On Stability Analysis of Power Grids with Synchronous Generators and Grid-Forming Converters under DC-side Current Limitation

TL;DR

This paper analyzes the stability of power grids with synchronous generators and grid-forming converters under DC-side current limits, comparing control strategies and providing stability conditions validated by simulations.

Contribution

It introduces stability analysis methods for GFCs with current limits, comparing control classes and extending results to generic systems.

Findings

Lyapunov and input-output stability conditions derived.

Sufficiency conditions for input-to-state stability established.

Simulation results validate the theoretical stability conditions.

Abstract

Stability of power grids with synchronous generators (SGs) and renewable generation interfaced with grid-forming converters (GFCs) under dc-side current limitation is studied. To that end, we first consider a simple 2-bus test system and reduced-order models to highlight the fundamental difference between two classes of GFC controls -- (A) droop, dispatchable virtual oscillator control (dVOC) and virtual synchronous machine (VSM), and (B) matching control. Next, we study Lyapunov stability and input-output stability of the dc voltage dynamics of class-A GFCs for the simple system and extend it to a generic system. Next, we provide a sufficiency condition for input-to-state stability of the 2-bus system with a class-B GFC and extend it for a generic system. Finally, time-domain simulations from a reduced-order averaged model of the simple test system and a detailed switched model of the GFC validate the proposed conditions.