time for this case is 50 ms, however only the time portion to 5 ms is shown in Figure 2.8 for comparison purposes.  2.7.2 Step Size Variations In this case study, we consider the step size variation for the results evaluation process, because the waveform shape for the output is sensitive to the selection of the step size. Figure 2.8 compares the base case results (solid line) for a step size of 50 p s with the results for a step size of 100 p s (dashed line). From Figure 2.8, we can observe how the waveform of the modified case data deviates from the base case.  38  Chapter 2. Intelligent Support System  100  Figure 2.8 Characteristic parameters and case study comparison for step size of 50 p. s (solid) and 100 p. s (dashed)  2.7.3 Fuzzy Logic Analysis In this case study, we consider upper and lower limits for the characteristic parameter change from the base case as follows:  -10.0 < AV  max  <10.0inV  -1.0 < AT „„ <1.0inms  39  Chapter 2. Intelligent Support System  These upper and lower limits were chosen based on experience gained by running many simulations with different step sizes [71].  From the observation of the simulation results, we could declare that the waveform is unacceptable i f the changes in the maximum voltage amplitude of the first peak (A V ) and max  the change in time of zero crossing (A T ) of the modified case data exceeds the upper zero  limits or if they go below the lower limits.  For the application of fuzzy logic, we segment the inputs, namely A V  max  and A T  , into  zer0  some overlapped regions by fuzzy sets in Figure 2.9, Figure 2.10. These regions correspond to linguistic labels such as "far low for A V  ". The output of the waveform comparison W  max  index  represents the matching between the base case and the modified case. W  index  can be defined  by fuzzy sets as shown in Figure 2.11.  1  FL  CL  FH  AV m a x  0  -10.0  10.0  Figure 2.9 The maximum voltage amplitude of the first peak  40  Chapter 2. Intelligent Support System  1.0  -1.0  Figure 2.10  0  The time of zero crossing  0.5  1.0  Figure 2.11 Output voltage waveform comparison The labels in the above figures are as follows:  F L = Far Low; C L = Close; F H = Far High; FS = Far Short; F L = Far Long; P = Poor Matching; F = Fair Matching; G = Good Matching.  Table 2.3 summarizes the rules that are used in the results evaluation process.  41  Chapter 2. Intelligent Support System  Table 2.3: Results evaluation rules FS  CL  FL  FH  P  F  P  CL  F  G  F  FL  P  p*  P  The rule table reads, for example at the cell marked with asterisk, as:  IF  AT  is Close  AV  is Far Low  W  is Fair Matching  zer0  AND THEN  max  index  There are different fuzzy reasoning methods [69]. For this problem, the popular Mamadnitype fuzzy reasoning mechanism is applied because the number of input-output variables is small.  For example, for a modified case study with characteristic parameters of A V  max  AT  zero  = 0.3 ms, and using Mamdani's direct method, the matching index is W  = 4 V and  index  « 0.7,  which is acceptable. The reasoning process for this given example is shown in Figure 2.12. From this example, we can conclude that the given case has a good similarity to the base case, hence it exhibits reasonably acceptable output.  Chapter 2. Intelligent Support System  Figure 2.12 Reasoning process  Chapter 2. Intelligent Support System  43  The fuzzy logic toolbox of M A T L A B Version 5.1, was used to implement the results evaluation process for all the derived rules of Table 2.3.  2.8 Summary This chapter has described an EMTP intelligent support system which allows the users of the E M T P to choose the closest case data from a case database that contains different types of simulation case studies. Based on this data, the users can modify their case to meet their particular targets. Also, the data validation and results evaluation process has been applied to a load energization study. The results evaluation process of the support system will advice the user about the acceptable range of the results obtained from the simulation.  The next chapter will present the development of a more realistic knowledge base for switching transient surges. The introduced knowledge base will help in selecting the proper model of representing power system components in the EMTP according to the problem specifications. It will help the user in checking the validity of the data used to represent the simulated transient phenomena before simulation. Also it will help in the evaluation of the results of the EMTP simulation, by using the knowledge of the phenomena being simulated.  Chapter 3 Switching Surge Transients 3.1 Introduction This chapter presents a knowledge base for switching transients overvoltages, and more specifically, for transmission line switching. A practical case of line energization is also presented in this chapter as a base case. The objective is to provide practical rules and modelling suggestions to evaluate switching transients simulations. These rules will be extracted by studying the switching transient phenomena in more detail.  The chapter begins by introducing a summary of different types of overvoltages in general. Section 2 then focuses on the switching overvoltages. This section describes briefly the origin and characteristics of switching overvoltages, the parameter that influence the switching overvoltages and means for limiting them. Section 3 describes a practical case of a three-phase  44  Chapter 3. Switching Surge Transients  45  transmission line energization. Section 4 then provides some modelling suggestions for the use of different E M T P models.  3.2 Switching Surge Transients-Background With the increasing operating voltage of transmission systems, switching surge overvoltages determine the insulation design rather than lightning overvoltages. The insulation level required to withstand the switching surge overvoltages can have significant influence on the cost of transmission systems. Therefore, an accurate estimation of the switching overvoltages under various conditions of operation is an important factor for the design of transmission systems [1][13].  3.2.1  Summary of Different Classes of Overvoltages  Overvoltages in power systems can be produced by a wide variety of phenomena, such as faults, switching operations and lightning strokes. It is not practical to design power equipment to withstand all types of overvoltages. The power engineer must seek a compromise between insulation or protection level and economics. The goals of insulation coordination studies are to select appropriate insulation levels for equipment and to choose protection devices so as to minimize damage and interruptions [17].  Overvoltages that can occur in power systems are classified according to their duration and frequency range: 1. Lightning Overvoltages: These are fast front transients, with front times in the order of microseconds. They are either caused by direct strokes to phase conductors and by back-  Chapter 3. Switching Surge Transients  46  flashovers, or by strokes to earth close to the line [18] [19]. 2. Switching Overvoltages: These result from the operation of switching devices, either during normal conditions or as a result of fault clearings. These transients have a duration from tens to thousands of microseconds. They belong to the category of slow front transients. The main operations that can produce switching overvoltages are line energization and re-energization, capacitor and inductor switching, occurrences of faults and breaker openings [1] [2]. 3. Temporary Overvoltages: These have frequencies near to or at a harmonic of the power frequency and they are known as long duration power frequency oscillations [20][21].  3.2.2  Source and Characteristic of Switching Overvoltages  In general, a switching operation in a power system changes the status of the system from those conditions existing before the switching to those existing after the operation. This will produce transient phenomena. The power frequency voltage before and after the switching operation may be of a different value due to the change in the state of the system. This means that the total amplitude of the overvoltage due to switching may be considered in two parts, namely a transient component which is superimposed on a power frequency component [1].  Switching transients usually show complex waveforms with frequencies in the range of 100 Hz to 1000 Hz superimposed on the power frequency.  Chapter 3. Switching Surge Transients  47  3.2.3 Parameters Influencing Switching Overvoltages There are number of parameters of the system and of the operating elements which influence overvoltages. O G R E Working Group 13.02 [1] presents these parameters as shown in Table 3.1 [1][13], based on an evaluation of a large amount of collected data on closing and reclosing overvoltages. This data is based on Transient Network Analyzer (TNA), computer and field test results. The evaluation shows the relative influence of the large number of parameters on overvoltages. The most important influencing parameters are explained below. In long transmission lines, the most important factors which affect the power frequency voltages on the line during normal operation, and the increase in voltages during a fault, are the length of the line and the degree of shunt compensation. Both parameters have a major indirect influence on the transient phenomena connected with the initiation or clearing of a fault, as well as with normal switching operations. Even the connection of a transformer at the end of a line can affect the overvoltages. Although one might think that the saturation of the transformer limits the increase in power frequency voltage, that is not so. Instead, the harmonics created by saturation and superimposed on the power frequency typically cause an increase in voltage.  Circuit breakers are less often the direct cause of high overvoltages in power systems than is generally assumed. Their operation is similar to that of an ideal circuit breaker, even when switching high short-circuit currents, switching capacitive current, and to a lesser extent in the case of low inductive currents. They interrupt the current mostly at its natural zero crossing  Chapter 3. Switching Surge Transients  48  point. Overvoltages are, on the other hand, caused by the switching process itself, the characteristic of the system and operation elements, as well as by switching operations and faults immediately prior to it. The circuit breaker itself, together with its closing resistance (the optimum value of which depends on the system characteristic) has a damping effect on switching surges.  There are two characteristics of the system itself which have a major influence On the increase in power frequency voltage and transient phenomena. One of them is the short-circuit power and the other is the system configuration. Low short-circuit power and feeding via a transformer only (inductive source), which occurs in the initial stages of setting up a system, cause much higher switching overvoltages than a high short-circuit power and feeding via transformers and transmission lines (complex system).  As shown in Table 3.1 [1][13], a distinction is made between those parameters inherent in the. switched  line,  the  circuit  breaker  and  the  supply  network.  It  should  be  clear that the influence of a single parameter cannot by itself determine the overvoltage, since mutual effects with other parameters are often important.  Chapter 3. Switching Surge Transients  49  Table 3.1 Network parameters influencing the switching overvoltages [1] Network parameter influencing the switching overvoltages  Influence on total overvoltage factors  1. Line side parameters - Positive and zero sequence inductance, capacitance and  Medium  resistance - Frequency dependence of the above line parameters  Medium  - Line length  Strong  - Degree of shunt compensation  Strong  - Degree of series compensation  Medium  - Line termination (open or transformer terminated)  Strong  - Presence and degree of trapped charges on the line with  Strong  out closing resistors - Presence and degree of trapped charges on the line with  Medium  closing resistors - Corona effects  Minor  - Saturation of reactors  Medium  - Damping or reactors  Minor  2. Circuit-breaker parameters - Max. pole span of contacts  Medium  - Dielectric closing characteristics  Minor  - Presence of closing resistors  Strong  - Value of closing resistor  Strong  - Insertion time of closing resistors  Medium  - Phase angle at instant of switching  Strong  3. Supply-side parameters - Service Voltage  Minor  - Service frequency  Minor  - Total short-circuit power  Strong  - Frequency-dependent damping factors of transformer and  Minor  generators - Inductive and complex network  Strong  - Parallel lines to switched line  Minor  - Ratio of positive to zero sequence impedance  Minor  Chapter 3. Switching Surge Transients  3.2.4  50  Switching Overvoltages in Closing and Reclosing Operations  Many measurements, and T N A and computer calculations of voltage surges occurring during closing and re-closing of transmission lines were compiled in [1 ] [13]. The results are shown in Figure 3.1. The following parameters were varied: 1. Closing or reclosing 2. Circuit breaker with or without closing resistors 3. Complex or inductive feeding systems 4. Shunt compensation greater or less than 50%. In most of the cases for > 50 % the degree of compensation was approximately 70%, while for the cases of < 50% mostly no compensation was employed [1].  The average values as well as the maximum and minimum values for the overvoltages were entered into the charts of Figure 3.1. It can be clearly seen that the highest overvoltages occur during reclosing without closing resistors, when the system consists of a feeding transformer only and no shunt compensation of the transmission line was provided. On the other hand, a simple charging of the line via closing resistors from a complex system, and with shunt compensation of the line, results in the lowest value of overvoltage.  From Figure 3.1 we can see that switching overvoltages are a function of various parameters of the system and the operating elements. At E H V levels, they are limited by shunt compensation, closing resistors, surge arresters and other measures taken during system operation. The  Chapter 3. Switching Surge Transients  51  overvoltages occurring at a particular location in the system must be known in order to decide on the use of particular equipment and its insulation [1].  In conclusion, faults and switching surges are daily occurrences in a system. The switching surges that they cause should not result in further faults or failure of the necessary switching operation. Overvoltages caused by switching on and off of lines, transformers, reactors and other equipment can be effectively reduced by shunt compensation, closing resistors, and surge arresters. Overvoltages which occur at the moment of fault initiation and fault clearing are, on the other hand, a function of the system configuration, the short-circuit power and the method of neutral grounding, and can be controlled or influenced only to a limited extent. Although switching surges are unavoidable, we can nevertheless reduce their frequency of occurrence and magnitude [13].  3.2.5 Definitions In the study presented in Figure 3.1, the following definitions are used [1]:  Inductive source: This expression refers to the supply side network which is fed exclusively through transformers with no lines or cables directly connected to the busbar.  Complex source: The supply side network includes one or more lines or cables directly connected to the busbar.  Variant: A variant is a single examined case in which all system, line and breaker parameters have a specified value, except those which must be varied to find a statistical distribution.  