Optimal pricing for residential demand response: A stochastic optimization approach

The problem of optimizing retail electricity price for residential demand response is considered. A two stage stochastic optimization is formulated in which the retailer optimizes the day ahead price in the first stage, and residential customers schedule their demands optimally in respond to the optimized retail price and in a distributed fashion. For the control of thermal dynamic loads, the optimal residential demand response policy is obtained based on a form of consumer surplus that captures the tradeoff between comfort level and cost. It is shown that the optimal control is an affine function of the retail price with a negative definitive factor matrix. The optimal retail pricing is obtained through a convex program that maximizes average profit or a form of conditional value at risk. Effects of incorporating renewable energy are also considered.