Real-time demand response with uncertain renewable energy in smart grid

We consider a set of users served by a single load serving entity (LSE) in the electricity grid. The LSE procures capacity a day ahead. When random renewable energy is realized at delivery time, it actively manages user load through real-time demand response and purchases balancing power on the spot market to meet the aggregate demand. Hence, to maximize the social welfare, decisions must be coordinated over two timescales (a day ahead and in real time), in the presence of supply uncertainty, and computed jointly by the LSE and the users since the necessary information is distributed among them. We formulate the problem as a dynamic program. We propose a distributed heuristic algorithm and prove its optimality when the welfare function is quadratic and the LSE's decisions are strictly positive. Otherwise, we bound the gap between the welfare achieved by the heuristic algorithm and the maximum in certain cases. Simulation results suggest that the performance gap is small. As we scale up the size of a renewable generation plant, both its mean production and its variance will likely increase. We characterize the impact of the mean and variance of renewable energy on the maximum welfare. This paper is a continuation of [2], focusing on time-correlated demand.