Correlated Equilibrium Power Flow in Distribution Networks Using Graphical Game Theory

Abstract

Modern power systems necessitate active management of distribution networks by Distribution System Operators (DSOs). A DSO can harness the flexibility capabilities of the nodes towards ensuring the safe operation of the distribution system, while optimizing a certain system objective. The objective-optimizing dispatch can be obtained by solving the Optimal Power Flow (OPF) problem. However, selfish nodes may deviate from the dispatch instruction by calculating a profitable deviation. Thus, an implementable solution needs to be not only optimal, but also an equilibrium, i.e., a point from which no node is willing to deviate. In this paper, we propose the adoption of correlated equilibrium as a solution concept that is generally more efficient than Nash and more relevant to this setting where the DSO acts as a coordinating entity. We formulate the problem of finding an efficient correlated equilibrium for distribution networks with discrete resources. The problem’s complexity is managed by exploiting the graphical structure and sparse connectivity of distribution networks, drawing on the methodology of graphical games. Simulations showcase that the proposed approach achieves an equilibrium with near-optimal efficiency, in contrast to the standard OPF approach which is shown to be unstable when each node selfishly optimizes its own objective.