We consider the decentralized control of radial distribution systems with controllable photovoltaic inverters and energy storage resources. For such systems, we investigate the problem of designing fully decentralized controllers that minimize the expected cost of balancing demand, while guaranteeing the satisfaction of individual resource and distribution system voltage constraints. Employing a linear approximation of the branch flow model, we formulate this problem as the design of a decentralized disturbance-feedback controller that minimizes the expected value of a convex quadratic cost function, subject to robust convex quadratic constraints on the system state and input. As such problems are, in general, computationally intractable, we derive a tractable inner approximation to this decentralized control problem, which enables the efficient computation of an affine control policy via the solution of a finite-dimensional conic program. As affine policies are, in general, suboptimal for the family of systems considered, we provide an efficient method to bound their suboptimality via the optimal solution of another finite-dimensional conic program. A case study of a 12 kV radial distribution system demonstrates that decentralized affine controllers can perform close to optimal.Index Terms-Distributed energy resources, energy storage, solar power generation, decentralized control, volt/var control.
I. INTROUDCTIONThe increasing penetration of distributed and renewable energy resources introduces challenges to the operation of distribution systems, including rapid fluctuations in bus voltage magnitudes, reverse power flows at distribution substations, and deteriorated power quality due to the intermittency of supply from renewables. These challenges are exasperated by the fact that traditional techniques for distribution system management, including the deployment of on-load tap changing (OLTC) transformers and shunt capacitors, cannot effectively deal with the rapid variation in the power supplied from renewable resources [1]. In this paper, we aim to address such challenges by developing a systematic approach to the design of decentralized feedback controllers for distribution networks with a high penetration of distributed solar and energy storage resources, in order to minimize the expected cost of meeting demand over a finite horizon, while respecting network and resource constraints. Related Work: Although current industry standards require that photovoltaic (PV) inverters operate at a unity power factor [2], the latent reactive power capacity of PV inverters can be utilized to regulate voltage profiles [3]-[8], and reduce active power losses [9]-[18] in distribution networks. A large swath of the literature on the reactive power management of PV Weixuan Lin (wl476@cornell.edu) and Eilyan Bitar (eyb5@cornell.edu) are with the inverters prescribes the solution of an optimal power flow (OPF) problem to determine the reactive power injections of PV inverters in real time [3]-[15]. The resulting OPF problem mus...
