Solving payment cost co-optimization problems

Current U.S. electricity markets select supply bids by using a bid cost minimization (BCM) auction mechanism but then settle the payments based on locational marginal prices (LMPs). The resulting payments can be significantly higher than the minimized bid costs. An alternative payment cost minimization (PCM) mechanism aiming to minimize the total payments has been discussed. Studies on single product problems have shown that PCM leads to reduced payments, but few results have been reported for the co-optimization of energy and other products. In view that co-optimization leads to a more efficient capacity allocation than optimizing each product individually, it is important to investigate the PCM co-optimization problems, and solve them in standard MIP solvers for a fair comparison with BCM. In PCM, prices are decision variables and need to be appropriately defined. We characterized marginal price-setting units by using logical constraints and converted them to linear forms since linearity is required by the standard MIP solvers. The nonlinear cross-product in PCM objective function, however, cannot be converted to linear forms. Based on our recent results on surrogate optimization, a method is developed to deal with nonlinearity. Prices are first fixed at their values at the previous iteration to obtain linear formulation, and are then updated using price definition if the surrogate condition is satisfied. Numerical testing results of small examples and a 24-bus example demonstrate the effectiveness and efficiency of the method.