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High frequency simulation of transformer windings for diagnostic tests Singh, Arvind 2006

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HIGH FREQUENCY SIMULATION OF TRANSFORMER WINDINGS FOR DIAGNOSTIC TESTS  by ARVIND SINGH B.Sc, The University of the West Indies, 2003  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE STUDIES  (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA February 2006  © Arvind Singh, 2006  ABSTRACT The change in business dynamics, brought on by the deregulation of the electricity industry has had an impact on the technical operations of the companies involved. To maintain competitiveness, industries must maintain a high level of efficiency and reliability. This has led to the shift to condition monitoring from scheduled maintenance schemes especially for expensive assets which are not immediately replaceable such as power transformers. High current surges impacting power transformers often cause winding deformations. These pose safety risks and heavy financial losses to the utility in spot market buying when failures occur. Long replacement times can have crippling financial effects on a company if there is no replacement for the transformer when a failure occurs. As a result of this diagnostic methods which estimate the transformer condition have become increasingly important.  These allow personnel to make decisions on replacing or  relocating a power transformer, in keeping with the financial objectives of the company. In this report an overview of the methods used in obtaining winding signatures used for condition monitoring is presented.  An equivalent circuit winding model based on  multiphase transmission line theory is developed which includes enough detail to allow for an accurate simulation. The circuit model for a specific transformer winding was implemented using Microtran software. The model was used to compare the response of the commonly used transadmittance signature to the characteristic impedance signature of the winding for different types of deformations (simulated by changing different capacitances in the model).  It was found that the methods were comparable in sensitivity with the transadmittance being only marginally better. The characteristic impedance signature however had the advantage of showing a constant percentage change over its frequency range for a given distortion. This makes it easier to quantify winding movement. The use of both methods in conjunction may serve as a more efficient method of classifying physical winding changes.  11  TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS INTRODUCTION SHIFT IN ENERGY ECONOMICS CHAPTER OUTLINE CHAPTER 1: TRANSFORMER FAILURE 1.1 INTRODUCTION 1.2 FAILURE DEFINITIONS Traditional (Critical Failure) definition Preventative (Non-critical Failure) definition 1.3 GENERAL CAUSES OF TRANSFORMER FAILURE CHAPTER 2: WINDING DISPLACEMENT 2.1 INTRODUCTION 2.2 GENERAL CAUSES OF WINDING DEFORMATION Natural Ageing Poor manufacturing or maintenance Short Circuit Forces Radial Movement Axial movement CHAPTER 3: DIAGNOSTIC METHODS 3.1 INTRODUCTION 3.2 COMMONLY USED WINDING DIAGNOSTIC METHODS Visual inspection Short circuit impedance Leakage reactance test Winding ratio test Winding resistance test Vibration test 3.3 COMPARISON TECHNIQUES Temporal Signatures Type based signatures Construction based signatures 3.4 FREQUENCY RESPONSE ANALYSIS (FRA) Swept Frequency Low Voltage Impulse CHAPTER 4: THE TRANSMISSION LINE DIAGNOSTICS METHOD.. 4.1 INTRODUCTION 4.2 TRAVELING WAVES ON TRANSFORMER WINDINGS 4.3 CHARACTERISTIC IMPEDANCE. 4.4 FREQUENCY DEPENDENCE (THE SKIN EFFECT) 4.5 APPLICATION OF THEORY TO WINDING MOVEMENT  iii  :  ,  ii iii v vi viii 1 1 3 5 5 5 5 5 6 12 12 12 12 12 12 13 14 16 16 16 16 17 17 17 17 17 18 19 19 19 21 21 21 25 25 25 27 29 30  Effect of separation on Z Derivation of measurement equations CHAPTER 5: TRANSFORMER MODELLING 5.1 INTRODUCTION 5.2 THE MULTIPHASE MODEL Intra-turn capacitance Capacitance from windings to external surfaces Inter-turn capacitance Modeling of Resistance 5.3 PROGRAM STRUCTURE Calculation of parameters Data file generation Running simulations Processing output files CHAPTER 6: MEASUREMENT AND MODELLING ISSUES 6.1 INTRODUCTION 6.2 EFFECT OF FREQUENCY ON MEASUREMENT 6.3 EFFECT OF LUMPING RESISTANCE 6.4 PHASE 'ERROR' CHAPTER 7: COMPARISON OF TLD AND FRA METHODS 7.1 INTRODUCTION 7.2 EFFECT OF WINDING RESISTANCE 7.3 WINDING BULGES 7.4 WINDING LOOSENING 7.5 WINDING COMPRESSION CHAPTER 8: DISCUSSIONS ...i 8.1 GENERAL 8.2 IMPULSE TESTS (FRA- LVI) 8.3 FUTURE WORK CHAPTER 9: CONCLUSIONS REFERENCES c  iv  :  ...  30 32 35 35 36 37 39 40 41 43 44 46 48 48 50 50 50 52 54 56 56 56 60 63 66 70 70 75 76 78 79  LIST OF TABLES Table 1: Sources of Transformer failures and causes of winding displacement [4] 10 Table 2: Transformer failures by component [4] 11 Table 3: Comparison of SFRA and FRA-LVI according to Tenbohlen and Ryder .22 Table 4: Comparison of SFRA and FRA-LVI according to Jeffery A. Britton 23 Table 5: Ability of FRA to detect various types of faults 24 Table 6 : Data for simulated transformer 50 Table 7: Results of simulation with different value of resistances at three important frequencies for fully distributed resistance 51 Table 8: Differences arising out of different lumped models 54 Table 9: Actual and measured percentage changes for Z signature for winding bulges 62 Table 10: Actual and measured percentage changes for TA signature for winding bulges 63 Table 11: Actual and measured percentage changes for Z signature for winding loosening 64 Table 12: Actual and measured percentage changes for TA signature for winding loosening , 66 Table 13: Actual and measured percentage changes for Z signature for winding compression 67 Table 14: Actual and measured percentage changes for TA signature for winding compression 68 Table 15: type of shifts exhibited by the Z and TA characteristics 73 c  c  c  c  v  LIST OF FIGURES Figure 1: Overview of processes taking place during a severe fault condition 6 Figure 2: Effect of severe fault conditions on withstand ability 7 Figure 3: Radial forces due to Current surge 13 Figure 4: Steady state flux orientation of winding 14 Figure 5: Radial flux experienced due to fast surges : 14 Figure 6: Illustration of time, construction and type based comparisons [7] 18 Figure 7: Illustration of Lumped Parameter approximation 26 Figure 8: Illustration of high frequency wave on a transmission line 26 Figure 9: High frequency pulse traveling along transformer winding [12] 27 Figure 10: Incremental length of line 27 Figure 11: capacitance to ground for unraveled winding 30 Figure 12: Winding between two static plates 31 Figure 13: Equivalent Circuit for Frequency dependent line 32 Figure 14: Mock Transformer at the HV Lab 34 Figure 15: Cross section of winding arrangement in a disk type transformer [13] 36 Figure 16: Multi-phase interconnection of windings... 37 Figure 17: Intra turn capacitance for a single coil of the transformer 38 Figure 18: Inner turn or core blocking intra turn capacitance 38 Figure 19: Actual electric field between windings and external surface 39 Figure 20: Approximated electric field between windings and external surface 39 Figure 21: Electric field assumed between windings 40 Figure 22: Separation of winding for capacitance distribution 41 Figure 23: Skin effect due to high frequency, current only flows through shaded region 42 Figure 24: Illustration of phase capacitance matrix for 2 pancakes with 5 turns each 45 Figure 25: Data file format, reproduced from the Microtran product manual [14] 46 Figure 26: Circuit set up for Microtran simulations 47 Figure 27: Algorithm for developed software 49 Figure 28: Simple test set up to explore the effect of lumping, Zc=200, v=200xl0 ms" 50 Figure 29: Relationship between Zc magnitude and phase shift between input and output currents for lossless line (R=0) 51 Figure 30: Resistance lumped at sending end of line 53 Figure 31: Resistance lumped at receiving of line 53 Figure 32: Resistance split between sending and receiving end of line 53 Figure 33: Variation of characteristic impedance phase angle with frequency 54 Figure 34: Z different values of input resistors 57 Figure 35 : Relatively constant separation between signatures 57 Figure 36: Change in Z for different winding resistances at different frequencies 58 Figure 37: Transadmittance characteristics for different values of input resistors 59 Figure 38: Separation between characteristics from R=l% signature 59 Figure 39: Change in TA for different winding resistances at different frequencies 60 Figure 40: |Z | signatures for variations in C 61 Figure 41: Percentage deviations from base plot for |Z | for variation in C 61 Figure 42: |TA| signatures for variations in C '.. 62 6  c  c  C  g  C  g  vi  g  1  Figure 43: Percentage deviations from base plot for |TA| for variation in C Figure 44: Actual plots for |Z | for variation in Cinter-tum Figure 45: Percentage deviationsfrombase plot for |Z | for variation in Cinter-tum Figure 46: Actual plots for |TA| for variation in Cinter-tum Figure 47: Percentage deviations from base plot for |TA| for variation in Cinter-tum Figure 48: Actual plots for |Z | for winding compression Figure 49: Percentage deviationsfrombase plot for |Z | for winding compression Figure 50: Actual plots for |TA| for winding compression Figure 51: Percentage deviations from base plot for |TA| for winding compression Figure 52: Transadmittance signature up to 10MHz for low line resistance Figure 53 : Percentage change in transadmittance signatures Figure 54 : Characteristic impedance signature up to 10MHz for low line resistance Figure 55: Percentage change in characteristic impedance signatures Figure 56: Unsymmetrical deformation causing turns on one pancake to link multiple turns on adjacent pancake g  C  C  C  C  vii  62 64 64 65 65 67 67 68 68 71 71 72 72 74  ACKNOWLEDGEMENTS I do not subscribe to the doctrine of individual agency. The work presented here though branded with my name has not emerged due to my sole effort. It takes an entire society to function in order for there to be the slightest progression of knowledge. Everyone, from the politicians that keep the country running smoothly to the janitors that keep the work environment clean and conducive to study are shareholders in any work of any level produced by the society. In keeping with usual standards however, and because this is not a philosophical treatise, I would like to thank my supervisors, Dr. K.D. Srivastava and Dr. J.R. Marti for taking me on as a student. I would also like to thank Dr. F. Castellanos of the University of the West Indies who acted unofficially in the capacity of a third supervisor. They have all provided valuable suggestions and advice at every stage of the project.  I should also mention the other members of the 'TLD' group Ben and of course Tom DeRybel, whose name should definitely find its way to the "Acknowledgements" of every report coming out of the power systems lab for his running and upkeep of the lab. I must also acknowledge the staff at Powertech labs especially Mr. John Vandermaar and Dr. Menguang Wang for cheerfully accomodating us when we needed to carry out physical experiments.  Lastly I would like to thank my family for supporting me  throughout my studies.  viii  INTRODUCTION  SHIFT IN ENERGY  ECONOMICS  Traditionally, Electric utilities were corporate monoliths. In most cases they existed as state owned monopolies. These could, for the most part, pass their losses directly on to their customers who had little choice but to accept the quality of service with which they were provided.  Recently this economic model of vertically integrated utilities was  replaced by multiple corporate entities. These provide unbundled services and employ market-driven decisions.  In theory, this would give more power to the consumer by  giving them a choice, much in the same way the telecommunications industry now operates. A network of energy generation companies has to make their product available through shared infrastructure, namely the electricity grid. The health of this grid can be severely affected by any independent power producer. Companies may incur heavy expenditures when other companies are affected by problems caused by them. In addition they may have to purchase power from other companies to fulfill their contractual agreements. It therefore becomes necessary to pay more attention to the state of critical assets and infrastructure. At the same time however, they must maintain competitive prices in order to survive financially and so cannot afford to replace equipment on a regular schedule.  