Using Dynamic Phasors To Model and Analyze Selective Harmonic Compensated Single-Phase Grid-Forming Inverter Connected to Nonlinear and Resistive Loads

In an islanded microgrid, a grid-forming inverter (GFMI) is required to maintain a stable sinusoidal voltage at nominal frequency and amplitude with minimal distortion regardless of loading conditions. As a result, the accurate design of GFMI control schemes in an islanded microgrid requires accurate understanding of the converter dynamics and system harmonics. Electromagnetic transient (EMT) simulations based on detailed switching models give an accurate picture of the GFMI's behaviour. However, EMT simulations take a relatively long time to produce accurate results in large-scale systems. On the other hand, conventional phasor models are unsuitable for harmonic studies. To address this limitation, this article leverages the dynamic phasor (DP) method to develop a new model of a single-phase GFMI connected to single-phase nonlinear (diode-bridge rectifier) and resistive loads. The benefit of the DP method lies in its inherent feature of transforming time-domain signals into slow-varying or DC signals, thereby enabling faster simulations. In this article, the relationship between the control gains of the proposed DP model and the conventional detailed model is established for the first time through small-signal and frequency-domain-based comparative analyses. User-written codes of the proposed DP model are scripted in MATLAB, and simulations on MATLAB/Simulink show that the proposed DP model results have a high degree of correlation with the detailed switching model results. A significant savings in computation time is exhibited by the proposed DP models. The simulation results are validated against experimental results to confirm the accuracy of the proposed DP model.