Analytical Verification of Performance of Deep Neural Network Based Time-Synchronized Distribution System State Estimation
This work addresses the need for trustworthy and robust state estimation in distribution systems, particularly for real-time applications with measurement uncertainties, but it is incremental as it builds on prior DNN-based estimators by adding analytical verification.
The paper tackles the problem of verifying the robustness of deep neural network-based state estimators for distribution systems to input perturbations by deriving analytical performance bounds and treating the DNNs as mixed-integer linear programming problems, validated on IEEE 34-node and real-world systems with incomplete observations.
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.