Small-Signal Stability-Constrained Optimal Power Flow for Inverter Dominant Autonomous Microgrids

This article details and solves a small-signal stability-constrained optimal power flow (SSSC-OPF) for inverter-based ac microgrids. To ensure a sufficient stability margin during optimal generation, a small-signal stability constraint is embedded into the conventional OPF formulation. This condition is enforced using a Lyapunov stability equation. A reduced-order model of the microgrid is adopted to alleviate the computational burden involved in solving the resulting SSSC-OPF. Even then, the resulting stability conditions are highly nonlinear and cannot be handled using the existing methods. To tackle the nonconvexity in the SSSC-OPF due to the presence of the nonlinear stability constraint, two distinct convex relaxation approaches, namely semidefinite programming and parabolic relaxations, are developed. A heuristic penalty function is added to the objective function of the relaxed SSSC-OPF, which is solved sequentially to obtain a feasible point. While off-the-shelf tools fail to produce any feasible point within hours, the proposed approach enables us to solve the SSSC-OPF in near real time. The efficacy of the proposed SSSC-OPF is evaluated by performing numerical studies on multiple benchmarks as well as real-time studies on a microgrid system built in a controller/hardware-in-the-loop setup.