Topological transient models of three-phase, three-legged transformer

The paper further develops a modeling concept of three-phase, three-legged transformer with tank walls represented as a distributed parameter structure. The circuital models proposed replicate accurately all possible zero-sequence impedances and losses of a three-winding transformer. Several model versions are compared to each other and to a conventional topological model with respect to their transient behavior during inrush and short circuit events, and in the presence of geomagnetically induced current (GIC). It was found that in all the cases considered, except that with a large GIC, all the models yield similar results. The reliability of the models is due to the representation of the tank walls behavior in a physical way, allowing one to observe the field distribution over the wall thickness as a function of transformer excitation. The modeled results are in a close agreement with positive and zero sequence data measured on a 25 MVA transformer as well as with inrush current test on a 300 kVA unit

Parameter estimation for transformer modeling

Large Power transformers, an aging and vulnerable part of our energy infrastructure, are at choke points in the grid and are key to reliability and security. Damage or destruction due to vandalism, misoperation, or other unexpected events is of great concern, given replacement costs upward of $2M and lead time of 12 months. Transient overvoltages can cause great damage and there is much interest in improving computer simulation models to correctly predict and avoid the consequences. EMTP (the Electromagnetic Transients Program) has been developed for computer simulation of power system transients. Component models for most equipment have been developed and benchmarked. Power transformers would appear to be simple. However, due to their nonlinear and frequency-dependent behaviors, they can be one of the most complex system components to model. It is imperative that the applied models be appropriate for the range of frequencies and excitation levels that the system experiences. Thus, transformer modeling is not a mature field and newer improved models must be made available. In this work, improved topologically-correct duality-based models are developed for three-phase autotransformers having five-legged, three-legged, and shell-form cores. The main problem in the implementation of detailed models is the lack of complete and reliable data, as no international standard suggests how to measure and calculate parameters. Therefore, parameter estimation methods are developed here to determine the parameters of a given model in cases where available information is incomplete. The transformer nameplate data is required and relative physical dimensions of the core are estimated. The models include a separate representation of each segment of the core, including hysteresis of the core, λ-i saturation characteristic, capacitive effects, and frequency dependency of winding resistance and core loss. Steady-state excitation, and de-energization and re-energization transients are simulated and compared with an earlier-developed BCTRAN-based model. Black start energization cases are also simulated as a means of model evaluation and compared with actual event records. The simulated results using the model developed here are reasonable and more correct than those of the BCTRAN-based model. Simulation accuracy is dependent on the accuracy of the equipment model and its parameters. This work is significant in that it advances existing parameter estimation methods in cases where the available data and measurements are incomplete. The accuracy of EMTP simulation for power systems including three-phase autotransformers is thus enhanced. Theoretical results obtained from this work provide a sound foundation for development of transformer parameter estimation methods using engineering optimization. In addition, it should be possible to refine which information and measurement data are necessary for complete duality-based transformer models. To further refine and develop the models and transformer parameter estimation methods developed here, iterative full-scale laboratory tests using high-voltage and high-power three-phase transformer would be helpful

Transformer Modeling for Low-And Mid-Frequency Electromagnetic Transients Simulation

