This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman operator, which provides a linear, infinite-dimensional representation of the nonlinear dynamics, and approximate a finite version that remains robust against spectral pollutions due to truncation. By computing $\epsilon$-approximate Koopman eigenfunctions using dynamics-adapted kernels in delay coordinates, we decompose the load dynamics into coherent spatiotemporal patterns that evolve quasi-independently. Our approach captures temporal coherent patterns due to seasonal changes and finer time scales, such as time of day and day of the week. This method allows for a more nuanced understanding of the complex interactions within power grids and their response to various exogenous factors. We assess our method using a large-scale dataset from a renewable power system in the continental European electricity system. The results indicate that our Koopman-based method surpasses a separately optimized deep learning (LSTM) architecture in both accuracy and computational efficiency, while providing deeper insights into the underlying dynamics of the power grid\footnote{The code is available at \href{https://github.com/Shakeri-Lab/Power-Grids}{github.com/Shakeri-Lab/Power-Grids}.

翻译：本文提出一种可解释的机器学习方法，在算子理论框架下表征电力系统负荷动态特性以实现电网负荷预测。我们采用Koopman算子描述负荷数据动态，该算子为非线性动态提供线性无限维表示，并通过逼近保持截断导致谱污染鲁棒性的有限维版本。通过在延迟坐标中使用动态自适应核函数计算$\epsilon$近似Koopman特征函数，我们将负荷动态分解为准独立演化的相干时空模式。该方法能捕捉季节性变化产生的时间相干模式，以及更精细时间尺度（如日内时段与星期周期）的动态特征。这种技术有助于更细致地理解电网内部复杂相互作用及其对外部因素的响应机制。我们使用欧洲大陆电力系统中可再生能源系统的大规模数据集评估该方法。结果表明：基于Koopman的方法在预测精度与计算效率上均优于独立优化的深度学习（LSTM）架构，同时为电网底层动态机制提供更深刻的见解\footnote{代码发布于\href{https://github.com/Shakeri-Lab/Power-Grids}{github.com/Shakeri-Lab/Power-Grids}。