Optimization of Inertia and Damping Coefficients in Virtual Synchronous Machine Based Grid Forming Inverters: From Selection to Implementation

`Virtual Synchronous Machine (VSM)' based grid forming (GFM) inverters are more attractive as they mimic the operation of the synchronous generator (SG). Unlike mechanical SG, VSM-based GFM inverter offers the flexibility to choose an appropriate level of virtual inertia and damping. However, ensuring the stability of VSM controllers remains a critical concern. This paper presents a detailed methodology for selecting these values using the `Lyapunov energy-like function' theory. Energy plots of the virtual SG underscore the necessity of selecting these optimal parameters to minimize energy and enhance stability. The eigenvalues of the VSM controller are used to verify the Lyapunov energy -like function. Moreover, a well-tuned LCL filter was introduced to enhance the inverter's performance. A meticulously tuned proportional -integral controller is applied to the VSM-based GFM inverter to enable the designed autonomous inverter to achieve its fast control action. The efficacy of the proposed methodology is validated in the MATLAB Simulink environment by demonstrating the stability of the proposed VSM-based GFM inverter under local load condition.