These competitive business dynamics have emphasized the need for proper and effective asset management schemes. Asset management can be broadly defined as the balancing of performance, cost and risk in order to maximize returns for the company. It requires proper alignment of corporate goals and management and technical decisions. It involves business processes and information systems that are able to make consistent and beneficial decisions on asset-level data. The general consensus among experts is that the key to optimizing the use of assets is minimizing the risk of failures and their effects.  1  Power transformers are the most expensive and most complex assets in substations. Outages due to power transformer failure cost the company money not only in replacement or repair costs but also in buying power from other companies to supply their customers, in environmental clean up costs, customer and collateral damage costs and increased insurance premiums. These costs can quickly run into millions of dollars in the space of just a few days. A case study carried out by Pacificorp [1] estimated the failure of a 520MVA transformer to reach US$17 Million in just 8 days. The following break down was given:  E q u i p m e n t costs: $3.5 M i l l i o n  Transformers: 3 M i l l i o n  Collateral Equipment damage Environmental clean up: $0.5 Million C o m p a n y Losses  Self-insured deductible: $1 Million Environmental clean up $0.5 Million Replacement Power on Spot market $1.5 Million per D A Y $100 per MWH spot market price $30 per MWH continuing production cost 500MW purchased on the spot market Total cost to purchase power = 500x(100+30)x24hrs =$1.56 M i l l i o n per day  Other important factors motivating the adoption of continuous monitoring systems for such critical assets such are high equipment costs and long replacement lead times. Power transformers cannot be bought off the shelf, and in general, because of their size, and cost and lifetime, back up units are not stored by companies. In some cases the replacement process may extend oyer a year. Given the heavy financial losses that can be incurred by an unexpected failure, traditional time based maintenance schemes have become untenable. As the estimated lifespan of the majority of in service power  2  transformers is approached, condition based monitoring techniques are becoming more integral to power system operations.  CHAPTER  OUTLINE  The report is organized in the following chapters: CHAPTER 1: TRANSFORMER FAILURE This section defines transformer failure in the traditional sense as well as in the sense of condition monitoring schemes. An overview of the general causes of transformer failure is given with specific focus on the failures related to winding movement. CHAPTER 2: WINDING DISPLACEMENT This section outlines some of the principal causes of winding deformations especially those arising from high current conditions.  CHAPTER 3: DIAGNOSTIC METHODS This section outlines comparison methods as well as common winding signatures used in practice with particular attention being paid to the "Frequency Response Analysis" (FRA) technique  CHAPTER 4: THE TRANSMISSION LINE DIAGNOSTICS (TLD) METHOD This section introduces the concept of traveling waves and develops the theory on which the TLD method is based.  CHAPTER 5: TRANSFORMER MODELLING This section presents considerations for developing a sufficiently detailed equivalent circuit transformer model based principally on the geometry of the transformer. The main features of the software developed for building the equivalent circuit transformer model are also presented.  3  C H A P T E R 6: M E A S U R E M E N T A N D M O D E L L I N G I S S U E S T h i s section l o o k s at errors a r i s i n g from measurement issues s u c h as the effect  of  standing w a v e s and m o d e l issues s u c h l u m p i n g o f resistances are investigated. A l o o k at phase ' e r r o r ' i n t r o d u c e d b y u s i n g m u l t i p h a s e elements is also presented.  C H A P T E R 7: C O M P A R I S O N O F T L D A N D F R A M E T H O D S In this section the transformer c i r c u i t m o d e l d e v e l o p e d is used to simulate different types of  fault  conditions  and to  c o m p a r e the  changes obtained  f r o m the  i m p e d a n c e and trans-admittance signatures.  C H A P T E R 8: D I S C U S S I O N S  G e n e r a l c o m m e n t s o n the results obtained and p r o p o s a l for further w o r k  C H A P T E R 9: C O N C L U S I O N S  4  characteristic  CHAPTER 1: TRANSFORMER FAILURE 1.1  INTRODUCTION  This section defines transformer failures in the traditional sense as well for condition monitoring schemes.  A n overview o f the general causes o f transformer failure is given  with specific focus on the failures related to winding movement.  1.2 FAILURE  DEFINITIONS  T r a d i t i o n a l (Critical Failure) definition A transformer is said to have failed when it is forced out o f service by a specific event that results in the inability o f the transformer to operate properly under nominal system conditions. Only the present state o f the transformer is considered i n deciding whether to keep the transformer in service or not.  That is, the transformer is considered to be  operational as long as it can operate under normal operating conditions. Preventative ( N o n - c r i t i c a l Failure) definition A transformer is said to have failed when it can no longer withstand the fault conditions for which it was originally designed. This means that the transformer may be operable in the traditional sense but could be classified as having failed because the next fault condition would cause it to fail.  It entails assessing how "fit" the transformer is and  making a decision as to whether it is safe to operate based not only on its present condition but on the probability o f catastrophic damage occurring by abnormalities that are likely to happen in the normal course o f operation.  5  1.3 GENERAL  CAUSES  OF TRANSFORMER  FAILURE  The behaviour o f a transformer depends on the physical state it is in, that is, the arrangement (shape, symmetry etc) o f the windings, and the condition o f the insulation (both paper and oil). When transformer ratings are specified, they relate to the voltages that the dielectrics can withstand before breakdown and the short circuit forces that can be endured by the structures that hold the windings in place. It follows therefore that transformer failures stem from exceeding o f the withstand capabilities i n these categories.  The transformer can be looked at as a combination o f three systems: electrical, mechanical and chemical. Figure 1 gives an overview o f how these interact during over current conditions.  High current, magnetic fields lead to high forces, expansion and contraction due to heating  Mechanical System  Heating Electrolysis Pyrolisis  Change in winding arrangements, nsulation thickness  Electrical system  Nonuniformities  Thermal / Chemical System  Change in dielectric causes change in circuit parameters like capacitance  High currents lead to heating, High electric field strength lead to dielectric breakdown  Figure 1: Overview of processes taking place during a severe fault condition  6  When these processes operate they always lower the strength of the transformer to future over-current events as shown in Figure 2. Fault withstand ability  Probability of ratings being exceeded  •  Tolerance level  Stability " Stable -  1  _  1+1  Number of severe over current events Figure 2: Effect of severe fault conditions on withstand ability  7  In the normal course of operation, the physical state of the transformer is stable. This means that the elastic limits of the clamps and windings have not been exceeded and the dielectrics have not broken down in any area. When a severe fault occurs that causes these elastic limits to be exceeded or the dielectrics to break down, then plastic deformation of windings or chemical changes in the insulation take place respectively.  The transformer does not return to its pre-fault physical state but moves to a new state instead. For example, clamps may be slightly stretched thus reducing the clamping pressure after the fault is cleared or gasses may be liberated in the oil. This new state that the transformer moves to has an altogether different set of ratings associated with it. As long as the new set of ratings is still acceptable then the transformer can be kept in service. If not taken out of service, the transformer can reach an unstable state where new dynamics have to be taken into consideration (e.g. vibrations of the winding if the clamp has been sufficiently loosened). In the normal course of operation, the state may continue to degrade till the transformer completely collapses.  Traditionally as long as the transformer was stable (up to 'n' faults on Figure 2) then it would be kept in service till the next scheduled maintenance time. However, in order to avoid critical failures the transformer has to be taken out of service at the "nth" short circuit at the latest in order to prevent the system going to an unstable state. Since the ratings decrease with the number of severe faults encountered then the probability of the new ratings being exceeded in a given time increases correspondingly and the time between severe over current events decreases.  The final mechanical or insulation breakdown of a transformer may be due to a number of primary causes. These include:  presence of oxygen and/or moisture, solid  contamination of the oil, manufacturing defects, transients due to lightning or switching, internal winding resonance, faults and overloads.  8  Several methods have been developed [2] over the years that can give some insight into the condition that the transformer is in. These include: Frequency Response Analysis (FRA), Dissolved Gas-in-oil Analysis (DGA), ratio measurements, winding resistance, short circuit impedance and loss, excitation loss and dissipation factor, capacitance and applied and induced potential. Among these methods FRA and DGA have emerged as the main methods of transformer diagnostics.  Although the primary causes of transformer failure have been mentionedd, they do not necessarily give direct insight into the physical state of the transformer. This is needed to determine how "fit" it is. In order to get this insight, measurable effects such as insulation degradation, change in oil properties and winding displacements have to be examined. A survey, [3], found that between 70 and 80% of failures can be traced back to short-circuit between winding turns. Table 1 shows that winding displacements can be associated with a number of different primary causes that account for a high percentage of transformer failures.  9  1975  1983  1998  Winding movement evident  32.3%  30.2%  12.4%  YES  13.6%  18.6%  21.5%  YES  10.6%  7.2%  2.9%  YES  10.4%  8.7%  13%  Overloading  7.7%  3.2%  2.4%  Moisture  7.2%  6.9%  6.3%  Inadequate  6.6%  13.1%  11.3%  2.6%  1.7%  0  2.1%  2.0%  6%  6.9%  8.4%  24.2%  Lightning Surges Line Surges/External Short Circuit Poor WorkmanshipManufacturer Deterioration of Insulation  YES  Maintenance Sabotage, Malicious Mischief Loose  YES  Connections All others  Table 1: Sources of Transformer failures and causes of winding displacement [4] From Table 1 it is possible to calculate that the average of failures related to winding displacement is 63.5% for the three years and 54.1% for the latest year (1998). Table 2 shows an excerpt from "Electricity Today" [5] outlining the percentage of transformer failures by component.  10  Transformer Component  Percentage  of  failures  component  is  responsible for  High Voltage Windings  48%  Low Voltage Windings  23%  Bushings  2%  Leads  6%  Off-load Tap Changers  0%  Gaskets  2%  Other  19% Table 2: Transformer failures by component [4]  From the table, just over 70% of transformer failures are due to winding related trauma. In fact the only element that causes more failures than the transformer windings are the on-load tap changers (not shown in Table 2) present in some transformers. These account for 41% of failures in transformers containing them while winding related failure accounts for approximately 19%.  11  CHAPTER 2: WINDING DISPLACEMENT 2.1  INTRODUCTION  The mechanical structure of a transformer may be compromised by a number of causes including: poor handling during transportation, poor manufacturing, natural ageing or over-current conditions brought on by system faults or lightning. This section briefly addresses the problems arising out of these conditions. 