Payment cost minimization with transmission capacity constraints and losses using the objective switching method

Deregulated electricity markets in the U.S. currently minimize total bid costs to select bids and their generation levels but determine payments based on market clearing prices. The inconsistency between auction and settlement mechanisms can lead to a significantly higher consumer payment. This gives rise to the “payment cost minimization,” an alternative auction mechanism that minimizes consumer payments directly. This paper formulates payment cost minimization problems with transmission capacity constraints and losses. DC power flow is used to model the transmitted power. The locational marginal prices are defined by “economic dispatch” and characterized by using the Karush-Kuhn-Tucker conditions. The formulation is converted to linear to be solved by the branch-and-cut method in standard commercial solver CPLEX´s MIP. Specific methods for the linear conversion are highlighted. The efficiency for solving this linear payment cost minimization model in CPLEX´s MIP is still low. The difficulties are studied by comparing the convex hulls of the two auction problems. To overcome the difficulties and improve the efficiency, the new “objective switching method” is developed which can be also used for solving other NP hard problems. Performance cuts are first generated to reduce the feasible region. The infeasibilities of originally discrete variables are then minimized within the reduced region to find one of many feasible near-optimal solutions with quantifiable quality. Numerical testing results of small examples and IEEE Reliability Test System demonstrate the effectiveness and efficiency of the model and the method.