Although locational marginal pricing (LMP) plays an important role in many restructured wholesale power markets, the detailed derivation of LMP as it is actually used in industrial practice is not readily available. This lack of transparency greatly hinders the efforts of researchers to evaluate the performance of these markets. In this paper, different alternating current and direct current optimal power flow models are presented to help us understand the derivation of LMP. As a byproduct of this analysis, we are able to provide a rigorous explanation of the basic LMP and LMP-decomposition formulas (neglecting real power losses) that are presented without derivation in the business practice manuals of the US Midwest Independent System Operator.
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