Mutually orthogonal LMP decomposition: Analysis of PJM network by null space approach

Under standard approach, locational marginal prices (LMPs) are generally decomposed into system marginal (energy) price (SMP), marginal congestion cost (MCC), and marginal loss cost (MLC). However, earlier work has shown that it is not possible to separate the standard decompositions of LMPs into three mutually orthogonal subspaces. It is also found that MLC term of standard LMP inherently depends on the selection of reference bus, due to their association with only a single direction (one dimensional space) in the set of admissible LMPs. On the other hand, the MCC term, constructed by the null space approach, is found to be independent of choice of reference bus. A key goal of this research is to develop efficient algorithms that provide conceptual and computational simplicity in characterizing the admissible set of LMPs. The key outcome of this work is an efficient algorithm that only requires the identification of a single null vector in a matrix known to be column-rank deficient by one, and hence achieves the goal of low cost computation. In this paper, we illustrate the usefulness of this fundamental null space approach by applying it on well-known PJM network by invoking one constraint at a time. The objective is to analyze the admissible LMP pattern in PJM network, by observing the behavior and relationship of MCC term - both magnitude and direction - to combined SMP/MLC term (marginal energy/loss basis vector).