# Improved PLL Design for Transient Stability Enhancement of Grid Following Converters Based on Lyapunov Method

## TL;DR

This paper introduces an improved PLL design with reset control for grid-following converters, enhancing transient stability by analyzing stability domains and employing Lyapunov methods to trigger resets, validated through case studies.

## Contribution

The paper proposes a novel PLL-reset control strategy based on Lyapunov functions to improve transient stability of GFL converters under large disturbances.

## Key findings

- Enhanced transient stability demonstrated in case studies.
- Lyapunov-based methods effectively trigger PLL resets.
- Improved stability domain analysis under various short circuit ratios.

## Abstract

Fluctuations in phase angle and frequency under large disturbances can lead to loss of synchronism (LOS) in grid-following (GFL) converters. The power angle and frequency of synchronous generators (SGs) correspond to rotor position and speed, whereas those of converters lack a direct physical counterpart in the real world and can thus be directly adjusted by control methods to prevent loss of synchronization. In this paper, an improved phase-locked loop (PLL) design with reset control for GFL converters is proposed to enhance transient stability. The stability domain (SD) of a GFL converter is first analyzed, and three forms of SD are identified under different short circuit ratios. Secondly, based on the characteristics of the three SD forms, two PLL-reset methods are proposed, including omega reset and omega&delta reset. Thirdly, to provide the triggering conditions for the PLL-reset control, the Lyapunov function of the GFL converter is constructed based on three methods: the approximation-based Lyapunov method, the Zubov method, and the analytical trajectory reversing method. All these methods are immune to the negative damping problem of PLL dynamics, which makes traditional energy-perspective Lyapunov functions invalid. Finally, the estimation accuracy of the three Lyapunov-based methods is analyzed, and the effectiveness of the PLL-reset control is verified in single-machine and multi-machine case studies.

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Source: https://tomesphere.com/paper/2509.00489