Day ahead dynamic pricing for demand response in dynamic environments

The problem of optimizing retail pricing of electricity for price-responsive dynamic loads is considered. For the class of day-ahead dynamic prices (DADPs), the problem of retail pricing is modeled as a Stackelberg game with the retailer as the leader and its customers the followers. It is shown that the optimal customer response to a DADP has an affine structure with a deterministic negative definite sensitivity matrix and a stochastic bias. With this structure, tradeoffs between consumer surplus and retail profit can be characterized by a convex region with a concave and non-increasing Pareto front, each point on the Pareto front corresponding to an equilibrium in a dynamic game with a particular payoff function; any consumer surplus-retail profit pair above the Pareto front is not attainable by any dynamic pricing scheme. The optimal DADP that maximizes the social welfare is shown to be that maximizes the consumer surplus thus making retail profit zero. Effects of renewable energy are also considered.