半无限优化的光滑化拟Newton法及其在最优潮流中的应用

Smoothing Quasi-Newton Method for Solving Semi-Infinite Programming with Application to OPF Problems

提出求解半无限优化(SIP)问题的一类新算法—光滑化拟Newton法.基于非线性互补函数(non linearcomp lem entary prob lem-NCP function),转化SIP问题的KKT系统为非光滑方程组,设计光滑化拟Newton法求解该方程系统.该方法的特点是在每步迭代中只需求解一个线性方程组系统,且算法具有较好的全局与局部超线性收敛性.利用该方法求解电力系统暂态稳定约束的最优潮流(optim al power flows w ith transient stab ility constraints-OTS)问题,计算结果显示该算法的有效性.

This paper presents a smoothing Quasi-Newton method for solving the semi-infinite programming（SIP）. Based on the nonlinear complementary problem（NCP） function, the KKT system of the SIP problem is reformulated to a system of nonsmooth equations. A smoothing Quasi-Newton method is designed to solve this system. The remarkable characteristic of the method is that it only solves a system of linear equations at each iteration; and it enjoys nice global and locally superlinear convergence. Finally, the algorithm is used to solve the optimal power flows with transient stability constraints（OTS） in power systems. Numerical results show the effectiveness of the proposed approach.