Load Scheduling With Price Uncertainty and Temporally-Coupled Constraints in Smart Grids

Recent years have witnessed the significant growth in electricity consumption. The emerging smart grid aims to address the ever-increasing load through appropriate scheduling, i.e., to shift the energy demand from peak to off-peak periods by pricing tariffs as incentives. Under the real-time pricing environment, due to the uncertainty of future prices, load scheduling is formulated as an optimization problem with expectation and temporally-coupled constraints. Instead of resorting to stochastic dynamic programming that is generally prohibitive to be explicitly solved, we propose dual decomposition and stochastic gradient to solve the problem. That is, the primal problem is firstly dually decomposed into a series of separable subproblems, and then the price uncertainty in each subproblem is addressed by stochastic gradient based on the statistical knowledge of future prices. In addition, we propose an online approach to further alleviate the impact of price prediction error. Numerical results are provided to validate our theoretical analysis.