# Data-Driven Learning-Based Optimization for Distribution System State Estimation

arXiv: https://arxiv.org/abs/1807.01671 · HTML: https://mlsanity.com/paper/1807.01671/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2018.

## Built on by (most cited first, 13 of 13)

- [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)
- [Massively Digitized Power Grid: Opportunities and Challenges of Use-inspired AI](https://mlsanity.com/paper/2205.05180/) (2022)
- [Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks](https://mlsanity.com/paper/2207.11465/) (2022)
- [Near Real-Time Distributed State Estimation via AI/ML-Empowered 5G Networks](https://mlsanity.com/paper/2207.11117/) (2022)
- [Heterogeneous Graph Neural Networks for Short-term State Forecasting in Power Systems across Domains and Time Scales: A Hydroelectric Power Plant Case Study](https://mlsanity.com/paper/2507.06694/) (2025)
- [Knowledge- and Data-driven Services for Energy Systems using Graph Neural Networks](https://mlsanity.com/paper/2103.07248/) (2021)
- [Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs](https://mlsanity.com/paper/2304.14680/) (2023)
- [Deep Learning-enabled MCMC for Probabilistic State Estimation in District Heating Grids](https://mlsanity.com/paper/2305.15445/) (2023)
- [Scalability and Sample Efficiency Analysis of Graph Neural Networks for Power System State Estimation](https://mlsanity.com/paper/2303.00105/) (2023)
- [Unsupervised anomaly detection in MeV ultrafast electron diffraction](https://mlsanity.com/paper/2505.13702/) (2025)
- [Learning a Generalized Model for Substation Level Voltage Estimation in Distribution Networks](https://mlsanity.com/paper/2510.16063/) (2025)
- [Learning Reduced-Order Dynamics with Singularity via Latent-Augmented Neural Ordinary Differential Equations](https://mlsanity.com/paper/2608.22142/) (2026)

## Abstract (arXiv)

Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used algorithms such as Gauss-Netwon perform poorly with the limited number of measurements typically available for DSSE, often require many iterations to obtain reasonable results, and sometimes fail to converge. DSSE is a non-convex problem, and working with a limited number of measurements further aggravate the situation, as indeterminacy induces multiple global (in addition to local) minima. Gauss-Newton is also known to be sensitive to initialization. Hence, the situation is far from ideal. It is therefore natural to ask if there is a smart way of initializing Gauss-Newton that will avoid these DSSE-specific pitfalls. This paper proposes using historical or simulation-derived data to train a shallow neural network to `learn to initialize' -- that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss-Newton. It is shown that this hybrid machine learning / optimization approach yields superior performance in terms of stability, accuracy, and runtime efficiency, compared to conventional optimization-only approaches. It is also shown that judicious design of the neural network training cost function helps to improve the overall DSSE performance.