Placing Grid-Forming Converters to Enhance Small Signal Stability of PLL-Integrated Power Systems

TL;DR

This paper theoretically analyzes how placing grid-forming converters in power systems improves small-signal stability by effectively strengthening the grid, using matrix perturbation theory and eigenvalue analysis, validated through simulations.

Contribution

It reveals the theoretical link between grid-forming converter placement and enhanced stability, providing a method to optimize their locations based on eigenvalue analysis.

Findings

Placement of grid-forming converters increases the smallest eigenvalue of the network Laplacian.

Optimal placement improves small-signal stability in large-scale power systems.

Simulation results confirm the theoretical predictions on test systems.

Abstract

The modern power grid features the high penetration of power converters, which widely employ a phase-locked loop (PLL) for grid synchronization. However, it has been pointed out that PLL can give rise to small-signal instabilities under weak grid conditions. This problem can be potentially resolved by operating the converters in grid-forming mode, namely, without using a PLL. Nonetheless, it has not been theoretically revealed how the placement of grid-forming converters enhances the small-signal stability of power systems integrated with large-scale PLL-based converters. This paper aims at filling this gap. Based on matrix perturbation theory, we explicitly demonstrate that the placement of grid-forming converters is equivalent to increasing the power grid strength and thus improving the small-signal stability of PLL-based converters. Furthermore, we investigate the optimal locations to place grid-forming converters by increasing the smallest eigenvalue of the weighted and Kron-reduced Laplacian matrix of the power network. The analysis in this paper is validated through high-fidelity simulation studies on a modified two-area test system and a modified 39-bus test system. This paper potentially lays the foundation for understanding the interaction between PLL-based (i.e., grid-following) converters and grid-forming converters, and coordinating their placements in future converter-dominated power systems.