Harmonic Stability Analysis of Microgrids with Converter-Interfaced Distributed Energy Resources, Part I: Modelling and Theoretical Foundations

This paper proposes a method for the Harmonic Stability Assessment (HSA) of power systems with a high share of Converter-Interfaced Distributed Energy Resources (CIDERs). To this end, the Harmonic State-Space (HSS) model of a generic power system is formulated by combining the HSS models of the resources and the grid in closed-loop configuration. The HSS model of the resources is obtained from the Linear Time-Periodic (LTP) models of the CIDER components transformed to frequency domain using Fourier theory and Toeplitz matrices. Notably, the HSS of a CIDER is capable of representing the coupling between harmonic frequencies in detail. The HSS model of the grid is derived from the dynamic equations of the individual branch and shunt elements. The system matrix of the HSS models on power-system or resource level is employed for eigenvalue analysis in the context of HSA. A sensitivity analysis of the eigenvalue loci w.r.t. changes in model parameters, and a classification of eigenvalues into control-design variant, control-design invariant, and design invariant eigenvalues is proposed. A case of harmonic instability is identified by the HSA and validated via Time-Domain Simulations (TDS) in Simulink.