Revenue Adequate Prices for Chance-Constrained Electricity Markets with Variable Renewable Energy Sources

In a commodity market, revenue adequate prices refer to compensations that ensure that a market participant has a non-negative profit. In this article, we study the problem of deriving revenue adequate prices for an electricity market-clearing model with uncertainties resulting from the use of variable renewable energy sources (VRES). To handle the uncertain nature of the problem, we use a chance-constrained optimization (CCO) approach, which has recently become very popular choice when constructing dispatch electricity models with penetration of VRES (or other sources of uncertainty). Then, we show how prices that satisfy revenue adequacy in expectation for the market administrator, and cost recovery in expectation for all conventional and VRES generators, can be obtained from the optimal dual variables associated with the deterministic equivalent of the CCO market-clearing model. These results constitute a novel contribution to the research of research on revenue adequate, equilibrium, and other types of pricing schemes that have been derived in the literature when the market uncertainties are modeled using stochastic or robust optimization approaches. Unlike in the stochastic approach, the CCO market-clearing model studied here produces uncertainty uniform real-time prices that do not depend on the real-time realization of the VRES generation outcomes. To illustrate our results, we consider a case study electricity market, and contrast the market prices obtained using a revenue adequate stochastic approach and the proposed revenue adequate CCO approach.