映射分裂方法及其在电力系统分析中的应用

为了求解复杂的非线性代数方程组，将线性代数方程组的矩阵分裂法推广至非线性方程组，提出了映射分裂法。该方法将复杂的非线性方程组的求解转化为一系列较简单的方程组的迭代求解问题，降低了解题复杂度。给出了映射分裂法的收敛性分析理论。介绍了映射分裂法在电力系统分析领域的应用成果，其中包括在潮流计算、状态估计和全局电力系统仿真建模中的应用。算例表明，各种基于映射分裂法提出的实用算法计算性能良好，能满足电力系统在线分析的要求

Mapping-splitting based method with applications to power system analysis

In order to solve complicated nonlinear algebraic equations, the matrix splitting based method for solving linear algebraic equations was generalized, then a new mapping splitting based method was presented in this paper. In the new method, solving complicated nonlinear algebraic equations was substituted by several iterations of solving simple algebraic equations. The convergence theory of the new method was proposed. Some applications of the method to power system analysis, including power flow calculation, state estimation and global power system simulation, were introduced and some digital tests are carried out. The results show that the performances of the practical mapping splitting based algorithms derived in the paper are good enough to meet the requests of power system analysis in the real time environment.