含铁心线圈励磁特性求取方法的探讨

为求取电力系统中含铁心线圈元件的励磁特性,选取13次多项式模拟瞬时值励磁特性,采用基于Leven-berg-Marquardt方法的非线性最小二乘法对实测数据进行参数估计以确定多项式的待定系数,从而单值确定有效值伏安特性,再转换为瞬时值励磁特性。计算实例表明该法可保证拟合精度,满足工程实际需要。

Calculation Method for Excitation Characteristic of Coil with Iron Core

In power system, it is important to obtain the instantaneous excitation characteristic of nonlinear inductive elements with magnetic cores such as power transformers, electromagnetic voltage transformers, reactors and so on, the instantaneous excitation characteristic influence electromagnetic transient phenomena. The direct testing method to acquire excitation characteristic is too complex to practice and the common method is that excitation characteristic is calculated according to effective volt-ampere characteristic, which is measured by applying voltage to the element. For theoretical research, analytical expression of excitation characteristic is necessary then a calculating method of the excitation characteristic of coil with iron core according to its volt-ampere characteristic is presented. In the paper, the instantaneous excitation characteristic is represented by a polynomial of the order thirteen with coefficients to be defined and the single-valued volt-ampere characteristic expression is obtained. With measured data, the volt-ampere characteristic can be acquired. The above-mentioned nonlinear curve-fitting problem is solved by the least-squares method and Levenberg-Marquardt method is used. The Levenberg-Marquardt method uses a search direction that is a cross between the Gauss-Newton direction and the steepest descent. The Gauss-Newton method is generally more effective when the residual is zero at the solution. However, such information is not always available beforehand, and the increased robustness of the Levenberg-Marquardt method compensates its occasional poorer efficiency. The main difficulty in the implementation of the Levenberg-Marquardt method is an effective strategy for controlling the size of scalar at each iteration so that it is efficient for a broad spectrum problems. The method used in this implementation is to estimate the relative nonlinearity of equation using a linear predicted sum of squares and a cubically interpolated estimate of the minimum. By a comparison with the calculated and experimental true saturation characteristic, it is observed that higher precision can be obtained especially in saturated regions, which is significant to study electromagnetic transient phenomena in power system.