A Faithful and Tractable Distributed Mechanism for Residential Electricity Pricing

Demand response (DR) programs incentivize consumers for using their elastic demand for demand shaping, supply-demand balancing, and other ancillary and network support services. This paper proposes a dynamic nonlinear pricing scheme for behind-the-meter distributed energy resources (DERs), such as residential batteries, plug-in electric vehicles, and smart appliances, participating in a DR program, based on distributed mechanism design concepts. The underlying method is a faithful mechanism that can overlay any tractable dual-decomposition algorithm that solves the DER management and coordination problem in a distributed fashion. Since electricity is a continuously produced and divisible commodity that cannot be invariably allocated or stored, the pricing scheme is designed to couple the negotiated allocations and the actual consumption in a proportionally fair way, which means that it assigns lower payments to consumers who require less energy and are more accurate in following these requirements. Specifically, this pricing scheme is based on the Lagrange multipliers, which are the byproducts of any dual-decomposition algorithm that solves the nonconvex DER management and coordination problem. As a result, and in contrast to most existing time-varying pricing schemes, this pricing strategy does not suffer from rebound peaks repercussions. Furthermore, the proposed distributed mechanism is proven to be asymptotically faithful, i.e., faithful when the number of households grows large, collusion proof and weakly budget balanced.