Complex Phase Analysis of Power Grid Dynamics

TL;DR

This paper introduces a complex phase-based modeling approach for power grid dynamics that remains invariant under linearization, improving stability analysis and system identification in inverter-based grids with renewable energy sources.

Contribution

It proposes a novel complex phase formulation that is independent of reference trajectories, enhancing robustness in modeling and analyzing power grid stability.

Findings

Complex phase offers invariant properties under linearization.

Enables robust system identification in realistic conditions.

Facilitates advanced stability analysis of inverter-based grids.

Abstract

With an increasing share of renewable energy sources, accurate and efficient modeling of grid-forming inverters is becoming crucial for system stability. Linear methods are a powerful tool for understanding dynamics close to an operating point, but usually depend on the reference trajectory. Thus, small deviations can render linear models invalid over time, posing a significant challenge in practice, and complicating theoretical analysis. As a solution, we show that the complex phase offers a robust formulation independent of reference phases and frequencies, thus preserving invariance properties under linearization. This enables robust system identification during realistic conditions and opens the road to powerful stability analysis of inverter-based grids.