RÉSUMÉ Dans cette thèse, de nouveaux modèles de transformateurs pour les transitoires électromagnétiques à basse fréquence ont été développés pour les appareils cuirassés. Ces modèles utilisent l'approche des inductances de fuite couplées, qui a l'avantage de ne pas nécessiter l'emploi d'enroulements fictifs pour connecter le modèle de fuite à un modèle topologique du noyau, tout en arrivant au même résultat en court-circuit que le modèle BCTRAN (matrice d'admittance indéfinie).Afin d'accroître le raffinement des modèles, il est proposé de partitionner les enroulements en bobines (agencement d'un ou de plusieurs tours de l'enroulement complet). Cependant, les mesures en court-circuit entre les bobines ne sont jamais disponibles, car on ne peut pas avoir accès à chaque bobine séparément en pratique. Pour combler cette lacune, une nouvelle méthode analytique basée sur la méthode des images a été développée, ce qui permet le calcul des inductances de court-circuit en 2-D entre des conducteurs de section rectangulaire. Les résultats de la nouvelle méthode convergent vers ceux obtenus par la méthode des éléments finis en 2-D. De plus, l'hypothèse que le champ de fuite est approximativement 2-D pour les transformateurs cuirassés a été validée à l'aide d'une simulation en 3-D avec un modèle plus complet de transformateur, incluant la cuve et les écrans magnétiques. Le produit de cette nouvelle méthode pour calculer les inductances de court-circuit entre les bobines a été utilisé pour calculer les inductances propres et mutuelles du modèle d'inductances de fuite couplées. Les résultats montrent, d'une part, que l'inductance de court-circuit totale des enroulements correspond bien aux mesures expérimentales et d'autre part, que le modèle d'inductances de fuite couplées donne des résultats identiques en court-circuit au modèle BCTRAN.En général, les inductances de fuite dans les modèles de transformateurs sont calculées à partir des essais en court-circuit et la branche de magnétisation est calculée à partir des essais à vide. De plus, on suppose généralement que les fuites sont négligeables pour le transformateur à vide et que le courant de magnétisation est infime pendant un court-circuit. Bien que l'hypothèse de perméabilité infinie soit valable pendant un court-circuit, car la force magnétomotrice dans le noyau est négligeable, on ne peut en dire autant de l'hypothèse selon laquelle les fuites sont négligeables à vide. En fait, le noyau ferromagnétique du transformateur commence à saturer à vide et une partie du flux magnétique fuit à l'extérieur du noyau. Pour prendre cela en compte, une méthode analytique novatrice est proposée dans cette thèse, qui permet d'enlever la contribution des flux de fuite lors des essais à vide afin de calculer correctement les branches de magnétisation des modèles proposés.Cependant, il doit être souligné que les courants de Foucault ont été négligés lors du développement de la nouvelle méthode analytique pour calculer les inductances de court-circuit (comme pour les autres méthodes analytiques).----------ABSTRACT In this work, new models are developed for single-phase and three-phase shell-type transformers for the simulation of low-frequency transients, with the use of the coupled leakage model. This approach has the advantage that it avoids the use of fictitious windings to connect the leakage model to a topological core model, while giving the same response in short-circuit as the indefinite admittance matrix (BCTRAN) model. To further increase the model sophistication, it is proposed to divide windings into coils in the new models. However, short-circuit measurements between coils are never available. Therefore, a novel analytical method is elaborated for this purpose, which allows the calculation in 2-D of short-circuit inductances between coils of rectangular cross-section. The results of this new method are in agreement with the results obtained from the finite element method in 2-D. Furthermore, the assumption that the leakage field is approximately 2-D in shell-type transformers is validated with a 3-D simulation.The outcome of this method is used to calculate the self and mutual inductances between the coils of the coupled leakage model and the results are showing good correspondence with terminal short-circuit measurements.Typically, leakage inductances in transformers are calculated from short-circuit measurements and the magnetizing branch is calculated from no-load measurements, assuming that leakages are unimportant for the unloaded transformer and that magnetizing current is negligible during a short-circuit. While the core is assumed to have an infinite permeability to calculate short-circuit inductances, and it is a reasonable assumption since the core's magnetomotive force is negligible during a short-circuit, the same reasoning does not necessarily hold true for leakage fluxes in no-load conditions. This is because the core starts to saturate when the transformer is unloaded. To take this into account, a new analytical method is developed in this dissertation, which removes the contributions of leakage fluxes to properly calculate the magnetizing branches of the new models. However, in the new analytical method for calculating short-circuit inductances (as with other analytical methods), eddy-current losses are neglected. Similarly, winding losses are omitted in the coupled leakage model and in the new analytical method to remove leakage fluxes to calculate core parameters from no-load tests. These losses will be taken into account in future work. Both transformer models presented in this dissertation are based on the classical hypothesis that flux can be discretized into flux tubes, which is also the assumption used in a category of models called topological models. Even though these models are physically-based, there exist many topological models for a given transformer geometry

