Gradient-enhanced physics-informed neural networks for power systems operational support

Mostafa Mohammadian, Kyri Baker, Ferdinando Fioretto

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The application of deep learning methods to speed up the challenging power system problems has recently shown very encouraging results. However, power system dynamics are not snapshot, steady-state operations. These dynamics must be considered to ensure that the optimal solutions provided by these models adhere to practical constraints to avoid frequency fluctuations and grid instabilities. Unfortunately, dynamic system models based on ordinary or partial differential equations are frequently unsuitable for direct application in control or state estimates due to their high computational costs. To address these challenges, this paper introduces a machine learning method to approximate the behavior of power systems dynamics in near real-time. The proposed framework is based on gradient-enhanced physics-informed neural networks (gPINNs) and encodes the underlying physical laws governing power systems. A key characteristic of the proposed gPINN is its ability to train without the need of generating expensive training data. The paper illustrates the potential of the proposed approach in both forward and inverse problems in a single-machine infinite bus system and a three-bus power network for predicting rotor angles and frequency, and uncertain parameters such as inertia and damping to showcase its potential for a range of power systems applications. The model exhibited high accuracy in predicting the variables, achieving a range of 0.533–4.092 and an average L2 relative error improvement of up to 13.30× compared to the PINN model. The computational performance of the proposed gPINN model was compared to a conventional solver, revealing a remarkable speed-up of 31 to 171 times faster in solving differential–algebraic systems of equations in power systems.

Original languageEnglish (US)
Article number109551
JournalElectric Power Systems Research
StatePublished - Oct 2023
Externally publishedYes


  • Deep learning
  • Optimal power flow
  • Physics-informed neural networks
  • Power system dynamics
  • Transfer learning

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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