Distributed tracking-ADMM approach for chance-constrained energy management with stochastic wind power in smart grid

This paper proposes a distributed strategy to the chance-constrained energy management for smart grid with penetration of stochastic wind power. The energy management model is constructed including chance constraints of spinning reserves for the sake of guaranteeing the maximum utilization of wind power on the basis of reliability. With the available wind power characterizing by Weibull distribution, the chance constraints can be converted into deterministic ones by the derived analytical form of inverse cumulative distribution function. Although the original problem is transformed into a typical convex optimization problem, the tight coupling of constraints presents challenges to the design of distributed strategy. As such, we formulate the problem into a compact form with each generator unit depending on individual decision variables, instead of the common form with decision vector being the collection of all local decision variables. Then, by developing a new initialization method and an adaptive weight matrix selection method, a distributed strategy based on tracking Alternating Direction Method of Multipliers (ADMM) is proposed to solve the model. The simulation results indicate that the proposed distributed strategy achieves comparable performance to the corresponding centralized scenario, and better performance than distributed consensus-based ADMM in the related literature. Moreover, the validity of the proposed distributed strategy is confirmed in one day chance-constrained energy management with stochastic wind power.