Sorta Solving the OPF by Not Solving the OPF: DAE Control Theory and the Price of Realtime Regulation

TL;DR

The study tackles the nonconvex ACOPF challenge by embedding grid physics into a differential-algebraic equation (NDAE) framework and designing a real-time, PMU-enabled feedback controller via a Lyapunov and $H_ ext{∞}$-based LMIs to compute a constant gain $K$ offline. This control-OPF approach avoids online nonconvex optimization, yet enforces the NDAE-encoded power-flow constraints and delivers stable, near-OPF generator dispatch under uncertainty and disturbances. Numerical case studies on standard networks show that control-OPF achieves costs close to OPF while providing improved transient stability (e.g., better frequency nadirs) and no constraint violations, effectively reducing the need for frequent ACOPF re-solves. Limitations include the absence of line-thermal constraint modeling within the NDAE and the lack of formal near-optimality guarantees, suggesting future work on incorporating line limits and robust stochastic formulations that extend to higher-fidelity renewables models.

Abstract

This paper presents a new approach to approximate the AC optimal power flow (ACOPF). By eliminating the need to solve the ACOPF every few minutes, the paper showcases how a realtime feedback controller can be utilized in lieu of ACOPF and its variants. By (i) forming the grid dynamics as a system of differential-algebraic equations (DAE) that naturally encode the non-convex OPF power flow constraints, (ii) utilizing DAELyapunov theory, and (iii) designing a feedback controller that captures realtime uncertainty while being uncertainty-unaware, the presented approach demonstrates promises of obtaining solutions that are close to the OPF ones without needing to solve the OPF. The proposed controller responds in realtime to deviations in renewables generation and loads, guaranteeing improvements in system transient stability, while always yielding approximate solutions of the ACOPF with no constraint violations. As the studied approach herein yields slightly more expensive realtime generator controls, the corresponding price of realtime control and regulation is examined. Cost comparisons with the traditional ACOPF are also showcased -- all via case studies on standard power networks.

Figures (10)

• Figure 1: Overall integrated framework of the proposed control-OPF
• Figure 2: Time-varying active/reactive power set-points provided by control-OPF and static set-points from ACOPF for three random step disturbances in load demand; above figures are for case 39 and below figures are for case 9 test system.
• Figure 3: Active and reactive power generated by all the generators and their respective limits, line flows and their maximum rating, and the overall modulus of all bus voltages for case 9 bus test system for Scenario A.
• Figure 4: Active and reactive power of a couple of generators and their respective limits, line flows, and their maximum rating, and the overall modulus of all buses voltages for case 39 bus test system for Scenario B.
• Figure 5: Generator frequencies under ten random disturbances in load and renewables for case 9, case 14, case 39, and case 57 test systems respectively.