基于辅助变量的潮流方程二次转折分岔点的直接算法

对于一个含单参数的潮流方程组，二次转折分岔是最简单的且最为普遍存在的一种分岔。在二次转折分岔点处，系统的Jacobi矩阵为秩降1的奇异阵。为了克服Jacobi矩阵的奇异性，可采用Moore—Spence系统来确定转折分岔点。然而，Moore—Spence系统具有很高的维数，给计算工作带来不便。该文通过引入辅助变量和辅助方程，得到一个求解潮流方程的Moore—Spence扩展系统的矩阵降阶新算法。该算法克服了潮流方程在分岔点处的奇异性所造成的求解困难，同时也解决了Moore Spence方程的高维数问题。

AN AUXILIARY-VARIABLE-BASED DIRECT METHOD FOR COMPUTING QUADRATIC TURNING BIFURCATION POINTS OF POWER FLOW EQUATIONS

For a given one-parameter power flow equation, the quadratic turning bifurcation is the simplest and generically existent bifurcation, where the Jacobian matrix of the equation becomes singular due to rank deficiency 1. To overcome the singularity of the Jacobian matrix, usual Newton method can be applied to the so-called Moore-Spence determining system to detect the quadratic turning point. But the Moore-Spence system has very high dimensionality and causes much complexity in factorization of its Jacobian matrix. By introducing an auxiliary variable and an auxiliary equation to form an extended Moore-Spence system, this paper derives an efficient matrix reduction technique. The high dimensionality of the Jacobian matrix can thus be reduced and the complexity involved in matrix factorization can be simplified.