On the Super-Lorenz Chaotic Model for the Virtual Synchronous Generator

Abstract

Distinguished from the previous virtual synchronous generator (VSG) using the power equation of the three-phase voltage-source inverter (VSI) as the swing equation, this brief considers a new VSG that utilizes the voltage equation of the dc-link capacitor of the three-phase VSI as the swing equation, which reflects directly the dynamics of the rotor of the synchronous generator compared to the previous power one. A novel control strategy for the new VSG is derived by comparing the ac-side voltage equations of the three-phase VSI with the stator voltage ones of the permanent-magnet synchronous generator. The swing equation and the ac-side voltage equations of the controlled three-phase VSI together constitute the complete model of the new VSG, which is further transformed into a super-Lorenz chaotic model by applying an affine transformation and a time-scaling transformation. The condition for the appearance of the Lorenz-like chaotic attractor in the super-Lorenz model is discussed. With variation of the bifurcation parameter, the chaos phenomenon appears and it devastates the stability of the inverter and the grid.