A Novel Robust Augmented Quotient Gradient System Method for AC Optimal Power Flow Part I: Theoretical Basis

Due to the non-convex characteristics of the alternating current optimal power flow (ACOPF) problem, most existing methods are restricted to obtaining Karush-Kuhn-Tucker (KKT) solutions. There are significant challenges associated with these solutions, including non-convergence and computational inefficiency. This first part of a two-part paper introduces a robust Augmented Quotient Gradient System (AQGS) method designed to resolve convergence issues in solving the ACOPF problem. The AQGS method demonstrates superior convergence performance, computational efficiency, and a zero-probability occurrence of saddle solutions. A novel dynamical AQGS system is established, then the local optimal solutions of the ACOPF and the regular stable equilibrium points of the AQGS system are shown to correspond one-to-one; the AQGS is demonstrated to be completely theoretically stable. Based on this theoretical foundation, an ideal numerical property is developed. The relevant theorems are visually demonstrated through ACOPF examples, which support the high-performance algorithms introduced in the second part of this two-part paper.