2.2 GENERAL  CAUSES  OF WINDING  DEFORMATION  Natural A g e i n g  Under normal operating conditions the components of the transformer will slowly deteriorate. The insulation will gradually lose its elasticity and may begin to crumble, clamps will loosen, and generally the structure undergoes a gradual weakening. Poor manufacturing or maintenance  Lax quality control in the manufacturing process can lead to a number of undesirable conditions such as loose brackets which lead to winding vibration, non-uniform surfaces which contribute to accelerated insulation break down and may lead to internal corona and partial discharge, oil impurity, and short circuit between turns. During maintenance it is not unheard of for equipment to be mistakenly left in the transformer tank. Many times these items would be magnetic materials that get pulled around the tank by the strong magnetic fields of the transformer under normal operation. When these collide with the windings they can quickly destroy insulation and cause short circuits Short Circuit F o r c e s  Given that standards in transit, manufacturing and maintenance have been upheld it is high current conditions that are the most serious threat to the transformer's structure. Under high current conditions, the transformer can undergo stresses over 100 times the forces it was designed to withstand. Consider a current surge entering one of the terminals of the transformer, distortion can be caused along two main directions: 1. Radial 2. Axial  12  Radial M o v e m e n t  RADIAL FORCES ON WINDING /  Current surge  Figure 3: Radial forces due to Current surge  The transient forces on the winding can exceed 100,0001bs in transformers as small as 10MVA [6] and are the principal source of winding deformation. This type of deformation is most dangerous because it has the ability to loosen and deform clamping structures. If this is left unchecked it can result in the entire winding structure coming apart with explosive results. This type of deformation also stretches the insulation and may cause cracks or brittleness and speeds the rate at which it naturally deteriorates.  13  Axial movement Axial movement is brought about by the non-uniform energization of the winding which induces radial flux. Consider the steady state flux orientation of the windings as shown in Figure 4.  Figure 4: Steady state flux orientation of winding  The grey arrows represent net flux directions while the solid black arrows show fluxes that have been cancelled by the arrows next to them. There is no net magnetic field inside the winding arrangement because the internal fields cancel each other. However, when a fast surge impacts the coil the majority of the current wave may be confined to a few windings or layers at a time and as such the surrounding windings experience net radial fluxes as shown in Figure 5 .  g % tjr ^  * * *  Figure 5: Radial flux experienced due to fast surges  14  *  This type of flux causes axially compressive forces to be exerted on the winding. In addition, the flux directions though principally axial may also have some radial components. These types of forces can cause the twisting of windings in addition to compression. This can result in rapid breakdown of insulation between layers leading to short circuits or partial discharge. Gases may become liberated in the oil, some of which are explosive, such as hydrogen. This represents a serious safety concern to both personnel and equipment.  15  CHAPTER 3: DIAGNOSTIC METHODS 3.1  INTRODUCTION  Methods to diagnose the condition of power transformers have become important tools for electrical utilities in recent years. The need for them arises from two main factors: 1. The majority of power transformers in service are approaching their life span so there is an increased risk of mechanical failure. 2. The operation of deregulated markets requires the use of critical assets to be optimized. This means transformers have to run as long as possible at their limits. The general principles involved in diagnosing the condition of windings are examined in this section. 3.2 COMMONLY  USED  WINDING DIAGNOSTIC  METHODS  The choice of diagnostic method used to estimate the condition of a winding is dependent on a number of criteria including:  •  Sensitivity to winding displacements  •  Sensitivity to noise  •  Sensitivity to measurement set up  •  Ability to diagnose and quantify type of deformation  Some of the most common methods to evaluate the state of a transformer are the following: Visual inspection  Visual inspection is the most reliable method to determine the winding condition. The transformer has to be taken out of service, drained and opened up to be inspected, the condition of clamps, windings and insulation can then be inspected to determine if there are any noticeable problems. This method requires trained and experienced personnel to carry out inspections and can lead to long out of service times for the transformer which is undesirable. This method is likely to be retained only as a final verification when a less invasive method detects the presence of a critical fault condition.  16  S h o r t circuit i m p e d a n c e  The low voltage winding terminals are shorted to each other and the input current voltage and power are measured. A deviation of 2% or greater is considered to be indicative of significant winding movement. This technique has to be performed offline in a test lab and is only effective for significant winding distortion. L e a k a g e r e a c t a n c e test  The short circuit impedance test set-up can also be used to calculate the new leakage reactance of the transformer. If the winding has expanded, the leakage reactance would increase as a consequence. This method is sensitive to certain types of distortion only, namely distortion that results in increased distance between the primary and secondary coil. It does not pick up distortions such as twisting of windings and is ineffective at high frequencies due to the skin effect. W i n d i n g ratio test  The winding ratio test is another offline test that can be used to detect faulty winding conditions. The transformer's voltage ratio is tested to ensure that the proper turns-ratio is present. This can be used to detect short circuited or open circuit conditions. W i n d i n g r e s i s t a n c e test  The winding resistance test is also an offline method. It operates on the principle that any change in the geometry of the conductor would show up as a change in the winding resistance. For example if the winding expands then the length of the winding would increase while the cross sectional area would decrease. This would cause an increase in the resistance of the winding. The technique requires highly sensitive equipment to detect fraction of an ohm changes. In addition since the temperature at which the experiments are carried out would influence the quality of the readings, temperature information has to be recorded as well to ensure repeatability when conducting future experiments. V i b r a t i o n test  Vibration testing involves the mounting of acoustic sensors on the tank wall of the transformer to sense the vibration of the transformer caused by the continuous magnetization and demagnetization of the core and windings. These acoustic signals  17  form the signature for the winding. This method has the advantage of being an online method; however the externally mounted sensors are highly susceptible to vibration noise from the external environment.  3.3 COMPARISON  TECHNIQUES  Transfer function signatures have become somewhat of an industry standard for transformer diagnostics, especially where the condition of the windings are concerned. The general approach to transfer function diagnostics is the comparison of a given transfer function of the transformer to a base signature that represents the transformer in a healthy condition.  The current signature of the transformer can be obtained by  measurements on the actual transformer. The base signature, however, is more difficult to acquire. Over the past few years three methods have been used to generate base signatures for power transformers [7]: 1. Temporal signatures 2. Construction based signatures 3. Type based signatures  Figure 6 illustrates the differences in these methods  Substation A. Trarrsformer 1.1996  Substation A, Transformer 1,2002  Substation B, Transformer 2.2002  Figure 6: Illustration of time, construction and type based comparisons [7]  18  Temporal  Signatures  Temporal signatures are simply the signature of the transformer obtained at an earlier date. This is the most reliable signature that can be used. When the transformer is new the signature is recorded and this serves as the reference for all future measurements. This data is usually not available though, since transformers have been in service for decades while condition monitoring techniques are relatively new. This means that alternate methods for obtaining baseline signatures usually have to be employed. Type based signatures  Type based signatures involve obtaining a signature from an identically constructed transformer that is known to be in good condition. This may typically be a relatively new transformer that has been installed at another substation or one that services a low fault area so that the only change in transfer function would arise from natural ageing. The main problem with this method is that even for identically specified transformers, winding designs over time may have changed, causing slightly different transfer functions, in addition, designs are made within a certain tolerance level so that there would be slight variations from one transformer to the next even if the winding designs used are identical. To solve this problem Christian and Feser [7] have proposed the statistical calculation of tolerance bands using transfer functions from a large group of same-type transformers to distinguish differences arising from winding distortions to differences arising from different manufacturing processes. Construction based signatures  Construction based signatures are used on multi-leg transformers where windings are not zigzag connected. The process entails using the windings on different legs as mutual references. Each winding is tested separately and then transfer functions compared. Christian and Feeser [7] find that the geometrical properties of the core-and-coil assembly as well as the type of vector group have noticeable effects on the comparability of the results of different legs.  The approach is not constrained to three-phase  transformers, where three single phase transformers are used the technique is equally viable. The technique of using windings as mutual references has the advantage of  19  requiring no past or external data for measurement. Measurements [7] show that the frequency responses of three windings are near identical.  The technique has the following advantages: the problem of different manufacturing techniques does not affect it since the windings are part of the same unit. Past data is not needed since asymmetries are evident from comparison of present data. Unless a three phase fault that symmetrically distorts all the windings occurs, which almost never the case, winding movement and distortion can always be ascertained.  The disadvantage of the technique is that if the three windings undergo change in their frequency response characteristics then the asymmetry would give misleading results, making the winding look like it has moved more or less than it actually has.  20  3.4 FREQUENCY  RESPONSE  ANALYSIS  (FRA)  Frequency response analysis involves measuring the trans-impedance or trans-admittance of the winding. This method has come to be somewhat of an industry standard, because of its high sensitivity to a number of different types of winding distortion. This method is based on the fact that a change in winding geometry results in a change of the RLC parameters of the winding. This results in the magnitudes and frequencies at which resonances occur to also change. There are two methods that are typically used to carry out the FRA measurements: 1. Swept Frequency 2. Low Voltage impulse Swept Frequency  Swept Frequency Frequency Response Analysis (SFRA) involves injecting a sinusoidal voltage into one end of the winding and then measuring the output current at the other end. The transadmittance is then calculated from the phasor quantities. This is repeated for a wide range of frequencies to obtain the transadmittance signature. White noise is also sometimes used as an injected quantity, since it contains all frequencies at equal power levels. The Fourier transform is then applied to the input and output measurements to obtain their phasor form representations and finally the transadmittance is calculated.  