  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.
