基于近似牛顿方向的多区域无功优化解耦算法

A Decomposition Algorithm Applied to Multi-area Reactive-power Optimization Based on Approximate Newton Directions

针对多区域电力系统的无功优化问题,提出了基于近似牛顿方向和GMRES算法的无功优化解耦算法。该算法以非线性原对偶内点法为基础,在迭代计算过程中构造近似牛顿方向,实现弱耦合系统的完全解耦,保证算法具有局部线性收敛特性,且其计算速度要比非线性原对偶内点法快。对于不能实现解耦的强耦合系统,以近似牛顿方向为初值和解耦对角阵作为预处理器,采用GMRES法求解,使算法具有良好的收敛性和较快的计算速度。以708节点系统作为试验系统验证所提算法的正确性和有效性,得到了满足所有等式和不等式约束的最优可行解。并以树型子系统分解法对其进行分解,对不同分解方案的计算结果进行了比较分析。

This paper presents a new decomposition algorithm for solving reactive-power optimization problem of multi-area power systems based on Generalized Minimal Residual （GMRES） method and approximate Newton directions. According to nonlinear primal-dual interior-point method, approximate Newton directions are constructed during iteration, and hence the weak coupling system can be fully decomposed. This decomposition method can converge locally to the optimum at a linear rate and is faster than the nonlinear primal-dual interior-point method. But strong coupling system, which can not be decoupled like the weak coupling one, can be further solved by means of a preconditioned GMRES algorithm. The approximate Newton direction and decoupled diagonal matrix provide initial values and preconditioner respectively for this algorithm. This preconditioned GMRES algorithm is fast and has a good convergence. Furthermore. Test cases based on a 708-bus system are used to validate the correctness and effectiveness of the proposed algorithm. At last, we obtain the optimization feasible solutions satisfying all equality and inequality constrains of test cases. Also a tree-like subsystem decomposition method is adopted to divide it and comparative studies for different decomposition schemes are reported.