Stochastic Planning of Distributed PV Generation
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Recent studies by electric utility companies indicate that maximum benefits of distributed solar photovoltaic (PV) units can be reaped when siting and sizing of PV systems is optimized. This paper develops a two-stage stochastic program that serves as a tool for optimally determining the placing and sizing of PV units in distribution systems. The PV model incorporates the mapping from solar irradiance to AC power injection. By modeling the uncertainty of solar irradiance and loads by a finite set of scenarios, the goal is to achieve minimum installation and network operation costs while satisfying necessary operational constraints. First-stage decisions are scenario-independent and include binary variables that represent the existence of PV units, the area of the PV panel, and the apparent power capability of the inverter. Second-stage decisions are scenario-dependent and entail reactive power support from PV inverters, real and reactive power flows, and nodal voltages. Optimization constraints account for inverter’s capacity, PV module area limits, the power flow equations, as well as voltage regulation. A comparison between two designs, one where the DC:AC ratio is pre-specified, and the other where the maximum DC:AC ratio is specified based on historical data, is carried out. It turns out that the latter design reduces costs and allows further reduction of the panel area. The applicability and efficiency of the proposed formulation are numerically demonstrated on the IEEE 34-node feeder, while the output power of PV systems is modeled using the publicly available PVWatts software developed by the National Renewable Energy Laboratory. The overall framework developed in this paper can guide electric utility companies in identifying optimal locations for PV placement and sizing, assist with targeting customers with appropriate incentives, and encourage solar adoption.