52  Chapter 3. Switching Surge Transients  Location of overvoltage: End of the line  Type of operation i closing  O reclosing  Closing resistor^ ® Yes  O No  Supply Network ^ • Complex O Inductive Shunt compensation #>50%  O < 50 %  No. of evaluated variants Max. Overvoltage  10  10  13  14  23  1.2  2.0  1.9  2.2  2.2 2.6 2.8 2.9  Mean Overvoltage  1.2  1.6  1.5 1.8  Min. Overvoltage  1.1  1.3  1.3  60  1.9 2.0  1.4 1.6 1.4  12  32  3  17  1.9 1.8  26  10  2.2  2.1  2.5 3.5 3.5 3.7  2.2 2.3 1.7  1.5 1.6 1.7  1.8 1.7  1.2 1.3  1.6  31  2.0 2.5  5  12  8  2.7 2.9  1.4 1.5 1.5 1.9  2.1  Figure 3.1 Evaluation of overvoltage factors dependent on type of operation and system [1]  Chapter 3. Switching Surge Transients  53  3.3 Switching Surge During Energization This section introduces a switching surge case study of a transmission line energization to be used as the base case for studying the transient phenomena. The network configuration for this case study is shown in Figure 3.2. The data comes from tests on the Jaguara-Taquaril line, which were conducted by the Brazilian utility company CEMIG. Field test data was made available for these test [6] [7] [8].  JAGUARA  [X]-matrix  TAQUARJL  Transmission Line 398 km, Transposed  © @©  Circuit Breaker with Closing Resistors, (all R = 400 ohms)  /////// Thevenin Equivalent for Generators and Transformers  [X]-matrix  ///////// Shunt Reactor  Figure 3.2 Network configuration for switching surge case study 3.3.1 Network Configuration 3.3.1.1  Feeding Network  The feeding network was a power plant with synchronous generators and transformers. The subtransient reactances of the generators and the reactances of the transformers could be reduced to a Thevenin equivalent circuit. The Thevenin equivalent impedance matrix was obtained from the positive and zero sequence impedances after conversion to phase quantities  54  Chapter 3. Switching Surge Transients  as shown below:  77.66 -22.25 -22.25 [*]  =  -22.25 77.66 -22.25  Q  -22.25 -22.25 77.66  These values were referred to the 345 k V side of the transformer. Immediately before the breaker closing, the voltage on the high side of the transformer was 328 k V (RMS, line to line). These are the values to be used for the voltage source behind the [X] matrix. In the simulation, voltages of 1.0 p.u. were used because the results were to be shown in p.u. of the pre-closing voltage of 328 kV. The phase angles were such that the voltage source of phase A passed through zero at t = 0, heading for negative values, or: v  =-1.0 cos (cot+ 90°)  p.u.  v =-1.0 cos (cot-30°)  p.u.  v =-1.0 cos (cot-150°)  p.u.  A  B  c  3.3.1.2  Shunt Reactor  The shunt reactor parameter ratings are: V j g = 440 k V , Q ting rat  n  ra  = 91 Mvar, X 0 . 3 5 X , wye connection solidly grounded. pos  From these parameters, the three-phase [X]-matrix was found as: 1666. -461. -461. -461. 1666. -461. Q. at 60 Hz. -461. -461. 1666.  z e r 0  =  Chapter 3. Switching Surge Transients  3.3.1.3  55  Transmission Line  The sequence parameters of the transmission line were: R R  p o s  zero  = 0.0503 Q/mile,  X  0.4957 Q/mile,  X  =  p o s  z e r o  = 0.6021 Q/mile,  C  = 2.061 Q/mile,  C  p o s  z e r o  = 18.98 nF/mile = 12.67 nF/mile  length = 247.36 miles = 398 km (parameters calculated at 60 Hz).  3.3.1.4  Circuit Breaker  The circuit breaker was equipped with closing resistors of 400 Q, which would be in series with the line when the auxiliary contacts were first closed. The closing resistors were then shorted out approximately 7 ms later as the main contacts closed. The closing times were determined from oscillographs as follows:  Phase  Auxiliary Contacts  Main Contacts  A  8.45 ms  15.85 ms  B  7.15 ms  14.45 ms  C  8.10 ms  15.10ms  The closing resistors with the resistance values of 400 Q are represented as switch resistances in the auxiliary contact switches.  The data file used for this case is shown in shown in Table A . l in Appendix D, while the output file is shown in Table A.2 in Appendix D.  Chapter 3. Switching Surge Transients  56  3.4 Modelling Suggestions This section presents some modelling suggestions for the simulation of line energizations. These suggestions will provide some practical rules which are based on some of the parameters listed in Table 3.1. These modelling suggestions will help the E M T P user to select the proper model and to understand the simulation results better.  3.4.1 Step Size When using the E M T P , the selection of the step size A t is of importance. On the basis of the highest expected frequency, and assuming that ten points would define one period of this frequency f  m a x  with sufficient accuracy, A t is given by [3]:  For the line energization case study, the maximum frequency f  m a x  is expected to be less than 2  kHz. A step size for this case study of 50 p s is therefore a reasonable choice. For At < 50 ps, the results are practically identical with At = 50\xs. When the step size A t is increased to 100 ps, the results are still accurate. However for 200 ps, the deviations become noticeable and the results are less accurate [14].  57  Chapter 3. Switching Surge Transients  The maximum frequency rule:  "If the maximum frequency in your system is f ,  then use the simulation step size of  max  1  „  The travel times for the transmission line are calculated as follows: x , = ijL^C,  (3.2)  x  (3.3)  0  = ljL\~C  Q  where x is the positive sequence travel time and x x  case, T j = 1.36328 ms and t  0  0  is the zero sequence travel time. In this  = 2.06432 ms.  For the existing distributed parameter line model in the EMTP, the step size A t must be less than the travel time of the shortest line in the network. This limitation has been overcome with the new line model presented in more detail in the next chapter. In the case here, the step size A t is less than the travel times T , and T . 0  The step size constraint rule:  "If the step size A t is larger than the travel time x of the shortest line in the network, then the new line model should be usedfor lines with x < At ".  Chapter 3. Switching Surge Transients  58  A l l line models have some discretization errors, except the lossless line if its travel time is an integer multiple of the step size. If this is not the case, then linear interpolation is used in the EMTP. Linear interpolation is believed to be a reasonable approximation for most cases, since the curves are usually smooth rather than discontinuous. If discontinuity or very sharp peaks do exist, then rounding T to the nearest integer multiple of A t may be more sensible than interpolation [4].  One simple rule that can be applied for checking whether the step size is suitable is to check if no further accuracy can be obtained if the step size is divided by two [3]. Step size accuracy rule:  "Ifyou want to check the accuracy of the simulation, then divide the used step size by 2 and run the simulation ".  Chapter 3. Switching Surge Transients  59  3.4.2 Transmission Line Models The Jaguara-Taquaril case has been simulated using the constant parameter line model, and good results were obtained. This is because there is very little zero sequence current in the results, it is the zero sequence parameters where frequency dependence is pronounced. In cases that have high zero sequence currents, the constant parameter line model is not the right model to be used. For comparison purposes, the transmission line was also represented with frequency-dependent parameters. 3.4.2.1 The Constant Parameter Line Model The simulation results for the constant parameter line model are shown in Figure 3.3, Figure 3.4 and Figure 3.5 for the voltages at the receiving end in phase A , phase B and phase C, respectively. For the receiving end at Taquaril, the differences between field test and computer simulation results is larger than at the sending end (not shown here). The exact reason for this difference is not sufficiently known. It could have been caused by the fact that the metering installation at Taquaril was relatively unreliable, consisting of a galvanometric oscillograph coupled to differential amplifiers placed inside a metallic cubicle without having any protection against the heat of the sun [7]. There was difficulty in calibrating the heat-sensitive amplifiers. At the sending end, a more reliable high-speed cathode ray oscillograph was used [7].  60  Chapter 3. Switching Surge Transients  2.5  1.5  0.5  -0.5  -1.5 0.005  0.015  0.01  0.02  0.025  T i m e (s)  Figure 3.4 Comparison between field test (solid) and constant parameter line model (dashed) in phase B  61  Chapter 3. Switching Surge Transients  TK  / /  x  l\ y  ^  _  _  \\ \\ / \ 1 0  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.5 Comparison between field test (solid) and constant parameter line model (dashed) in phase C 3.4.2.2  The Frequency Dependent Line Model  Figure 3.6 gives the tower configuration of the line. This geometry and the characteristic of the conductors are needed to calculate the frequency dependent line parameters for both positive and zero sequence. The conductor characteristics were taken from [11], [12].  A l l the parameters, including series resistance and shunt conductance, are modeled as continuously distributed along the line's length in this line model. It is based on the synthesis by rational functions, in the frequency domain, of the line propagation function and characteristic impedance. These rational approximations correspond to a sum of simple partial fractions in the time domain [4].  Chapter 3. Switching Surge Transients  62  The E M T P input data file for this line model is produced by the auxiliary program fdData. This file contains the partial fractions expansion of the characteristic impedance and propagation function for the zero sequence and positive sequence mode [10].  The fdData input file for this case is shown in Table A. 3 in Appendix D. The E M T P input data file for the case with the frequency dependent line model is shown in Table A.4 in Appendix D.  The simulation results for the frequency dependent line model are shown in Figure 3.7, Figure 3.8 and Figure 3.9 for phase A , phase B and phase C, respectively.  Chapter 3. Switching Surge Transients  63  G r o u n d wires at tower  Phase conductors at tower G r o u n d wires at m i d s p a n  Phase conductors at m i d s p a n  Figure 3.6 Tower configuration of Jaguara-Taquaril line. A l l measurements in meters, earth resistivity = 100 Q m  64  Chapter 3. Switching Surge Transients  i'l >  0  0.005  0.01  0.015  0.02  0.025  T im e (s)  Figure 3.7 Comparison between field test (solid) and frequency dependent line (dashed) in phase A  / N  if  V  \\  //  \  \  I/  \./[ 0  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.8 Comparison between field test (solid) and frequency dependent line (dashed) in phase B  Chapter 3. Switching Surge Transients  0  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.9 Comparison between field test (solid) and frequency dependent line (dashed) phase C  Chapter 3. Switching Surge Transients  3.4.2.3  66  Comparison Between the Two Line Models  The simulation results for the frequency dependent line model are compared with those of the constant parameter line model in Figure 3.10, Figure 3.11 and Figure 3.12. From these results we can observe that the voltages at the receiving end are almost identical, except for a 10% difference in the peak which is caused by a less damped high frequency oscillation in the constant parameter line model. This is because the zero sequence parameters have the strong frequency dependence, but the zero sequence current flowing in the network is small compared to the phase currents. The zero sequence current for this case is shown in Figure 3.13. The currents for the three phases A , B and C are shown in Figure 3.14.  If the zero sequence current is relatively high, then the constant parameter line model will not give accurate results as compared to the frequency dependent line model. This is because the higher frequency damping in zero sequence cannot be accurately represented with the constant parameter line model.  67  Chapter 3. Switching Surge Transients  Figure 3.10 Comparison between frequency dependent line (solid) and constant parameter line (dashed) in phase A  T i m e (s)  Figure 3.11 Comparison between frequency dependent line (solid) and constant parameter line (dashed) in phase B  68  Chapter 3. Switching Surge Transients  ff v \ =  0.5  *  V  u  0  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.12 Comparison between frequency dependent line (solid) and constant parameter line (dashed) in phase C x  10  Time (s)  Figure 3.13 Zero sequence current for Jaguara case study  69  Chapter 3. Switching Surge Transients  4,  x10  3  1  1 1  J  L__/AttJ  1 / /  1 1 /  •  /  - -1  \  1 L '  *?  v  \  r if r\ V V : \  V  v  '',  - / - ^ ; - / - T ; -  \ \-\  /  ^v '  i  \'  N  !  -3  1. 1  0  0.005  i i 0.015  0.01  Y /V  ' I \  "i  0.02  0.025  Time (s)  Figure 3.14 Three phase currents for Jaguara case study 3.4.2.4  The Single-Phase Energization Case Study  A case of single-phase energization is presented to show a situation where the results from the constant parameter line model differ more from those of the frequency dependent line model. The simulation results are shown in Figure 3.15 and Figure 3.16 for phases A and B, and C, respectively. The voltages in the unenergized phases B and C are identical, and result from coupling effect to the energized phase.  In this case the zero sequence current is equal to the single phase current of phase A . It is shown in Figure 3.17. The case was slightly modified from the three-phase energization case: there was no closing resistors, and the voltage in the feeding network was at the peak value  Chapter 3. Switching Surge Transients  70  when the circuit breaker closed. This produced more higher frequencies than closing at zero voltage. If we compare this zero sequence current to that of the three phase energization, we can see that for this case the zero sequence current is much larger. This makes a difference in choosing the proper model. If we look at the positive sequence inductance of the overhead line we can see that it is practically constant, as shown in Figure 3.18, while the positive sequence resistance remains more or less constant until the skin effect in conductors becomes noticeable, as shown in Figure 3.19. The zero sequence inductance is shown in Figure 3.20 and zero sequence resistance is shown in Figure 3.21. Both are very much frequency dependent, due to the skin effect in the earth return.  The frequency dependent model includes information about the variation of the parameters with frequency. This is an important consideration when the ground return mode (zero sequence) is involved. In these cases, the frequency dependent line model will give more accurate representation for a wide range of frequencies contained in the transient phenomena, as compared to the constant parameter line model.  71  Chapter 3. Switching Surge Transients  3  0.5  h  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.16 Comparison between frequency dependent line (solid) and constant line (dashed) for phase B and C  72  Chapter 3. Switching Surge Transients  T i m e (s)  Figure 3.17 Zero sequence current and current in phase A 1.8,  1.55  ,  ,  -i  -2  10  ,  ,  1  0  10  ,  .  ,  '  :  -i  10 Frequency (Hz)  10  2  ,  ,  l  4  6  10  Figure 3.18 Positive sequence inductance of the three-phase line  73  Chapter 3. Switching Surge Transients  10  Frequency (Hz)  Figure 3.19 Positive sequence resistance of the three-phase line  12  10  = E  8  E  o  6  10  10  10 Frequency (Hz)  10  10  Figure 3.20 Zero sequence inductance of the three-phase line  Chapter 3. Switching Surge Transients  74  Frequency (Hz)  Figure 3.21 Zero sequence resistance of the tree-phase line  The zero sequence current rules: "If the zero sequence current is small, then use the constant parameter line model".  "If the zero sequence current is high and contains high non-power frequencies, then the frequency dependent line model should be used".  Chapter 3. Switching Surge Transients  75  3.4.3 Shunt Compensation Shunt reactors are usually modelled as a simple lumped inductance with a series resistance. A parallel resistance may be added for more realistic high frequency damping [14].  