Load scheduling with price uncertainty and coupling constraints

This paper investigates the load scheduling problem in smart grids. Due to the uncertainty of future electricity prices, the statistical knowledge is utilized in the load scheduling process. Instead of resorting to stochastic dynamic programming that is generally prohibitive to be explicitly solved, load scheduling is formulated as an optimization problem with coupling constraints. Dual decomposition and stochastic gradient are proposed to solve the optimization problem. That is, the problem is first decoupled into a series of separable subproblems, and then price uncertainty is addressed by stochastic gradient based on probability distributions of future prices. An online approach improves the performance of load scheduling by alleviating the impact of price prediction error. Numerical results are provided to validate our theoretical analysis.