fML )  Y=  ul  Low Voltage Impulse  The Low voltage impulse method or (FRA-LVI) involves injecting a low voltage pulse at the input and recording the current at the output terminal. The input and output waveforms are then processed in the same way as is done with white noise in SFRA measurements. There has been much debate about which of these methods is actually better. Tenbohlen and Ryder [8] have explored the relative advantages and disadvantages of the methods, which are summarized below. They conclude that SFRA is the superior method.  21  FRA LVI Disadvantages  SFRA Advantages •  High signal to noise ratio  •  Wide frequency range  •  Adaptable (better  frequency resolution  •  frequency  at  Only  one  equipment  as  higher  frequency  components have less energy.  increments •  low  Frequency resolution is fixed and poor at low frequencies  frequencies) •  Signal to noise ratio decreases with  piece  •  of measuring  needed  Several pieces of equipment needed (function generator, rogowski coil,  (Network  digital oscilloscope)  analyzer) •  Difficult to filter out broad band noise  •  SFRA Disadvantages Time taken to make  each  measurement  long  is  relatively  •  FRA LVI Advantages Time taken to make  each  measurement is short (typically one minute).  (several minutes)  Table 3: Comparison of SFRA and FRA-LVI according to Tenbohlen and Ryder  Jeffery A. Britton of Phoenix technologies has also compared these methods [9] and has put forward the following comparisons  FRA LVI Disadvantages  SFRA Advantages •  •  Intuitive and straightforward  Sensitive to noise can have a drastic effect on transfer function results  •  Repeatability not of a high standard without the use of very expensive equipment  22  •  SFRA Disadvantages Network analyzer traditionally used which does not have power  to  •  sufficient  the transformer, thus minimizing  excite  the effect of the external circuit  appreciably  setup.  windings at high frequencies due to •  large inductive load. •  FRA LVI Advantages Voltage and currents measured at  Low inductance shunts may be used  excite  to reduce damping compared to 50  windings at very high frequencies  ohm internal impedance of network  due to high capacitive load of  analyzer in SFRA.  Insufficient  power  to  insulation system. •  Low level signals result in high measurement  errors  repeatability  especially  and  poor  on high  current windings. •  Extremely  sensitive  to  measurement set up since cable lengths may exceed 50 feet. Table 4: Comparison of S F R A and F R A - L V T according to Jeffery A . Britton  The comparisons show that the main downfall of SFRA relates to the equipment used to take measurements. If it were possible to take measurements at the transformer terminals with a sufficiently strong signal then SFRA would clearly be a better option for diagnostics. Since the Transmission Line Diagnostics (TLD) technique described in the next section utilizes the same measurements as SFRA and takes them at the transformer terminals, it is assumed that the SFRA would indeed be the superior choice to FRA LVI for comparisons.  Ryder, proponent of SFRA, describes [10] the key indicators of damage when comparing SFRA signatures as:  23  • • •  Changes to the overall shape of the graph. The creation of new resonant frequencies or the elimination of existing resonant frequencies. Large shifts in existing resonant frequencies.  Through a series of case studies he put forth the information in table 5 regarding the ability of FRA to detect fault conditions.  Detectable?  Nature of Fault  No core earth  Probably not detectable laboratory conditions.  Multiple core earths  Usually not detectable  Foreign object  Not detectable.  except under  Additional turns on yoke Detectable. Detectable. Additional turns on limbs Short-circuited turns  Detectable.  Mechanical damage to windings Detectable. Detectable if very severe. -to core Windings undamped  Probably not detectable laboratory conditions.  Loose turns  Detectable.  "Normal" ageing  Detectable if very severe.  except  under  Table 5: Ability of FRA to detect various types of faults  As stated earlier, FRA has become somewhat of an industry standard due to its sensitivity, however the quantification of the differences in the transfer function and extracting insightful information about the nature of the winding deformations from these differences are still being researched. Solutions varying from neural networks to simple correlations have been used to different degrees of success.  24  CHAPTER 4: THE TRANSMISSION LINE DIAGNOSTICS METHOD 4.1  INTRODUCTION  This proposed method [11] relies on the use of the frequency-dependent characteristicimpedance of the transformer as its signature. It arises out of the conceptualization of the winding as a traveling wave medium on which voltage and current waves propagate. When energy is input to the medium, the energy goes toward developing magnetic and electricfields.The rate at which these fields are developed, as well as the quantity of flux that is produced both influence the propagation characteristics. The magnetic fields can be represented by circuit inductance while the electric fields can be represented by circuit capacitance. Both of these are directly related to the geometry of the winding so winding displacements will be reflected in the changes in propagation characteristics.  4.2 TRAVELING  WAVES  ON TRANSFORMER  WINDINGS  Traditionally, traveling wave theory has been used in transient simulations for long lines (>150km) when lumped parameter models no longer give accurate results. The winding of a power transformer however has been estimated to be between 1.5 and 2km long. This may seem very short even for a short line model (<40km), however, the fact is that energy is always transmitted as traveling waves. The lumped parameter model arises when the speed at which the energy propagates is very much greater than the rate at which the energy level changes. Another way of looking at this is that the wavelength of the applied signal is much greater than the length of the line (see Figure 7).  25  Relatively short tine  Figure 7: Illustration of Lumped Parameter approximation  Figure 7 shows that the whole winding sees approximately the same potential. For a given length of winding the lower the frequency of the input signal, the better the lumped parameter approximation becomes, or vice versa.  When the length of the winding  becomes long compared to the wavelength of the line, the situation illustrated in Figure 8 arises.  Relatively Long line  0  Relatively short wavelength or relatively high frequency Figure 8: Illustration of high frequency wave on a transmission line  The speed at which the energy propagates is no longer sufficient to assume that the line is at a single potential and therefore one end of the line may be at an altogether different potential to the other end.  This means that although lumped parameter networks are sufficient for modeling transformer windings at low frequencies such as power system frequencies of 60Hz, at high frequencies in the megahertz range, this approximation becomes invalid. At these  26  frequencies pulses applied to the transformer would not be seen by the whole winding at the same time by instead propagate down the winding as shown in Figure 9.  I V Figure 9: High frequency pulse traveling along transformer winding [12]  It is possible to conclude that at high frequencies the traveling wave model would be more suitable as a circuit representation of the winding. It follows that a signature based on the main parameter associated with the traveling wave can be used as a signature, namely the characteristic impedance, Z . c  4.3 CHARACTERISTIC  IMPEDANCE  An incremental length of line dx can be represented as shown in Figure 10.  Figure 10: Incremental length of line  27  The incremental series impedance, Z and the incremental shunt admittance, Y are defined as: (1)  Z = R +jo>L dx  dx  Y = G* + ja>C  (2)  lt[  From the circuit equations a set of differential equations is developed and the system can be expressed as the wave equations: dV  - — = ZI  (3)  - — = YV dx  (4)  dx  Where V and I are phasors The general solution for this system of equations is given by: V = K e*  Where y = 4ZY  +Ke  v  x  %  Substituting this back in the original equation: Where Z =  V = ^ e - v - ^ e *  z  z.  = c  J—  c  R(o)) + jcvL(cv) z, ^G(co) + jo)C(cv)  1Y  c  At sufficiently high frequencies, due to skin effect (discussed in the next section), the frequency dependent  resistance  can be modeled asR^.  Also,  for practical  considerations the shunt conductance is negligible. Equation 5 reduces to:  2  _  ^R4G> + jcoL(co) jcoC{co)  _  I  \jy[cvC((0)  R  +  L(co)  C(cv)  At very high frequencies current flows on the skin of the conductor alone, so that the inductance is completely external. Since the conductor is comprised of free moving charges there is no steady state electric field within the conductor so that the capacitance is due to external flux alone. The equation is reduced to the following at high frequencies:  28  L(a>)  L 'EXTERNAL  C(co)  C,EXTERNAL  (6)  Which is constant  4.4 FREQUENCY  DEPENDENCE  (THE SKIN  EFFECT)  Skin effect is the name given to the phenomenon whereby AC current tends to flow closer to the surface of a conductor as frequency is increased. This is due to the current being guided by a medium (copper) of a different permeability than the medium surrounding it (oil paper insulation). increases with depth.  As a result the inductance of the conductor  As frequency is increased the inductive reactance  jcoL  also  increases resulting in higher impedance at the centre of the conductor which forces current to flow to the outside.  This affects the velocity of propagation because the velocity with which current wave propagates is related to the rate at which the electric and magnetic fields it generates can develop. This is dependent on the permittivity and the permeability of the medium in which the fields are generated. At low frequencies current still flows at a relatively large depth inside the conductor. This means that there are two media involved in propagation, the copper winding and the insulation around it. The wave speed is limited by the higher permittivity of the copper and so travels more slowly. As frequency increases, the current flows increasingly to the surface of the winding. A greater percentage of the fields are generated in the external medium. At very high frequencies, the current flows on the skin of the conductor. Approximately all of the fields are developed in the external insulating medium and consequently the wave is allowed to propagate at its fastest. The wave propagation speed is entirely independent of the geometry of the winding or the capacitance and inductance. However, it is related to the capacitance and inductance through the equation below (assuming very high frequency):  29  v can be calculated from readily available values of ju and s, thus if either the  CEXTERNAL  or LEXTERNAL is known the other can be calculated.  4.5 APPLICATION  OF THEORY  Effect o f s e p a r a t i o n o n Z  TO WINDING  MOVEMENT  c  Consider first an unraveled winding, which can be represented as a transmission line  Unravelled winding  Figure 11: capacitance to ground for unraveled winding  The rectangular construction of the windings allows us to calculate the capacitance of the winding to ground by using the well known equation for parallel plate capacitors: C =  4  (8)  Since the cross sectional area per unit length remains the same as well as the permittivity of the insulation the only factor seen to influence the capacitance is the distancefromone surface to another.  If the distance, 'd', changes, there is a corresponding change in the capacitance; the inductance is correspondingly scaled in the opposite direction, since the L C product must remain the same (the velocity remains constant). This scaling is reflected exactly in the characteristic impedance as the following equations illustrate:  30  c  -y  VSA 2  2  2  Z =d.K  (ll)  c  A change i n the distance, d, is reflected by a proportional change i n Z . The actual model c  is not this simple, however, since the winding is coiled as shown i n Figure 12.  lllilBIIEIII  OUTER -  iiiiieiieni  STATIC PLATE  m i n i m i iiiiiiiiii  INNER STATIC PLATE  1IBI1III1I11 llllllllllll Figure 12: Winding between two static plates  The external capacitance is not due to a single source, e.g. capacitance to ground or capacitance.  There are also capacitances between adjacent turns and between adjacent  layers. A s a result the simple relationship between the characteristic impedance and the capacitance may not hold true.  31  Derivation of m e a s u r e m e n t e q u a t i o n s  The equations developed thus far deal with Z in terms of the circuit parameters L and C, c  for diagnostic purposes however these are not directly measurable.  