The main purpose of shunt compensation in E H V systems is to limit the power frequency overvoltages. Since the total overvoltage factors on closing and reclosing depend approximately linearly on the power frequency overvoltages, shunt compensation also has an important effect on the magnitude of the total overvoltages. Table 3.2 shows the steady-state nodal voltages for the network of Figure 3.2 when shunt compensation is included at the sending end, while Table 3.3 shows the steady-state nodal voltages for the same network without shunt compensation. The total overvoltages will in general be higher for networks having little or no shunt compensation as compared with cases with more shunt compensation. Figure 3.22, Figure 3.23, and Figure 3.24 show the comparison between the overvoltages with and without shunt reactors at the receiving end for phase A , phase B and phase C, respectively.  Table 3.4 shows the steady-state nodal voltages for the same network if the same shunt reactor at the sending end is also placed at the receiving end. As we can observe, the overvoltages are reduced even more than in the other two cases.  For 100% compensation, we need a shunt reactor at both ends of the line with a positive sequence value of —— I = |o)C pos  X  2  1. In this case, the voltages at both ends would be identi-  Chapter 3. Switching Surge Transients  76  cal under no-load condition as shown in Table 3.5. This can easily be shown with the nominal tc -circuit of equation (1.1). In practice, 100% compensation is avoided because of the danger of resonance. 1 X  pos  Typically degrees of compensation are 50% to 70%. In that case,  1 k = 2-coC"P" / x 100 —— where k is the percentage of compensation.  The shunt compensation rule: "If you want to have k% shunt compensation for the line, then place a shunt reactor with a 1 1 positive sequence value of —— = - c o C pos  X  2  k I x —— at both ends of the line ". 1  0  0  Table 3.2:Network steady-state nodal voltages with shunt compensation NAME  MAGNITUDE  JAG  0.8289  TAQ  0.9518  Table 3.3:Network steady-state nodal voltages without shunt compensation NAME JAG TAQ  MAGNITUDE 0.8770 1.007  77  Chapter 3. Switching Surge Transients  Table 3.4:Network steady-state nodal voltages with shunt compensation doubled NAME  MAGNITUDE  JAG  0.8228  TAQ  0.9098  Table 3.5Network steady-state nodal voltages with 100% shunt compensation NAME JAG TAQ  2.5  MAGNITUDE 0.710 0.7120  1  1 .5  g  if  0.5  -0.5 h  V  •1 .5  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.22 Overvoltages with shunt reactor (solid) and without shunt reactor (dashed) in phase A  Chapter 3. Switching Surge Transients  0  0.005  78  0.01  0.015 Time  0.02  0.025  (s)  Figure 3.23 Overvoltages with shunt reactor (solid) and without shunt reactor (dashed) in phase B  0  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.24 Overvoltages with shunt reactor (solid) and without shunt reactor (dashed) in phase C  Chapter 3. Switching Surge Transients  79  3.4.4 Trapped Charges In switching surge studies, one must also simulate cases where it is assumed that the line to be energized has trapped charges on it, while the feeding network behind the circuit breaker will be in normal ac steady-state condition. This produces the highest overvoltages in the network. This applies to lines without shunt reactors only, because shunt reactors connected to the line (or inductive potential transformers) would drain off the trapped charges. The severity of the overvoltages in cases with trapped charges depends on the polarity of the trapped charges and the inserting instants of the breaker poles. There are two ways of simulating trapped charges in the EMTP: 1. Use the override "initial conditions" feature of the EMTP. 2. Let the circuit breaker opening action of switches trap a charge, before the circuit breakers are closed again.  To show the effect of trapped charges on switching surges, the following simulation was performed with trapped charges of + 1.0, - 1.0, + 0.5 pu voltages on phases A , B , and C respectively. The voltage waveforms for trapped charges are shown in Figure 3.25, Figure 3.26, and Figure 3.27.  The trapped charges rule:  "Ifyou want to simulate trapped charges in the EMTP, then use the override "initial conditions" feature of the EMTP, or let the circuit breaker opening action of switches trap a charge before the circuit breakers are closed again ".  Chapter 3. Switching Surge Transients  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.25 Effect of trapped charges on switching surge (1.0 p.u. on phase A)  =•  o  0.005  0.01  0.015  0.02  0.025  T i m e (s)  Figure 3.26 Effect of trapped charges on switching surge (-1.0 p.u. on phase B)  Chapter 3. Switching Surge Transients  1.5  1  0.5  7  81  -  o  <u J> -0.5 o >  -  -1  -  -1.5  -  -2 -2.5 _3 I 0  i 0.005  i 0.01  i 0.015  i 0.02  I 0.025  T i m e (s)  Figure 3.27 Effect of trapped charges on switching surge (0.5 p.u. on phase C) 3.4.5 Feeding Network In most switching transient studies, the generators are modelled as voltage sources behind subtransient reactances, the non-switched lines with constant parameter models, and the transformers with their short-circuit impedances. How extensive the feeding network has to be modelled depends on the particular case. O G R E Working Group 13.05 [3] recommends for normal switching operations "that the detailed model of the system in general must comprehend the part of network up to the second substations behind that of the operating circuit breaker. For line energization and re-energization exact representation only up to the first substations is sufficient in most cases".  Chapter 3. Switching Surge Transients  82  Often, a network equivalent which approximately represents the frequency response characteristic of the entire feeding network is used to simplify its representation [57] [58] [59].  In Figure 3.1 the distinction is made between inductive and complex source feeding networks. The results presented in [1] show that the overvoltages with complex feeding networks are typically 10% to 15% less than those with an inductive source, especially when no closing resistors are used.  The feeding network rules:  "Ifyou want to model the feeding network for normal switching operations, then the detailed model of the system must include the part of the network up to the second substations behind that of the operating circuit breaker ".  "Ifyou want to model the feeding network for line energization and re-energization then line models only up to the first substations are sufficient in most cases ".  "If the feeding network is complex, then the resulting overvoltages are typically 10% to 15% less than those with an inductive source ".  3.4.6 Closing Resistors Circuit breakers are often equipped with closing resistors, which are inserted in series with the circuit for a short period of time before the main breaker contacts closed. Figure 3.1 shows that closing resistors are one of the most effective ways to reduce the switching overvoltages [1]. When shunt compensation is present, the effect is more assured. The selection of the opti-  Chapter 3. Switching Surge Transients  83  mum pre-insertion resistor value depends on the line shunt compensation, the short circuit power of the feeding network and the length of the line. For example, shorter lines have higher optimum pre-insertipn resistors.  A n example for the importance of closing resistors in reducing overvoltages is shown in Figure 3.28, Figure 3.29, and Figure 3.30 for phases A , B and C, respectively. The closing resistors rule:  "If the circuit breaker has one-step closing resistors, then model each pole with two switches, one for the auxiliary contacts with the resistor and one for the main contact".  /  j  i  /  I  \  \ \  \  \ \  j  J f  /3  y  \  \  \/ ! i  0  0.005  0.0 1  0.015 T i m e  0.02  0.025  (s)  Figure 3.28 Overvoltages with closing resistors (solid) and without closing resistors (dashed) at phase A  Chapter 3. Switching Surge Transients  84  \  \ \  / V  i  '"•'X./ 0  0.005  0.01  0.015 Time  0.02  0.025  (s)  Figure 3.29 Overvoltages with closing resistors (solid) and without closing resistors (dashed) at phase B  3  1 2 i  /  \ \  \ -2  i 0  0.005  0.01  0.015 Time  0.02  0.025  (s)  Figure 3.30 Overvoltages with closing resistors (solid) and without closing resistors (dashed) at phase C  Chapter 3. Switching Surge Transients  85  3.4.7 Line Length Table 3.1 shows that the total overvoltages are strongly affected by the line length. The increase in the total overvoltages with the increasing line length is primarily due to the increase of the power frequency voltage, which is further a function of the shunt compensation and the short-circuit power of the feeding network. The transient overvoltage shows no clear dependence on the length of the switched line, but is influenced by closing resistors [1]. The given line energization case is simulated with a shorter line length of 125 miles and compared with the original simulation results. The effect of the line length is shown in Figure 3.31, Figure 3.32, and Figure 3.33 for phases A , B and C, respectively.  As we can observe, the overvoltages for the longer line are higher than those for the shorter one. This is because of the Ferranti rise effect phenomenon [15]. The rise in the receiving end voltage due to the Ferranti effect can be explained with a voltage divider equation, using the series impedance R'l+joL'l  of the re -circuit and the shunt impedance - — - — at the receiv|/©C7  ing end of the n -circuit. Since R' « coZ,' on high voltage lines, we can ignore the resistance and get: 1 1.  1 •<dC7 1 1.  1 •<dC7  +;'©Z7  1 (o Z'C7 12 2  (3.4) 2  86  Chapter 3. Switching Surge Transients  Or  V  2  V  (3.5)  2  2  AV  2  This shows that the relative voltage drop  is negative, which means a voltage rise, and  that this relative voltage rise is proportional to the square of the line length.  0.005  0.01  0.015  0.02  0.025  Time (s)  Figure 3.31 The effect of line length on the overvoltages in phase A : original line (solid), shorter line (dashed)  Chapter 3. Switching Surge Transients  87  X  \  0  0.005  0 .0 1  0.0 1 5 Time  / ' *•'  0.02  0.02 5  (s)  Figure 3.32 The effect of line length on the overvoltages in phase B : original line (solid), shorter line (dashed)  A*'  0  0.005  0.0 1  f  0.0 1 5 Time  0.02  0.025  (s)  Figure 3.33 The effect of line length on the overvoltages in phase C: original line (solid), shorter line (dashed)  Chapter 3. Switching Surge Transients  88  3.4.8 Closing Angle and Pole Span The closing angles of the three breaker poles are the phase angles of the source side voltages at the instant of electrical closure of the contacts. These angles have a strong influence on the line closing and reclosing overvoltages as they determine the initial conditions for the transients. For transients, when they are not controlled, undesired closing instants of the three poles may occur, but only within the limits of the breaker's pole span. The pole span is the time between the first and the last pole to close. When all the three breaker poles close simultaneously, the overvoltages are smaller than those of random closing. When closing resistors are used, the resistor insertion time should exceed the pole span of the breaker [1].  3.4.9 Statistical Switching Transient voltage and current magnitudes depend upon the instant on the voltage waveform at which the circuit breaker contacts close electrically. A statistical switching case study typically consists of 100 or more separate simulations, each using a different set of circuit breaker closing times. Statistical methods can then be used to process the peak overvoltages from all the simulations.  The switching overvoltages that occur in any specific system arrangement follow a statistical distribution. The distribution function of the amplitude of the switching overvoltages does not behave according to a normal Gausssian distribution. There exists a minimum and a maximum overvoltage magnitude that cannot be exceeded due to technical reasons.  Chapter 3. Switching Surge Transients  89  The procedure for assessing the statistical distribution of overvoltages can be presented as follows: 1. Generate the input data file. 2. Run the case many times with different closing times to get a large enough random sample for the phase voltages. 3. Apply statistical methods to the phase voltages to get their statistical distribution. 4. Determine the protective level of the system considering both reliability and economy. A n extensive statistical analysis for the Jaguara-Taquaril case has been done in [16].  Statistical switching rule: "To design the insulation of the line, run 100 cases or more, with statistical variation of the closing angles and pole spans. Normally, the 2% value on the cumulative frequency distribution curve is used to design overvoltages ". 3.4.10 Derived Practical Rules from the Knowledge Base From the knowledge base presented in the previous sections, several practical rules can be obtained. Some of these derived rules are presented in Table 3.6. These rules could be included in the proposed rule-based systems.  Chapter 3. Switching Surge Transients  90  Table 3.6: Some derived rules from the knowledge base for switching surge transients Parameters  Derived Rules If the maximum frequency in your system isf , then use the simulation step size max  f  Step Size  1  If the step size A t is larger than the travel time t of the shortest line in the network, then the new line model should be usedfor lines with At > t If you want to check the accuracy of the simulation, then divide the used step size by 2 and run the simulation again  Transmission Line Models  If the zero sequence current is small, then use the constant parameter line model If the zero sequence current is high and contains high non-power frequencies, then the frequency dependent line model should be used If you want to have k% shunt compensation for the line, then place a shunt reac-  Shunt Compensation  tor with a positive sequence value of - — = i r o C pos 1  2  /x  at both ends of the  1 0 0  line If you want to simulate trapped charges in the EMTP, then use the override "ini-  Trapped Charges  tial conditions" feature of the EMTP or let the circuit breaker opening action of switches trap a charge before the circuit breakers are closed again If you want to model the feeding network for normal switching operations, then the detailed model of the system must include the part of the network up to the second substations behind that of the operating circuit breaker  Feeding Network  If you want to model the feeding network for line energization and re-energization then line models only up to the first substations are sufficient in most cases If the feeding network is complex, then the resulting overvoltages are typically 10% to 15% less than those with an inductive source If the circuit breaker has one-step closing resistors, then model each pole with  Closing Resistors  two switches, one for the auxiliary contacts with the resistor and one for the main contact To design the insulation of the line, run 100 cases or more, with statistical varia-  Statistical Switching  tion of the closing angles and pole spans. Normally, the 2% value on the cumulative frequency distribution curve is used to design overvoltages  Chapter 3. Switching Surge Transients  91  Also, from the information presented in Figure 3.1 we can derive various rules for the results evaluation process. These rules can be formulated based on the average values, as well as the maximum and minimum values for the overvoltages. For example, i f the overvoltages occur during reclosing without closing resistors, when the system consists of a complex feeding network and no shunt compensation of the transmission line is used, then the maximum overvoltage should not exceed 3.5 p.u. The same scenario can be repeated for different system conditions.  