This paper investigates large fluctuations of locational marginal prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form $$\mathbb{P}(\mathbf{\text{LMP}}\notin \prod _{i=1}^n[{\alpha }_i^{-},{\alpha }_i^{+}]),$$ where LMP is the vector of LMPs at the n power grid nodes, and α⁻, ${\mathit{\alpha }}^{+}\in {\mathbb{R}}^n$ are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply–demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modelling uncontrollable renewable generation. We use techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations, and are validated numerically on the IEEE 14-bus test case.

This article is part of the theme issue ‘The mathematics of energy systems’.

本文研究了由可再生能源发电概况的波动引起的批发能源市场中位置边际价格 (LMP) 的大幅波动。具体来说，我们研究以下形式的事件 $$\mathbb{磷}(\mathbf{\text{LMP}}\notin \prod _{\mathrm{一世}=1}^n[{\alpha }_{\mathrm{一世}}^{-},{\alpha }_{\mathrm{一世}}^{+}]),$$ 其中LMP是n 个电网节点的 LMP 向量，α ⁻，${\mathit{\alpha }}^{+}\in {\mathbb{电阻}}^n$是价格阈值的向量，指定了不希望出现的价格。通过利用电网中供需匹配机制的结构，我们将 LMP 视为确定性分段仿射，随机输入过程的可能不连续函数，对不可控制的可再生发电进行建模。我们使用大偏差理论中的技术来确定极端价格飙升发生的最可能方式，并根据经历价格飙升的可能性对电网节点进行排名。我们的结果是在高斯波动的情况下得出的，并在 IEEE 14 总线测试用例上进行了数值验证。

这篇文章是主题问题“能量系统的数学”的一部分。