Model Reduction and Dynamic Aggregation of Grid-forming Inverter Networks

This paper presents a model-order reduction and dynamic aggregation strategy for grid-forming inverter-based power networks. The reduced-order models preserve the network current dynamics as well as the action of the inverter current-reference limiter. Inverters based on droop, virtual synchronous machine, and dispatchable virtual oscillator control are considered, a generic model for all three control strategies is presented, and a smooth function approximation is utilized to represent the action of the current-reference limiter. The network is assumed to be composed of lines with homogeneous <inline-formula><tex-math notation="LaTeX">$l/r$</tex-math></inline-formula> ratios. Given such a system, our approach involves three steps. First, time-domain Kron reduction is used to reduce the dimensions of the electrical network model. Next, dynamic aggregate models are developed for parallel-connected inverters. Finally, singular perturbation analysis is used to systematically eliminate fast-varying dynamics in both the network model and the grid-forming inverter single/aggregate models. Numerical simulation results benchmark the response of the reduced-order aggregate models against the full-order models from which they are derived, and we demonstrate significant savings in computation cost with limited loss of accuracy.