3.5 Summary The following sections have been covered in this chapter: an overview of switching transient overvoltages, the parameters that influence the switching overvoltages, the means for limiting the switching overvoltages, a practical case study of transmission line energization, and modelling suggestions for the simulation of line energizations based on the parameters that influence the switching overvoltages.  Using the knowledge presented in this chapter as a starting point should increase the knowledge of E M T P users about transients phenomena, and how to apply this knowledge to the use of the E M T P for more complex studies. A n understanding of power system transient phenomena is needed before sufficient expertise can be claimed; there is no other alternative for understanding the fundamentals of transient phenomena and what their effects are expected to be, and this is what this chapter is partially trying to answer.  Chapter 3. Switching Surge Transients  92  The next chapter presents a new transmission model for short lines and cables based on one of the rules that was suggested for a knowledge base for switching surges. This rule suggests that i f the travel time is smaller than the step size then the new line model should be used to get proper results.  Chapter 4 Transmission Line Model 4.1 Introduction This chapter presents a new E M T P line model for the representation of short overhead transmission lines and cables [64] [72] [73]. This model overcomes the limitation of using a time step size not larger than the travel time. The interpolation errors inherent in this line model produce a filtering effect for higher frequencies.  For simulating short transmission lines and cables in electromagnetic transients programs of the E M T P type [5], nominal TC -circuits are usually used when the travel time x is less than the time step size At. This TC-circuit approximation is used because the constant parameter line models [4] as well as the frequency dependent line models [61, 62] require that the step size should not be larger than the travel time.  93  Chapter 4. Transmission Line Model  94  In this chapter, a new modelling approach is presented which overcomes the time step size constraint for short lines. This modelling approach was suggested in the previous chapter when the step size A t is larger that the travel time x, which is the case for short lines and cables.  The constant parameter line model will be used to explain the approach, and to keep the derivation simple.  The new line is tested for two case studies. The first one is a case of transmission line energization, with data taken from the Jaguara-Taquaril line tests discussed in the previous chapter [6] [7] [8]. Simulation results for this case show that the new line model gives results for a short line which are close to the constant parameter line model results, while results with a tz circuit show unrealistic high frequency oscillations.  The new transmission line model is also tested for the case of a drive system which involves power electronics devices [80]. In this case, the new line model is used to represent a short cable. The n -circuit and the constant parameter line models would give unrealistic voltage waveforms.  4.2 Transmission Line Models-Background Transmission lines and underground cables are the main transmission links in power systems. Transmission lines usually extend over many kilometers and are affected by a wide variety of phenomena, from short circuits, to switching surges and to lightning discharges. To simulate  Chapter 4. Transmission Line Model  95  these and other related phenomena in a power system simulation program, accurate transmission line models need to be developed. A number of transmission line and underground cables have been developed and successfully implemented in the E M T P . The Power Systems Research Group in the Department of Electrical and Computer Engineering at the University of British Columbia has developed a number of line models for electromagnetic studies in the past twenty years [60] [61] [62] [66] [67].  To introduce the proposed line model properly, the best known and widely used transmission line models in the E M T P are briefly reviewed. A comprehensive review of different transmission lines and their features is presented in [4] and [68].  4.2.1 The 71-Circuit The 7t-circuit is the simplest representation of a transmission line. Here, the line is represented with lumped elements: a series impedance and two shunt admittances for the complete line or for line segments if cascade connections of TC -circuits are used. This model is also used by the Transient Network Analyzer. This model is a good choice for steady-state applications. However, the 7t -circuit is not the best choice for transient solutions because it cannot represent the frequency dependent parameters and one must also accept the unrealistic oscillations caused by the lumped parameters of the circuit even for short lines. The cascade connection of 7t -circuits may still be useful for untransposed lines.  Chapter 4. Transmission Line Model  96  4.2.2 The Constant Parameter Line Model The constant parameter line model was the first line model used in the E M T P [5]. In this line model, the capacitance and the inductance are evenly distributed along the line while the losses are lumped in three places along the line. This line model has a constraint that the step size must be smaller than the travel time.  4.2.3 The Frequency Dependent Line Model The frequency dependent line model is one of the most successful models for considering the frequency dependence of the parameters of the transmission line in the E M T P . This model is very accurate for both single-phase lines and for multi-phase lines.This line model has the same step size constraint as the constant parameter line model.  The line model presented in this chapter overcomes the mentioned step size constraint of the constant parameter and the frequency dependent line models. This is important for short lines as well as for transient stability analysis.  4.3 Transmission Line Model For Long Lines Before introducing the new line model, let us review the lossless line model that is implemented in the E M T P , based on Bergeron's method [9]. Figure 4.1 shows the equivalent circuit from which the model's most important property is immediately clear: Both terminals k and m are galvanically separated. The currents into the two terminals k and m are given by:  97  Chapter 4. Transmission Line Model  G  0  0  G  c  c  v*(0 + «(0  (4.1)  v  where the history vector is known from the currents and voltages of preceding time steps h (t) k  M O  "0  G  0 1  0_  _i q  G  c  c  hi*-*)  (4.2)  and where G is the reciprocal of the surge impedance Z : c  c  G = Jc'/L c  (4.3)  Equation (4.2) shows that the conditions at one end depend on what happened at the other end at travel time x earlier.  As long as the step size A t is less than the travel time x, those conditions at the far end at time (t - x ), which appear at the near end at instant t, can be retrieved from "history" tables.  4.4 The New Line Model For Short Lines The concept of this new line model was suggested in [63]. The model equations were derived and implemented in MicroTran (UBC-version of the EMTP) in co-operation with S. Henschel [64]. The new line model allows a smooth transition from electromagnetic transients phenomena to very slow dynamic phenomena, and vice versa. The use of the new line model for switching between electromagnetic transients and stability simulations with variable step size was described in [64] and [78]. The work here [72] [73] concentrates on using the new line model for electromagnetic transient studies.  98  Chapter 4. Transmission Line Model  ©  >-°  Lit) m'-^ vjt)  (m)  o  G,  Figure 4.1 Lossless line model using Bergeron's method The integration method used in the E M T P is the trapezoidal rule of integration. With this rule, we assume that a variable changes linearly as a straight line between two adjacent points. Therefore, i f two solutions x(t) and x(t- At) were known, they could be linearly interpolated to yield x(t-x)  provided that At > x . The variable x could either be a voltage or a  current. These interpolated values can then be used to compute the history vector in equation (4.2).  The interpolation formula is: x(t-x) where  = ax(t) + bx(t - At)  (4.4)  Chapter 4. Transmission Line Model  By replacing the past values in equation (4.2) with the interpolated values, we can obtain a new model for the lossless line:  1+a  '•*(') I-a  2  >(0  -2a  "v*(0 + h(t) 2 v (t) h (t) 1 +a -2a  m  (4.5)  m  The history vector, whose values are obtained from the previous time step, is equal to: bG  \ ( 0  c  I-a  2  _*»(')_  b I-a  2  v (t-At)  a -1  k  -1 a a -1  i (t-M) k  -1 a_ i (t-At) m  From equation (4.6) we can observe that the conductance matrix also possesses off-diagonal elements, so that the line equations can no longer be solved independently for both ends.  Equations (4.5) and (4.6) are only used if Ar < x ; otherwise the E M T P automatically replaces them with equations (4.1) and (4.2).  The history vector of the new line model requires only values of the previous time step, so that the history memory of this model is extremely short.  The equivalent circuit of this new line model for the single-phase case is shown in Figure 4.2.  100  Chapter 4. Transmission Line Model  2a  ® i  I®  c '-a  CZr-  U  -C  Figure 4.2 Lossless transmission line model  4.5 Interpolation Error Analysis Interpolation with equation (4.4) produces errors which depend on frequency. It is therefore best to show them in the frequency domain. The errors of the new line model are derived here for the open and short-circuit responses, and the results are compared with those of the exact solution. The new line model equations (4.5) and (4.6) can be transformed into the frequency domain as follows, with I and V being phasors:  l+a  2  \-a  +  2  2  where:  -2a  -2a  1 +a V  .  (4.7)  V  .  Chapter 4. Transmission Line Model  101  V I-a  at  +  7  vj  a(t-  At)  (4.8)  ia(t-At)  a -1  k  1  -1 a  I-a'  y^it-At)  a -1 -1 a  e  ij  a(t-At)  After dividing equations (4.7) and (4.8) by el™ , we obtain the phasor equation  kk  km  Y  Y  Y  k  Y  mk  mm  ~v~  k  (4.9)  Ym_  where: -GAa •kk  + 2abe~ ^ ]  (a + 2abe  At , , 2 ~2j(aAt  + b^e  +o e  + 1)  (4.10)  - 1)  2G (a + be- ) jaAt  c  mk ~~  (4.11)  Y  (a + 2aoe  +6 e  - 1)  The exact solution for the lossless line model with constant parameter can be obtained from: -1 cos cox jsincox j sin cox  (4.12)  -1 coscox [ysincox ysincoxj If the receiving end is short circuited, the receiving end voltage equals zero (V  m  short-circuit current ratio is given as:  = 0) and the  Chapter 4. Transmission Line Model  102  Y  (- )  =  k  J  4  mk  13  I  On the other hand, if the receiving end is open-circuited, the receiving end current equals zero {l = 0) and the open-circuit voltage ratio is given as: m  V  Y  b  m _  mk  k  mm  (4.14)  Equations (4.13) and (4.14) represent the short and open-circuit responses of the transmission line model at any given frequency <u .  Figure 4.3 compares the magnitude of the short-circuit response for the exact frequency response (solid line), with that of the new line model (dashed lines from bottom to top), for step sizes A^ equal 1.3 x, 1.6x, 1.9x and 2.2x, respectively. The values were obtained for Z = 100 Q and x= 50  lis.  Figure 4.4 compares the magnitude of the open-circuit response for the exact model (solid line), with that of the new line model (dashed lines from bottom to top), for the same step sizes.  From the results shown in Figure 4.3 and Figure 4.4, it can be seen that the short and opencircuit responses of the new line model show a strong filtering effect, which becomes more emphasized as the simulation step size is increased. In a time domain simulation with At > x, this effect results in averaging of the transient voltage and current oscillations. The results with this filtering effect may come closer to reality. To prove this, comparisons with  103  Chapter 4. Transmission Line Model  frequency dependent line models should be done in future research.  The results obtained in the frequency domain can also be duplicated in the time domain at a given frequency using the E M T P . The comparison between the time domain simulation and the frequency domain results shows that both answers are practically identical. The E M T P data file for the new line model is shown in Table A . 5 in the Appendix D. The time domain simulation for the currents I and I at this point (At = 1.3x and/= 1000 Hz) are shown in m  k  Figure 4.5 and Figure 4.6. From these two figures, we can calculate the short-circuit response for the given point using equation (4.13). The results obtained are practically equal to the L short circuit response that is measured in the frequency domain as — « 0.98 . h The interpolation error analysis for the new line model, as compared with other line models and the exact solution, was implemented in M A T L A B environment and it is presented in Appendix C.  104  Chapter 4. Transmission Line Model  F r e q u e n c y (Hz)  Figure 4.3 The short-circuit ratio  Figure 4.4 The open-circuit ratio  105  Chapter 4. Transmission Line Model  0.03  0.1 9 5  0.1 9 6  0.1 9 7 T i m e ms  0.1 9 8  0.1 9 9  Figure 4.5 The Current I response in the time domain m  i  Time ms  Figure 4.6 The current I response in the time domain k  0.2  Chapter 4. Transmission Line Model  106  4.6 The Lossy Line Model To represent the losses approximately, lumped resistances are inserted at both ends and in the middle of two lossless line sections, as shown in Figure 5. This approach is also used for the polyphase case [64]. The lossy line model was implemented in MicroTran (UBC-version of the EMTP). The connec subroutine for this implementation is presented in Appendix B.  i^R/4 1M. o—WV—of)  ®  ©  R/2 i |  ig. R/4MI  le—VA—of)  lo—W\—0  ©  ®  ©  ®  Figure 4.7 Schematic of a lossy line model  4.7 Case Studies In order to demonstrate the usefulness of the proposed line model, a time domain simulation of transmission line energization and adjustable speed drive cases are used. The results and analyses are presented in this section.  4.7.1 Transmission Line Energization A transmission line energization case is shown in Figure 4.8. The data comes from the Jaguara-Taquaril tests conducted by a Brazilian utility company [6] [7] [8].  To show the performance of the new line model as compared with other E M T P line models, the transmission line is divided into two sections. The longer section is represented by a  Chapter 4. Transmission Line Model  107  constant parameter line model, while the short section is to be represented by different line models, including the constant parameter line model, the TC -circuit and the new line model. The main and auxiliary contacts of the circuit breaker close at times specified in [65] for an unfaulted line energization case, between 7.15 and 15.85 ms. A single-phase to ground fault is assumed to occur in phase A at 10 ms. From the field test results for the case of the unfaulted line energization, we found that the constant parameter line model provides results which come close to the field test results [65]. The performance of the new line model for the case of the faulted line energization is compared with the response of the constant parameter line model.  The response of the constant parameter line model is shown in Figure 4.9. The travel time T of the short line is 4.31 p s. The simulation step size is chosen to be 4 p s, as the constant parameter line model requires that the simulation step size At should not be larger than the travel time x of the shortest line.  Figure 4.10 shows the response produced by the new line model for a step size At slightly larger than the travel time x of 4.31 s p . From Figure 4.10, we can see that the response of the new line model agrees very well with that of the constant parameter line model.  