Chance-Constrained Optimization of Energy Storage Capacity for Microgrids

The optimal storage capacity is a crucial parameter for stable and reliable operation of microgrids in an islanded mode. In this context, an analytical method is developed to robustly formulate and analyze energy storage capacity deploying chance constrained stochastic optimization. More specifically, the goal is to determine an appropriate size for an energy storage to reach a specific loss of load probability (LOLP) in a microgrid with large penetration of renewables considering generation and load forecast error. The total cost is minimized over optimal storage capacity as well as over generators power, while accounting for generation and storage power and energy constraints. It is postulated that the shortage/surplus power will be derived from/injected to the storage system. However, due to stochastic nature of load and renewables and an inevitable forecast error, the renewable generation output or the load power may not be accurately acquired. Thus, the total storage power and energy constraints are posed as chance constraints, for which conservative convex approximations are employed for tractability. In particular, to overcome the difficulty brought about by the large size of the optimization problem, a separable (distributed) structure is pursued, and the dual decomposition method is adopted to obtain optimal solutions. Numerical tests verify the effect of prior knowledge in modeling the uncertainty in optimal choice of storage capacity.