Mechanism Design for Demand Response Programs

Demand Response (DR) programs serve to reduce the consumption of electricity at times when the supply is scarce and expensive. The utility informs the aggregator of an anticipated DR event. The aggregator calls on a subset of its pool of recruited agents to reduce their electricity use. Agents are paid for reducing their energy consumption from contractually established baselines. Baselines are counter-factual consumption estimates of the energy an agent would have consumed if they were not participating in the DR program. Baselines are used to determine payments to agents. This creates an incentive for agents to inflate their baselines. We propose a novel self-reported baseline mechanism (SRBM) where each agent reports its baseline and marginal utility. These reports are strategic and need not be truthful. Based on the reported information, the aggregator selects or calls on agents to meet the load reduction target. Called agents are paid for observed reductions from their self-reported baselines. Agents who are not called face penalties for consumption shortfalls below their baselines. The mechanism is specified by the probability with which agents are called, reward prices for called agents, and penalty prices for agents who are not called. Under SRBM, we show that truthful reporting of baseline consumption and marginal utility is a dominant strategy. Thus, SRBM eliminates the incentive for agents to inflate baselines. SRBM is assured to meet the load reduction target. SRBM is also nearly efficient since it selects agents with the smallest marginal utilities, and each called agent contributes maximally to the load reduction target. Finally, we show that SRBM is almost optimal in the metric of average cost of DR provision faced by the aggregator

Numerical solution of the Lyapunov equation by approximate power iteration

AbstractWe present the approximate power iteration (API) algorithm for the computation of the dominant invariant subspace of the solution X of large-order Lyapunov equations AX + XAT + Q = 0 without first computing the matrix X itself. The API algorithm is an iterative procedure that uses Krylov subspace bases in computing estimates of matrix-vector products Xv in a power iteration sequence. Application of the API algorithm requires that A + AT < 0; numberical experiments indicate that, if the matrix X admits a good low-rank solution, then API provides an orthogonal basis of a subspace that closely approximates the dominant X-invariant subspace of corresponding dimension. Analytical convergence results are also presented