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Probabilistic LMP forecasting under AC optimal power flow framework: Theory and applications

机译：交流最优潮流框架下的概率LMP预测：理论与应用

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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.
机译：本文提出了一种分析方法，用于研究电力批发市场中负荷预测不确定性对位置边际价格（LMP）的影响。负载的随机性会通过市场结算模型（也称为最佳潮流（OPF）问题）在LMP中带来不确定性。这项工作建立在交流电OPF的基础上，后者是对功率损耗进行精确建模的实际问题的近似表示。在负载是正态分布的随机变量的情况下，首先将ACOPF下的概率LMP概念检查为混合随机变量，同时假设连续值和离散值。然后，利用LMP与负载模型，公式化了概率LMP的概率密度函数（PDF）和累积密度函数（CDF），并证明了几乎在任何地方都是可微的。派生的PDF公式揭示了一个有趣的事实，即使负载呈正态分布，LMP也不会遵循正态分布。相反，由于LMP阶跃变化现象，其PDF呈现分段的部分正态分布模式。此外，推导了概率LMP的期望值及其敏感性。所提出的分析方法对于电力市场参与者评估和对冲与LMP不确定性相关的金融风险很有用。在改进的PJM 5总线系统和IEEE 118总线测试系统上将举例说明该方法的有效性和有效性。

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