A stochastic distribution system planning method considering regulation services and energy storage degradation.

• A stochastic distribution system planning with energy storage degradation is solved. • Energy arbitrage and regulation services are co-optimized for siting and sizing. • A Gaussian mixture model is adopted to generate stochastic scenarios. • A modified progressive hedging algorithm which outperforms Gurobi is introduced. With the trend of energy storage participating in ancillary service markets, it is still computationally burdensome to incorporate the rapidly changing real-time signals in the long-run distribution system planning. In this paper, a two-stage stochastic programming is proposed for the distribution system with energy storage, where the storage degradation and ancillary service revenue for frequency regulation are both considered. For this purpose, the problem is formulated as a mixed-integer linear programming optimizing the overall planning cost, including investment and maintenance cost, power transaction cost and revenue from regulation services. A degradation penalty is added in the objective to avoid excessive charge/discharge when providing regulation services, thus further benefiting the economy of the distribution system. The model also considers uncertainties of load demand and electricity prices. A Gaussian mixture model is adopted to characterize these uncertainties and a set of representative scenarios are sampled. To accelerate the optimization, a modified progressive hedging with parallel computing is proposed. It is demonstrated through a 33-bus distribution system that the proposed algorithm has a speed approximately 15 times as fast as the state-of-art commercial software Gurobi when solving the model in 100 scenarios. For this case study, considering degradation penalty has been shown to extend energy storage lifespan by one year. [ABSTRACT FROM AUTHOR]