Stochastic optimization for siting and sizing of renewable distributed generation and D-STATCOMs

Abstract

This paper presents a novel methodology for the optimal placement and sizing of distributed renewable generators and D-STATCOMs in electrical distribution systems. The problem is formulated as a mixed-integer second-order cone stochastic model with an objective function that minimizes the investment costs of purchasing and installing D-STATCOMs, wind turbines, photovoltaic systems, and small hydropower plants, as well as the expected value of energy purchase cost by the distribution company. A two-stage stochastic programming formulation addresses uncertainties in electrical demand, energy prices, wind-based distributed generation, solar-based distributed generation, and small hydropower-based distributed generation. Stochastic scenarios are generated using the k-means clustering technique. Moreover, a relaxed convex model is proposed to reduce the number of candidate nodes for installation, significantly improving computational efficiency while ensuring optimality. The proposed methodology’s accuracy, efficiency, and robustness are validated on two benchmark distribution systems with 70 and 136 nodes, respectively. The results demonstrate that the simultaneous integration of distributed renewable generators and D-STATCOMs effectively reduces operational costs and energy losses, achieving a loss reduction of 42.3% and 13.6% for the 70-node and 136-node test systems, respectively, while enhancing voltage regulation and improving the loading of network components. Furthermore, the model estimates the cost reductions required for solar and wind technologies to become economically viable under uncertainty, providing a practical tool for policymakers to design effective financial incentives. This feature is particularly relevant for developing countries, where high capital costs and limited public resources hinder renewable energy integration.