An SQP Method Combined with Gradient Sampling for Small-Signal Stability Constrained OPF

TL;DR

This paper introduces a novel SQP method combined with gradient sampling to solve small-signal stability constrained optimal power flow problems, effectively handling nonsmooth spectral abscissa functions and ensuring convergence.

Contribution

The paper develops a new SQP algorithm with gradient sampling for SSSC-OPF, guaranteeing convergence despite nonsmooth spectral functions, which was not possible with previous methods.

Findings

Method guarantees global convergence to stationary points.

Validated on multiple power system test cases.

Effective in handling nonsmooth spectral abscissa functions.

Abstract

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.