Analytical model for placing and sizing photovoltaic systems in electricity distribution networks

In recent times, the power distribution operators are focusing on integrating distributed renewable energy resources, such as photovoltaic (PV) units, into the grid in response to increasing electric demand and limited fossil fuel resources. However, stochastic availability of renewable energy poses obstacles in seamless and efficient integration of PV systems into current electricity distribution networks. Challenges include placing and sizing PV installations under solar irradiance uncertainties. Also, the stochasticity present in the problem may lead to high thermal losses due to potentially reverse power flows in periods of high generation. Considering these issues, the present work develops a formulation for optimally placing and sizing PV units to achieve minimum installation and maintenance costs, and network operation costs while satisfying necessary operational constraints. A radial distribution network with substation and user nodes is considered. The formulation includes 1) binary variables that represents the existence of PV units; the apparent power capability of the inverter; 3) for each user node and scenario, real power capability of the inverter and reactive power injected by PV inverter; 4) real and reactive power flows going into node. The constraints include the existence of PV, the inverter’s capacity, PV module area limits. The problem is formulated as a Mixed integer convex program. To show the applicability and efficiency of the proposed formulation, numerical tests are conducted on an IEEE 34-node feeder, while the output power of PV systems is modeled through publically available solar irradiance data from the National Renewable Energy Laboratory (NREL) PVWatts website.