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

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.