A Quotient Gradient System-Based Trust-Tech Method for Computing Solutions of Multiple/All Feasible Components of ACOPF Models: Theory and Methodology

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Abstract
Alternating Current Optimal Power Flow (ACOPF) model is nonconvex and generally has multiple local optimal solutions (LOSs) distributed across multiple feasible components of its feasible region. In this paper, a novel, theory-based dynamic method, named QGS-TT, is proposed to compute multiple feasible solutions located in different disconnected feasible components. The proposed method incorporates a dynamic transformation that converts the feasible region of ACOPF problem into the union of regular stable equilibrium manifolds (RSEMs) through the construction of a quotient gradient system (QGS). Furthermore, the Transformation Under Stability Retaining Equilibria Characterization (Trust-Tech, TT) methodology is extended to explore the solution space in a tier-by-tier manner systematically. Starting from an arbitrary initial point, assisted by a QGS-based numerical method to detect the existence of, and then computation of other feasible components, supported by the stability boundary theory (properties). Five numerical studies are conducted on the IEEE 2-, 9-, 39-, 118-, and 500-bus systems, each of which exhibits multiple OPF solutions with significantly different objective function values. Regarding computational performance, it will be shown that the method is significantly faster than an existing one.
Funding Information
  • National Natural Science Foundation of China (52407109)
  • National Science Foundation (2328248)
  • Natural Science Foundation of Jiangsu Province of China (BK20240593)
  • Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (24K1B470018)
  • China Southern Power Grid Company, Ltd Science and Technology Program (000005KC24010004)

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