The transition toward low-inertia power systems demands modeling frameworks that provide not only accurate state predictions but also physically consistent sensitivities for control. While scientific machine learning offers powerful nonlinear modeling tools, the control-oriented implications of different differentiable paradigms remain insufficiently understood. This paper presents a comparative study of Physics-Informed Neural Networks (PINNs), Neural Ordinary Differential Equations (NODEs), and Differentiable Programming (DP) for modeling, identification, and control of power system dynamics. Using the Single Machine Infinite Bus (SMIB) system as a benchmark, we evaluate their performance in trajectory extrapolation, parameter estimation, and Linear Quadratic Regulator (LQR) synthesis. Our results highlight a fundamental trade-off between data-driven flexibility and physical structure. NODE exhibits superior extrapolation by capturing the underlying vector field, whereas PINN shows limited generalization due to its reliance on a time-dependent solution map. In the inverse problem of parameter identification, while both DP and PINN successfully recover the unknown parameters, DP achieves significantly faster convergence by enforcing governing equations as hard constraints. Most importantly, for control synthesis, the DP framework yields closed-loop stability comparable to the theoretical optimum. Furthermore, we demonstrate that NODE serves as a viable data-driven surrogate when governing equations are unavailable.

翻译：向低惯量电力系统的转型要求建模框架不仅能提供准确的状态预测，还需具备物理一致的灵敏度以用于控制。尽管科学机器学习提供了强大的非线性建模工具，但不同可微分范式对于控制导向的意义仍未得到充分理解。本文对物理信息神经网络、神经常微分方程以及可微分编程在电力系统动态的建模、辨识与控制方面进行了比较研究。以单机无穷大母线系统为基准，我们评估了它们在轨迹外推、参数估计以及线性二次调节器综合中的性能。我们的结果揭示了数据驱动灵活性与物理结构之间的根本权衡。NODE通过捕捉底层向量场展现出优异的外推能力，而PINN由于依赖时间相关的解映射，其泛化能力有限。在参数辨识的反问题中，尽管DP和PINN均能成功恢复未知参数，但DP通过将控制方程作为硬约束实现了显著更快的收敛速度。最重要的是，对于控制综合，DP框架产生的闭环稳定性可与理论最优值相媲美。此外，我们证明了当控制方程不可用时，NODE可作为一个可行的数据驱动替代模型。