Recently, we demonstrated success of a time-synchronized state estimator using deep neural networks (DNNs) for real-time unobservable distribution systems. In this letter, we provide analytical bounds on the performance of that state estimator as a function of perturbations in the input measurements. It has already been shown that evaluating performance based on only the test dataset might not effectively indicate a trained DNN's ability to handle input perturbations. As such, we analytically verify robustness and trustworthiness of DNNs to input perturbations by treating them as mixed-integer linear programming (MILP) problems. The ability of batch normalization in addressing the scalability limitations of the MILP formulation is also highlighted. The framework is validated by performing time-synchronized distribution system state estimation for a modified IEEE 34-node system and a real-world large distribution system, both of which are incompletely observed by micro-phasor measurement units.

翻译：近期，我们展示了利用深度神经网络（DNN）对实时不可观测量配电系统进行时间同步状态估计的成功案例。本文针对该状态估计器在输入测量扰动下的性能，给出了解析界限。已有研究表明，仅基于测试数据集评估性能，无法有效指示训练后的DNN处理输入扰动的能力。为此，我们通过将DNN建模为混合整数线性规划（MILP）问题，从解析角度验证其对输入扰动的鲁棒性与可信度。同时，本文强调了批归一化在解决MILP模型可扩展性限制方面的作用。通过在修改后的IEEE 34节点系统及实际大规模配电系统（两者均由微型相量测量单元实现部分观测）上进行时间同步状态估计，验证了所提框架的有效性。