# Physics Informed Neural Networks for Phase Locked Loop Transient Stability Assessment

arXiv: https://arxiv.org/abs/2303.12116 · HTML: https://mlsanity.com/paper/2303.12116/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Transient Stability Analysis with Physics-Informed Neural Networks](https://mlsanity.com/paper/2106.13638/) (2021)
- [Lyapunov Functions Family Approach to Transient Stability Assessment](https://mlsanity.com/paper/1409.1889/) (2014)

## Built on by (most cited first, 3 of 3)

- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [Enhanced physics-informed neural networks (PINNs) for high-order power grid dynamics](https://mlsanity.com/paper/2410.07527/) (2024)
- [Neural Controlled Differential Equations for EMT-Level Surrogate Modeling of Grid-Forming Inverters](https://mlsanity.com/paper/2607.16258/) (2026)

## Abstract (arXiv)

A significant increase in renewable energy production is necessary to achieve the UN's net-zero emission targets for 2050. Using power-electronic controllers, such as Phase Locked Loops (PLLs), to keep grid-tied renewable resources in synchronism with the grid can cause fast transient behavior during grid faults leading to instability. However, assessing all the probable scenarios is impractical, so determining the stability boundary or region of attraction (ROA) is necessary. However, using EMT simulations or Reduced-order models (ROMs) to accurately determine the ROA is computationally expensive. Alternatively, Machine Learning (ML) models have been proposed as an efficient method to predict stability. However, traditional ML algorithms require large amounts of labeled data for training, which is computationally expensive. This paper proposes a Physics-Informed Neural Network (PINN) architecture that accurately predicts the nonlinear transient dynamics of a PLL controller under fault with less labeled training data. The proposed PINN algorithm can be incorporated into conventional simulations, accelerating EMT simulations or ROMs by over 100 times. The PINN algorithm's performance is compared against a ROM and an EMT simulation in PSCAD for the CIGRE benchmark model C4.49, demonstrating its ability to accurately approximate trajectories and ROAs of a PLL controller under varying grid impedance.