Real-Time Pricing with uncertain and heterogeneous consumer preferences

Consumer demand profiles and fluctuating renewable power generation are two main sources of uncertainty in matching demand and supply. This paper proposes a model of the electricity market that captures the uncertainties on both, the operator and the user side. The system operator (SO) implements a temporal linear pricing strategy that depends on real-time demand and renewable generation in the considered period combining Real-Time Pricing with Time-of-Use Pricing. The announced pricing strategy sets up a Bayesian game among the users with unknown, heterogeneous and correlated consumption preferences. The explicit characterization of the optimal selfish user behavior using the Bayesian Nash equilibrium solution concept allows the SO to derive pricing policies that influence demand to serve practical objectives such as minimizing peak-to-average ratio or attaining a desired rate of return while at the same time hedging renewable generation uncertainty.