以特征值为判据的异步发电机自激建压过程分析

Analysis of Voltage Build-up for Self-excited Induction Generator Based on Eigenvalues

为研究自激电容对异步发电机空载暂态建压过程的影响并确定最小建压电容值,采用了以状态方程矩阵特征值计算为基础的分析方法。从自激异步发电机αβ坐标系下的等值电路出发,推导了异步发电机空载建压时的状态方程,通过对状态方程进行局部线性化,进而计算出线性状态矩阵的特征值。根据不同自激电容值所对应特征值实部的符号并应用系统稳定性理论,以此判断电容为该值时电压是否得以建立,空载暂态建压过程的仿真波形与实验波形较为一致,说明了分析方法的有效性。把特征值实部绝对值选为目标函数并结合一维优化方法计算了异步发电机空载最小建压电容值,此值与传统方法计算结果相吻合,进一步证实了分析方法的正确性。

An analysis approach based on eigenvalues of the state equation matrix is utilized to study the effect of the self-excited capacitances on the no-load transient voltage build-up and determine the minimum build-up capacitance of an induction generator. The state equations of the induction generator for no-load voltage build-up are deduced, which are resulted from the equivalent circuits in αβreference frame of the machine. With the state equations locally linearized, the eigenvalues of the linear state matrix are obtained. According to the real-part sign of the eigenvalues at different capacitances and the system stability theory, whether the voltage is built up or not is judged for the specific capacitance. The agreement between the simulation results and the experimental ones for no-load transient voltage build-up shows the validity of the presented analysis approach. The minimum capacitance for no-load voltage build-up is computed by one-dimensional optimization method with the absolute value of real-part of the eigenvalue selected as the object function, which corresponds to that obtained by the traditional method and further confirms the correctness of the presented method.