Real-Time Power System State Estimation and Forecasting via Deep Unrolled Neural Networks

Liang Zhang, Gang Wang, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


Contemporary power grids are being challenged by rapid and sizeable voltage fluctuations that are caused by large-scale deployment of renewable generators, 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, existing power system state estimation (PSSE) schemes become computationally expensive or often yield suboptimal performance. To bypass these hurdles, this paper advocates physics-inspired deep neural networks (DNNs) for real-time power system monitoring. By unrolling an iterative solver that was originally developed using the exact ac model, a novel model-specific DNN is developed for real-time PSSE requiring only offline 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 its competing alternatives, including the widely adopted Gauss-Newton PSSE solver.

Original languageEnglish (US)
Article number8754766
Pages (from-to)4069-4077
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number15
StatePublished - Aug 1 2019

Bibliographical note

Funding Information:
Manuscript received February 25, 2019; revised May 25, 2019; accepted June 20, 2019. Date of publication July 3, 2019; date of current version July 12, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Sotirios Chatzis. This work was supported by the National Science Foundation under Grant 1508993, Grant 1509040, Grant 1514056, and Grant 1711471. This paper was presented in part at the IEEE Global Conference on Signal and Information Processing, Anaheim, CA, USA, November 26–29, 2018. (Corresponding author: Gang Wang.) The authors are with the Digital Technology Center and the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:;; Digital Object Identifier 10.1109/TSP.2019.2926023

Publisher Copyright:
© 1991-2012 IEEE.


  • Power system state estimation
  • data validation
  • forecasting
  • least-absolute-value
  • proximal linear algorithm
  • recurrent neural networks


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