The short-term forecasting of real-time locational marginal price (LMP) and network congestion is considered from a system operator perspective. A new probabilistic forecasting technique is proposed based on a multiparametric programming formulation that partitions the uncertainty parameter space into critical regions from which the conditional probability distribution of the real-time LMP congestion is obtained. The proposed method incorporates load generation forecast, time varying operation constraints, and contingency models. By shifting the computation cost associated with multiparametric programs offline, the online computation cost is significantly reduced. An online simulation technique by generating critical regions dynamically is also proposed, which results in several orders of magnitude improvement in the computational cost over standard Monte Carlo methods.
Several techniques have been proposed to approximate the LMP distribution at a future time. In @cite_8 , a probabilistic LMP forecasting approach was proposed based on attaching a Gaussian distribution to a point estimate. The advantage is that the technique can incorporate various point forecasting methods. The disadvantage, on the other hand, is that network effects are not easy to incorporate. The authors of @cite_6 and @cite_11 approximate the probabilistic distribution of LMP using higher order moments and cumulants. These methods are based on representing the probability distribution as an infinite series involving moments or cumulants. In practice, computing or estimating higher order moments and cumulants are very difficult; lower order approximations are necessary.
@cite_11 @cite_6 @cite_8
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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. In power market studies, the forecast of locational marginal price (LMP) relies on the load forecasting results from the viewpoint of planning. It is well known that short-term load forecasting results always carry certain degree of errors mainly due to the random nature of the load. At the same time, LMP step changes occur at critical load levels (CLLs). Therefore, it is interesting to investigate the impact of load forecasting uncertainty on LMP. With the assumption of a certain probability distribution of the actual load, this paper proposes the concept of probabilistic LMP and formulates the probability mass function of this random variable. The expected value of probabilistic LMP is then derived, as well as the lower and upper bound of its sensitivity. In addition, two useful curves, alignment probability of deterministic LMP versus forecasted load and expected value of probabilistic LMP versus forecasted load, are presented. The first curve is designed to identify the probability that the forecasted price in a deterministic LMP matches the actual price at the forecasted load level. The second curve is demonstrated to be smooth and therefore eliminates the step changes in deterministic LMP forecasting. This helps planners avoid the possible sharp changes during decision-making process. The proposed concept and method are illustrated with a modified PJM five-bus system and the IEEE 118-bus system.