  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.
