The integration of machine learning with domain-specific physics is transforming the design, monitoring, and control of electricity systems, where data scarcity, limited interpretability, and the need to enforce physical laws constrain purely data-driven models. Physics-informed machine learning (PIML) addresses these limitations by embedding governing equations directly into the learning process, yielding accurate, efficient, and scalable solutions for Industry 4.0 applications. This article reviews hybrid PIML architectures for electricity systems, including physics-informed neural networks (PINNs), Deep Operator Networks (DeepONets), Fourier Neural Operators, Extreme Learning Machine-enhanced PINNs, graph-based PINNs (PIGNNs), and domain-decomposition PINNs. Each approach is examined through case studies spanning field analysis, fault detection, digital twins, surrogate modeling, and control optimization. The review shows that embedding Maxwell's equations and other first-principles constraints substantially improves predictive accuracy under sparse and noisy data, reduces simulation time by orders of magnitude relative to finite element methods, and enhances generalization across operating regimes. Hybrid frameworks consistently outperform purely data-driven baselines on parameter sensitivity, dynamic behavior, and robustness, while supporting real-time digital-twin calibration and uncertainty quantification. Persistent challenges include training instability for stiff multi-scale problems, computational cost of high-fidelity models, and the absence of standardized benchmarks. The findings demonstrate that PIML enables a paradigm shift from black-box data-driven methods to transparent, physics-informed strategies, positioning the field for sustained innovation in resilient and intelligent electricity systems.

翻译：机器学习与领域特定物理知识的融合正深刻变革电力系统的设计、监测与控制。在数据稀缺、可解释性有限以及需强制执行物理定律的约束下，纯数据驱动模型面临挑战。物理信息机器学习通过在训练过程中直接嵌入控制方程，克服了这些局限性，为工业4.0应用提供了精确、高效且可扩展的解决方案。本文综述了面向电力系统的混合物理信息机器学习架构，包括物理信息神经网络、深度算子网络、傅里叶神经算子、极限学习机增强型物理信息神经网络、基于图的物理信息神经网络以及区域分解物理信息神经网络。通过涵盖场分析、故障检测、数字孪生、代理建模和控制优化等领域的案例研究，对各方法进行了分析。综述表明：在稀疏和噪声数据条件下，嵌入麦克斯韦方程组及其他第一性原理约束可显著提升预测精度；相较有限元方法，仿真时间降低数个数量级；并能增强跨运行工况的泛化能力。混合框架在参数灵敏度、动态行为和鲁棒性方面持续优于纯数据驱动基线，同时支持实时数字孪生标定与不确定性量化。当前持久挑战包括：刚性多尺度问题中的训练不稳定性、高保真模型的计算成本，以及标准化基准的缺失。研究结论表明，物理信息机器学习正推动从黑箱数据驱动方法向透明化物理信息策略的范式转变，为构建弹性智能电力系统的持续创新奠定基础。