Fast algorithm for multi-period locational marginal price

Locational marginal price (LMP) is widely used in various electricity markets. It is one the most successful and important pricing scheme. In this paper, we established a linear programming model called d-LP algorithm to obtain the optimal Lagrange multipliers. So that we can directly get the optimal multipliers and the LMPs without solving the SCED problem. Based on detailed analysis of the multi-period security constrained economic dispatch (SCED) model, we decomposed the multi-period SCED formulation into single-period Lagrange function and individual unit sub-problems at each period. Then we obtained the piecewise linear concave relationship between the optimal value of each individual unit sub-problem and the Lagrange multipliers. We proved that the proposed method is effective by analyzing the numerical results of the typical IEEE 24-bus system.