A study of commitment cost in approximate extended Locational Marginal Prices

In the current wholesale electricity markets of the US, Locational Marginal Prices (LMPs) are determined in the economic dispatch process with fixed commitment decisions. Certain fast start resources at generation limits may not be the marginal unit to set LMPs. Costs associated with commitment decisions may not be incorporated either, resulting in significant uplift payments. Extended LMPs (ELMPs) have been obtained from the convex hull of the total cost function to address these issues. To practically implement ELMPs, an approximate model has been developed. In this model for fast start resources to set prices, commitment related costs are allocated to individual intervals, and the resulting cost curves are convexified. Start-up cost is coupled across time and should be appropriately allocated to individual intervals. In this paper, the allocation is studied by time-decoupling an integral relaxed unit commitment problem. The interaction of commitment related cost across time is analyzed from the resulting Lagrangian multipliers. It can be computationally expensive to obtain the optimal multipliers. Instead of solving the dual problems, a generic allocation study is conducted by using the Karush-Kuhn-Tucker (KKT) conditions. The study shows that start-up cost is allocated to peak generation intervals. This provides a mathematical guideline to determine the allocation practice when developing approximate ELMPs. Numerical results show that following the allocation study, approximate ELMPs are obtained close to ELMPs and can effectively incorporate major features of ELMPs.