## 2 Implementation of VI-Based Inverters
### Vsg  
VSG is essentially based on conventional inverter hardware with a controller that emulates the inertial response of an SG in response to any frequency changes. VSG control strategy allows the operation of grid-connected inverters to produce VI [39]. The adoption of VSG has attracted significant attention because of its equivalent operating mechanism as an SG to provide a practical scheme for grid-connected RES [40]. The emulation of releasing or absorbing kinetic energy imitates the characteristic of an SG. VSG is different from SG in terms of the ability to modify VI by the microprocessor during frequency variation. Hence, self-tuning algorithms are crucial to vary the VI to minimize frequency variation. Compared to a conventional droop controller that provides frequency regulation only, VSG provides dynamic frequency control based on the derivative of the frequency measurement. This control is similar to the inertial power release or absorption by an SG during a \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Application** & **Ref.** & **Type of VSM/VISMA** & **Highlights of the Control Strategy** \\ \hline DC Microgrids & [33] & VSM for DC Microgrids & VSM is designed to improve the inertia of DC microgrid and reduce the fluctuation of the DC bus voltage. \\ \hline MMC & [34] & VSM for MMC & VSM control strategy is applied for MMC to operate and control it as an SG. \\ \hline General & [32] & Enhanced VSM & The enhanced VSM (eVSM) exhibits larger inertia which eliminates the requirement of a large DC-link element or BESS. \\ \hline Microgrid & [35] & VSM with EES for a stand-alone microgrid & ESS is integrated by VSM-based inverter to the grid and a double second-order generalized integrator PLL to regulate frequency during transient conditions. \\ \hline Load & [36] & Load VSM & Load virtual synchronous machine topology and corresponding control strategy to mimic the characteristics of an SM. \\ \hline General & [37] & Optimal design of the VI and damping coefficient & H2 norm objective function is utilized to calculate the coefficient values for VSM. \\ \hline Smart grids & [38] & VSM for distributed control of power converters in smart grids & A VSM is designed to provide smart grid support and allow a seamless transition between grid-connected or islanded operation. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Current VSM merits and demerits. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metrics** & **Demerits** \\ \hline - Suppress grid disturbances - Automatic synchronization and power-sharing ability - For both stand-alone and microgrid operation - Conceptual simplicity & - Long TET because of Park Transformation Numerical instability Complex PLL implementation \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of selected VISMA and VSM implementations. power imbalance. VSG requires pre-synchronization before connecting to the power grid. It is executed by either a conventional PLL or phase angle regulator [41]. \(\Delta\omega\) represents the change in angular frequency, and \(d\Delta\omega/dt\) is defined as the rate of change of \(\Delta\omega\). \(K_{D}\) represents the damping constant while \(K_{I}\) represents the inertial constant. The damping constant is similar and adopted from frequency droop concept. It helps to stabilize frequency and reduce minimum (nadir) frequency. The inertial constant dampens RoCoF by providing fast dynamic frequency response, based on the frequency derivative. This characteristic is crucial for an isolated, islanded, or standalone grid, which exhibits high initial RoCoF. The inertial response acts as a safety measure, which prevents the unnecessary tripping of the protection relay. Since VSG involves \(d\)-\(q\) transformation, it is based on the \(d\)-\(q\) current control approach. VSG is based on a current-controlled inverter. Hence, the current references are generated for the current controller based on the reference power from equation (1). The \(d\)-axis current reference is computed using Equation (2).