油–纸绝缘结构瞬态电场计算的状态空间有限元法

A State-space Finite Element Method for the Calculation of Transient Electrical Field in Oil-paper Insulation Construction

针对换流变压器油–纸绝缘结构中瞬态电场的计算问题,利用罚函数法整合有限元边界条件,建立了完整的以节点电位为变量的状态方程。采用状态空间法对方程进行求解,将方程的输入项进行级数展开,由方程积分形式的解析解得到具有较高精度的数值解。同时为模拟边界电位的阶跃变化,在级数中引入了冲激函数。通过1个有解析解的简单模型,验证了所述计算方法的有效性和计算精度。该方法既可用于求解换流变压器油–纸绝缘结构中的极性反转瞬态电场计算问题,还可用于求解热扩散问题以及其他可用抛物型偏微分方程描述的瞬态物理过程计算问题。

In order to solve the transient electrical field in oil-paper insulation construction of converter transformer,a state equation was built based on the finite element method.The boundary conditions were combined into the equation by means of penalty method.The state space method was used to solve above equation.Firstly,the input of the equation was expanded into series,the precise numerical solution was obtained from the analytic solution in integral form.Then,an impulse function was introduced into the series expansion to simulate the step change of the boundary potential.Finally,the accuracy and validity of this method were verified with a simple model and its analytic solution.This method not only can be used to calculate the transient electric field under polarity reversal voltage in oil-paper insulation construction of converter transformer,but also can be applied to solve the heat diffusion problem and other physical problems which can be described as parabolic partial differential equations.