Risk-constrained stochastic optimal allocation of energy storage system in virtual power plants

This paper aims to develop a decision-making procedure for efficient placement and sizing of energy storage system (ESS) within virtual power plants (VPPs) premises under the uncertainty of market price. The main aim is to minimize the overall cost of VPP within a fixed time horizon planning. The understudy VPP consists of wind turbine, photovoltaic system, curtailable loads, ESS, and diesel generators in which the VPP trades electricity with the upstream grid. The proposed framework investigates both optimal power and optimal energy of ESS based on the available budget for investment. To hedge against the uncertainty of investment, an efficient risk management manner based on the concept of conditional value at risk is applied. Moreover, from the reliability point of view, two reliability indices: the loss of load expectation and energy expected not served, are evaluated under different levels of investment to assess the impact of ESS on VPP reliability. The proposed model is formulated as a mixed-integer nonlinear programming problem and is solved by the well-known General Algebraic Modeling System commercial software package. The effectiveness of the proposed risk-based opti-mization approach is demonstrated through vigorous case studies and comprehensive cost-benefit analysis.