Research On Field-circuit Coupling Problem Of Element-by-Element Finite Element Method

For large power equipment,its physical size is very large.When using the finite element method to analyze the electromagnetic field of the power equipment,in order to ensure the calculation accuracy,a large number of meshes need to be divided,resulting in the calculation scale is too large to be solved by the traditional finite element method.Therefore,parallel algorithms have attracted more and more attention of researchers,and have been applied to the numerical analysis of the physical fields of large electrical equipment.In this paper,the field-circuit coupling mathematical model,solution method and verification of Element-by-Element（EBE）finite element method are studied.Firstly,this paper deduces the direct field-circuit coupling mathematical model of the traditional finite element method for simultaneous solution of magnetic field and circuit equation.Combined with the basic theory of EBE finite element method,besides the node correlation matrix which reflects the local to global mapping relationship,the branch correlation matrix which connects the elements and branches is proposed,and the field-circuit coupling mathematical model of EBE finite element method is established.The EBE finite element method field-circuit coupling model with one branch and two branches in the calculation domain is deduced respectively.The model can be extended to the case that the calculation domain contains multiple branches.The process of solving this model by preconditioned conjugate gradient method is presented,the boundary condition treatment of field-circuit coupling solution by EBE finite element method is given,and the corresponding algorithm program is developed by C++ programming language.The above algorithm and program are applied to calculate the magnetic field and winding current of a single-phase power transformer.The main magnetic field and excitation current when the secondary side is open,and the leakage magnetic field and the currents in high and low voltage winding when the secondary side is short-circuited are calculated respectively.The commercial software ANSYS Maxwell is used to simulate the magnetic field and current of the same transformer structure model under the same parameters and excitation conditions.The results are compared with the calculation results obtained by the self-programming software,and the correctness and reasonableness of the field-circuit coupling model and the program of the EBE finite element method has been verified.