Risk-averse placement and sizing of photovoltaic inverters in radial distribution networks

A risk-averse strategy is presented for optimal placement and sizing of photovoltaic (PV) inverters in distribution networks under solar irradiance and load uncertainty. By modeling uncertainties through a finite set of scenarios, a two-stage stochastic program is formulated. First-stage decisions comprise binary placement variables, area, and apparent power capacity of PV units. Second-stage decisions are PV reactive power compensations and power flows. The objective accounts for PV installation costs, expected thermal losses and a risk measure thereof. The formulation amounts to a mixed-integer second-order cone program and is tested on the IEEE 34-node test feeder.