Dynamic Power Distribution System Management with a Locally Connected Communication Network

Coordinated optimization and control of distribution-level assets enables a reliable and optimal integration of massive amount of distributed energy resources (DERs) and facilitates distribution system management (DSM). Accordingly, the objective is to coordinate the power injection at the DERs to maintain certain quantities across the network, e.g., voltage magnitude, line flows, and line losses, to be close to a desired profile. By and large, the performance of the DSM algorithms has been challenged by two factors: 1) the possibly nonstrongly connected communication network over DERs that hinders the coordination; and 2) the dynamics of the real system caused by the DERs with heterogeneous capabilities, time-varying operating conditions, and real-time measurement mismatches. In this paper, we investigate the modeling and algorithm design and analysis with the consideration of these two factors. In particular, a game-theoretic characterization is first proposed to account for a locally connected communication network over DERs, along with the analysis of the existence and uniqueness of the Nash equilibrium therein. To achieve the equilibrium in a distributed fashion, a projected-gradient-based asynchronous DSM algorithm is then advocated. The algorithm performance, including the convergence speed and the tracking error, is analytically guaranteed under the dynamic setting. Extensive numerical tests on both synthetic and realistic cases corroborate the analytical results derived.