  Coordinated optimization and control of distribution-level assets can enable
a reliable and optimal integration of massive amount of distributed energy
resources (DERs) and facilitate 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, or line losses, to be close to a desired profile. By and large, the
performance of the DSM algorithms has been challenged by two factors: i) the
possibly non strongly connected communication network over DERs that hinders
the coordination; ii) 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 (NE) 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.
