Equivalence Analysis of Virtual Synchronous Machines and Frequency-Droops for Inertia Emulation in Power Systems with Converter-Interfaced Renewables

Abstract

In converter-based AC microgrids, the frequency-droop is widely applied. As a considerable share of installed capacity is replaced by renewable generation, the virtual synchronous machine (VSM) algorithm is presented to address stability issues caused by low-inertia converter interfaces. Recently, droop control loops are also modified to improve stability. The VSM and the frequency-droop are both derived from the property imitation of synchronous generators (SGs) while researched independently. In this paper, by simplifications in the steady state, the expression of the inertia emulation of the VSM algorithm based on the second-order SG model is linearized as a first-order ordinary differential equation. In frequency-droop loops, as the instantaneous power components are commonly passed through a low-pass filter for disturbance rejection, the system function of the droop control can also be transformed into a first-order ordinary differential equation, which is equivalent to that of the VSM under certain conditions. In terms of the inertia constant, the swing equation is normalized under per unit representation. By the same simplification in the VSM linearization, the equivalence between the linearized VSM and the SG is also demonstrated. Therefore, the equivalence among SGs, the VSM, and the frequency-droop are summarized, which provides insights for coordinative control of power converters integrated into current SG dominating power systems. For a specific synchronous generator, the equivalence conditions are verified by simulation.