An electricity market operator solves a social welfare maximization model to determine market prices and generation. If the cost functions include nonconvexities such as binary variables, then linear prices generally do not exist such that all firms agree that the market operator's generation instructions are optimal. We define a "minimum disequilibrium" (MD) model which selects market prices and generation quantities to minimize the total of all firms' apparent loss of profit. The MD model is, however, difficult to solve. Gabriel, Conejo, Ruiz and Siddiqui recently proposed an extension of the mixed complementary problem type of model, which allows for integer variables and is solved as a mixed integer program. We show that the approach of Gabriel et al. provides an approximate solution to the MD model, and the approximation is exact in some circumstances. The approximation to the MD model is illustrated and compared with current, ad hoc fixes to the problems caused by nonconvexities in real markets.
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