Low-frequency Transformer Model Considering Hysteresis Behavior And Its Application In Ferroresonance

Power transformer is one of the most important equipment in power systems.The operation condition of a transformer directly affects the security and stability of power systems.With the development of power grids interconnection,the switching of circuit breaker is much more frequent.The possibility of transformer faults caused by the low-frequency electromagnetic transients,such as ferroresonance and inrush currents,increases.Thus,an accurate low-frequency transformer model can provide the basis for the electromagnetic transient simulation in power systems.However,the structures of power transformer are complicated,the types of power transformer are various,and the operating status of power transformer are more and more complex.It is difficult to build a unified magnetic circuit and electrical circuit transformer electromagnetic transient model.In addition,most of the existing hysteresis models are used to magnetic property analysis.These models are usually based on the magnetic parameters,however,the typical EMTP-type software usually uses the electrical parameters to build the model.The existing hysteresis models with magnetic parameters can hardly be used to power equipment modeling,such as transformer modeling.Therefore,in this thesis,a frequency-dependent winding model and an iron core model of different three-phase transformers are built for low-frequency electromagnetic transient simulation.A novel dynamic hysteresis model with anisotropy is proposed for transformer iron core modeling.The optimization algorithm of iron core parameters and estimation method of winding parameters are studied.The methods for implementing the voltage-driven hysteresis reactor and building the transformer low-frequency electromagnetic transient model in EMTP-ATP are investigated.Finally,the low-frequency transformer model is verified by the ferroresonance experiments.The main work of this thesis are as follows:(1)The models of frequency-dependent winding resistances,leakage inductance and capacitance are obtained based on the structures of transformer winding and iron core.The electrical circuits of three-phase three-legged,three-phase five-legged and three-phase shell-type iron cores are obtained based on the principle of duality.The Cauer circuit is applied to model the transformer tank based on the nonuniformity of zero-sequence flux distribution and the saturation level of transformer tank under different excitations.(2)Based on the classical JA model,the dynamic JA hysteresis model and its inverse model are derived from the energy balance equation.The hybrid JA hysteresis reactor considering anisotropy is then obtained by revising the Langevin anhysteretic magnetization curve.Different solution algorithms which are used to solve the hybrid JA hysteresis reactor are discussed and compared in Matlab program.The properties of the hybrid JA hysteresis model and classical JA model are compared.The results show that the hybrid JA hysteresis reactor can represent the hysteresis property of much more materials than the classical JA model.The influences of parameters on the proposed JA hysteresis loops are discussed to lay the foundation of later parameter estimation.Finally,the three-phase three-legged,three-phase five-legged and three-phase shell-type low-frequency transformer models using the hybrid JA hysteresis reactor are obtained.(3)The differential evolution-shuffled frog leaping algorithm is proposed to calculate the parameters of the hybrid JA hysteresis reactor.The hysteresis loops under 1.0 T and 1.5 T obtained from the genetic algorithm,simulated annealing algorithm,differential evolution algorithm and differential evolution-shuffled frog leaping algorithm are compared with the experiment results.Finally,the transformer inrush current of a three-phase five-legged transformer is used to verify the accuracy of the proposed model.The inrush currents obtained from the hybrid JA hysteresis reactor and the existing R//L model are compared with the experiments,and the errors are also discussed.(4)A voltage-driven dynamic ψ-i JA reactor model is proposed,and its implementation in EMTP-ATP is also discussed.The no-load excitation characteristics of a toroidal GO core under 50 Hz and 150 Hz are measured,and two different expressions of dynamic ψ-i JA differential equations are compared based on the above differential evolution-shuffled frog leaping algorithm.The characteristics of the proposed voltage-driven dynamic reactor are studied based on the ramp-up tests and the harmonic excitation tests.Finally,the fundamental and subharmonic ferroresonance experiments using a single-phase transformer and a three-phase transformer are carried out,respectively.The simulation results obtained from the proposed voltage-driven dynamic ψ-i JA reactor are compared with the experiment by the nonlinear dynamic analysis method to verify the accuracy of the low-frequency transformer model based on EMTP-ATP in this thesis.The results of this thesis show that the error of the steady-state peak voltage of ferroresonance which is obtained from the proposed low-frequency transformer model is less than 5 %,the waveform similarities for ferroresonance are higher than 0.9.The work of this thesis covers the shortages of various three-phase low-frequency transformer modeling considering hysteresis behavior,facilitates the low-frequency transformer model considering the hysteresis reactor with the EMTP-ATP,and also lays the foundation for obtaining a wide-frequency transformer model.