The Subgradient Simplex Cutting Plane Method for Extended Locational Marginal Prices

In current electricity markets of the USA, locational marginal prices (LMPs) are obtained from the economic dispatch process and cannot capture costs associated with commitment decisions. The extended LMPs (ELMPs) were established as the optimal Lagrangian multiplier of the dual of the unit commitment and economic dispatch problem. Commitment related costs are included and uplift payments are minimized. To obtain ELMPs, the dual problem should be solved with multiplier optimality and computational efficiency. Subgradient methods suffer from the multiplier zigzagging difficulty. Cutting plane methods encounter computational complexity issues in calculating query points. In this paper, a subgradient simplex cutting plane method is developed to obtain ELMPs. Transmission is not considered for simplicity, while key features of ELMPs are still captured. By innovatively using subgradients and simplex tableaus, query points are efficiently obtained through an adaptive three-level scheme. A query point along the subgradient is easily calculated at Level 1. As needed, Level 2 obtains Kelley´s query point and Level 3 obtains the Chebyshev center, both by pivoting simplex tableaus. Numerical results show that the optimal multiplier is efficiently obtained.