On the problem of controlling shiftable prosumer devices with price signals

Price-based control approaches can be derived from the Lagrangian relaxation of the unit commitment problem and provide a scalable framework for solving practical sized optimization problems. The framework postulates an iterative gradient based-pricing mechanism, in which the price signal is used to negotiate the energy exchange between individual market participants. Within this framework shiftable prosumer devices induce non-convex, non-continuous utility functions, which can cause divergence of the gradient based pricing mechanism resulting in market failures. This paper proposes a new simple but efficient method to deal with this problem by exploiting the concept of randomized price offsets.