## 4 Comparison of VI-Based Inverters
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **VSM** & **VSG** & **Synchronver** \\ \hline Converter type & & VSC & \\ \hline Inverter type & & Current-controlled & Voltage-controlled \\ \hline Based on & SM & SG \\ \hline Model order & Up to seventh order & Up to second order \\ \hline Complexity & High & Medium \\ \hline Grid mode & & Yes \\ \hline Standalone mode & Not applicable & Yes \\ \hline Grid viewpoint & Different than SG & As an SG \\ \hline Dependency on the tracking & & Yes \\ of ref. I or V & & \\ \hline Cost & & High \\ \hline General mathematical model & \(\frac{d\omega_{\text{total}}}{dt}=\frac{p}{\tau_{e}}-\frac{p}{\tau_{e}}-\frac{p_{ f}}{\tau_{e}}\) & \(P_{VSC}=P_{0}+K\omega\frac{d\omega_{\text{total}}}{dt}+K_{\text{D}}\Delta\omega\) & \(P_{\text{set}}+D_{p}(f_{\text{ref}}-f_{\text{grid}})-P_{0}=J\omega\frac{d\omega }{dt}\) \\ \hline Algorithm Implementation & Moderate–higher order & Hard–parameters difficult to adjust and dependent on unstable PLL & Easy–second-order SG model and can operate with or without PLL \\ \hline Readiness for commercial & & \\ and industrial inverter & & Ready for full commercialization: ABB, Schneider Electric, FREQCON \\ \hline Readiness for the grid or & Hydro-Québec Tansénergie’s (HQT’s) Canada; National Grid Electricity System Operator (NGESO), \\ power system operator & Great Britain; Electric Reliability Council of Texas grid; South African Grid Code \\ \hline Research and Development & & VSYNC project (EU), 2007; IÉPE & Synchrotronver– European \\ (R\&D) Funding & SYNDEM & Group; ISE Lab; Kawasaki \\  & & Heavy Industries (KHI) & Co. \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Technical comparison between VI-based inverters. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Type of Inverter** & **Grid-Fomming** & **Grid-Following** \\ \hline VI-based Inverters & Synchronverter and VSM & VSG \\ \hline Function & Supporting the grid & Following the grid \\ \hline Source behavior from grid viewpoint & Voltage source & Current source \\ \hline Set grid voltage and frequency & Yes & No (Follow the grid) \\ \hline Provide active and reactive power to the load via voltage & Yes & Inject active and reactive power \\ \hline Response & Slow response due to large inertia & Fast response to the intermittent \\ \hline Inertial response & Yes & No \\ \hline Buffer & Yes & No \\ \hline Instable due to intermittent irradiance (PV) or wind & No & Yes \\ \hline Support weak grid operation & Yes & No \\ \hline Islanding & Yes & No \\ \hline Deviation from the nominal frequency & Higher & Lower \\ \hline RoCoF & & Similar \\ \hline Peak power injection during disturbance & Smaller & Larger \\ \hline Injection of active power & Not application & Yes \\ \hline The manipulation of frequency of voltage & Yes & Not application \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Key differences between grid-forming and grid-following inverter. Various control methods of VI-based inverters are developed and designed to improve power quality, disturbance rejection, and voltage or current tracking of the inverter output, as shown in Figure 13. The grid-forming and grid-following inverters can be implemented based on different types of controller. The controller is responsible for optimizing and manipulating voltage or current to generate PWM for an inverter. the inner-loop voltage and current control is the most common control strategy for VI-based inverters. Different developed control strategies are used according to the characteristics of inverter topologies. The control strategies are developed from simple approaches to complex mathematical methods. In general, a conventional proportional integral derivative (PID) is the most commonly used control strategy. However, it exhibits several critical drawbacks including performance degradation during the disturbance. The topology of VI is still a relatively new concept from the year 2007. Its proposed implementations are fragmented and solely depend on the preference and research objectives of the researches.