数值延拓法在非线性直流电场间接耦合计算中的应用

Application of Numerical Continuation Method in Nonlinear DC Electric Field Indirect-coupling Calculation

高压直流设备的材料电导率取决于场强和温度的大小,高度非线性的电场分布可能导致数值求解的发散,而迭代初值的选择是计算收敛的关键之一。为此,提出了一种非线性直流电场间接耦合计算新方法,将原直流场问题转化为特定参数下的同伦方程,以削弱电导率的非线性为出发点,构造了2个具有明确物理意义的同伦方程,并采用数值延拓法对真解进行跟踪,从而扩大初始解的收敛域。以±200 kV直流模注型接头为例,利用数值延拓法结合Steffensen迭代公式计算得到了其电场分布,而采用传统间接耦合方法则会出现数值发散,最后对影响算法收敛性的迭代公式、同伦方程和延拓步长等因素进行了探讨。所提方法有助于提高非线性直流电场计算的大范围收敛性,可有效改善由迭代初值选取不当引起的数值发散问题。

The material conductivity of HVDC equipment depends upon both electric field and temperature. Highly nonlinear electric field distribution may lead to divergence of numerical solution, and selection of initial values is one of the keys to converge. For this reason, a novel approach for nonlinear DC electric field indirect-coupling calculation was proposed in this paper, where the original DC electric field problem was translated into homotopy equations at a special parameter. To weaken nonlinearity of conductivity, two homotopy equations with clear physical meaning were constructed and the numerical continuation method was adopted to track true solution, thus expanding the convergence domain of initial solution. Taking ±200 kV DC extrusion molded joint as an example, the electric field distribution was computed based on numerical continuation method and Steffensen iterative formula, while traditional indirect-coupling method would gave rise to iterative divergence. Finally, the iterative formulae, homotopy equations and continuation step, affecting convergence of the algorithm, were discussed. This study helps to enhance global convergence in nonlinear DC electric field calculation and overcome numerical divergence due to improper selection of initial values.