Research And Application Of Fast Calculation Method Of Distributed Capacitance For Multi-conductor Based On Finite Element Method

The distributed capacitance parameter of multi-conductor is the basis of electromagnetic transient analysis.In order to accurately and efficiently obtain the distributed capacitance between multi-conductors of complex structures,this paper first deduces the equations with the inductance as the quantity to be solved based on the electromagnetic field theory,and gives the automatic calculation method of the coefficient matrix of the equations for each non-zero element.According to the finite element method,the space energy is calculated as the right term element of the equations,and the induction coefficient matrix is obtained after solving the equations.The proposed method is applied to solve a two-conductor transmission line model problem with an analytical solution,and the results are compared with the analytical solution to verify the effectiveness of the proposed method.Secondly,the calculation of distributed capacitance by the traditional finite element method is based on the energy method,so each time a distributed capacitance parameter is calculated,the finite element equation of n×(n+1)/2 times needs to be solved.For the problem of parameter extraction of distributed capacitance between large scale multi-conductors,due to the large number of conductors,the theory based on automatic calculation method and its calculation method will take a lot of time.Therefore,by studying the relationship between the nodal charge and potential in the electrostatic field,a fast method to calculate the distributed capacitance of multiple conductors based on finite element method is proposed.In this method,n distributed capacitance parameters can be obtained after each finite element equation calculation.Only n times of finite element equation solution is needed to obtain the distributed capacitance between multiple conductors,which greatly improves the calculation efficiency.The method is used to calculate the distributed capacitance parameters of the two-core shielded cable model,which verifies the effectiveness of the method.Finally,the method proposed in this paper is applied to three examples: the distributed capacitance between the line conductors of a typical six-conductor tower type(double-circuit on the same tower)in the PSCAD/EMTDC software,the distributed capacitance between turns of a transformer winding and the inductance matrix between three conductors of printed circuit board multilayer medium.During analysis,based on the parameters of the research object,a finite element simulation model is established based on Ansys software,the dielectric constant around the multi-conductor is set,and a semicircular or rectangular truncated boundary is used,and the influence of the truncated boundary size and the number of grids on the calculation results of the distributed capacitance parameters is analyzed.