The response of the nominal TC-circuit line model is shown in Figure 4.11. This response is simulated for the same step size as for the new line model. From Figure 4.11, we can observe that the response of the nominal TC -circuit line model does not match the results of the  Chapter 4. Transmission Line Model  108  constant parameter line model. Also, it fails to duplicate the maximum peak overvoltage which are shown for both the new line model and the constant parameter line model. This is because the nominal TC -circuit model is not accurate enough to represent the high frequency transients involved in the switching action.  From these results we can see that the new line model is more accurate than the TC -circuit for the representation of short lines.  JAGUARA  [X]-matrix -,  r  i © ©©  .  TAQUARIL  n  m  Circuit Breaker with Closing Resistors, (R = 400 ohms)  1.2 km  i  396.2 km  • • •  i ]  J  J!  7777777-  777777777-  Thevenin Equivalent Circuit for Generators and Transformers  Shunt Reactor  [X]-matrix  Figure 4.8 Transmission line energization  109  Chapter 4. Transmission Line Model  v[JAGA](1) 0.18  0  10  20  30  40  Time (ms)  Figure 4.9 The constant parameter model response  Figure 4.10 The new line model response  50  Chapter 4. Transmission Line Model  110  v[JAGA](1  Figure 4.11 The pi-circuit line model response 4.7.2 Power Electronics Case Study Power electronics devices are becoming very common in industrial power systems, for example in adjustable speed drives (ASD) which are often found in oil exploitation and mining [65]. A S D ' s are used because they allow a more flexible motor operation, above and below rated speed. ASD's generate harmonics, which are analyzed in this study [80]. The drive system studied is a square wave inverter with 480V output. It has a step-up transformer 480:1350V, with a 135 HP motor rated 950 V . The motor is connected through a 2.5 km long submarine cable. Since the converter is operating at a very low switching frequency, low harmonics are generated. The basic components of this adjustable drive system are shown in Figure 4.12.  Chapter 4. Transmission Line Model  111  The step-up transformer at the inverter is used because the semiconductor switches are, in this type of system, usually of low voltage rating. The power supply was represented by a voltage source behind a reactance. This representation is permissible when the drive system represents a small load compared to the short-circuit level of the supply system. If this is not the case, a frequency-dependent network would have to be used, or a detailed generator model in case of an isolated pumping system. The converter can be divided into three parts: rectifier, D C link, and inverter. The semiconductors in the rectifier are either diodes or thyristors, depending on the inverter type (voltage or current) and on the switching strategy, Pulse Width Modulation (PWM) or Pulse Amplitude Modulation (PAM).  This implies that the input voltage (or current) in the inverter will contain characteristic harmonics of the diode or thyristor bridge, together with the characteristic harmonics generated by the inverter. The DC link has the function of filtering the rectifier output, so as to produce as much as possible a ripple free voltage (or current).  The inverter has switches which are capable of conducting and interrupting the current at predetermined times. They are mostly Insulated Gate Bipolar Transistors (IGBT) with antiparallel diodes. The harmonics on the inverter side are reflected through the D C link to the converter input.  This leads to inter-harmonics, which may coincide with a multiple (or sub-multiple) of the supply frequency during some specific operating frequencies. Harmonic instability can arise when anti-resonances in the supply system coincide with a multiple or sub-multiple of the  Chapter 4. Transmission Line Model  112  resonance in the drive system.  The aforementioned phenomena stress the importance of representing both converter stages (rectifier and inverter). Besides small resistances to account for conduction losses, all semiconductors were treated as ideal. Experience has shown that, for studies of the complete drive system, the modelling with ideal switches is sufficiently accurate in MicroTran, because this version uses the Critical Damping Adjustment (CDA) scheme to eliminate numerical oscillations. Other E M T P versions may require more complicated modelling to dampen numerical oscillations.  Figure 4.13 shows the voltage waveform of the field test recording conducted at the given drive system, at the sending end of the submarine cable between phase A and B. The field test waveform is asymmetric due to grounding problems while measuring the voltage. These measurements were done on an oil platform where fluctuations can occur in the ground voltage [80].  Figure 4.14 shows the simulation results with the new line model used for the representation of the submarine cable. The travel time for the short cable is 18.31 LIS, while the simulation step size is chosen to be 30 (is (At > x). From Figure 4.14 we can observe that the proposed model gives very reasonable answers. The filtering effect for high frequencies seems to be similar to the damping effect caused by skin effect in the actual cable.  Figure 4.15 show the simulation results for the n -circuit line model. This response is  113  Chapter 4. Transmission Line Model  simulated with the same step size of the new line model of 30 p s ( A r > x ) .  Figure 4.16 show the simulation results for the constant parameter line model for a step size of 18 p s ( A r < T ) .  When we compare the field test recording of Figure 4.13 with the responses of the TC -circuit and the constant parameter line models, we can observe that the responses of these two models are unrealistic. This is because the new line model has a filtering effect for high frequencies similar to the damping effect caused by skin effect in the actual cable.The new line model does not have the step size constraint of the constant parameter line mode, which is especially important for short lines and cables.  V,out  Submarine cable  Figure 4.12 The power electronics case  114  Chapter 4. Transmission Line Model  2000  1  1500 1 000  1  1  1  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  — ^ - / |  i  : IT  i  i  i  t  i  500  i  i  0  Ik.  -500  r  i  r i  i i  -1000  i  i  i  i  i  i i i  -1 500  J  -2000 0.124  -  -  i  i  i  i  i i  0.126  0.128  0.13  0.1 32  0.1 34  0.136  0.138  0.14  0.142  Time ms  Figure 4.13 The field test recording for the drive system  2000  I I I  1500  1  _  1  1 1 1  1000 500  1  •—  1  1  0 O >  Y 1  1  -500  L  T  -1000  L  n  1 I \  -1500  .__  pu-  i  -2000  L v .  k u ^ .  _ _ i  0.125  0.13  0.135 Time ms  0.14  Figure 4.14 Simulation results for the new line model  0.145  115  Chapter 4. Transmission Line Model  o  >  -2000  0.125  0.145  Figure 4.15 Simulation results for the TC -circuit line model  Figure 4.16 Simulation results for the constant parameter model  Chapter 4. Transmission Line Model  116  4.8 Summary This chapter describes a new transmission line model for the representation of short transmission lines and cables. This model is an extension of the constant parameter line model of the EMTP. It overcomes the limitation of requiring a time step size not larger than the travel time. This new line model can represent the transient phenomena accurately in the low frequency region. The new line model was tested with two practical case studies. Simulation results show that the new line model may provide more accurate answers for transient studies as compared with the nominal TC -circuit line model as well as the constant parameter line model.  Chapter 5 Conclusions and Future Work 5.1 Overview The E M T P is widely used for simulating fast transient effects in electric power systems. However, using the E M T P and similar programs is not easy. Although the use of the program may be made more user-friendly with customized pre-/post-processors, such as graphical user-interfaces, the difficulty of proper modeling of the target power system remains basically unchanged. This is because of the high level of expertise required for the analysis of a large variety of transient phenomena.  In the preceding chapters, the research objectives of developing an E M T P support system for the simulation and analysis of power system transients were outlined, and the implementation of the proposed prototype intelligent system has been presented in more detail. Also, a  117  Chapter 5. Conclusions and Future Work  118  knowledge base for switching surge overvoltages has been introduced. Finally, a new E M T P line model for representing short transmission lines and cables has been implemented. This line model was developed to overcome the step size constraint of the constant parameter and frequency dependent line models in the EMTP.  The conclusions and recommendations for future work are presented in the following sections.  5.2 Conclusions The main accomplishments of this research are summarized below:  5.2.1 The Prototype Intelligent Support System This dissertation has introduced an intelligent support system that supports the users of the E M T P in studying diverse transient phenomena in electric power systems. The support system assists the users to choose a base case data from a case database that contains various simulation cases as a starting point. When the modifications have been made to the base data to meet the user's particular purpose, the support system checks the validity of the data. Through the validation process the data set cannot only be made more appropriate, but the inexperienced user can learn the reasonable range of parameters and proper usage of the models. The results evaluation process of the support system can give hints to the user about the acceptable range of results obtained from the simulation.  Chapter 5. Conclusions and Future Work  119  5.2.2 Switching Surge Overvoltages This thesis has introduced a knowledge base for switching surge transients. From this knowledge base, some practical rules were derived for switching surge transients. The objective of this part of the thesis was to develop simple and approximate rules for the support system. These practical rules and the modelling suggestions were validated either by simulations or verified by interviews with E M T P experts. The modelling suggestions will help the EMTP user to select the proper model and to gain some insight into the case study being simulated.  5.2.3 New Transmission Line Model This thesis described a new E M T P transmission line model for the representation of short overhead lines and cables. It overcomes the limitation of using a time step size not larger than the travel time. The error analysis for the short and open-circuit responses shows that the new line model has a filtering effect for higher frequencies. In a comparison with actual field test measurements, it could be shown that the new line model is suitable for a reasonable representation of cables, whereas both the TC -circuit and the constant parameter line models produced unrealistic high frequency oscillations.  5.3 Recommendations for Future Work The following are some recommendations for future directions of research activities for the development of a support system for electric power system transients. 1.  The case database should be expanded to include more case data from different power system transient studies.  Chapter 5. Conclusions and Future Work  120  2. The complete scheme of the Case-Based Reasoning (CBR) presented in [39][40] with indexing, case storage and retrieval, could be used to improve the design of the proposed case database. 3. The expanded data validation process should then help the user in selecting the proper models based on more rules derived from the knowledge base. 4. The results evaluation should be expanded to provide the user with more modeling experience in the overall picture of the simulated system. Also, the information presented in Figure 4.1 about overvoltages magnitudes for different system conditions could be for the results evaluation process. 5.  The existing knowledge base should be expanded to include more types of transient case studies. The derived practical rules would be used in the proposed E M T P support system.  6.  The new line model with At > x should be extended to the more accurate frequency dependent line model which has been used extensively for cases with At < x, and from single-phase to multi-phase models.  Bibliography [1] CIGRE Working Group 13-02 Switching Surges Phenomena in E H V Systems, "Switching Overvoltages in E H V and U H V Systems with Special Reference to Closing and Reclosing Transmission Lines," Electra, Vol. 30, pp 70-122, 1973. [2] CIGRE Working Group 13.05, "The Calculation of Switching Surges (I). A Comparison of Transient Network Analyzer Results," Electra, Vol. 19, pp. 67-78, 1971. [3] CIGRE Working Group 33.02, "Guidelines for Representation of Network Elements When Calculating Transients", Paris, 1990. [4] H . W. Dommel, EMTP Theory Book, Microtran Power System Analysis Corporation, Vancouver, B.C., Canada, 1992. [5] H . W. 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Malik, "Expert Systems in Electric Power Systems - A Bibliographical Survey," IEEE Trans, on Power Systems, Vol. 4, No. 4, pp. 1355-1361, October 1989. [37] A. Germond and D. Niebur, "Survey of Knowledge-Based Systems in Power Systems:Europe,", Proceedings of The IEEE, Vol.80, No. 5, pp. 732-744, May 1992. [38] CIGRE Report "Application of Expert Systems to Education and Training of Power System Engineers", TF 38.06.05, Electra, Vol. No. 165, pp. 97-127,April 1996. [39] J. Hseih and C. Liu, " A n Integrated Knowledge- and Algorithm- Based Method for Power Converter Design," IEEE Power Electronics Specialists Conference Record, pp. 13161323, March 1992. [40] J. Hseih and C. Liu, "Intelligent System as a Computer A i d for Power Converter Designs," Engineering Intelligent Systems, Vol. 1, No. 1, pp. 21-30, June 1993.  Biblopgraphy  126  [41] M . Huneault, et al, " A Study of Knowledge Engineering Tools in Power Engineering Applications," IEEE Trans, on Power Systems, Vol. 9, No. 4, pp. 1825-1832, November 1994. [42] J. Martin and S. Oxman, Building Expert Systems- A Tutorial, Prentice Hall, 1988. [43] Young D., et al, "Development of a Practical Expert System for Alarm Processing" IEE Proceedings-C, Vol. 139, No. 5, pp. 437-447, Sept. 1992. [44] Artificial Intelligence Section, CLIPS Reference Guide, CLIPS Version 6.0, Lyndon B. Johnson Space Center, 1993. [45]Knowledge Systems Laboratory, Fuzzy CLIPS User's Guide, Fuzzy CLIPS Version 6.02A, Institute for Information Technology, National Research Council Canada, 1994. [46] W. Mettrey, " A Comparative Evaluation of Expert System Tools", IEEE Transactions Computer Magazine, pp. 19-31, February 1991. [47] W. Mettrey, "Evaluation of A l Languages and Knowledge Engineering Environments", Northern Telecom Report KBS-88-009, Research Triangle Park, N C , 1988. [48] W. Mettrey, " A n Assessment of Tools for Building Large Knowledge-Based Systems", Al Magazine, Vol. 8, No. 4, pp. 81-89, Winter 1987. [49] L. Brownston et al., Programming Expert Systems in OPS5, An Introduction to RuleBased Programming, Addison Wesley, Reading. Mass., 1985. [50] COMDALE/X  user's manual, Comdale Technologies (Canada) Inc., 1986-1993.  [51]T. Niimura, H.W. Dommel, J.R. Marti, "An Intelligent Guide to Support E M T P Simulation", Stockholm Power Tech. Conference, June 1995, Stockholm, Sweden.  Biblopgraphy  127  [52] A. Ibrahim T. Niimura, H.W. Dommel, J.R. Marti, "Case-based Approach for Transient Analysis Modeling Using EMTP", The International Conference on Power Systems Transients, Seattle, Washington, June 1997. [53] F.L Alvarado, et al., EMTP Workbook, Vol. 1-3, EPRI Report EL-4651s, 1986-89. [54] Electromagnetic Transients Program (EMTP), Version 2.0: Revised Application Guide, EPRI Report EL-7321s, 1991. [55] A. Greenwood, Electrical Transients in Power Systems, John Wiley & Sons, 1991. [56] M . El-Hawary, Electric Power Systems, Reston Publishing Company, 1983. [57] A. Ibrahim, M . Salama, "Frequency Dependent Network Equivalents for Electromagnetic Transient Studies", The International Journal of Electrical Power & Energy Systems, Vol. 21, pp. 395-404, August 1999. [58] A. Ibrahim, M . M . A . Salama, "Frequency Dependent Network Equivalent for A C Power System Using the QZ Algorithm, "IEEE Canadian Conference on Electrical and Computer Engineering CCECE/CCGEI'95,  Montreal, Canada, Vol. No. 3/4, 1995, pp. 56- 59.  [59] A . Ibrahim, M . M . A . Salama, "Frequency Dependent Network Equivalent Algorithm for A C Power Systems, "IEEE Canadian Conference on Electrical and Computer Engineering CCECE/CCGEI'96,  Calgary, Canada, Vol. No. 2,1996, pp. 639-642.  [60] F.J. Marcano, Modelling of Transmission Lines Using Idempotent Decomposition, M.S. Thesis, The University of British Columbia, Department of Electrical and Computer Engineering, Vancouver, B C , Canada, August 1996  Biblopgraphy  128  [61] J. Marti, "Accurate Modelling of Frequency-Dependent Transmission Lines in Electromagnetic Transients Simulations," IEEE Trans, on Power Apparatus and Systems, V o l . PAS-101, pp. 147-157, January 1982. [62] F. Castellanos, J. Marti, "Full Frequency-Dependent Phase-Domain Transmission Line Model," IEEE Trans, on Power Systems, Vol. 12, No. 3, pp. 1331-1339, August 1997. [63] W. Meyer, H . Dommel, "Numerical Modelling of Frequency Dependent Transmission Line Parameters in an Electromagnetic Transients Program," IEEE Trans, on Power Apparatus & Systems, Vol. PAS-93, pp. 1401-1409, September/October 1974. [64] S. Henschel, A . I. Ibrahim, H. W. Dommel, "Transmission Line Model for Variable Step size Simulation Algorithms", The International Journal of Electrical Power & Energy Systems, Vol. 21, pp. 191-198, January 1999. [65] A . Lima, R. Stephan, and A Pedroso," Modelling the Electrical Drive System for Oil Exploitation," International Power System Transients Conference, pp. 234-239, June 1997. [66] H. V . Nguyen, Simulation of Lighting Surges on Transmission Lines, Ph.D. Thesis, The University of British Columbia, Department of Electrical and Computer Engineering, Vancouver, B C , Canada, February 1996. [67] L. Marti, Simulation of Electromagnetic Transients in Underground Cables with Frequency Dependent Modal Transformation Matrices, Ph.D. Thesis, The University of British Columbia, Department of Electrical and Computer Engineering, Vancouver, B C , Canada, November 1986.  Biblopgraphy  129  [68] H. W. Dommel and J.R. Marti, "Overhead Transmission Line Models for Steady State and Transient Analysis," The Canadian Electrical Association, Power Planning & Operation Section, March 1985. [69] K. Tanaka, An Introduction to Fuzzy Logic for Practical Applications, Springer-Verlag, 1997. [70] A . Ibrahim, T. Niimura, H . Dommel, "An Intelligent Support System for the Analysis of Electric Power System Transients" The International Conference on Intelligent Systems and Control, June 1-3, 1998, Halifax, Canada. [71] A. Ibrahim, D. Lindenmeyer, T. Niimura, H . Dommel, "An Intelligent Support System for the Results Evaluation Analysis of Electric Power System Transients" IEEE Canadian Conference CCECE/CCGEF98,  Waterloo, Canada, Vol. No. 1, May 24-28,1998.  [72] A. Ibrahim, S. Henschel, H . W. Dommel, T Niimura, "Transmission Line Model For Large Step Size Simulations", The IEEE Canadian Conference CCECE/CCGEF99,  Edm-  onton, Alberta, Canada, May 1999. [73] A . Ibrahim, S. Henschel, A . C. Lima, H. Dommel, T. Niimura, " A New E M T P Line Model For Short Overhead Lines And Cables ", Submitted to the IEEE Transactions on Power Delivery. [74] A. Ibrahim, T. Niimura, H . Dommel, "An Intelligent Support System for the Analysis of Electric Power System Transients", Submitted to The International Journal of Intelligent Systems and Control.  Biblopgraphy  130  [75] J. Mahseredjian and F. Alvarado, "Creating an Electromagnetic Transients Program in Matlab: MatEMTP," IEEE/PES Winter Meeting, Paper 96 W M 098-4 PWRD, January, 1996. [76] O. Nayak, G. Irwin and A . Neufeld, "GUI Enhanced Electromagnetic Transients Simulation Tools" IEEE Computer Applications in Power, Vol. 8, No. 1, pp. 17-22, January 1995. [77] R. S. Rosales, Simulation environment for a real-time power system simulator, M.S. Thesis, The University of British Columbia, Department of Electrical and Computer Engineering, Vancouver, B C , Canada, 1997. [78] Sebastian Henschel, Analysis of Electromagnetic and Electromechanical Power System Transients with Dynamic Phasors, Ph.D. Thesis, The University of British Columbia, Department of Electrical and Computer Engineering, Vancouver, B C , Canada, February 1999. [79] H. W. Dommel, Notes on Power Systems Analysis, E L E C 463 Course Notes, The University of British Columbia, Department of Electrical and Computer Engineering, Vancouver, B C , Canada, 1975. [80] A . Delima, H. Dommel, and R. Stephan, "Modelling Adjustable Speed Drives with Long Feeders", IEEE Transactions on Industrial Electronics, V o l . 47, No. 3, pp. 549-556, June 2000.  Appendix A The Case Database The E M T P support system currently supports the following cases. Some of these cases are from the E M T P workbook [53]: 1. Switching Transients: 1. Overhead Line Energization II. Overhead Line Re-energization with Trapped Charges III. Capacitor Switching IV. Cable Energization V . Transformers and Shunt Reactor Energization VI. Load Energization 2. Fault Analysis:  131  Appendix A. The Case Database  132  I. Single Line-to-Ground Fault of an Overhead Line II. Single Line-to-Ground Fault of an Overhead Line with Frequency Dependence III. Transient Stability Analysis with a Three-Phase Short-Circuit IV. Load Rejection 3. Resonance Analysis: I. Ferro-resonance Analysis  A . l Switching Transients Analysis The switching transients analysis menu of the E M T P support system case database has the following cases which will be described briefly.  A.1.1 Overhead Line Energization The selection of the overhead line models depends on how accurate the transmission lines should be represented in terms of simulation step size. The following cases are included in the overhead line energization sub-menu:  A.l.1.1 Energization of Transposed Line In this configuration shown in Figure A . l , a transposed three-phase transmission line is represented by the constant-parameter line model. The constant-parameter model is a distributed parameter line model without frequency dependence. If the effect of transmission line on overall transient phenomena is the matter of interest, you should model the transmission line by a distributed-parameter line model. On the other hand, the source circuit representations  Appendix A. The Case Database  133  can be simplified. It may be more practical to assume a CB between Busl and the transmission line in the three-phase line energization of this example (There may be other load on the bus).  —•  # BU S I B \  THEVB  THEVC  1  B U ! J1A  THEVA  BUS12A  • |*  / BUS12B  -nr  A/W  BUS13A  rrrv  frr\  BUS13B  • 51C \ / BlLJS12C • Transposed  , BU  Distributed— parameter line  3^ S 3  Figure A . l Transposed transmission line. A.l.1.2 Energization of Untransposed Line If the transmission line is untransposed, the user must supply the modal transformation matrix. If the user has, for example, only positive- and zero-sequence parameters of the target circuit, he or she can use fdLine support program for modal parameters with detailed configuration of towers. This sample power system shown in Figure A.2 includes a long overhead transmission line between B K R 1 and Bus2. Bus 2 is assumed no-load, and the opening circuit breaker BKR1 leaves the unloaded (capacitive) line charged. The voltage sources are represented by Thevenin equivalents. The timing of breaker open or close action will influence the magnitude and polarity of trapped charges and the resultant overvoltage when reclosed.  134  Appendix A. The Case Database  THEVA THEVB  JTTX  rm.  THEVC  SRC1A,  BU$1A  BUS12A  SRCIB^. BUS IB  BUS12B  SRCIC^^U^IC,  BUS12C  —•  ^—i  BUS13A BUS13B  —•rTT  ^ BUS13C  Untransposed -Distributed— parameter line  ^  ^  ^  "3 i 3 S >> > r  I  I  Figure A.2 Untransposed transmission line  A.l.1.3 Reclosing into a Line with Trapped Charges This sample power system shown in Figure A.3 includes a long overhead transmission line between B K R 1 and Bus2. Bus2 is assumed no-load, and the opening circuit breaker BKR1 leaves the unloaded (capacitive) line charged. The voltage sources are represented by Thevenin equivalents. The timing of breaker open or close action will influence the magnitude and polarity of trapped charges and the resultant overvoltage when reclosed.  135  Appendix A. The Case Database  coupled-^ -circuit  Transposed Distributedparameter line  l3US12A BUS12B  r m  r r r >  bUS12C  Transposed _ Distributed- . parameter line  BUS13A  BUS13B r m  r r o  r r r  BUS13C  ^  AAAr AAA-  r r o  Transposed _ Distributed- J parameter line  Figure A.3 Reclosing of overhead lines with trapped charges A. 1.2 Capacitor Switching The main point in capacitor switching is:  a. Charging current upon energization. b. Overvoltages by irregular breaker opening sequences (particularly, when breaker gets stuck). The capacitor switching sub-menu has the following cases:  A.l.2.1 Capacitor Bank De-energization This example shown in Figure A.4 simulates the breaker opening actions when the threephase capacitor bank is energized by a three-phase source. The neutral grounding is considered by a separate capacitor. In this example, breakers are assumed to operate in correct sequence.  Appendix A. The Case Database  136  A.l.2.2 Capacitor Bank Re-energization with a Circuit breaker Stuck This example shown in Figure A.4 simulates the breaker opening actions when the threephase capacitor bank is energized by a three-phase source. The neutral grounding is considered by a separate capacitor. In this example, breaker in phase-b gets stuck. Breaker between BUSB and B A N K B opening is delayed to half-cycle (8.3 ms) after the first zero current.This example simulates the breaker opening actions when the three-phase capacitor bank is energized by a three-phase source.  There is a recommendation on neutral grounding of capacitor banks in ANSI C37.99, pp.2425 (Guideline on protection relaying). Neutral grounding practice of capacitor banks are also summarized in the IEEE Standards. The neutral grounding branch is necessary for the EMTP. Without such branch the program stops due to zero diagonal element. It is reasonable to assume some stray capacitance in phase to ground.  SRCEA  •  BUS Aw  Ww—  SRCEB . . . SRCEC  BUSB BUSC  v  BANKA BANKB BANKC  BANKN JKN^  Figure A.4 Capacitor bank De-energization  Appendix A. The Case Database  137  A.l.2.3 Capacitor Bank De-energization with Transformers This sample network shown in Figure A.5 considers the de-energization of capacitor banks connected in parallel to transformer. Upon opening the breakers, transient recovery voltages across breaker contacts develop and it can result in breaker restrike. Also, the saturation of a transformer can lead to a resonant condition.  In a practice circuit configuration we consider the de-energization of capacitor banks connected in parallel to transformer. Upon opening the breakers, transient recovery voltages across breaker contacts develop more than 2.0 p.u. This can result in breaker restrike. Also, the presence of a transformer can lead to a resonant condition due to transformer saturation.  Source impedance is represented by lumped R - L . The transformer is represented by ideal transformers and saturation is included on the low voltage side by piece-wise linear inductances (Type-93 for MicroTran). Phase-b breaker is assumed stuck for another cycle. Results may differ due to the residual flux in the transformer.  138  Appendix A. The Case Database  B1*KSA BR230A  SOURCA  —•  SOURCB f— • —  /  Y  Y  W \ A , ,—•—  V  BRKSBy, BR230B HRKSCvBR23pC BR115C  S0URCC  -Auto transformer BR115B  I—•—  coupled-^ circuit  BR115A 11 B'RTERA HRTERB I I — 0  NEUTRL I I —  Figure A . 5 Capacitor switching with transformers  A.1.3 Cable Switching Cable modeling in the present MicroTran version of the E M T P is not resolved at this point. The difficulties are mainly due to frequency dependence and variety of connections of multiphase cables. The single-phase modeling of cables given here is only valid for submarine cables where we can neglect mutual coupling. Otherwise, we need to model mutual coupling of cables, TC -models are practically inaccurate except for steady-state calculation. fdLine support program may be used to obtain impedance for single-phase cables but so far there had not been such an attempt. A l l the following examples neglect the effect of frequency on modal parameters and modal transformation matrices.  A. 1.3.1 Three-Phase Cable Energization In this sample circuit shown in Figure A. 6 cables are modeled as single-phase two mode lines (one sheath mode) assuming that all sheaths voltages are the same. This modeling neglects the mutual coupling of each phase. Such assumption is only valid for submarine cables.  Appendix A. The Case Database  A. 1.3.2  139  Three-phase Cable Energization with Crossbonding  In this example shown in Figure A.7 cables are assumed as crossbonded. By crossbonding the sheath of one phase in one cable section is connected to the sheath of a different phase in the next cable section. In the sample model, cables are represented by multi-sectioned TC -circuits.  . . , SRCIA.  THEVA  BUS1A~  rrrxA A / \ / - « — ^ ~  THEVB  rm  Sm  THEV<  . . . SRC1B  BUS12A y^ -MSH12A *" ^ BUSlffiyp SH12B  BUS1B  X  A A A , - . - ^ - . - ^ SRC1C  BUSIC  X  BUS13A  nr  __BUS129 -p_ SH12C T  Single-phase distributedparameteT circuit  BUS13B B U S 1 3 C  Figure A.6 Three-phase cable switching  THEVA THEVB  rrrx  BUS12A r m -•—h  .rm_  ^ B U S l ^ ^ ^ ^ ^ U S l ^ B ^  THEVCl  SRClCx Thevenin impedance ~  —  _Load.  BUS13B  BUS13C BUSIC , BUS12C TTTrans Multi-sectioned formers .coupled-^ circuit A  A  Figure A.7 Cable switching with crossbonding  BUS13A  Appendix A. The Case Database  140  A.1.4 Transformer Switching When an unloaded transformer is energized, there can result large and often distorted inrush current due to nonlinear inductance of transformer core. The major factor of concern are, therefore: i) Current magnitude (typically, 2-5 times that of the rated current); ii) Harmonic component (such as rectified DC wave).  The inrush current will vary with source voltage phase and remnant flux. The transformer switching sub-menu has the following cases:  A. 1.4.1 Transformer and Shunt Reactor Energization In this example shown in Figure A.8, the single-phase transformer with no load is considered. If a transformer is unloaded, the equivalent circuit will be reduced (from the T-circuit) to a single reactor (of the transformer core) as shown in the figure. The inrush current will vary with source voltage phase and remnant flux.  The modeling of transformer (core) may then involve the following properties:  i) Nonlinear reactance of the transformer core;  ii) Hysteretic curve; iii) Remnant flux.  Appendix A. The Case Database  141  The current vs. flux saturation curve inductance can be modeled by piece wise linear nonlinear inductance (Type-93). The current vs. flux curve can be obtained from point-by-point voltage vs. current curve supplied by transformer manufacturer using C O N V E R T subroutine included in the EMTP.  [Further Remarks] (a) Remnant flux is included in Type-93 piece-wise linear inductance as initial value. (b) In a three-phase transformer (bank or three-phase core) the three-phase core should be such modeled as the sum of remnant flux being zero.  (c) A large resistance (typically 10 x 6 Q ) across the nonlinear inductance is designed to serve as hysteresis. Similarly, a large inductance (10 x 20H) may be used to model flux.  (d) There is a conversion program available for saturable transformer data which is present in other versions of EMTP.  