A method of  calculating Z from measurable data is needed. c  Traditionally, characteristic impedance measurements, such as those used to measure the characteristic impedance of co-axial cables, involve open and short circuit tests. The open and short circuit input impedances are measured and the characteristic impedance is found by the following equation:  Z = J z x Zshort Ay  c  open  .  R + jcoL G  +  (12)  jaC  The open circuit impedance is the inverse of the shunt admittance ( short circuit impedance gives the series impedance (R+jcoL).  -  ) and the  G + jcoC  This measurement method  however, would require offline testing of the transformer. Since the eventual aim of the Transmission Line Diagnostic method is to have online measurements then a different method must be derived.  The equivalent circuit for the frequency dependent line as well as the derivation of the measurement equations are given on the following page:  =lk=!>  Zc  Zc  Ekh  Figure 13: Equivalent Circuit for Frequency dependent line  Ekh-(V - Z I ) e ^  (13)  Z I0e -yi  (14)  m  E =(V + mh  k  c  m  c  32  -\m=  Applying Kirchoff s voltage law Ve +  ZJke*  yl  k  Vk  = ZI + c  Z I =Z I e c  k  c  y i  m  m  +  V  (15)  Ve  (16)  m  yi  m  From (15) +V  7 T  (17)  Substituting for this in equation (16):  {K-zj,  v -z i = k  c  k  m)  By cross multiplication:  (v -z i Xv zj )=(v z i \K =vk  c k  k+  k  m+  c m  m  ZJ ) m  2  m  (18)  It can be seen that the value of the characteristic impedance is obtainable through a simple equation involving measurable voltages and currents. These variables are all phasors. The output voltage and current is measured across an output resistor and the input voltage and currents are measured at the transformer terminals. In practice a swept frequency approach is used because of the inherently higher signal to noise ratio it involves. For testing purposes, the mock transformer constructed in the Department's High Voltage Lab last year (see Figure 14) was used.  33  Figure 14: Mock Transformer at the H V L a b  This device facilitated a rough verification of the theory. However, since the method is sensitive to the construction of the transformer, the mock transformer is not ideal to test the effectiveness of the technique on large power transformers. Although some experiments were carried out at Powertech Labs, these so far could only verify that a signature of the expected form is obtained by measurement. Since simulating distortions could destroy a power transformer or for the least result in very high repair costs, it is necessary to develop a detailed transformer model that allows distortions to be simulated and the differences between signatures to be quantified.  34  CHAPTER 5: TRANSFORMER MODELLING 5.1  INTRODUCTION  The transformer is one of the most complex electrical elements in a substation. For power flow studies or even short circuit studies its complex nature is often trivialized as an inductance.  However for the purpose of diagnostics, where the response of the  windings is measured over a range of frequencies, such simplifications cannot be made. Lumped (RLC) models are currently the most prevalent circuit models being used for studying the transfer functions of transformers. These models break the winding into sections containing as a series inductance and resistance with a lumped capacitance to ground as well as a lumped capacitance from section to section representing the inter-turn capacitance. It is not uncommon for windings to be split into as much as 60 or 70 sections for this type of model.  A model must be developed that is detailed enough to accurately depict the phenomena being simulated yet simple enough to allow simulation on available modern computing facilities. To determine how detailed the model should be, the physical layout of the transformer (particularly the winding arrangement) must be studied. In this, section a useful Transmission Line model of the transformer is developed for diagnostic simulations. • At this point it should be remembered that the characteristic impedance becomes constant and a quantifiable measure of winding displacement at high frequencies. The model developed will, therefore, focus on capacitive considerations.  35  5.2 THE MULTIPHASE  MODEL  Figure 15 shows a typical arrangement for a disk type transformer.  Figure 15: Cross section of winding arrangement in a disk type transformer [13]  Common assumptions used for the modeling of overhead transmission lines such as negligible proximity effect, uniform electric fields etc. can be called into question for the analysis of a transformer. In reality, there is capacitance from every surface on the inside of the transformer to every point of the winding. The distances between surfaces may vary, for example, the static shield is slanted, and corners of the tank are further from the windings than the centres of the tank walls. The close packing of the windings also brings in phenomena such as proximity effect.  Most of these irregularities, however, are negligible or can be averaged out without significant loss of accuracy. A cross section of the transformer such as the one shown in figure 15 reveals that, unlike a transmission line there is a capacitance from the winding to itself (due to coiling) corresponding to the capacitance between turns and the capacitance between layers. Since the turns and layers are coupled to eachother a single phase line cannot be used to represent the winding.  36  A more realistic approach is to use the multiphase line representation.  The entire  winding cross section as shown in Figure 15 would be viewed as a multiphase system, with each turn of each layer corresponding to a phase. The end of each phase is then connected to the start of the next phase to represent the winding as shown in Figure 16.  Figure 16: Multi-phase interconnection of windings  The transmission lines in the model use constant parameter (CP) representation. These lines are high frequency approximations to frequency dependent transmission lines. The parameters that need to be specified for these lines are the capacitance and inductance matrices. As discussed earlier, the process adopted is to estimate the capacitance based on winding construction and then calculate the inductance which is obtainable through the equation relating inductance, capacitance and velocity of propagation.  Some  considerations in modeling the capacitance of the windings are outlined in the following sub-sections.  Intra-turn c a p a c i t a n c e  Capacitance arises from the electric field between a plane and any other surface that does not lie on that plane. For this reason there is no capacitance from one point of a horizontal transmission line to a point further down that line. In the case of transformers however, the winding is coiled so that there is capacitance between every point on a coil to every other point (see Figure 17). 37  Figure 17: Intra turn capacitance for a single coil of the transformer  The capacitance of a transmission line to itself cannot be modeled. The model would, therefore, have to contain transmission lines of such a small size that they would be relatively straight, not curved. This would require an extraordinary amount of transmission lines to model even a single turn. However, the space between the turn is occupied by other turns or the core which in effect blocks the electric flux that would give rise to the intra turn capacitance. This means that the intra-turn capacitance is greatly reduced as shown in Figure 18. Inner tum or core blocking o„  t e r  turn  i  n  "  a ,  u  r  n  eapacitive «i»  Figure 18: Inner turn or core blocking intra turn capacitance  From Figure 18 it can be seen that as the distance between the turns decreases the intraturn capacitance also decreases.  The only separation between the turns is the oil-  impregnated paper (a relatively small distance), hence this capacitance can be neglected.  38  C a p a c i t a n c e f r o m w i n d i n g s to external s u r f a c e s  A basic assumption made is that the capacitance to any surface is due to a uniform electric field, that is, both surfaces form a parallel plate capacitor, the area of which is set to the area of the winding surface involved, (see figure 19 and 20). Electric field dispersion  External surface, Static plate or Core  Windings  Figure 19: Actual electric field between windings and external surface Uniform I JElectric Field  External surface, Static plate or Core  Windings  Figure 20: Approximated electric field between windings and external surface  This is not at all a poor assumption since the edge effects of adjacent windings interact to produce a net flux perpendicular to the winding and external surfaces. Only the edge effects of the top and bottom windings would not have this interaction. However, considering total height of the winding structure then these can be ignored.  39  Inter-turn c a p a c i t a n c e The capacitance between turns is treated in a similar way to capacitance from the turns to external surfaces in that the edge effects are neglected. The electric fields that are assumed present are those directly above, below and directly to the side o f a turn. Figure 21 shows the electric field distribution considered.  The dotted lines are examples o f  fluxes that would be ignored.  ^  innr P I P P n r -  f  ML  ^  h.illU  Figure 21: Electric field assumed between windings  Apart from these two assumptions o f uniformity, the only other assumption with respect to the modeling o f the capacitance is its dependence on location o f the turn in the winding structure. Since capacitance is dependent on the electric field, turns at different locations of the windings would experience different net electric fields. For example the turn on the top left corner o f Figure 21 has only capacitance to two turns while the one at the centre has capacitance to 4 turns. To model this, the winding was separated into 9 main sections as illustrated i n Figure 22.  40  OUTER  TOP  Figure 22: Separation of winding for capacitance distribution  The capacitance for each of the nine sections can be separately specified. This allows the user to determine whether the capacitances (to ground for instance) should be distributed equally throughout the length of the winding or should it be confined to a particular set of windings alone.  Modeling of Resistance  Although both the inductance and the resistance are dependent on the skin effect the inductance is taken to be constant at the value of the external inductance while the resistance is altered at every simulated frequency. Two options are provided for the calculating of the resistance. The first is simply an application of Lord Rayleigh's observation that at sufficiently high frequencies the resistance is proportional to the square root of the applied frequency  Though this is traditionally applied to overhead cables that have circular construction it can also be shown to be true for conductors of rectangular construction. Consider the  41  rectangular section of dimensions x and y below through in which current is flowing through the shaded region:  Figure 23: Skin effect due to high frequency, current only flows through shaded region  A  DC  A  hf  A  hf  = xy = xy - (x - 2d)(y =2xd  2d)  + 2yd + 4d  2  pi A  (19)  2xd + 2yd + 4d'  1 where  k = — T =  d - skin depth =  *-  _  Jc  *  —  k  .k  (20)  r  2x-p= + 2 v - ^ + 4 —  V7  V7  asf->oof:R=  /  p  k  v7  (2x + 2y)  (21)  R = Kjf where K =  l  — k(2x + 2y)  42  Using this method the resistance of the winding at a known high frequency is entered; the value of the constant K is calculated and used to recalculate the resistance at every new frequency.  The second option allows the user to enter the conductor dimensions, the conductivity and permeability of the rectangular conductor. Using the conductivity and permeability the skin depth at a particular frequency is calculated, the resistance is then calculated by using the area through which current flows and the resistivity of the conductor. This method is expected to be more accurate for lower frequency simulations where the high frequency approximations made do not hold. For the general application of this model proposed (high frequencies) both methods should give roughly the same results.  By either method the resistance calculated is the resistance corresponding to the length of the winding section used and is placed in series with winding section.  5.3 PROGRAM  STRUCTURE  The software was developed in the MATLAB v7.04 programming environment for data processing while the Microtran Circuit Simulator (an external program), was used for carrying out simulations. The entire simulation process involved four main stages sequentially run in the order below: 1. Calculation of parameters. 