Fast Calculation Method of Magnetic Field and Short-Circuit Electromagnetic Force of Transformer Based on Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method
Wang Qingyu1, Tian Songbo1, Zeng Qiang2, Wu Zehua3, Cheng Jianwei3
1. School of Electrical Engineering Xi’an Jiaotong University Xi’an 710049 China; 2. Dongguan Power Supply Bureau Guangdong Power Grid Corporation Dongguan 523000 China; 3. CSG Electric Power Research Institute Guangzhou 510663 China
Abstract：Short-circuit faults have a significant impact on the internal state of the transformer. When a sudden short-circuit accident, the transformer will be subjected to short-circuit current impact in a very short period of time, and the electromagnetic force borne by the windings will increase sharply, which may lead to winding deformation or even destruction. For the digital transformation of new power systems, the rapid analysis of the internal dynamic process of the transformer under the action of short-circuit current can effectively support the system decision-making and overhaul strategy. However, subject to the traditional numerical calculation methods, in the calculation of transient nonlinear magnetic field, the solution of each time step is a nonlinear problem, which requires multiple iterations of calculation and high computational time cost, and it is difficult to meet the requirements of digital application in the field of physical field simulation of power equipment. In order to improve the efficiency of online short-circuit resistance analysis and evaluation of transformers, this paper proposes a fast calculation method based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). electromagnetic force of transformer based on POD and DEIM. Firstly, the nonlinear transient control equations for the calculation of transformer electromagnetic force are derived based on the Galerkin finite element method; secondly, using the POD method, a reduced order model is established to reduce the order of the finite element equations and improve the computational efficiency; then, in order to solve the inefficiency of the POD method for solving the nonlinear problems, the nonlinear terms in the finite element equations are processed by interpolation method based on the DEIM algorithm. which reduces the formation time of the nonlinear stiffness matrix in each iteration step and further improves the computational efficiency. Finally, this paper establishes a short-circuit electromagnetic force calculation model based on the actual distribution of 220 kV transformer windings, and validates the proposed reduced-order algorithm by comparing it with commercial simulation software. In this paper, the effectiveness of the POD-DEIM order reduction algorithm in 220 kV transformer short-circuit electromagnetic force is investigated, and the following conclusions are obtained: (1) Using the POD method, the order reduction subspace is constructed by singular value decomposition and selecting the eigenvectors as constructing the order reduction subspace, so that the order of the equation is reduced from 204 232 to 6. (2) Combining DEIM with POD, the interpolation points in the nonlinear terms are constructed by selecting the interpolation matrix, which reduces the update time of the nonlinear terms in each iteration step, reduces the overall solution time of the equation (from 1 299 s to 132.6 s). (3) The computational results of the POD-DEIM reduced-order algorithm are basically consistent with those of the COSOL software and the full-order model, and the maximum relative error of the internal leakage flux of the transformer and the short-circuit electromagnetism of each winding is no more than 3.5%; in terms of the computational time, the computational efficiency of the reduced-order model is improved by a factor of 9.8 compared with that of the COSOL software and the full-order model. The results suggest that the reduced-order algorithm has a certain value of application in the rapid computation of short-circuit electromagnetic force in power transformers.
王青于, 田淞铂, 曾强, 吴泽华, 程建伟. 基于本征正交分解和离散经验插值的变压器磁场及短路电磁力快速计算方法[J]. 电工技术学报, 2025, 40(19): 6167-6179.
Wang Qingyu, Tian Songbo, Zeng Qiang, Wu Zehua, Cheng Jianwei. Fast Calculation Method of Magnetic Field and Short-Circuit Electromagnetic Force of Transformer Based on Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method. Transactions of China Electrotechnical Society, 2025, 40(19): 6167-6179.
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