Modeling for harmonic analysis of ac offshore wind power plants

This Ph.D. dissertation presents the work carried out on the modeling, for harmonic analysis, of AC offshore wind power plants (OWPP). The studies presented in this Ph.D. thesis are oriented to two main aspects regarding the harmonic analysis of this type of power system. The first aspect is the modeling and validation of the main power components of an AC offshore wind power plant. Special emphasis is focused on the modeling of wind turbines, power transformers, submarine cables, and the interaction between them. A proposal of a wind turbine harmonic model is presented in this dissertation to represent the behavior of a wind turbine and its harmonics, up to 5 kHz. The distinctive structure of this model consists of implementing a voltage source containing both the fundamental component and the harmonics emitted by the converter. For the case of transformer and submarine cables, the frequency-dependent behavior of certain parameters is modeled for frequencies up to 5 kHz as well. The modeling of the frequency-dependent characteristics, due to skin and proximity effect, is achieved by means of Foster equivalent networks for time-domain simulations. Regarding the interaction between these power components, two complementary modeling approaches are presented. These are the Simulink®-based model and an analytical sequence network model of the passive components of the OWPP. A description of model development and parameterization is carried out for both modeling approaches considering a scenario that is defined according to a real offshore wind power plant. On the other hand, the second aspect of this Ph.D. thesis is oriented to the analysis of the issues that appear in offshore wind power plants in relation to harmonic amplification risk, compliance of grid codes in terms of harmonics and power factor, and the design of effective solutions to improve the harmonic emission of the facility. The technical solutions presented in this Ph.D. thesis cover aspects regarding modulation strategies, design of the connection filter of the grid side converter and management of the operation point of the grid side converter of wind turbines. This last by means of changing the setpoint of certain variables. As inferred, these are solutions from the perspective of the wind turbine manufacturer

Modeling and Analysis of Power Transformers under Ferroresonance Phenomenon

La Ferroresonancia és un dels fenòmens transitoris més destructius dels sistemes de potència. Associa inductàncies no lineals i capacitancias del sistema, iniciant-se de maneres diferents, el que fa molt difícil la seva caracterització. Per evitar les conseqüències de la ferrorresonancia cal entendre el fenomen, predir-i identificar-lo, per poder evitar-ho o eliminar-lo. No obstant això, el seu comportament complex no permet analitzar usant mètodes lineals. A causa de les no linealitats, la solució d'un circuit ferrorresonante s'obté generalment usant mètodes en el domini del temps; típicament, mètodes d'integració numèrica per ordinador, com ara el EMTP. Algunes eines per a l'enteniment, classificació i predicció de la ferrorresonancia es presenten en aquest estudi: mapes de Poincaré s'utilitzen per identificar el fenomen; Diagrames de Bifurcació s'utilitzen per detallar la ubicació dels canvis abruptes en estudis paramètric; Mapes 3D i 4D s'implementen per generalitzar el comportament complex del sistema. D'altra banda, els transformadors són sens dubte l'equip que requereix un modelatge més detallat. Els paràmetres utilitzats en el model han de ser adequats específicament per al tipus d'estudi a realitzar, d'una altra manera, les simulacions podrien no reproduir els casos correctament. En aquesta tesi, es presenten els detalls per modelar transformadors monofàsics i trifàsics. A més, es presenten noves tendències per representar fenòmens físics com el cicle d'histèresi.La Ferrorresonancia es uno de los fenómenos transitorios más destructivos de los sistemas de potencia. Asocia inductancias no lineales y capacitancias del sistema, iniciándose de maneras diferentes, lo que hace muy difícil su caracterización. Para evitar las consecuencias de la ferrorresonancia es necesario entender el fenómeno, predecirlo e identificarlo, para poder evitarlo o eliminarlo. Sin embargo, su comportamiento complejo no permite analizarlo usando métodos lineales. Debido a las no linealidades, la solución de un circuito ferrorresonante se obtiene generalmente usando métodos en el dominio del tiempo; típicamente, métodos de integración numérica por ordenador, tales como el EMTP. Algunas herramientas para el entendimiento, clasificación y predicción de la ferrorresonancia se presentan en este estudio: mapas de Poincaré se utilizan para identificar el fenómeno; Diagramas de Bifurcación se utilizan para detallar la ubicación de los cambios abruptos en estudios paramétrico; Mapas 3D y 4D se implementan para generalizar el comportamiento complejo del sistema. Por otro lado, los transformadores son sin duda el equipo que requiere un modelado más detallado. Los parámetros utilizados en el modelo deben ser adecuados específicamente para el tipo de estudio a realizar, de otra manera, las simulaciones podrían no reproducir los casos correctamente. En esta tesis, se presentan los detalles para modelar transformadores monofásicos y trifásicos. Además, se presentan nuevas tendencias para representar fenómenos físicos como el ciclo de histéresis.Ferroresonance is one of the most destructive transient phenomena in power systems. It involves the association of nonlinear magnetizing inductances and capacitances, and may be initiated in many different ways, making very difficult its characterization. To prevent the consequences of ferroresonance it is necessary to understand the phenomenon, predict and identify it, to finally avoid it or eliminate it. However, it cannot be analyzed or predicted by computation methods based on linear approximation. Because of nonlinearities, the solution of a ferroresonant circuit is usually obtained using time-domain methods; typically, a computer-based numerical integration method such as the EMTP. Tools for discerning, classifying and predicting ferroresonance are collected in this study: Poincaré maps are used to describe the time behavior of a system; Bifurcation Diagrams are utilized to detail the locations of all the abrupt changes in parametric study; 3D and 4D Maps can be implemented to generalize a complex system behavior. On the other hand, transformers are unquestionably the equipment demanding most detailed modeling. The parameters used in the model should be adequate specifically for the type of study to be performed, other way, the simulation may not reproduce the real cases. In this thesis, details are presented to modeling single- and three-phase transformers. In addition, new trends are presented to address important physical phenomenon such as hysteresis cycle

