Physics-Guided Deep Neural Networks for Power Flow Analysis

Xinyue Hu, Haoji Hu, Saurabh Verma, Zhi Li Zhang

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable due to system dynamics, and uncertainties, making traditional numerical approaches infeasible. To address these concerns, researchers have proposed data-driven approaches to solve the PF problem by learning the mapping rules from historical system operation data. Nevertheless, prior data-driven approaches suffer from poor performance, and generalizability, due to overly simplified assumptions of the PF problem or ignorance of physical laws governing power systems. In this paper, we propose a physics-guided neural network to solve the PF problem, with an auxiliary task to rebuild the PF model. By encoding different granularity of Kirchhoff's laws, and system topology into the rebuilt PF model, our neural-network based PF solver is regularized by the auxiliary task, and constrained by the physical laws. The simulation results show that our physics-guided neural network methods achieve better performance, and generalizability compared to existing unconstrained data-driven approaches. Furthermore, we demonstrate that the weight matrices of the proposed neural networks embody power system physics by showing their similarities with the bus admittance matrices.

Original languageEnglish (US)
Article number9216092
Pages (from-to)2082-2092
Number of pages11
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - May 2021

Bibliographical note

Funding Information:
Manuscript received March 19, 2020; revised July 28, 2020; accepted September 27, 2020. Date of publication October 7, 2020; date of current version April 19, 2021. This work was supported in part by NSF under Grants CNS-1814322, CNS-1831140, CNS-1901103, and CNS-1952085, in part by US DoD DTRA DTRA under Grant HDTRA1-14-1-0040, and in part by an Amazon AWS ML Research Award. Paper no. TPWRS-00427-2020. (Corresponding author: Xinyue Hu.) The authors are with the Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, United States (e-mail:;;;

Publisher Copyright:
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  • Power flow analysis
  • data-driven analysis
  • neural networks
  • physics-guided learning
  • power flow solver


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