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

arXiv: https://arxiv.org/abs/2311.06973 · HTML: https://mlsanity.com/paper/2311.06973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 12 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Adversarial Attacks and Defenses in Images, Graphs and Text: A Review](https://mlsanity.com/paper/1909.08072/) (2019)
- [Understanding Batch Normalization](https://mlsanity.com/paper/1806.02375/) (2018)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Neural Network with Unbounded Activation Functions is Universal Approximator](https://mlsanity.com/paper/1505.03654/) (2015)
- [Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks](https://mlsanity.com/paper/2006.11029/) (2020)
- [Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications](https://mlsanity.com/paper/1910.01624/) (2019)
- [Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning](https://mlsanity.com/paper/1811.02756/) (2018)
- [Is Machine Learning in Power Systems Vulnerable?](https://mlsanity.com/paper/1808.08197/) (2018)
- [State and Topology Estimation for Unobservable Distribution Systems using Deep Neural Networks](https://mlsanity.com/paper/2104.07208/) (2021)
- [Neural Network Virtual Sensors for Fuel Injection Quantities with Provable Performance Specifications](https://mlsanity.com/paper/2007.00147/) (2020)
- [Transmission Line Parameter Estimation Under Non-Gaussian Measurement Noise](https://mlsanity.com/paper/2208.13105/) (2022)
- [Detailed Primary and Secondary Distribution System Model Enhancement Using AMI Data](https://mlsanity.com/paper/2105.14161/) (2021)

## Built on by (most cited first, 1 of 1)

- [Creating Temporally Correlated High-Resolution Profiles of Load Injection Using Constrained Generative Adversarial Networks](https://mlsanity.com/paper/2311.12166/) (2023)

## Abstract (arXiv)

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.