2. Data file generation. 3. Running Simulations. 4. Processing output files.  The process is now completely automated and does not require Microtran to be run separately by the user as was the case in earlier software iterations. The following subsections outline the main responsibilities of each stage of the simulation process.  43  Calculation of parameters  The program requires the user to input the following data regarding the transformer winding to be tested: •  Number of turns per pancake.  •  Number of pancakes.  •  Turn length.  •  Inter pancake capacitance.  •  Inter turn capacitance.  •  Capacitance to ground.  •  Capacitance to static plates.  • •  Velocity of propagation. Transformer MVA.  •  Transformer kVA.  •  Resistance at a specified high frequency.  •  Amplitude of signal.  •  Vector of frequencies to be simulated.  The number of turns per pancake, number of pancakes and the capacitances specified are used to generate the capacitance matrix which is of the following form for a system with 5 turns and 2 pancakes.  44  -c„ -c„  0  0  0 0  0 0  0  Z^tt.3  0  0  0  -c„  0  -c  ip  0  0  -c.  0  0  -c.  0  0 0  0  0  Figure 24: Illustration of phase capacitance matrix for 2 pancakes with 5 turns each  The number of matrices on the diagonal is equal to the number of pancakes and the size of each of these matrices corresponds to the number of turns. The following points should be noted:  •  The inter pancake couplings form the diagonal elements of the off diagonal matrices.  •  There is no inter-turn capacitance C„ in the off diagonal matrices  •  The Diagonal elements are the sum of all included capacitances including the inter turn; inter pancake and ground capacitances.  •  The off diagonal elements, namely C and C„ are fixed while the sums calculated ip  for the diagonal elements can be changed according to the position of the winding (outer-top, middle-top etc).  Once this matrix is obtained, it is used to calculate the inductance matrix using the equation relating capacitance inductance and velocity:  [^EXTERNAL  EXTERNAL  45  V  (22)  The capacitance matrix is then diagonalized by a similarity transformation. It should be noted that the same matrix that diagonalizes the capacitance matrix also diagonalizes the inductance matrix. Data file g e n e r a t i o n  The transformer includes a number of large multiphase systems that need to be simulated at a number of frequencies so the data files become exceedingly long, approximately 1500 lines, and therefore cannot be written by hand. The data file format for Microtran is reproduced in Figure 25.  Item "1" '21 [31 S [41 $  [51 S "6" i  [S"  s  s  Description CASE IDENTIFICATION CARD. TIME CARD. LINEAR AND T R U E NONLINEAR BRANCHES. Blank line to terminate section '31. SWITCHES AND PIECEWISE LINEAR BRANCHES. Blank line to terminate section [4], SOURCES.  Blank line to terminate section '51. USER-SUPPLIED INITIAL CONDITIONS. NODE V O L T A G E S OUTPUT. POINT-BY-POINT USER-DEFINED SOURCES. Blank line to terminate the data ease. NEXT D A T A CASE Blank line to terminate the set of cases.  Figure 25: Datafileformat, reproduced from the Microtran product manual [14]  The data file is a text file that is read by columns. Node names were pre assigned based on the layer and turn of the winding as shown in Figure 26.  46  Knpnt  -AAA  -A/W-  Mnpnt  1  Source resistance  Uw  H  Uw Uw  mrw  AAA  w  n  UAA  . /777m Figure 26: Circuit set up for Microtran simulations  In the above circuit the nodes on the sending end of the transmission line are named 'k' followed by the pancake number 'np' and then the turn number 'nt' which it represents. The receiving end is named'm' followed by 'np' and 'nt' for the pancake and turn which it represents. The lumped resistance represents losses and the lumped inductance is the propagation leakage. The details of the data card formats are available in the Microtran Reference manual and shall not be reproduced here.  The root name of the data case is specified by the user, e.g. 'base_case' and the program generates a sequence of cases bearing this name for each frequency in the vector of frequencies specified.  For example if five frequencies are specified the program will  generate the following files:  base_casel.dat base_case2.dat base_case3.dat base_case4.dat base case5.dat 47  Running simulations  Running Microtran has been automated in two ways in the Matlab program. The first method entails saving all the generated data files into the same folder as the Microtran executable programme. All "*.dat"filesshould be configured to open with the Microtran executable. The "winopen" function in Matlab is then used to open the file. The second method uses the command prompt to run Microtran and does not require files being placed in special folders or being configured to open using the Microtran executable. In this method the dos prompt was used to open Microtran from Matlab, passing it the name of a the simulation file for microtran to run. The output file is in the same directory of the input file specified.  P r o c e s s i n g o u t p u t files  Once the output files have been generated, the program can search for these files which have the same names as the inputfilese.g. base_casel.out base_case2.out base_case3.out base_case4.out base_case5.out  The output data from Microtran is formatted. By counting a predetermined number of spacesfromthe end of the file the voltage and current output data can be extracted. This is done for each file and a value of characteristic impedance, trans-admittance and transimpedance are calculated. When all the files are read the points are automatically plotted along with the numerical differences and the percentage difference between the plots (if two plots are specified). The following chart summarizes the entire program  48  READ INPUT DATA  BUILD CAPACITANCE MATRIX  Calculate Leakage and propagation inductances  yes —  Compute new resistance and Generate data file for current frequency  •  Run microtran simulator for all data files  Extract data from output files  Calculate: Characteristic Impedance, Trans-admittance Trans-impedance  Plot: Characteristic Impedance, Trans-admittance Trans-impedance  Figure 27: Algorithm for developed software  49  CHAPTER 6: MEASUREMENT AND MODELLING ISSUES 6.1  INTRODUCTION  This section explores the influence of the frequencies at which measurements are taken, the influence of lumping elements and phase error. The data for the transformer simulated is given in Table 6.  Number of turns Number of pancakes/layers Length of turn Inter-pancake capacitance Inter-turn capacitance Surge velocity Power rating Voltage rating Input resistance Output resistance  Value  Units  20 12 10 27.28 158 200x10 900 525 150 1  metres pF pFm" ms" MVA kV Ohms Ohms 1  1  b  Table 6 : Data for simulated transformer  6.2 EFFECT  OF FREQUENCY  ON  MEASUREMENT  The frequencies at which characteristic impedance measurements are taken can affect the accuracy of the results. To illustrate this a simple test was done (the test set up is shown in figure 28). *  ST-  \  100  10.0  f\) v  Figure 28: Simple test set up to explore the effect of lumping, Zc=200, v=200x!0'ms t  50  RESISTANCE  0 (IDEAL PROPAGATION) 1x10* 1x10"  m #25kH%  200 200 200  1  200  52.;>(>54 1.29E+05 1.31 E+04 22R.005A  217.7542 365 3291  200 200 200 200 200.0244  200.2049  204.8852  w75kH/. 200  200  JxlO" 10 50 too 500  IZcl  C#5kHz 0  201.2167 204.K939 274,2021  200.5507 202.2181 241.4878  Table 7: Results of simulation with different value of resistances at three important frequencies for fully distributed resistance  Table 7 shows that for the ideal case, frequencies of 25 kHz and 75 kHz produce accurate results while at 50 kHz the value is 0. Figure 29 shows the relationship between Z and c  the phase shifts between the input and output currents for some key frequencies. ZC CHARACTERISTICS  ' sir Figure 29: Relationship between Zc magnitude and phase shift between input and output currents for lossless line (R=0).  From figure 29 it can be seen that when the input and output currents are completely in phase (0°) or completely out of phase (180°) the results are erroneous (since there is no resistance the CP line should have a perfectly horizontal characteristic). The plots  51  suggest that there is an element of periodicity affecting the results. Errors of similar types occur at 50 kHz andl50kHz and 100 kHz and 200 kHz. This interval of 100 kHz corresponds to the characteristic frequency of the line.  This behaviour is due to standing waves being produced. When the input signal is periodic the delay corresponds to a phase shift and at multiples of the characteristic frequency the receiving end of the line falls in phase with the sending end of the line. Since there has been no loss over the length of the line the voltage and current waveforms ,at the receiving end are indistinguishable from the voltage and currents at the sending end.  These frequencies in effect make the line look like a node. The measurement  equation then becomes undefined since  Vk=V  m  and  h=I  m  yielding  Zc=0/0.  This  phenomenon is noticeable even for sizeable values of resistance such as 10Q as can be seen from Table 6.  When the resistance increases to over fifty ohms, however, the results for 50 kHz begin to look more accurate.  This is due to the fact that the output parameters have  significantly smaller magnitudes because of the high losses. When the output falls in phase with the input they are not equal magnitude so that the numerator of the measurement equation (18) does not go to zero.  6.3 EFFECT OF LUMPING RESISTANCE Transient simulations are needed for impulse testing. Due to restrictions in Microtran regarding the size of the specified resistance compared to the size of the characteristic impedance of a line (R/4 < Zc/10) it was not possible to add the resistances directly into the transmission line element. These had to be added externally in series to the transmission line elements. To explore the effect of lumping on the model, consider the following four cases: a transmission line with a distributed resistance of 1000Q (2km=1000Q); 1000Q lumped at the sending end of the line (Figure 30); 1000Q lumped at the receiving end of the line  52  (Figure 31);  and the resistance split equally between the sending and receiving end  (Figure 32).  The frequencies chosen were the quarter, half and three-quarter frequencies of the characteristic frequency of the line (velocity/line length). These were specifically chosen because the lossless transmission line corresponds to a pure delay.  Vk  100  10.0  ( \ )  Figure 30: Resistance lumped at sending end of line  2  1000.0 C P  Vk  10.0  ( \ )  Figure 31: Resistance lumped at receiving of line  Vk  Vk  500.0  2  500.0 C P  —A-o  .  . . .  Vm  100  10.0  f\)  Figure 32: Resistance split between sending and receiving end of line  53  Location  Z at 2 5 k H z / ohms c  Distributed  Z at 5 0 k H z / ohms c  365.3291  Z at 75kHz / ohms c  274.2021  249.4978  Front  205.0015  3.0307e+003  205.0015  Back  39.1868  18.2793  39.1868  Back and F r o n t  538.5236  500.6786  538.5236  Table 8: Differences arising out of different lumped models.  Table 8 shows that the results for the distributed line are the most accurate. It shows a general decreasing trend with increasing frequency as expected. The lumped models however give oscillating results (first decreasing and then increasing or vice versa). It is therefore necessary to have as little lumping as possible for accurate simulation.  6.4 PHASE 'ERROR'  Characteristic impedance phase angle vs frequency  frequency / Hz  x to"  Figure 33: Variation of characteristic impedance phase angle with frequency  Figure 33 shows that the phase angle is in the region of 88 to 90 degrees when at high frequencies the angle should be approximately 0 degrees. This error is only seen in the multiphase model. This indicates that the inter turn capacitances may act as leakages that  54  provide alternate signal paths to the main path along the winding thus introducing phase shift.  It may also be due to the steady state measurement of the voltages and currents and the equation used to calculate the characteristic impedance (18). At high frequencies the multiphase transformer looks like a capacitive network. In steady state, therefore, the current leads the voltage by 90 degrees (verifiedfromdata). This is in turn reflected in the Characteristic impedance value as calculated by equation 18.  The large trough at 1MHz is an illustration of the error introduced by measurements at frequencies around the characteristicfrequency.In this case, it is the characteristic frequency not of the entire winding or an individual turn but of a multiphase section (pancake, 200m).  