Analytical Verification of Performance of Deep Neural Network Based Time-Synchronized Distribution System State Estimation

TL;DR

This paper analytically evaluates the robustness of deep neural network-based distribution system state estimation against input perturbations, providing bounds and validation on real and simulated systems.

Contribution

It introduces an analytical framework using MILP to verify DNN robustness in distribution system state estimation, addressing scalability with batch normalization.

Findings

Analytical bounds on DNN performance under input perturbations.

Validation on IEEE 34-node and real-world distribution systems.

Demonstrated robustness and trustworthiness of DNN estimators.

Abstract

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.