Research On Fast Calculation Method Of Nonlinear Electromagnetic Field Based On POD

With the rapid development of computer technology,the numerical analysis method represented by finite element method is widely used in the design and performance analysis of modern electrical equipment.However,the performance analysis of electrical equipment such as motor and transformer is a time-varying,nonlinear problem,and the finite element method is very time-consuming.In some cases where sensitivity analysis,optimization design and high real-time requirements such as digital twin are needed,direct finite element solution is not an optimal choice.Due to the nonlinear characteristics of magnetic properties of iron core materials and the complexity of geometric models,the traditional finite element method can not meet the requirements of high efficiency in the performance analysis of electrical equipment such as motors and transformers.Therefore,based on the Proper Orthogonal Decomposition（POD）method,this paper studies the model order reduction technology of nonlinear electromagnetic field problems of electrical equipment,which provides an accurate and fast calculation method for dealing with the nonlinear problems of electrical equipment.This paper introduces several commonly used model order reduction techniques,briefly analyzes their mathematical principles,and studies the applicable fields of various model order reduction techniques.The POD method is discussed in detail,its principle is derived mathematically,and a fast computing technique based on this method for nonlinear analysis of electromagnetic field is proposed.Taking an electric locomotive traction transformer as an example,the proposed method is applied to analyze the no-load magnetic field of traction transformer.In order to discuss the accuracy of the no-load magnetic field calculation results,the selection of the core point of different position,compared with the traditional finite element simulation and calculation result of the proposed rapid analysis method,analyses the error.The core of magnetic field was calculated under different saturation degree,and compared the order model fall in different degree of saturation calculation result of the differences.Aiming at the problem that the error distribution of the reduced order model is uneven at different positions,the influence of the position selection of snapshot matrix on the calculation error is studied.Aiming at the above model,the prediction results of the reduced order model under different truncation positions and different combinations of interpolation polynomial orders are discussed.The error sources of the improved reduced order model and the original model are analyzed,and the variation rule of the error with the polynomial orders and truncation positions is summarized.Based on the above research results,an adaptive method to determine the optimal number of snapshots for nonlinear problems is proposed to achieve a balance between solving efficiency and solving accuracy.