# Real-time Power System State Estimation and Forecasting via Deep Neural Networks

arXiv: https://arxiv.org/abs/1811.06146 · HTML: https://mlsanity.com/paper/1811.06146/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2018.

## Built on by (most cited first, 30 of 32)

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- [Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers](https://mlsanity.com/paper/2207.11417/) (2022)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
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- [Embedding Power Flow into Machine Learning for Parameter and State Estimation](https://mlsanity.com/paper/2103.14251/) (2021)
- [Physics-Informed Neural Networks for Accelerating Power System State Estimation](https://mlsanity.com/paper/2310.03088/) (2023)
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- [Attention-based Deep Neural Networks for Battery Discharge Capacity Forecasting](https://mlsanity.com/paper/2202.06738/) (2022)
- [Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks](https://mlsanity.com/paper/2207.11465/) (2022)
- [Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding](https://mlsanity.com/paper/2309.06195/) (2023)
- [Robust Power System State Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.05874/) (2025)
- [PowerGNN: A Topology-Aware Graph Neural Network for Electricity Grids](https://mlsanity.com/paper/2503.22721/) (2025)
- [Deep Learning for Intelligent Demand Response and Smart Grids: A Comprehensive Survey](https://mlsanity.com/paper/2101.08013/) (2021)
- [Near Real-Time Distributed State Estimation via AI/ML-Empowered 5G Networks](https://mlsanity.com/paper/2207.11117/) (2022)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Knowledge- and Data-driven Services for Energy Systems using Graph Neural Networks](https://mlsanity.com/paper/2103.07248/) (2021)
- [Robust stabilization of polytopic systems via fast and reliable neural network-based approximations](https://mlsanity.com/paper/2204.13209/) (2022)
- [Towards Practical Physics-Informed ML Design and Evaluation for Power Grid](https://mlsanity.com/paper/2205.03673/) (2022)
- [Robust and Fast Data-Driven Power System State Estimator Using Graph Neural Networks](https://mlsanity.com/paper/2206.02731/) (2022)
- [Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs](https://mlsanity.com/paper/2304.14680/) (2023)
- [Fast Transient Stability Prediction Using Grid-informed Temporal and Topological Embedding Deep Neural Network](https://mlsanity.com/paper/2201.09245/) (2022)
- [Scalability and Sample Efficiency Analysis of Graph Neural Networks for Power System State Estimation](https://mlsanity.com/paper/2303.00105/) (2023)
- [Resilient Temporal GCN for Smart Grid State Estimation Under Topology Inaccuracies](https://mlsanity.com/paper/2410.16008/) (2024)
- [DLMMPR:Deep Learning-based Measurement Matrix for Phase Retrieval](https://mlsanity.com/paper/2511.12556/) (2025)

## Abstract (arXiv)

Contemporary power grids are being challenged by rapid voltage fluctuations that are caused by large-scale deployment of renewable generation, electric vehicles, and demand response programs. In this context, monitoring the grid's operating conditions in real time becomes increasingly critical. With the emergent large scale and nonconvexity however, the existing power system state estimation (PSSE) schemes become computationally expensive or yield suboptimal performance. To bypass these hurdles, this paper advocates deep neural networks (DNNs) for real-time power system monitoring. By unrolling an iterative physics-based prox-linear solver, a novel model-specific DNN is developed for real-time PSSE with affordable training and minimal tuning effort. To further enable system awareness even ahead of the time horizon, as well as to endow the DNN-based estimator with resilience, deep recurrent neural networks (RNNs) are also pursued for power system state forecasting. Deep RNNs leverage the long-term nonlinear dependencies present in the historical voltage time series to enable forecasting, and they are easy to implement. Numerical tests showcase improved performance of the proposed DNN-based estimation and forecasting approaches compared with existing alternatives. In real load data experiments on the IEEE 118-bus benchmark system, the novel model-specific DNN-based PSSE scheme outperforms nearly by an order-of-magnitude the competing alternatives, including the widely adopted Gauss-Newton PSSE solver.