Probabilistic LMP Forecasting under AC Optimal Power Flow Framework: Theory and Applications


This paper presents an analytical approach for studying the impact of load forecasting uncertainty on locational marginal price (LMP), in electricity wholesale market. The random nature of load brings in uncertainty in LMP through a market clearing model, also known as an optimal power flow (OPF) problem. This work is built on alternating current OPF, a close representation of the actual problem where power losses are accurately modeled. In the context of load being a normally distributed random variable, the probabilistic LMP concept under ACOPF is firstly examined to be a mixed random variable assuming both continuous and discrete values. Then, with the LMP versus load model, the probability density function (PDF) and cumulative density function (CDF) of probabilistic LMP are formulated and shown to be differentiable almost everywhere. The derived PDF formulation reveals an interesting fact that LMP does not follow a normal distribution even when load is normally distributed. Rather, its PDF presents a piece-wise partial normal distribution pattern due to the LMP step-change phenomenon. Further, the expected value of the probabilistic LMP and its sensitivity are derived. The proposed analytical approach can be useful for power market participants in evaluating and hedging financial risks associated with LMP uncertainty. The validity and effectiveness of the proposed method will be exemplified on a modified PJM 5-bus system and the IEEE 118-bus test system.


Electrical and Computer Engineering

Keywords and Phrases

Critical Load; Locational Marginal Price; Optimal Power Flows; Power Markets; Probabilistic LMP; Acoustic Generators; Commerce; Electric Load Forecasting; Normal Distribution; Random Variables; Electric Load Flow; AC Optimal Power Flow (ACOPF); Critical Load Level; Optimal Power Flow; Power Market

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Article - Journal

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© 2012 Elsevier, All rights reserved.

Publication Date

01 Jul 2012