A Saddle-Point Equilibrium Model for Optimal Operation of Hybrid Renewable Energy Systems

Abstract

Mixed hybrid renewable energy systems comprising wind, solar, storage, and electrolyze assets are increasingly owned by market-based competitors rather than centralized operators; thus, conventional economical dispatch formulations do not adequately model strategic bidding behaviors and self-interested capacity dispatch by diverse players. This paper formulates saddle point equilibrium for optimal hybrid system operation as a Nash equilibrium game between competing agents under common network and market clearing conditions. By dualizing the linking constraints with a generalized lagrangian, constrained equilibrium turns into unconstrained saddle point, and the corresponding equilibrium set can be shown to equal solution set for monotone variation inequality formulation over compound strategy space.  Saddle point equilibrium' existence and uniqueness are derived under pseudo gradient' operator of game by a Generalized Monotonicity and Coercivity properties.  A distributed primal dual algorithm is presented that involves agents' sub-gradient steps and Coordinator's multiplier update, then the study establishes linear rate for convergence under meteoric  sub-regularity, and analyze communication complexities for computation that connect iteration count with structure of power system network and heterogeneity of assets. Finally, numerical example is given, that illustrate rate of convergence for both pure and accelerated distributed methods and show agent's price tend towards common equilibrium.