Demand response in presence of multiple suppliers

In demand side management electricity consumers are systematically encouraged by a load serving entity (LSE) to adjust their electricity demand to reduce overall costs. Li et al. [1] have presented such an iterative demand response program. In each iteration it sends price signals to the consumers against their demands for each hour of the day ahead, and smart consumer appliances adjust their usage accordingly to maximize their utility given the prices. The price signal is the marginal cost based on a single quadratic and piecewise smooth cost function. We extend previous work to allow multiple cost functions one for each supplier, and require that the LSE optimizes procurement jointly with the demand response. The price signal is then based on the optimal cost of procurement from all suppliers, computed using sequential quadratic programming (SQP). However, when the number of cost functions grows computing the price signal in each iteration becomes a bottleneck. Therefore, we also introduce an approximation technique based on knowledge compilation, in which the procurement problem is first represented in discrete form in propositional logic, and compiled into a tractable form known as decomposable negation normal form (DNNF). The DNNF is then used for efficient computation of near optimal prices in each iteration.