Research On Frequency-domain Algorithm For Nonlinear Electromagnetic Field Of Transformer Under Non-sinusoidal Excitation

During the manufacture and operation of electrical equipment,it is of great significance to effectively analyze the electromagnetic field inside the equipment.Therefore,the study of numerical method for accurate analysis of large electrical equipment has important academic significance and engineering application value.Sponsored by the National Key Research and Development Program of China under grant 2017YFB0902703 and the National Natural Science Foundation of China under grant 51777073,a frequency-domain decomposition algorithm based on harmonic balance method is proposed to solve the nonlinear problems such as dc bias and AC-DC hybrid electric field of converter transformer.In this paper,a fixed-point frequency domain algorithm based on the magnetic scalar potential and current vector potential is presented by using the complex exponential to approximate periodic variables.The dc biased problem in a laminated core is investigated and analyzed by the proposed method,in which the edge element is used to interpolate the current vector potential.The frequency-domain finite element equation is assembled to solve the two-dimensional nonlinear magnetic field taking electromagnetic coupling into account.The fixed-point permeability is introduced to decompose the coefficient matrix and decouples harmonic solutions,which reduce the memory requirements and computational time significantly.A laminated core model is employed to carry out the dc biasing experiment.The calculated results are compared with the experimental ones to verify the validity of the proposed method in computation and analysis of dc biased problems.In further research,the frequency-domain decomposition algorithm is applied to analyze the AC-DC hybrid electric field of converter transformer under multi-harmonic excitation.Compared with two algorithms,the traditional harmonic balanced method and the time step method,the proposed method can decompose the stiffness matrix according to the harmonic order,by which the memory consumption and computation time can be remarkably reduced.To verify the effectiveness of the proposed algorithm,a typical model of the oil-paper insulation structure is taken for instance,and the results obtained by the proposed algorithm is compared with two algorithms.And it can be applied to analyze the compound electric field problems of the actual converter transformer.The electric field distribution of a ±500 kV converter transformer is calculated and analyzed considering the nonlinear relationship between the electric field and the medium conductivity.