Figure A.8 Transformer switching  142  Appendix A. The Case Database  A.1.5 Load Energization The load energization sub-menu includes the following cases:  A.l.5.1 Simple Switching (Single-Phase) This configuration shown in Figure A. 9 represents an energization of a single-phase R-L load from an ideal source through a transmission line represented by a % -circuit. Single-phase representation of an originally three-phase circuit can be inaccurate because of the difference in voltage phases at the moment of CBs closing.  SRC  Busl  Busl2  Busl3  Figure A. 9 Simple switching (single-phase)  A.l.5.2 Simple Switching (Three-Phase) A short transmission line can be represented by coupled % -circuits as shown in Figure A. 10. For fast transient solutions, however, distributed-parameter line models are generally better. You can use the n -models only when the traveling time is less than a reasonable time-step A t.  Appendix A. The Case Database  143  The source voltage should be converted into the line to ground peak voltage. The three-phase R - L load can be calculated by the base k V / M V A (if their values are given in p.u.). Singlephase representation of an originally three-phase circuit can be inaccurate due to the difference in voltage phase of original phases at the moment of CBs closing.  Appendix A. The Case Database  Figure A. 10 Simple switching (three-phase)  Appendix A. The Case Database  145  A.2 Fault Analysis Modeling considerations for fault analysis are summarized as follows:  (a) Source  In most cases Thevinin equivalent of the source is used. Simplification of voltage source into a Thevinin equivalent depends on the time-scale of simulation. Generally, such simplification is valid only for initial 2-3 cycles. For the analysis of longer time-scale, e.g. generator stability analysis, we need a detailed machine model.  (b) Lines  It is advisable to use a frequency-dependent model for an overhead line wherever data are available. Frequency-dependent model for underground cables is not available at present. For the frequency-dependent model input, detailed information of tower geometry is needed.  Using the R E B U I L D option in fdLine support program, we can approximate the tower geometry of a frequency-dependent line. The conductor geometry assumed by R E B U I L D option by fdLine is triangular. The height of conductors is given at the center of the triangle. Also, the program can guess the ground resistivity by default.  (c) Fault  Fault can be represented by a switch between a line and the ground with possible grounding resistance. To specify a fault location (distance from source, etc.), the user can split a line into  Appendix A. The Case Database  146  two portions simply dividing by the distance. Further Remarks:  Fault impedance is normally resistive but nonlinear (voltage-dependent) rather than timevariant. However, the tower footing resistance in lightening surge analysis can be better assumed as time-varying.  A.2.1 Single-Line to-Ground of an Overhead Line In this example shown in Figure A . 11 we consider a single-phase fault at the end of a long transmission line. The 120 mile transmission line is represented by a constant-parameter line model. The modeling does not include the frequency dependence of the line parameters.  A.2.2 Single-Line to-Ground with Frequency Dependence The test system shown in Figure A . 12 is used for B P A field test comparison. The source impedance is modeled by lumped inductance. The transmission line is represented by a frequency-dependent line. Support program fdLine is used to calculate equivalent tower geometry (separate data set is required for the fdLine option).  147  Appendix A. The Case Database  GEN3A  >l|—(  Transposed Distributedparameter line_  coupled-jj circuit  rrrx.A/VV V^GEN3B  -k-  Vrn.  GEN3C •1—  BKR1A • BKR1B •BKR1C -•-t-c  •  BUS2B  •  BUS2C •  THEVA,  rrrx.  ^THEVO-yy^  A  BUS7B \ A  \ BUS7C  coupled-^ circuit  BUS1A -I • BUS1B  Transposed .Distributed- _ parameter line  BUSIC  Figure A. 11 Single-line to-ground fault  SOURCA  —•  _  r Y Y  ^_BRKRA^  SOURCB -• SOURCC  pro.  I SENDA "•—I—I  I RECVA ZH #  BRKRC Frequency_dependent Distributedparameter line  BUS2A  .FAULT  Figure A. 12 Fault analysis with frequency dependence  Y  Appendix A. The Case Database  148  A.2.3 Three-phase Short-Circuit for Transient Stability A three-phase to ground fault case is given in this example as shown in Figure A . 13. The system configuration is given in the single-line diagram (but the actual data are three-phase). The fault is initiated at t=30ms, and CBs at Bus-1 clears the faulted line after 100 ms.  Line-to-ground fault and line-to-line short circuit are considered here.  The phenomena of concern may include: i) Fault current on various paths from the source(s); ii) Voltages during post-fault;  iii) Generator stability. Modeling considerations include:  (a) For line-to-ground fault overhead lines should be modeled by frequency dependent model.  For short-circuit studies, overhead lines can be represented by constant parameter model. If in doubt, it is advisable to use frequency-dependent line model.  (b) Saturation of transformers should be included because the fault voltage is likely to produce harmonics.  149  Appendix A. The Case Database  step-up 13.8kV Transformer  ®-l_39 BUS3  Infinite Bus THEVI  Transmission line Thev. Equiv.  BUS7  230kV  BUS1  X  Transmission line  BUS12  BUS13  BRK1 Fault  Figure A. 13 Transient stability analysis A.2.4  Load Rejection  The problem of load rejection often arises when radially connected generation is switched off at load end. The load rejection generally results in overvoltage by the following reasons:  i) Switching surge from a heavily loaded line to an unloaded line; ii) The Ferranti effect (at the open end);  iii) Generator overspeeding.  The magnetic saturation in generator step-up transformer may result in ferroresonant oscillations. The overvoltage conditions can influence the lightening arrester selection.  In the sample circuit note the following modeling considerations: •  A synchronous machine model is used for a sinusoidal voltage source.  •  If the switching surge and the Ferranti effect are only concerned the source can be modeled by a sinusoidal voltage source behind the subtransient reactance.  15U  Appendix A. The Case Database  •  To represent the saturation of the transformer, a combination of ideal transformers and Type-93 nonlinear inductances are used for MicroTran. Some manual conversion of data may be needed for type-51 synchronous machines from Type-59 in other versions of EMTP.  The single-line diagram of a test system is shown in Figure A . 14 (Actual data is three-phase). A synchronous machine model is used for a sinusoidal voltage source. The step-up transformer with saturation is represented by a combination of ideal transformers and Type-93 nonlinear inductances.  BUSl  BUS6  ©  © Figure A. 14 Load rejection  A.3 Ferro-resonance Analysis In this example shown in Figure A . 15, a three-phase transformer bank is energized in only two phases and the ferro-resonance results from the interactions between the transformer and the capacitance among phases. A transformer is modeled by the T-equivalent with the core represented by nonlinear (piece-wise linear) inductance. Ferro-resonance can occur when a nonlinear inductor resonates with a capacitor, typically  Appendix A. The Case Database  i 51  when a high-voltage transmission line without load can act as a capacitance. Ferro-resonance may exhibit variety of distorted waveforms, typically sub-harmonic resonance.  A transformer is modeled by the T-equivalent with the core represented by nonlinear (piecewise linear) inductance as shown in the figure. The T-equivalent circuit is not valid for multiphase transformer cases because of the difference in positive- and zero-sequence impedances. At least the ideal transformer is needed in multi-phase cases. The support program BCTran can deal with such coupling effect.  BUSl  © Figure A . 15 Ferro-resonance analysis  Appendix B EMTP Connec Subroutine for the New Line Model SUBROUTINE  CONNEC(IPHASE,ISTEP,ZTHEV,X,Y,NONLAD,NONLE,  1 CURR,VOLD,VOPEN,VNONL,ILAST1,VZERO,T,DELTA2,IWHERE,  ICHECK,ITMAX,  2 *) IMPLICIT NONE C  PROCEDURE ARGUMENTS: INTEGER*4 REAL* 8  C  IPHASE,ISTEP,NONLAD,NONLE,ILAST1,IWHERE,ICHECK,ITMAX ZTHEV,X,Y,CURR,VOLD,VOPEN,VNONL,VZERO,T,DELTA2  INTERNAL VARIABLES: INTEGER*4 REAL*8  I,K,L,DEN,MEM,MAXMEM,CNT ZC,TAU,DT,A,FACT,RMAT,ZMAT,HIST,HVEC(IPHASE)  PARAMETER  (MAXMEM=3 0)  DIMENSION  ZTHEV(*),X(*),Y(*),NONLAD(*),NONLE(*),ILAST1(*),CURR(*)  +  VOLD(*),VOPEN(*),VNONL(*),VZERO(*),RMAT(3),ZMAT(3),  +  HIST(2,MAXMEM)  152  153  Appendix B. EMTP Connec Subroutine for the New Line Model  SAVE  CNT,MEM,HIST  C C  CONNEC  C  With t h i s r o u t i n e we hope t o connect another v e r s i o n of a  C  l i n e model t o MICROTRAN. While o t h e r l i n e models  C  r e q u i r e t h a t the time s t e p DT be l e s s than o r e q u a l the  C  t r a v e l i n g time TAU,  C  l i m i t a t i o n . The v e r s i o n implemented  C  s i n g l e phase l i n e s . Purpose of t h i s implementation i s  C  t o g a i n more i n s i g h t of the b e h a v i o r and c h a r a c t e r i s t i c s of  C  t h i s model.  C  A d e s c r i p t i o n of the s u b r o u t i n e arguments o n l y i n c l u d e s those  C  arguments t h a t are a c t u a l l y used. For more d e t a i l s  C  the MICROTRAN Manual  C  F o l l o w i n g i s a d e s c r i p t i o n of v a r i a b l e s used i n t h i s s u b r o u t i n e :  the new  model t r i e s t o overcome t h i s h e r e i n can o n l y handle  (9/1992, S e c t i o n 8.6)  consult  o r Dr. H.W.  Dommel.  C C  A  C  r a t i o of time s t e p DT minus t r a v e l i n g time TAU the time s t e p DT:  C  A = (DT-TAU)/DT  for  DT  >  TAU  C  A = 0.0  for  DT  <=  TAU  C  AUX1  auxiliary  variable.  C  AUX2  auxiliary  variable.  C  AUX3  auxiliary  variable.  C  AUX4  auxiliary  variable.  C  CNT  index counter f o r h i s t o r y memory HIST  C C  and  Every time i t reaches MEM, CURR  (ring  i t resets i t s e l f  storage). t o one.  a v e c t o r c o n t a i n i n g the c u r r e n t s of the p r e v i o u s time  Appendix B. EMTP Connec Subroutine for the New Line Model  154  C  s t e p on i n p u t . T h i s v e c t o r i s m o d i f i e d a t t h e end o f  C  t h i s procedure t o c o n t a i n the new c u r r e n t s o f the  C OUTPUT).  current  time  step  on o u t p u t  (SUBROUTINE INPUT &  C  DELTA2  H a l f t h e i n t e g r a t i o n time step DT (SUBROUTINE INPUT).  C  DT  t h e c u r r e n t time s t e p .  C  FACT  a factor f o r notational  C  HIST  i n t e r n a l memory f o r h i s t o r y v a l u e s . E s p e c i a l l y needed  convenience.  C  i f DT<TAU. A t each time step, the h i s t o r y v a l u e s a r e  C  c a l c u l a t e d from past v o l t a g e s and c u r r e n t and s t o r e d  C  i n t h i s memory. A f t e r a time span TAU they a r e c a l l e d  C  from the memory.  C  HK, HM  h i s t o r y c u r r e n t sources  C  I  auxiliary variable.  C  a t nodes K and M.  IKM,IMK c u r r e n t s o f the p r e v i o u s time s t e p a t nodes K ( f l o w i n g  C  from K t o M) and M ( f l o w i n g i n the o p p o s i t e  direction).  C  K  auxiliary variable.  C  MAXMEM  maximum p o s s i b l e number o f memorable h i s t o r y v a l u e s .  C  MEM  number o f used memory MEM <= MAXMEM.  C  RMAT  m a t r i x c o n t a i n i n g the l i n e impedance. Hence, i t i s the  C  i n v e r s e o f the l i n e admittance m a t r i x .  C  scheme i s e x p l a i n e d under ZTHEV.  I t s storage  C  VK, VM  v o l t a g e s o f the p r e v i o u s time s t e p a t nodes K and M.  C  VOLD  a v e c t o r c o n t a i n i n g the v o l t a g e s o f the p r e v i o u s  C C  step VOPEN  C C  (SUBROUTINE INPUT).  a v e c t o r c o n t a i n i n g the open c i r c u i t v o l t a g e s o f the e x t e r n a l network  X, Y  time  (SUBROUTINE INPUT).  parameter v e c t o r . X ( l ) c o n t a i n s t h e c h a r a c t e r i s t i c  Appendix B. EMTP Connec Subroutine for the New Line Model  C  l i n e impedance  C  time TAU (SUBROUTINE  C  ZC  C  ZMAT  C  characteristic  155  ZC, and Y ( l ) c o n t a i n s t h e t r a v e l i n g INPUT).  impedance:  ZC = s q r t ( L / C )  m a t r i x c o n t a i n i n g t h e sum o f t h e l i n e impedance m a t r i x RMAT and the Thevenin impedance  matrix of the external  C  network ZTHEV. A f t e r t h e s u b r o u t i n e c a l l o f REDUCE  C  the m a t r i x w i l l c o n t a i n t h e n e g a t i v e i n v e r s e o f i t s  C  p r e v i o u s c o n t e n t . I t s s t o r a g e scheme i s i d e n t i c a l  C  t o t h e one o f ZTHEV.  C  ZTHEV  m a t r i x c o n t a i n i n g the Thevenin e q u i v a l e n t impedance o f  C  t h e e x t e r n a l network  (SUBROUTINE INPUT).  C  i t i s a 2x2 m a t r i x s t o r e d such t h a t  In t h i s case  C  ZTHEV(1) = element[1,1]  C  ZTHEV(2) = element[1,2] = element[2,1]  C  ZTHEV(3) = element[2,2]  C  ZTHEV(4) = element[1,3]  C  ZTHEV(5) = element[2,3]  C  ZTHEV(6) = element[3,3]  C  ZTHEV(7) = element[1,4]  C  ZTHEV(8) = element[2,4]  C  ZTHEV(9) = element[3,4]  C  ZTHEV(10)= element[4,4]  ZC=X(1) TAU=Y(1) DT=2.0D0*DELTA2 A=0.ODO  Appendix B. EMTP Connec Subroutine for the New Line Model  IF  (DT.GT.TAU)  156  A=(DT-TAU)/DT  FACT=ZC/(A**2-l.ODO) C  Initialization IF  o f h i s t o r y memory (zero i n i t i a l  conditions only):  (ISTEP.EQ.l) THEN MEM=1+INT(TAU/DT) CNT=0 IF  (MEM.GT.MAXMEM) THEN PRINT*, "CONNEC: Not enough h i s t o r y memory." PRINT*, " STOP "PROGRAM  Use a b i g g e r  time  step."  TERMINATED"  END IF DO 1=1,MEM DO K=l,IPHASE HIST(K,I)=0.ODO END DO END DO END IF C  RMAT i s the i n v e r s e admittance m a t r i x : RMAT(1)=-(A**2+l.ODO)*FACT RMAT(2)=-2.0D0*A*FACT RMAT(3)=RMAT(1)  C  We now b u i l d t h e combined impedance DO 1=1,(IPHASE**2+IPHASE)/2 ZMAT(I)=ZTHEV(I) END DO ZMAT(1)=RMAT(1)+ ZMAT(1) ZMAT(2)=RMAT(2)+ZMAT(2)  ZMAT=RMAT+ZTHEVenin:  157  Appendix B. EMTP Connec Subroutine for the New Line Model  ZMAT(3)=RMAT(3)+ZMAT(3) ZMAT(6)=RMAT(1)+ZMAT(6) ZMAT(9)=RMAT(2)+ZMAT(9) ZMAT(10)=RMAT(3)+ZMAT (10) ZMAT(15)=RMAT(1)+ZMAT(15) ZMAT(20)=RMAT(2)+ZMAT(20) ZMAT(21)=RMAT(3)+ZMAT(21) C  The next command s h o u l d read ZMAT and r e p l a c e i t by i t s n e g a t i v e i n v e r s e : CALL  REDUCT(ZMAT,21,0)  C  From here on ZMAT c o n t a i n s  -(ZMAT) (-1).  C  C a l c u l a t e t h e h i s t o r y v a l u e s from q u a n t i t i e s o f t h e p r e v i o u s s t e p and  C  s t o r e them i n t h e h i s t o r y memory. The q u a n t i t i e s o f t h e l a s t s t e p a r e :  A  I=l+MOD(CNT-1+MEM,MEM) DEN=A+1.ODO HIST(1,I)=(A/ZC*VOLD(1)-1.0D0/ZC*VOLD(2)+A*CURR(1)-CURR(2))/DEN HIST(2,I)=(-1.0D0/ZC*VOLD(1)+A/ZC*VOLD(2)-CURR(l)+A*CURR(2))/DEN HIST(3, I) = (A/ZC*VOLD(3)-1.0D0/ZC*VOLD(4)+A*CURR(3)  -CURR(4))/DEN  HIST(4,I)=(-1.ODO/ZC*VOLD(3)+A/ZC*VOLD(4)-CURR(3)+A*CURR(4))/DEN HIST(5,I)=(A/ZC*VOLD(5)-1.0D0/ZC*VOLD(6)+A*CURR(5)-CURR(6))/DEN HIST(6,I)=(-1.0D0/ZC*VOLD(5)+A/ZC*VOLD(6)-CURR(5)+A*CURR(6))/DEN C  Get t h e h i s t o r y v a l u e s f o r t h e c u r r e n t s t e p from t h e h i s t o r y memory.  C  I f t h e memory c o n t a i n s more than one h i s t o r y v a l u e , use i n t e r p o l a t i o n : IF  (MEM.GT.l) THEN 1=1+MOD(CNT+MEM,MEM) K=1+MOD(CNT+1+MEM,MEM) DO L=l,IPHASE HVEC(L)=HIST(L,I)+(HIST(L,K)-HIST(L,I))*(REAL(MEM)*DT-TAU)/DT  Appendix B. EMTP Connec Subroutine for the New Line Model  15 8  CURR(L)=VOPEN(L) END DO ELSE 1=1+MOD(CNT+MEM,MEM) DO L=l,IPHASE HVEC(L)=HIST(L, I) CURR(L)=VOPEN(L) END DO END I F CNT=I C  C a l c u l a t e t h e new c u r r e n t s : CURR = YMAT*VOPEN + YMAT*RMAT*H HVEC(1)=RMAT(1)*HVEC(1)+RMAT(2)*HVEC(2) HVEC(2)=RMAT(2)*HVEC(1)+RMAT(3)*HVEC(2) HVEC(3)=RMAT(1)*HVEC(3)+RMAT(2)*HVEC(4) HVEC(4)=RMAT(2)*HVEC(3)+RMAT(3)*HVEC(4) HVEC(5)=RMAT(1)*HVEC(5)+RMAT(2)*HVEC(6) HVEC(6)=RMAT(2)*HVEC(5)+RMAT(3)*HVEC(6) CALL TIMES(IPHASE,-ZMAT,HVEC) CALL TIMES(IPHASE,-ZMAT,CURR) DO L=l,IPHASE CURR(L)=CURR(L)+HVEC(L) END DO RETURN END SUBROUTINE CONNEC  c  C C  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  M u l t i p l i c a t i o n of a matrix with a vector:  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  =  :  =  c  C C  Appendix B. EMTP Connec Subroutine for the New Line Model  SUBROUTINE TIMES(IPHASE,MAT,VIN) real*8  VIN(IPHASE),VOUT(IPHASE),MAT((IPHASE**2+IPHASE)/2)  INTEGER I,K,M,IPHASE K=l M=l DO 1=1,IPHASE VOUT(I)=0.0D0 END DO DO 1=1,(IPHASE**2+IPHASE)/2 IF  (K.EQ.M) THEN VOUT(K)=VOUT(K)+MAT(I)*VIN(K) M=M+1 K=l  ELSE VOUT(K) =VOUT(K) +MAT(I) *VIN (M) VOUT(M) =VOUT(M) +MAT(I) *VIN(K) K=K+1 END IF END DO DO 1=1,IPHASE VIN(I)=VOUT(I) END DO END SUBROUTINE TIMES  159  Appendix C Interpolation Error Analysis %  This error analysis  compares t h r e e d i f f e r e n t l o s s l e s s  %  t r a n s m i s s i o n l i n e m o d e l s i n t h e f r e q u e n c y d o m a i n f r o m 0.001  %  t o 10000 Hz.  function  ret=analysis(TimeStep,StepsPerPeriod,Charlmp,TravelTime)  clc; c l g ; if  (exist('Charlmp') &  exist('TravelTime')),  Zc=CharImp; Tau=TravelTime; else, Zc=100; Tau=0.00005; end; logflag=0;  % use l o g a r i t h m i c  frequency  160  scale.  