Joint day-ahead power procurement and load scheduling using stochastic alternating direction method of multipliers

In this work, we consider the joint day-ahead power bidding and load scheduling problem for the smart grid system, in the presence of uncertain energy demand and renewable energy generation. We formulate the problem as a convex stochastic program in which the renewable energy generation and energy demand are modeled as random variables. The objective is to minimize the cost in the day-ahead market as well as the cost due to real-time power imbalance, by simultaneously selecting: 1) the amount of power to buy in the day-ahead market and 2) the schedule for the controllable load. We propose a stochastic alternating direction method of multipliers (S AD-MM) to solve the resulting convex stochastic optimization problem and analyze its convergence. The effectiveness of the proposed approach is demonstrated via numerical experiments using real solar power data.