发表机构
KU Leuven; Flemish Institute for Technological Research (VITO); EnergyVille（荷语鲁汶大学; 弗拉芒技术研究所; 能源谷）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非高斯不确定性下配电网状态估计，提出硬约束物理信息因子图神经网络，结合闭式似然与可微优化层，实现物理可行且鲁棒高效的估计。
AI 中文摘要
鲁棒且准确的状态估计是主动配电网可靠运行与监测的基础。传统的数值估计器，如加权最小二乘法，计算速度较慢，并且在存在受非高斯噪声影响的稀疏量测时，常常面临收敛问题。物理信息神经网络最近作为一种有前景的替代方案出现，通过在目标函数中引入基于残差的惩罚项来纳入物理原理，这可以提高对噪声的鲁棒性和计算效率。然而，这种基于惩罚的方法不能保证在推理过程中严格强制执行物理约束，并且对合理的概率不确定性建模提供的支持有限。为解决这些局限性，我们提出了一种新颖的硬约束物理信息因子图神经网络（HCP-PINN），将配电网状态估计表述为因子图上的概率约束估计问题。所提出的方法通过灵活的、基于闭式似然的损失函数显式建模非高斯（伪）量测不确定性。它进一步结合了一个基于可微优化的估计层，该层严格强制执行非线性等式约束和量测一致性，在训练和推理过程中都产生物理上可行的状态估计。据我们所知，这是首个将硬物理约束与非高斯不确定性建模相结合的基于PINN的配电网状态估计框架，适用于不平衡三相网络。数值实验表明，与深度学习基准方法和数值估计器相比，所提出的方法提供了更准确且物理上一致的状态估计，同时在现实量测场景下表现出对网络模型误差更强的鲁棒性和更高的计算效率。
英文摘要
Robust and accurate state estimation is fundamental for the reliable operation and monitoring of active distribution networks. Conventional numerical estimators, such as weighted least squares, are computationally slower and often suffer from convergence issues in the presence of sparse measurements affected by non-Gaussian noise. Physics-informed neural networks have recently emerged as a promising alternative by incorporating physical principles through residual-based penalty terms in the objective, which can improve robustness to noise and computational efficiency. However, such penalty-based approaches do not guarantee strict enforcement of physical constraints during inference and provide limited support for principled uncertainty modeling. To address these limitations, we propose a novel Hard-Constrained, Physics-Informed Factor Graph Neural Network (HCP-PINN) that formulates distribution system state estimation as a probabilistic constrained estimation problem on a factor graph. The proposed approach explicitly models non-Gaussian (pseudo-)measurement uncertainty through flexible, closed-form likelihood-based loss functions. It further incorporates a differentiable optimization-based estimation layer that strictly enforces nonlinear equality constraints and measurement consistency, producing physically feasible state estimates during both training and inference. To the best of our knowledge, this is the first PINN-based DSSE framework to combine hard physical constraints with non-Gaussian uncertainty modeling for unbalanced three-phase networks. Numerical experiments demonstrate that the proposed method delivers more accurate and physically consistent state estimates than deep learning benchmarks and numerical estimators, while exhibiting greater robustness to network model errors and improved computational efficiency under realistic measurement scenarios.
CommentsPreprint. Submitted to Sustainable Energy, Grids and Networks
