Multi-Time Co-optimization of Voltage Regulators and Photovoltaics in Unbalanced Distribution Systems

In distribution systems with high penetrations of solar energy, co-optimizing the operation of voltage regulators (VRs) with off-unity power factor inverters of photovoltaics (PVs) becomes imperative for confining nodal voltages within ANSI limits and ensuring an adequate number of tap actions. The framework proposed in this article minimizes the energy import from the substation (or maximizes the solar utility), the line losses, and the diurnal VR actions (VRAs) to reduce their maintenance costs and optimally coordinate with PV Var compensation. This is subject to the physical and security constraints of unbalanced distribution systems for which we build upon the rank-relaxed semidefinite programming branch flow model (SDP BFM). Departing from approximate VR models, we formulate an accurate model with nonuniformly-operated discrete tap positions. We overcome the computational complexity of solving the multi-time MISDP problem and the trilinearity emanating from VR incorporation by the application of Generalized Benders Decomposition (GBD). Also, to efficiently accommodate a large instance of binary variables, we accelerate the GBD's convergence with additional constraints on tap positions to reduce the search region. The merits of the proposed algorithm are demonstrated on the modified IEEE 37-bus and 123-bus test feeders for an hourly day-ahead optimization.