# Physics-Informed Deep Neural Network Method for Limited Observability State Estimation

arXiv: https://arxiv.org/abs/1910.06401 · HTML: https://mlsanity.com/paper/1910.06401/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems](https://mlsanity.com/paper/2102.06349/) (2021)
- [Embedding Power Flow into Machine Learning for Parameter and State Estimation](https://mlsanity.com/paper/2103.14251/) (2021)
- [Robust Power System State Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.05874/) (2025)
- [Robust, Deep, and Reinforcement Learning for Management of Communication and Power Networks](https://mlsanity.com/paper/2202.05395/) (2022)
- [Learning Without Adversarial Training: A Physics-Informed Neural Network for Secure Power System State Estimation under False Data Injection Attacks](https://mlsanity.com/paper/2604.22784/) (2026)

## Abstract (arXiv)

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.