161  Appendix C. Interpolation Error Analysis  f p r i n t f ( 1 , HARMONIC A N A L Y S I S OF \n' ) ; 1  L O S S L E S S TRANSMISSION L I N E MODELS  ret=l; j=sqrt(-1); ToDeg=180/pi; Huge=l.0E20;  StepsPerDecade=50; fmin=100.; fmax=10000.0; dlogf=l/StepsPerDecade; decades=loglO(fmax)-loglO(fmin); df=(fmax-fmin)/(l+decades*StepsPerDecade) ; 8 - * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ o  ** %  EXACT LOSSLESS L I N E MODEL  9.******************************************** o  k=0; f=fmin; while  (f>=fmin & f<=fmax),  w=2*pi*f; Ad(l,l)=cos(w*Tau) ; Ad(1,2)=-1; Ad(2,1)=-1; Ad(2,2)=cos(w*Tau) ;  Appendix C. Interpolation Error Analysis  D=Zc*j*sin(w*Tau); Adl=Ad/D;  % Open C i r c u i t  Gain,  S h o r t - C i r c u i t Susceptance  and Reactance  k=k+l; G(k, 1 ) = - A d l ( 2 , 1 ) / A d l ( 2 , 2 ) ; Z(k,1)=Adl(1,1)/Adl(2,1);  grf (l,k)=f; grf(2,k)=abs(G(k,l)); if  (logflag),  g r f ( 2 , k ) = 2 0 * l o g l 0 ( a b s ( G ( k , 1 ) ) ) ; end;  %grf(3,k)=angle(G(k,1))*ToDeg; grf (4,k)=abs(Z(k,l) ) ; if  (logflag),  g r f ( 4 , k ) = 2 0 * l o g l 0 ( a b s ( Z ( k , 1 ) ) ) ; end;  grf(5,k)=angle(Z(k,1))*ToDeg;  if  (logflag), logf=loglO(f) ; newf=logf+dlogf ; f=10^(newf);  else, f=f+df; end; end;  163  Appendix C. Interpolation Error Analysis  %disp('Done. Press any key t o c o n t i n u e . ' ) ; pause;  3 . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * o  ** %  60-Hz STEADY-STATE MODEL  9-****************************************** o  ** k=0; f=fmin; w=2*pi*60; Ad(l,l)=cos(w*Tau); Ad(1,2)=-1; Ad(2,1)=-1; Ad(2,2)=cos(w*Tau); D=Zc*j*sin(w*Tau); Adl=Ad/D;  while  (f>=fmin & f<=fmax),  % Open C i r c u i t  Gain,  Short-Circuit  k=k+l; G(k,3)=-Adl(2,1)/Adl(2,2); Z ( k , 3 ) = A d l ( 1 , 1 ) / A d l ( 2 , 1) ; grf (l,k)=f; g r f ( 1 4 , k ) = a b s ( G ( k , 3) ) ;  Susceptance and Reactance  164  Appendix C. Interpolation Error Analysis  if  (logflag),  g r f ( 1 4 , k ) = 2 0 * l o g l 0 ( a b s ( G ( k , 3 ) ) ) ; end;  grf(15, k)=angle(G(k,3))*ToDeg; grf(16, k)=abs(Z(k, 3 ) ) ; if  (logflag),  g r f ( 1 6 , k ) = 2 0 * l o g l 0 ( a b s ( Z ( k , 3 ) ) ) ; end;  grf(17,k)=angle(Z(k,3))*ToDeg;  if  (logflag), logf=loglO(f) ; newf=logf+dlogf ; f=lCT(newf);  else, f=f+df; end; end;  %disp('Done. Press  %  any key t o c o n t i n u e . ' ) ;  pause;  NOMINAL P I - C I R C U I T MODEL  o  ** k=0; f=fmin; while  (f>=fmin & f<=fmax),  w=2*pi*f; Ad(l,1)=1-0.5*(w*Tau)"2;  Appendix C. Interpolation Error Analysis  Ad(1,2)=-1; Ad(2,1)=-1; Ad(2,2)=1-0.5*(w*Tau)^2; D=Zc*j *w*Tau; Adl=Ad/D;  Open C i r c u i t  Gain, S h o r t - C i r c u i t Susceptance and Reactance  k=k+l; G(k,4)=-Adl{2;1)/Adl(2,2); Z(k,4)=Adl(1,1)/Adl(2,1);  grf(22,k)=abs(G(k,4)); if  (logflag),  g r f ( 2 2 , k ) = 2 0 * l o g l 0 ( a b s ( G ( k , 4 ) ) ) ; end;  grf(23,k)=angle(G(k,4))*ToDeg; grf(24,k)=abs(Z(k,4)); if  (logflag),  g r f ( 2 4 , k ) = 2 0 * l o g l 0 ( a b s ( Z ( k , 4 ) ) ) ; end;  grf(25,k)=angle(Z(k,4))*ToDeg;  if  (logflag), logf=logl0(f);  newf=logf+dlogf ; f=10"(newf); else, f=f+df;  Appendix C. Interpolation Error Analysis  166  end; end; % d i s p ( ' D o n e . P r e s s any k e y t o c o n t i n u e . ' ) ; p a u s e ;  ** %  NEW  TRANSMISSION L I N E MODEL  if  ( e x i s t ( ' S t e p s P e r P e r i o d ' ) = = 0 ) , StepsPerPeriod=2; end;  if  (exist('TimeStep')==0),  TimeStep=0; end;  StepsPerPeriod=max(2,StepsPerPeriod);  % Nyquist  Criterion  flim=l/(StepsPerPeriod*Tau); if  (TimeStep>0), f l i m = m i n ( f l i m , 1 / ( S t e p s P e r P e r i o d * T i m e S t e p ) ) ;  lim(l,l:2)=[flim,flim]; 1 i m ( 2 , 1 : 2 ) = [-Huge, Huge ] ; fixed=[1.3; figure; for  1.6; 1.9; 2 . 2 ] ;  hold;  ii=l:4  k=0;  nlim=0;  f=fmin; Dt=TimeStep; while  (f>=fmin & f<=fmax),  end;  Appendix C. Interpolation Error Analysis  if  (nlim==0 & f > f l i m ) ,  nlim=k; end;  if  (TimeStep==0), T = l / f ;  D t = f i x e d ( i i ) * T a u ; end;  w=2*pi*f; a=(Dt-Tau)/Dt; b=l-a; Ad(l,1)=-(a~2+2*exp(-j*w*Tau)*a*b+exp(-2*j*w*Tau)*b"2+l); Ad(l,2)=2*(a+b*exp(-j*w*Tau)); Ad(2,1)=2*(a+b*exp(-j*w*Tau)); Ad(2,2)=-(a 2+2*exp(-j*w*Tau)*a*b+exp(-2*j*w*Tau)*b^2+l); A  D=Zc*(a"2+2*exp(-j*w*Tau)*a*b-l+exp(-2*j*w*Tau)*b^2); Adl=Ad/D; % Open C i r c u i t  Gain,  S h o r t - C i r c u i t Susceptance and Reactance  k=k+l; G(k,2)=-Adl(2,1)/Adl(2,2); Z(k,2)=Adl(1,1)/Adl(2,1); % Absolute  Values:  g r f (6,k)=abs(G(k,2) ) ; unitl='p.u.'; if  (logflag),  g r f ( 6 , k ) = 2 0 * l o g l 0 ( a b s ( G ( k , 2 ) ) ) ; u n i t l = ' d B ' ; end;  grf(7,k)=angle(G(k,2))*ToDeg; grf(8,k)=abs(Z(k,2)); unit2='p.u.'; if  (logflag),  g r f ( 8 , k ) = 2 0 * l o g l 0 ( a b s ( Z ( k , 2 ) ) ) ; unit2='dB'; end;  grf(9,k)=angle(Z(k,2))*ToDeg; % Absolute Deviation:  Appendix C. Interpolation Error Analysis  DG1=(G(k 2 ) - G ( k , l ) ) ; % / G ( k , l ) DZ1= (Z (k 2) - Z ( k , l ) ) ; % / Z ( k , l ) DG2=(G(k 3) - G ( k , 1 ) ) ; % / G ( k , 1 ) DZ2= (Z (k 3) - Z ( k , l ) ) ; % / Z ( k , l ) DG3=(G(k 4) - G ( k , 1 ) ) ; % / G ( k , 1 ) DZ3= (Z (k 4 ) - Z ( k , l ) ) ; % / Z ( k , l )  g r f ( 1 0 , k =abs(DG1); g r f ( 1 1 , k =angle(DG1)*ToDeg; grf(12,k =abs(DZl);  •  g r f ( 1 3 , k)=angle(DZ1)*ToDeg; grf(18,k)=abs(DG2); grf(19,k)=angle(DG2)*ToDeg; grf(20,k)=abs(DZ2); grf(21,k)=angle(DZ2)*ToDeg; grf(26,k)=abs(DG3); grf(27,k)=angle(DG3)*ToDeg; grf(28,k)=abs(DZ3); grf(29,k)=angle(DZ3)*ToDeg; if  (logflag), logf=logl0(f); newf=logf+dlogf; f=10 (newf); A  else, f=f+df;  Appendix C. Interpolation Error Analysis  end; end; if  (nlim==0  & flim>=fmax),  fprintf(1,'\nPress  nlim=k;  end;  nlim=max(nlim,1);  any  key  to  continue.\n );  any  key  to  continue.\n');  1  pause; fprintf(1,'\nPress pause;  av=0; for  s2=0;  maxpk=-Huge;  minpk=Huge;  i=l:size(grf,2), maxpk=max([maxpk,grf(2,i),grf(6,i),grf(14,i),grf(22,i)]); minpk=min([minpk,grf(2,i),grf(6,i),grf(14,  i),grf(22,i)]);  av=av+(grf(2,i)+grf(6,i)+grf(14,i)+grf(22,i))/  (4*size(grf,2));  end; for  i=l:size(grf,2), s2=s2+((av-grf(2,i))~2+(av-grf(6,i)) 2 A  ...  +(av-grf(14,i))~2+(av-grf(22,i)) 2)/(4*size(grf,2)); A  end; s=sqrt(s2); up=av+s; lo=av-s;  figure(1); subplot (2,1,1) ; semilogx(grf(1,:),grf(2,:),'y-',  ...  Appendix C. Interpolation Error Analysis  g r f (1, : ) , g r f (6, : ) , ' c — ' , . . . lim(l, :),lim(2, :),'w-.'); axis([fmin,fmax,lo,up]); %  v=axis;  v(1:2)=[fmin,fmax];  title('Open-Circuit  axis(v);  (G=Vm/Vk w i t h  lm=0)');  ylabel(unitl); subplot(2,1,2); s e m i l o g x ( g r f (1, : ) , g r f ( 3 , : ) ,  1  y-', ...  g r f (1, : ) , g r f (7, : ) , • c — ' , . . . g r f (1, : ) , g r f (15, : ) , ' g . ' , . . . grf(1,:),grf(23,:),'r:',... lim(l,:),lim(2,:),'b-.'); v=axis;  v=[fmin,fmax,-190,190];  axis(v);  ylabel('Degrees'); xlabel(  av=0; for  1  s2=0;  Frequency  [Hz] ' ) ;  maxpk=-Huge;  minpk=Huge;  i=l:size(grf,2), maxpk=max([maxpk,grf(4,i),grf(8,i),grf(16,i),grf(24,i)]); minpk=min([minpk,grf(4,i),grf(8,i),grf(16,i),grf(24,i)]); a v = a v + ( g r f ( 4 , i ) + g r f ( 8 , i ) - i - g r f ( 1 6 , i ) + g r f (24 , i ) ) / ( 4 * s i z e ( g r f , 2) ) ;  end; for  i=l:size(grf,2), s2=s2+((av-grf(4,i)) 2+(av-grf(8,i)) A  A  2  +(av-grf(16,i)) 2+(av-grf(24,i)) 2)/ A  A  ... (4 * s i z e  (grf,2));  Appendix C. Interpolation Error Analysis  end;  s=sqrt(s2) ; up=av+s; lo=av-s;  figure(2); subplot(2,1,1); s e m i l o g x ( g r f ( 1 , : ) , g r f ( 4 , :) , 'y-' , . . . g r f (1, : ) , g r f (8, : ) , ' c — ' , . . . lim(l,:),lim(2,:),'w-.'); axis([fmin,fmax,lo,up]);  % f o r p.u.  %  axis([fmin,fmax,-150,50]);  % f o r dB  %  v=axis; v(1:2)=[fmin,fmax];  axis(v);  title('Short-Circuit  (Z=Im/Ik w i t h Vm=0)')  ylabel(unit2); subplot(2,1,2); semilogx(grf(1,:),grf(2,:), y-', 1  ...  g r f (1, : ) , g r f (6, : ) , ' c — ' , . . . lim(l,:),lim(2,:),'w-.'); axis([fmin,fmax,lo,up]); %  v=axis; v(1:2)=[fmin,fmax]; title('Open-Circuit ylabel(unitl);  f i g u r e (3) ; subplot(2,1,1);  axis(v);  (G=Vm/Vk w i t h  lm=0)');  Appendix C. Interpolation Error Analysis  semilogx(grf(1,1:nlim),grf(10,1:nlim),'c—',... grf(1,1:nlim),grf(18,1:nlim),'w.',... grf(1,1:nlim),grf(2 6,1:nlim),'r:'); v=axis; v(1:2)=[fmin,flim]; title('Deviations unit3(1:9)='DG  axis(v);  from t h e Exact S o l u t i o n  (Absolute  [p.u.]';  ylabel(unit3); subplot(2,1,2); semilogx(grf(1,1:nlim),grf(12,1:nlim),'c--',... grf(1,1:nlim),grf(20,1:nlim),'w.',... grf(1,l:nlim),grf(28,l:nlim),'r:'); v=axis; v(1:2)=[fmin,flim]; unit4(1:9)='DZ  [p.u.]';  ylabel(unit4); xlabel('Frequency  [Hz]');  axis(v);  Values)'  Appendix D Input & Output Data Files for EMTP Table D.l :Data input file for the switching surge case stu< * File  "JAGUARA.DAT".  JAGUARA TAQUARIL LINE ENERGIZATION w i t h CP LINE 50.000e-6  60.  .025 0  1S1A  JAGTA  77.65  2S1B  JAGTB  -21.95  77.65  3S1C  JAGTC  -21.95  -21.95  1JAGA 2JAGB  -461.  3JAGC  -461.  C The c o n s t a n t p a r a m e t e r l i n e  1666. -461.  TAQA  .5178 2.0385.01288247.36  -2JAGB  TAQB  .055 0.603  -3JAGC  TAQC  $  End o f l e v e l  $  .01899247.36  1: L i n e a r and n o n l i n e a r e l e m e n t s  = = = = = = = = = = =  JAGTA JAGA  0 0084  1. 0  400 .  JAGTB JAGB  0 0071  1. 0  400 .  JAGTC JAGC  0 0081  1 .0  400.  JAGTA JAGA  0 0158  1 .0  JAGTB JAGB  0 0144  1. 0  JAGTC JAGC  0 0151  1. 0  = = =  End of  level 2  1666.  model  -1JAGA  = =  77.65  1666.  S w i t c h e s a n d p i e c e w i =e l i n e a r  elements  14S1A  -1 0  60 .0  90.  -1 0  14S1B  -1 0  60 .0  -30 .  -1 0  14S1C  -1 0  60. 0  210 .  -1 0  173  Appendix D. Input & Output Data Files for EMTP  174  Table D.2:0utput file for switching surge case study M i c r o T r a n v2.08-32 Date: 11/10/97 Time: 14:28:31 (C) C o p y r i g h t M i c r o t r a n Power System A n a l y s i s C o r p o r a t i o n , 1985 t o 1996. (C) C o p y r i g h t The U n i v e r s i t y o f B r i t i s h Columbia, 1979 t o 1995. A l l Rights Reserved. Input f i l e : j a g u a r a . d a t Output f i l e : jaguara.OUT Plot f i l e : jaguara.PLO JAGUARA  TAQUARIL LINE ENERGIZATION  DELTA-T=5.OOOOOOE-05 T-MAX=2.500000E-02 ISHORT=0 ISWITCH=0 IOSCIL=0 IFREE=0  IFLUX=0 ISMOOTH= 0 EPSILON=l.OOOE-08  PULSE=0.000E+00  (R IN OHM, X IN OHM FOR 60.0 HZ, C IN MICROFARAD) RECORD OF INPUT - BRANCH DATA S1A JAGTA 1 0.000E+00 7.7S5E+01 O.OOOE+00 SIB JAGTB 2 0.OOOE+00-2.195E+01 0.000E+00 O.O00E+O0 7.765E+01 0.000E+00 SIC JAGTC 3 0.000E+00-2.195E+01 0.000E+00 0.000E+00-2.195E+01 0.000E+00 0.000E h00 7.765E+01 0.000E+00 JAGA 1 0.000E+00 1.666E+03 0.000E+00 JAGB 2 O.OOOE+00-4.610E+02 0.000E+00 0.000E+00 1.666E+03 0.000E+00 JAGC 3 0.000E+00-4.610E+02 0.000E+00 0.000E+00-4.610E+02 0.000E+00 0.000E +oo i.eesE+03 O.OOOE+OO -1 JAGA TAQA 5.178E-01 2.038E+00 1.288E-02 2.474E+02 0 0 Zc= 647.94 Tau=2. 06432E-03 -2 JAGB TAQB 5.500E-02 6.030E-01 1.899E-02 2.474E+02 0 0 Zc= 290.22 Tau=l. 36328E-03 -3 JAGC TAQC 4.0000E+02 SWT JAGTA JAGA 0.0000E+00 0.0000E+00 8.4000E-03 1.0000E+00 4.0000E+02 SWT JAGTB JAGB 0.0000E+00 0.0000E+00 7.1000E-03 1.0000E+00 4.0000E+02 SWT JAGTC JAGC 0.0000E+00 0.0000E+00 8.1000E-03 1.0000E+00 O.O000E+O0 SWT JAGTA JAGA 0.0000E+00 O.OOOOE+OO 1.5800E-02 1.0000E+00 SWT JAGTB JAGB 0.0000E+00 O.OOOOE+00 0.000OE+00 1.4400E-02 1.0000E+00 SWT JAGTC JAGC 1.5100E-02 1.0000E+00 0.0000E+00 0.0000E+00 O.00OOE+00 RECORD OF INPUT - SOURCE DATA 14 S1A 0 -1.00000E+00 6.00000E+01 9.00000E+01 1.00000E+75 14 SIB 0 -1.00000E+00 6.00000E+01 -3.00000E+01 1.00000E+75 14 SIC 0 -1.00000E+00 6.00000E+01 2.10000E+02 1.00000E+75  O.OOOOOE+00  0.00000E+00  -1.00000E+00  0.00000E+00  0.00000E+00  -1.OOOO0E+00  0.O0000E+OO  0.00000E+00  -1.00000E+00  STEADY-STATE CALCULATIONS COMPLETE. TRIANGULAR MATRIX WITHOUT SWITCH-NODES HAS 6 ELEMENTS RESULTS SAVED ON F I L E FOR PLOTTING. PLOTS WILL USE EVERY FIRST 6 RESULTS ARE NODE VOLTAGES NEXT 0 RESULTS ARE BRANCH VOLTAGES NEXT 0 RESULTS ARE CURRENTS FINAL 0 RESULTS ARE SYNCHRONOUS MACHINE VARIABLES STEP TIME JAGA JAGB JAGC TAQA SWITCH JAGTB SWITCH JAGTC SWITCH JAGTA SWITCH JAGTB SWITCH JAGTC SWITCH JAGTA . MAGNITUDES  TO JAGB TO JAGC TO JAGA TO JAGB TO JAGC TO JAGA 1.37704E+00  AT T= CLOSES CLOSES AT T= CLOSES AT T= CLOSES AT T= CLOSES AT T= CLOSES AT T= 1.57055E+00  7 10000E-03 8 10000E-03 8 .40000E-03 1 .44000E-02 1 .51000E-02 1 .58000E-02 1. 52643E+00  1 CALCULATED POINTS ONLY  TAQB  TAQC  2 .24479E+00  Appendix D. Input & Output Data Files for  175  EMTP  Table D.3:The fd Data input file for Jaguara case study * FD DATA FILE FOR JAGUARA CASE line-model  BALANCED  .1  10  8  METRIC 1 3333 066998  4  30 38  -8.5  22 91  8.31  2  457 2  0  2 3333 066998  4  30 38  0. 0  22 91  8.31  2  457 2  0  3 3333 066998  4  30 38  +8 . 5  22 91  8.31  2  457 2  0  0 5  4 .188  4 50  9 14  -6 .25  30 05  19.43  0 5  4 . 188  4 50  9 14  + 6 . 25  30 05  19.43  100.  1000.  . ctlfit  398.09  15-1-1 0 0  *  NPOLES  * * * * *  *  IQUICK  | | | |  *  IDYNAM  | | |  *  I ALL  *  ICALC  .outfit  | | | 1 1  176  Appendix D. Input & Output Data Files for EMTP  Table D.4:Input data file for Jaguara case study using frequency dependent line model *  File  "JAGUARA.DAT".  C LINE ENERGIZATION. FROM: H.W. DOMMEL ET AL, CASE STUDIES FOR ELECTROMAGNETIC C TRANSIENTS, MAY 1983 (LATEST REVISION JAN. 1991). JAGUARA TAQUARIL LINE ENERGIZATION w i t h FD LINE MODEL 9.1553e-6  60.  .025 0  1S1A  JAGTA  77.65  2S1B  JAGTB  -21.95  77.65  3S1C  JAGTC  -21.95  -21.95  1JAGA  1666.  2JAGB  -461.  3JAGC  -461.  -1  JAGA  TAQA  -2  JAGB  TAQB  -3  JAGC  TAQC  $  = =  1666. -461. TESTFD.PUN  End o f l e v e l 1: L i n e a r and n o n l i n e a r elements  = = = = = = = = = = = =  0.0084  1.0  400.  JAGTB JAGB  0.0071  1.0  400.  JAGTC JAGC  0.0081  1.0  400.  JAGTA JAGA  0.0158  1.0  JAGTB JAGB  0.0144  1.0  JAGTC JAGC  0.0151  1.0  End o f l e v e l 2: Switches and p i e c e w i s e  C The o s c i l l o g r a m s from t h e f i e l d C d i r e c t l y with the f i e l d  test  1666.  -13  JAGTA JAGA  $ = = =  77.65  l i n e a r elements  t e s t had t h e wrong p o l a r i t y .  = = = = = = = = To compare  o s c i l l o g r a m s , we r e v e r s e t h e p o l a r i t y o f  C t h e source v o l t a g e s here 14S1A  -1.0  60.0  90.  -1.0  14S1B  -1.0  60.0  -30.  -1.0  14S1C  -1.0  60.0  210.  -1.0  $ = = = JAGA  End o f l e v e l 3: Sources JAGB  JAGC  TAQA  TAQB  = = = = = = = = = = = = = = = = = = = = = = = TAQC  $ = = =  End o f l e v e l 4: U s e r - d e f i n e d v o l t a g e output  $ = = =  L e v e l 5: End o f data case  = = = = = = = = = = = = =  = = = = = = = = = = = = = = = = = = = = = =  177  Appendix D. Input & Output Data Files for EMTP  Table D.5:Error analysis in time domain  *  Case i d e n t i f i c a t i o n  card  C E r r o r a n a l y s i s f o r the new l i n e model i n time domain  Time c a r d 65e-6  *  .  0.1  .  .  1  .  .  .  .  2  Lumped RLC b r a n c h 10  3  .001  1  C The new l i n e model 92  2  11  100  50.e-6  9999999. 92  3  21  100  50.e-6  9999999. $  = =  End o f l e v e l  $ = = =  End o f l e v e l  1: L i n e a r and n o n l i n e a r elements 2: S w i t c h e s and p i e c e w i s e l i n e a r  = = = = = = = = = = = = elements  = = = = = = = =  +  *  .  14  . 1  $ = = = X $ = = =  .  .  . 1  End o f l e v e l  .  .  Voltage o r current  sources  4000 3: S o u r c e s  = = = = = = = = = = = = = = = = = = = = = = =  **** A l l v o l t a g e s w i l l be p r i n t e d **** L e v e l 5: End o f d a t a case  = = = = = = = = = = = = = = = = = = = = = =  

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