Contribution for the Study of Inductive Fault Current Limiters in Electrical Distribution Grids

Inductive type fault current limiters with superconducting tapes are emerging devices that provide technology for the advent of modern electrical grids, helping to mitigate operational problems that such grids can experience as well as preventing the often-costly upgrade of power equipment, namely protections. The development of such limiters leads to several design challenges regarding the constitutive parts of those devices, namely the magnetic core, primary winding and superconducting secondary. Fault current limiters are required to operate at overcurrents during a certain amount of time. The operation at such currents can lead to harmful effects due to mechanical, electromagnetic and thermal stresses, especially in the superconducting tape. Since the operation principle of fault current limiters envisaged in this thesis is based on the superconducting-normal transition of superconducting materials, the study of its transient behaviour is an important research subject. In this work, an electromagnetic methodology based on the characteristics of the constitutive parts of the limiters, previously developed and compared to finite element modelling simulations with very similar results, is simulated and validated with experimental results. Furthermore, the current in the superconducting tape is modelled from experimental results with the purpose of predicting the temperature of the material during normal and fault operation conditions, by employing a thermal-electrical analogy. These results are also compared to experimental measurements. A fast simulation tool, with computation times in the order of minutes, is also developed in Simulink, from Matlab environment. With the developed simulation tool, it is possible to quickly predict the transient electromagnetic-thermal behaviour of an inductive type fault current limiter operating in electrical grids, namely the line current and primary linked flux, as well as current and temperature in the superconducting tape

Transformer Thermal Assessment under Geomagnetically Induced Current Conditions

Power transformers are one of the most critical and expensive pieces of equipment in power systems. The widespread use of the transformer in power grids and its high cost make the lifetime and reliability of this apparatus highly important. Although some factors affect the reliability of transformers, thermal and electrical stresses are the main reasons for transformer failure. As a result, transformer thermal modeling is essential in the design and operation stage to represent the thermal behavior of transformers during normal operation or transient phenomena. However, the multi-physics behavior of transformers and the nonlinear and frequency-dependent parameters make this modeling a challenging task. This thesis aims to develop a more accurate transformer model for representing the thermal behavior of transformers, especially during transient phenomena such as Geomagnetically Induced Current (GIC). To fulfill this goal, it is necessary to perform several tasks in different fields, such as geometry and material modeling, electromagnetic studies, and investigation into computational fluid dynamic (CFD) analysis of transformers. First, the GIC phenomenon and its impact on the transformer are briefly explained. Then, a comprehensive literature review of existing transformer thermal models is performed to find their drawbacks. A 3-phase, 3-leg transformer is then subjected to an electromagnetic-thermal study in both normal and GIC conditions. It is shown that the structural parts, including the tank, clamps, and tank shunts, are saturated with a small amount of GIC. However, the transformer core becomes saturated with larger currents, resulting in additional stray losses in the structural parts. The findings show that the most vulnerable part is the tank, as the hot spot temperature (HST) of the tank approaches 372.14 0C, which is double the permissible limit, under 66.6A GIC per phase. Finally, a new approach is proposed to determine the HST of OIP bushing based on the FEM-modified thermal equivalent circuit (TEC) model. The proposed model can accurately estimate the HST of the bushings under normal and GIC conditions. Furthermore, a detailed thermal analysis is performed to investigate the impact of different parameters such as load, ambient temperature, and top oil temperature on the thermal performance of bushings

