An SQP Method Combined with Gradient Sampling for Small-Signal Stability   Constrained OPF
  Small-Signal Stability Constrained Optimal Power Flow (SSSC-OPF) can provide additional stability measures and control strategies to guarantee the system to be small-signal stable. However, due to the nonsmooth property of the spectral abscissa function, existing algorithms solving SSSC-OPF cannot guarantee convergence. To tackle this computational challenge of SSSC-OPF, we propose a Sequential Quadratic Programming (SQP) method combined with Gradient Sampling (GS) for SSSCOPF.At each iteration of the proposed SQP, the gradient of the spectral abscissa unction is randomly sampled at the current iterate and additional nearby points to make the search direction computation effective in nonsmooth regions. The method can guarantee SSSC-OPF is globally and efficiently convergent to stationary points with probability one. The effectiveness of the proposed method is tested and validated on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system, and IEEE 54-machine 118-bus system. 
Peijie Li, Junjian Qi, Jianhui Wang, Hua Wei, Xiaoqing Bai, and Feng   Qiu
math.OC