A new high accuracy method for calculation of LMP as a random variable

The Locational Marginal Pricing (LMP) is a dominant approach in energy market operation and planning to identify the nodal price and to manage the transmission congestion. Considering the uncertainties associated with the input data of load flow, the LMP can be considered as a stochastic variable. Therefore calculation of LMP as a random variable can be very useful in power market forecasting studies. In this paper, LMP has been calculated with Cumulant & Gram-Charlier (CGC) method and compared with Monte Carlo and point estimation method. This method combines the concept of Cumulants and Gram-Charlier expansion theory to obtain Probabilistic Distribution Functions (PDF) and Cumulative Distribution Function (CDF) of LMP. It has significantly reduced the computational time while maintaining a high degree of accuracy. The method described in this paper applied to PJM test system. The sensitivity of LMP with variation of load has also been calculated and compared with deterministic calculation.