Duality derived topological model of single phase four limb transformers for GIC and DC bias studies

Geomagnetic disturbances brought about by solar activity cause geo-electric fields in the Earth that drive geomagnetically induced currents through the earthed neutrals of transformers and through power transmission networks. The flow of these currents causes the magnetic cores of transformers to half-wave saturate. Saturated transformers pose problems for power system operators since they can cause harmonics, transformer heating, mal-operation of protection relays, generator heating and vibration, and consume a large reactive power that can cause voltage collapse. Network studies of slow transient phenomena such as transformer half-wave saturation require appropriate models with parameters that represent the transformer transient state aptly. In this thesis a novel duality derived reversible model is developed of a single phase four limb transformer. The test transformers' non-step lap butt type core joints are shown to be problematic and the model is developed further to include the core joints. Due to the irregular core stacking method joint parameter determination is at best an approximation and the model is reduced to a duality compliant equivalent pi model for accuracy reasons. The pi model parameters and saturation characteristics are determined through laboratory testing and a complete pi model is presented. An understanding of a single phase transformer's physical behavior to slow transients is undertaken through the use of appropriately developed test circuits. Search coils are used extensively to understand the transformer core's behaviour through flux mapping of the core and stray flux in the surrounding air space when the transformer saturates. Three phase testing is included using a three phase bank of test transformers. The electrical measurements of waveforms are analysed and fast Fourier transforms carried out to obtain the harmonic components. The effect on a motor load of the distortion caused by transformer half-wave saturation is determined. A novel method of determining the effective core joint area of the problematic non-step lap butt type core joints is developed and a joint utilization factor is proposed that can be used in the absence of transformer manufacturer design information about this joint type in other transformer models

Development of a finite element matrix (fem)three-phase three-limb transformer model for Geomagnetically Induced Currents (GIC) experiments

Geomagnetically Induced Currents (GIC) have been a growing concern within power system operators and researchers as they have been widely reported to lead to power system related issues and material damage to system components like power transformers. In power transformers, GIC impacts are evidenced by part-wave saturation, resulting in transformers experiencing increased presence of odd and even harmonics. The three-phase three-limb (3p3L) transformer has been found to be the most tolerant to high dc values compared to other core types. The research was based on a hypothesis which reads “transformer laboratory testing results can be used as a guide towards developing suitable Finite Element Matrix (FEM) models to be used for conducting GIC/DC experiments”. This study thus investigates the response of a 15 kVA 3p3L laboratory transformer to dc current, emulating the effects of GICs. GIC and dc current are the same under steady state conditions, and hence mentioned interchangeably. Laboratory tests conducted identified two critical saturation points when the transformer is exposed to dc. The early saturation point was identified to be at around 1.8 A/phase of dc (18% of rated current), while the deep saturation point was at around 15 to 20 A/phase of dc (about 72% of rated current). Further analysis showed that holes drilled on the transformer can lower the transformer knee-point by about 26%, depending on the size and location of the holes. The holes hence end up affecting the operating point of the transformer due to losses occurring around the holes. A transformer FEM model was developed following the laboratory exercise, where it was concluded that a 2D model leads to grossly erroneous results, distorting the magnetizing current by about 60% compared to the laboratory results. A solid 3D model improved performance by about 30% as it took the transformer's topological structure into consideration. The 3D model was then refined further to include joints and laminations. It was discovered that laminations on the transformer need to be introduced as stacks of the core, with each core step split into two, allocating a 4% air gap space between stacks. Refinement of the T-joints proved that the joints have a relatively high influence on the transformer behaviour, with their detailed refinement improving the transformer behaviour by about 60%. The final FEM model was used for dc experiments. The results of such experiments showed close resemblance to the laboratory results, with saturation points identified in FEM lying within 10% of the laboratory identified saturation points. Overall, the various investigation methods explored showed that the hypothesis was satisfactorily proven true. Laboratory results functioned as a guide in developing the model, offering a reference case