Optimal robust allocation of distributed modular energy storage system in distribution networks for voltage regulation

This paper addresses the optimal robust allocation (location and number) problem of distributed modular energy storage (DMES) in active low-voltage distribution networks (DNs) with the aim of reducing voltage deviations. In the proposed allocation problem, a novel centralized-local control framework (CLCF) is designed for DMES for voltage regulation, where the droop coefficients setting schedule are optimally determined. Besides, in order to address the uncertainties and correlation between active and reactive power injections, the proposed DMES allocation problems are formulated as robust optimization models under the novel correlated polyhedral uncertainty set (CPUS) to avoid over-conservatism of solutions. Moreover, to make the proposed nonlinear nonconvex allocation problem computationally trackable, it is decoupled into operation and planning (siting and sizing) optimization stages. The operation problem is relaxed into a mixed-integer second-order cone programming problem using mixed-integer reformulation, dual linear program and second-order cone program. In planning stage, a recursive algorithm is employed to determine the capacity boundaries to identify the optimal number of DMESs. Through case studies, the effectiveness and advantages of the optimal allocation methods was demonstrated in an actual rural low-voltage DN in China.