55  CHAPTER 7: COMPARISON OF TLD AND FRA METHODS 7.1  INTRODUCTION  In this section the transformer model developed is used to simulate different types of fault conditions. Changes obtained from the Characteristic Impedance and trans-admittance signatures are also compared. The program developed also computes the trans-impedance signature which is simply the inverse of the trans-admittance signature. Those plots, however, are not reproduced in the main body of this report as its strengths and shortcomings are the same as those of the trans-admittance. Simulations are performed up tofrequenciesof 3MHz which is higher than the limit of 2MHz used in the physical experiments performed at Power Tech Labs.  The winding deformations simulated are divided into four main categories 1. Changes in line resistance 2. Winding bulging 3. Winding loosening 4. Winding compression  7.2 EFFECT  OF WINDING  RESISTANCE  The basic simulations have shown lumping to be critical to obtaining good results. The multiphase model uses 240 sections of line, this means the external line resistance is somewhat, though not fully, distributed. The code was amended to fully distribute the resistance using the exact pi-circuits in steady state solution. The line resistances were specified as a percentage of Zb - For the purpose of simulations the percentage was ase  varied between 1% and 200%. Although resistances above of 10% of Zb seen in reality they are simulated for the sake of illustration.  56  ase  may never be  Comparison of Zc signatures for different values of line resistance  frequency / Hz  Figure 34: Z different values of input resistors c  Figure 34 shows that as the resistance increases there is a corresponding upward shift of the characteristic impedance. Separation between signatures -R=10% - R=50% -R=100% - R=200%  E  300  8! E  1 0 0  Frequency /Hz  Figure 35 : Relatively constant separation between signatures  Figure 35 shows the separation between the signatures.  Except for the initial slight  oscillation the separation between the curves remains relatively constant.  57  Variation of differences in Zc at different frequencies  Resistance as a percentage of Zbase /%  Figure 36: Change in Z for different winding resistances at different frequencies c  Figure 36 shows that the percentage change in Zc with the percentage change in resistance is almost linear. The separation between the plots is due to the fact that the separations are not exactly constant over the frequency range. As the frequency increases the separation between the signatures (Figure 34) also increases slightly. It should be noted however that the higher frequency plots of Figure 36 seem to be closer together. This is because at higher frequencies the signatures level off.  It would be better,  therefore, to use higher frequency measurements in any attempt to quantify the winding movement from the plots.  58  frequency/Hz  *">*  Figure 37: Transadmittance characteristics for different values of input resistors  Figure 37 shows the transadmittance signatures for the same cases as Figure 33. The separation between the curves varies considerably with frequency, unlike the case of the characteristic impedance. Figure 38 shows the differences of the plots at different frequencies.  frequency/Hz  Figure 38: Separation between characteristics from R=l% signature  59  * 10°  Resistance / percent of Zbase  Figure 39: Change in TA for different winding resistances at different frequencies  Figure 39 shows that specific frequencies cannot be chosen to analyze the differences between the transadmittance plots as can be done for the characteristic impedance.. Transadmittance characteristics are not monotonically decreasing functions like the characteristic impedance, but contain resonant peaks.  The frequency range used for  simulation does not show any resonant peaks, however, figure 37 shows that the plots for low values of line resistance seem to be bent upward, in the shape of the low frequency side of a resonant peak. The plots for higher values of resistance do not have this shape indicating that their resonant peaks may be at higher frequencies. These resonances make the interpretation of the Transadmittance signatures more complicated than the characteristic impedance signature. 7.3 WINDING  BULGES  The winding bulge case is simulated by assuming that all the ground capacitance of the winding is to the tank. When the winding bulges, the windings come closer to the tank and so the ground capacitance increases. The parameter data borrowed for the model [15] did not specify distance to tank, so the capacitance is changed by percentage. Figure 4shows the deviation of the Z signatures for 5%, 10%, 15% and 20% increases in the c  capacitance to ground.  60  Comparison of Zc signatures for changes in capacitance to ground - Baseline signature - 5% increase - 10% increase - 1 5 % increase  :  - 20% increase  w  10000 k  E  frequency / Hz  Figure 40: |Z | signatures for variations in C C  g  Percentage change from baseline signature for change in ground capacitances  - * —  10%  -e—  15%  — i — 20%  frequency / Hz  mo"  Figure 41: Percentage deviations from base plot for |Z | for variation in C C  g  Figure 41 shows that the percentage change between the plots remains relatively constant throughout the frequency range. The measured percentage changes are related to the' actual change in capacitance through a simple scaling factor: Actual  change  = Measured  61  change  x K  Actual percent Change /% 5 10 15 20  Scaling factor (K) 2.0858 2.1649 2.2244 2.3021 .  Measured percent change /% 2.3971 4.6192 6.7433 8.6879  Table 9: Actual and measured percentage changes for Z signature for winding bulges c  Table 9 shows that the scaling factor remains relatively constant (10% change from smallest to largest). This indicates that the measured percentage change can be used to directly estimate the physical bulge of the winding if the scaling factor can be determined. -»  Comparison of TA signatures for change in capacitance to ground  x 10  -  baialina ilgnatu 5% Incna** 10% Incraas* 15% tncr»a»* 20% incraai*  frequency / Hz  Figure 42: |TA| signatures for variations in C  g  Percentage change in TA from baseline signature for changes in ground capacitance  frequency/Hz  > 10  Figure 43: Percentage deviations from base plot for |TA| for variation in C  62  g  Actual percent Change /% 5 10 15 20  Measured percent change /% 2.8597 5.6444 8.3345 10.9169  Scaling factor (K) ' 1.7484 1.7717 1.7997 1.8320  Table 10: Actual and measured percentage changes for T A signature for winding bulges  Figure 43 and table 10 show that the transadmittance signatures exhibit similar behaviour to the characteristic impedance signatures in that the percentage change in the signatures are relatively constant. This however can only be said because no resonances have been encountered. The change in characteristic has the effect not only of changing the magnitude of the resonant points but also thefrequencyat which they occur making the separation of the signatures change dramatically around those points.  For this type of deformation both characteristics respond similarly to the increase in capacitance with an downward shift in the difference characteristics being evident. The trans-admittance however is marginally more sensitive with changes varying between 2.9% and 11%. The characteristic impedance signatures varied between 2.4% and 8.7%  7.4 WINDING LOOSENING Windings may become loose when they experience radial forces that stretch the clamps that hold them in place beyond their elastic limits. The result is that the winding becomes slightly unwound and the space between the turns increases. This is modeled as an decrease in the inter-turn capacitance of the winding. From the case data [15] the interturn separation is 3.5mm. Increases of 1mm, 2mm, 5mm and 10mm are modeled.  63  Comparison of Zc signatures for changes in inter-tum capacitance  frequency / H z  Figure 44: Actual plots for |Z | for variation in C  C  i n t e r  .  t u r  Comparison of percentage change in Zc signatures for decreases in inter-tum capacitance  frequency / Hz  Figure 45: Percentage deviations from base plot for |Z | for variation in Ci„, ,-tur C  Winding loosening / m m  Percent change in Cjnter-turn/  1 2 5 10 Table 11: Actual and  ^  Averarge measured  c  Scaling factor (K)  percent change / %  1.6659 13.1926 21.9780 1.4409 25.0101 36.0360 1.0600 55.1708 58.4795 0.7734 95.4251 73.8007 measured percentage changes for Z signature for winding loosening c  64  Figure 45 shows that the percentage changes are still relatively constant throughout the frequency range. However, the scaling factor between the percentage change in capacitance and the measured percentage change vary widely.  This means that the  percentage change that is measured is not a direct indication of how much the winding has separated as in the case for winding bulges.  Comparison of TA signatures for change in inter-tum capacitance  frequency / Hz  Figure 46: Actual plots for |TA| for variation in C ter-turn in  Comparison of percentage changes in TA signatures for decrease in inter turn capacitance  -- 1 m 5m mm m -- 2 m 10m m  a-a-a-a-a-H" - e - s -  frequency/Hz  •  Figure 47: Percentage deviations from base plot for |TA| for variation in  65  xio*  C  inte  r-turn  Winding loosening /mm 1 '2 5 10  Percent change in (\ 10/ *-Mnter-turn' '*> 21.9780 36.0360 58.4795 73.8007  Averarge measured percent change /% 33.5670 53.2875 80.1580 93.2565  Scaling factor (K) 0.6548 0.6763 0.7296 0.7914  Table 12: Actual and measured percentage changes for TA signature for winding loosening  Here also the percentage changes remain relatively constant but the measured percentage but the scaling factors vary too much to be considered a direct indication of the winding movement.  Once again the change in capacitance has caused a corresponding unidirectional shift in both of the'characteristics. This time the Zc characteristic increases since the capacitance is being decreased however the Trans-admittance characteristic decreases just as it did in the case where the capacitance to ground was being decreased.  This time, the  characteristic impedance signature showed a greater range in the percentage changes from approximately 13% to 95% while the transadmittance signature showed a range of 33% to 93%.  7.5 WINDING COMPRESSION Winding compression basically creates the opposite effect to winding loosening. When a radial force is experienced, the windings are forced outward..This force is mustfirstdo the work of compressing the insulation before the force is transferred to the clamps that keep the winding in place, if the clamps are strong enough to not undergo plastic deformation then the windings may not become loose after the surge but remain in a compressed state. Since the insulation is compressed the turns are closer together and so the inter-turn capacitance increases.  Simulations were performed to simulate  compressions of 1mm, 2mm and 3mm with the baseline signature corresponding to a separation of 3.5mm. To simulate this, the inter-turn capacitance had to be increased proportionally.  66  Comparison of Zc signatures for inrease in inter turn capacitance  frequency / Hz  Figure 48: Actual plots for |Z | for winding compression C  Comparison of percentage change of Zc signatures for increase in inter turn capacitance - 2mm - 3mm  frequency /Hz  Figure 49: Percentage deviations from base plot for |Z | for winding compression C  Scaling factor (K)  Percent change in  Averarge measured  compression / m m  Cinter-turn/%  percent change / %  1  39.2157  15.2065  2.5789  2  129.0323  33.7825  3.8195  3  545.4545  60.1935  9.0617  Winding  Table 13: Actual and measured percentage changes for Z signature for winding compression c  67  Comparison of TA signatures for increases in inter turn capacitance  frequency  Figure 50: Actual plots for |TA| for winding compression Comparison of percent change in TA signatures with increase in inter turn capacitance - datal - data2 - data3  frequency /Hz  Figure 51: Percentage deviations from base plot for |TA| for winding compression Winding  Percent change in  Scaling factor (K)  /% 0.6047 64.8471 39.2157 1 0.5768 223.6866 . 129.0323 2 0.5532 986.0275 545.4545 3 Table 14: Actual and measured percentage changes for TA signature for winding compression  compression / m m  c  Averarge measured percent change / %  ^-'inter-turn' ' «  68  The Trans-admittance signature is extremely sensitive to this type of deformation, exhibiting between 65% and 987% deviations, while Zc exhibits a range of between 15% and 60%, which is still quite sensitive but as not sensitive as the trans-admittance.  