Accelerated Distributed Hybrid Stochastic/Robust Energy Management of Smart Grids

The uncertainties of renewable energy, loads, and electricity prices pose significant challenges to the economical and secure energy management of smart grids. In this article, a hybrid stochastic/robust (HSR) optimization method is developed to minimize the overall cost of all units. The proposed approach takes advantage of stochastic programming, robust optimization, and distributed optimization methods while considering various system constraints. First, stochastic electricity price scenarios are selected by the Latin hypercube sampling method. Second, the uncertainties of renewable energy generation and loads are managed by the proposed robust optimization method under each price scenario. Then, an improved distributed optimization method is proposed to solve the formulated HSR optimization problem, which considerably enhances the convergence with the accelerated gradient method. Numerical case studies of both small-scale and large-scale power systems demonstrate the accuracy, effectiveness, and scalability of the proposed distributed HSR approach. Additionally, the optimality and convergence of this proposed distributed algorithm are mathematically proven and analyzed.