## 5 Future Research  
This section points out the outlook for future research directions of VI-based inverters, including main challenges and limitations, ESS for VI emulation, and market trend of VI. Fundamentally, the main idea of VI is to regulate the grid frequency especially for the interface of RES to the power grid. The active power droop from synchronverter shares the same objectives with different implementation and approach. The VI concept enables a static power electronics converter to emulate the dynamic characteristic of an SM or SG. SM is a general category that constitutes both SM and SG. Essentially, VSM, VSG, and synchronverter share similar topologies. VSM is based on SM while VSG and synchronverter are based on SG. The implementation of VI is flexible and versatile. Various microcontrollers, DSP, or computers including dSpace, Microchip, and Texas Instrument (TI) are applicable to emulate VI with suitable sensors, interface, and configuration. The emulation of VI can be integrated with AI to improve transient response and steady-state error. A fuzzy adaptable logic controller based on a differential evolution algorithm is developed specifically for VI-based frequency regulation [83]. The inertial response of a PV system can be improved by using battery ESS. The combination of droop and inertia emulation [84] is possible to enable the ability to operate at a setpoint of active power and thus guarantee the system frequency stability [85]. VI and conventional active power-frequency droop control are the common approaches to regulate the active power output of the inverter-based generator in maintaining nominal frequency at all time. VI exhibits lower overshoot, better damping, and slower frequency transients compared to the droop [86]. The applications of VI-based inverters are versatile in unifying and synchronizing different sources of energy into modern power system [87]. Figure 14 illustrates the application of VI-based inverters in the modern power system to replace SM. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Order of** & **Model** & \begin{tabular}{c} **Reference Voltage** \\ **Implementation** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **Direct PWM** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **Current** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **Power** \\ **(P&Q)** \\ \end{tabular} & **Merit** & **D****Emerit** \\ \hline Seventh-order & Electric, magnetic, & & & & & Full & Highly complex \\ model & swing equation of & & & & & representation of & and high \\  & stator and rotor & & & & SG dynamics with & computational \\  & winding & & & & & all parameters & burden \\ \hline Fifth- or & Electric, magnetic, & & & & & Best balance & Only stator \\ fourth-order & & swing equation of & & & & between & winding is \\ model & stator winding & & VSM & Possible & VSM & N/A & complexity and computational & considered \\  & & & & & & computational & seventh-order \\  & & & & & & model \\ \hline Second-order & Swing equation and & & & & & Most common & Lack of some \\ model & voltage amplitude is & & & & scheme of & parameters \\  & given by the reactive & & & & research & & computer to \\  & power controller & & & & & for a simple and & \\  & & & & & close imitation & model \\ \hline First-order & \begin{tabular}{c} Inertial emulation by \\ power response \\ calculated from grid \\ voltage tracking \\ \end{tabular} & N/A & N/A & Possible & \begin{tabular}{c} VSYNC \\ and VSG \\ \end{tabular} & \
\begin{tabular}{c} Simplest and \\ fastest \\ implementation \\ \end{tabular} &
\begin{tabular}{c} Incapable of \\ isolated operation \\ and insufficient \\ modeling \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of VSM, VSG, and synchronverter in term of swing equation model order. Normally, IEEE 9-Bus test system is widely used for the performance assessment of VI-based inverters. The pole-zero plot, Nyquist diagram, and Lyapunov stability [88] are the most common stability assessments for VI-based controller design.