Although this type of deformation is simply the opposite, of the loosening case, the transadmittance now has a greater range than the characteristic impedance. This means that as the windings become more separated the characteristic impedance signature becomes more sensitive but if they become compressed the transadmittance will tend to become more sensitive.  69  CHAPTER 8: DISCUSSIONS 8.1  GENERAL  Measurements become increasingly inaccurate as multiples of the half wavelength of the signal approaches the length of the winding. At these points the input and output waves are either fully in phase or fully out of phase, causing standing waves. It has been shown that with small values of line resistance this may cause the value of Z to be very much c  larger or smaller than the expected value. Higher values of resistance seem to have a stabilizing effect on the characteristic since the energy loss caused by them reduce the similarity of the input and output waveforms. This means that at high frequencies the accuracy of the model should improve since the resistance increases proportionally with the square root of the frequency. This is why there was no evidence of discontinuities in the simulations done (the resistance becomes high in the Megahertz range). The previous section compared the sensitivity of the characteristic impedance signature to the trans-admittance signature for different types of winding deformations. In the case of the winding bulging both showed similar levels of discrimination with the transadmittance being only marginally better.  For this type of deformation, the  percentage change between the baseline signature and the signature after deformation could be directly related to the actual percentage change in capacitance. This was true for both the characteristic impedance and trans-admittance signatures. However, the range of frequencies was too low to see any resonances in the transadmittance signature. Figure 52 shows a transadmittance plot up to 10MHz that illustrates the presence of resonances, while Figure 53 shows the percentage deviation over the frequency range. Figures 54 and 55 are the corresponding characteristic impedance plots.  70  Figure 52: Transadmittance signature up to 10MHz for low line resistance  201  1  1  ;  Percentage change in TA signatures [  i  Figure 53 : Percentage change in transadmittance signatures  71  Comparison of Zc signatures for low line resistance - 20% change in capacitance to ground - baseline signature  frequency / Hz  Figure 54 : Characteristic impedance signature up to 10MHz for low line resistance  Percentage change between Zc signatures  frequency / Hz  Figure 55: Percentage change in characteristic impedance signatures  Figure 53 shows a variation of about 10% with an average of approximately 11-12% deviation. This indicates that in the presence of resonances the approximately constant  72  relationship between the change in capacitance and the measured percentage difference does not exist any longer. In the case of the characteristic impedance the variation is approximately 0.5% with an average of about 8.65%. The dip toward the end is caused by standing waves produced at the characteristic frequency (10MHz) of the turns.  The data at problematic frequencies can be discarded without any loss in information for the characteristic impedance signature. This can be done first plotting all points then looking for changes in the sign of the gradient. When the gradient between two points is positive these points can be discarded. The percentage change would then exhibit even less variation indicating that the characteristic impedance can still be used.  Winding compression and loosening involved changing the same capacitance. They were simulated separately to emphasize the fact that as the windings came closer together the transadmittance signature became more sensitive and as they went further apart the characteristic impedance became more sensitive. If a record of past signatures are kept (not just one baseline signature), it may be possible to tell how the winding is moving based on how the relative magnitude of percentage deviation noticed in each signature changes.  The methods also responded differently from each other for different types of distortions. That is, a certain type of deformation may cause an increase in the trans-admittance while it causes a decrease in the characteristic impedance. Table 15 summarizes this behaviour for the three types of deformations examined.  DISTORTION TYPE  Z  c  SHIFT TYPE  T A SHIFT TYPE  BULGE  Decrease  Decrease  LOOSEN  Increase  Decrease  COMPRESS  Decrease  Increase  Table 15: type of shifts exhibited by the Z and TA characteristics c  73  This combination of the characteristic impedance and trans-admittance signatures can form the beginning of a primitive winding deformation classifier. Table 15 shows that a combination of both methods allows us to uniquely classify deformation types.  Although these deformations have been dealt with separately, in practice they would occur in combination. When a radial force is experienced it is likely that the insulation would become compressed and the windings would bulge, or after the windings have expanded due to the initial force and the clamps exceeded their elastic limits the winding would become loose as well as wider.  Unsymmetrical deformations may also occur, causing some windings to bulge more than others. Deformations such as these have major implications for the capacitance matrix that is built for the model. The capacitance matrix is built based on the grid like geometry of the winding structure. If some windings expand more than others the symmetry of the grid is broken. Turns may no longer have other turns exactly above and below and on either side as shown in Figure 56 below.  EXPANDED " PANCAKE  m  it  Figure 56: Unsymmetrical deformation causing turns on one pancake to link multiple turns on adjacent pancake  In situations such as these the capacitance matrix would have to be constructed to mirror this re-distribution of flux. Not only would the inter-pancake capacitances be affected but the capacitance from the winding to external structures such as the core or the tank  74  would no longer be equal. Windings may also become twisted such that turns no longer lie on a single plane. The model does not have the capability to deal with such complex deformations, however, the intention of condition monitoring is to pick up deformations in their early stages before such serious conditions manifest.  8.2 IMPULSE  TESTS  (FRA- LVI)  The original intention of the work presented was to compare the FRA-LVI method to the TLD method, however the impulse technique involves taking the Fourier transform of the input and output voltage and current waves to obtain phasor information for calculation of the trans-admittance or trans-impedance. This technique, however, is best suited for transient analyses since the Fourier transform assumes that the waveforms being analyzed are undamped whereas transients are by nature heavily damped. Transient signal frequencies have finite energy. Since the resistance of the line increases with frequency some frequencies would be attenuated faster than others. The problem can be illustrated by taking the hypothetical situation of the finite energy of a particular frequency being dissipated after two seconds. If the sample window is large, say ten seconds, then the Fourier transform would represent this frequency by a constant amplitude signal over the entire ten seconds, even though it is only there for two seconds in actuality.  This false representation would cause an erroneous representation of the winding transadmittance. Jayalalitha [16] shows that different transfer functions are obtained for different wave shapes such as chopped waves and impulse waves. He similarly finds that the transfer functions obtained by impulse tests "ignore the finite energy deterministic nature of the input" and proceeds to use winding current as a basis for detecting partial discharge.  The signatures produced by impulse testing, however, are still valid signatures.  If  properly done they can be very similar to the actual transadmittance signatures gained from swept frequency methods. 75  8.3 FUTURE  WORK  The model can be improved by using to a frequency dependent line model. For steady state simulations this can be done roughly on the current CP-line system by changing the velocity at every frequency step. If transient simulations are required however, then the model would have to be rebuilt using FD-line models in Microtran. The reason for this is that the line resistances are lumped at the line ends for transient simulations in the CPline model while they remain fully distributed in the FD-Line model. The difficulty with constructing an FD line model would be the modeling of the frequency dependent inductance. References [17] and [18] discuss the modeling of skin effect inductance by ladder networks, while [19] and [20] discuss the quantification of skin effect in a system of rectangular conductors.  The FD-line model data can also be obtained from a transformer when it is taken offline and used as a basis to construct a software representation as close as possible to the actual winding. If this, along with the modeling of deformations can be done with a sufficient level of accuracy then the model can be used to generate deformation signatures to train neural networks which can then be used to analyze the actual datafromthe transformer.  An additional benefit of the FD-line model is that it can be used in time domain reflectometry simulations.  Time domain reflectometry can be used to pinpoint  discontinuities on the winding, however because it is very sensitive to lumping and is a time domain method, the CP line can no longer be used since it lumps the line resistance for transient simulations.  Work also needs to be done in developing an intelligence based system that utilizes the data from both the characteristic impedance and transadmittance signatures to reliably diagnose the type of winding deformation.  The system accuracy was limited by the fixed column widths that Microtran used for data entry. The Microtran simulator was not designed to cater for such a complex multiphase  76  system which involves very small lengths of transmission lines.  The model suffered  limitation from both truncation errors and limited number of phases available for use in a multiphase element. These problems need to be remedied if the model is to be used in matching the measured impedances of real transformers.  77  CHAPTER 9: CONCLUSIONS The model behaved as expected.  Simple functions can be written to change the  capacitance matrix if more complex deformation cases need to be simulated. The model can be used to find additional patterns (such as the changes in the sensitivity of the transfer functions) which can aid in the classification of deformation types.  The simulations showed that the characteristic impedance signature is comparable to the transadmittance signature in terms of ability to detect changes in winding geometry. In addition to this, in some cases it can also be used to directly quantify the winding movement.  Both methods rely on the same measured data therefore a combination of both can be used to improve the ability to distinguish between deformation types. This would be more reliable than using either signature in isolation since each signature involves a different property of the winding and so behaves differently for different types of winding displacement. In future, other signatures may easily be added to improve the analysis, provided that they do not need extra input or output data.  The model should be rebuilt using frequency dependent line elements to increase accuracy.  This would also facilitate experiments using impulse methods and  investigation into time domain reflectometry.  78  REFERENCES [1]  Augenstein, B. Fox, W. Fischer, P. "Outsourced Monitoring and Reliability of Critical Assets", Distributech,  [2]  Serveron  Corporation  p. 6. (2003).  Wang, M. Vandermaar. A.J. "Review of condition assessment of power transformers in-service", IEEE  Electrical  Insulation  Vol. 18, No. 6.  Magazine,  pp. 12-25. (2002).  [3]  Franklin, A.C. Franklin, D.P. "The J&P Transformer Book 11 Edition: A th  Practical Technology of The Power Transformer", Butterworth  & Co. Ltd,  p. 629.  (1983). [4]  Jiang, Q. "Diagnostic of transformer winding movement", MaSc thesis, University  [5]  of British  Columbia.,  pp. 7-8. (2004).  Tanguay, F. "Transformer Maintenance: The Cheapest Form of Insurance Part 1 :The Transformer Killers", Electricity  [6]  No. 1, pp. 5-9. (2002).  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