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

Pullaguram D., Madani R., Altun T., Davoudi A.

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, vol.69, no.7, pp.7318-7328, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1109/tie.2021.3102454
  • Journal Name: IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, Civil Engineering Abstracts
  • Page Numbers: pp.7318-7328
  • Keywords: Power system stability, Microgrids, Optimized production technology, Inverters, Stability criteria, Numerical stability, Mathematical model, AC microgrids, convex optimization, inverters, optimal power flow, relaxation, small-signal stability, OPF
  • Yozgat Bozok University Affiliated: Yes

Abstract

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.