# Virtual Synchronous Machine Control of RES Plants in Isolated Power Systems
### Proposed Solution  
VSC with VSM control is one of the most promising control schemes for imitating the dynamic response of a SG [19]. Through VSM control, it is possible to achieve a behavior \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control Strategy** & & **Characteristics** & & **Issues** \\ \hline \multirow{8}{*}{SG model-based} & \(\bullet\) & Voltage-source implementation & \multirow{2}{*}{\(\bullet\)} & \multirow{2}{*}{Numerical instability} \\  & \(\bullet\) & Accurate replication of SG dynamics & & \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Frequency derivative not required & \(\bullet\) & Need for a current limiter to protect the device during short-circuits \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Need for a Phase locked loop (PLL) for & & \\  & \(\bullet\) & Synchronization & & \\  & \(\bullet\) & Black-start capability & & \\ \hline \multirow{8}{*}{Swing equation-based} & \(\bullet\) & Governor is modeled as a first-order lag element & \(\bullet\) & Numerical instability Power and frequency oscillations \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Frequency derivative not required & \(\bullet\) & Need for a current limiter to protect the device during short-circuits \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & \multicolumn{1}{c}{} & \multirow{2}{*}{Higher Rate of Change of Frequency} \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Need for a PLL for synchronization & & \\ \hline \multirow{4}{*}{Frequency-power response-based} & \(\bullet\) & Straightforward implementation & \(\bullet\) & Instability due to PLL, particularly in weak grids \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Current-source implementation & \(\bullet\) & Frequency derivative required, system susceptible to noise \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Inherent overcurrent protection & & \\ \hline \multirow{8}{*}{Droop-based} & \multirow{8}{*}{\(\bullet\)} & Communication-less & \multirow{2}{*}{\(\bullet\)} & \multirow{2}{*}{Slow transient response} \\  & & & & \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Very common & & \\ \cline{1-1} \cline{3-5}  & \(\bullet\) & Classical droop control implementation & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Features and concerns of different VSM control strategies (built starting from [8]). similar to that of a SG, but the converter is not guarded against overcurrent. Thus, the converter input current needs to be limited by a vector-current controller (VCC) [20; 21]. In this paper, the VSM control combined with a vector-current controller is applied to the converters that are assumed to be installed in the small island of Pantelleria. Initially, the hourly generation and demand of the island (data provided by the local utility SMEDE) are analyzed during typical winter and summer days. For both seasons, hour-by-hour power system inertia is calculated, and the most critical situations based on a reduced inertial response are identified. Subsequently, an equivalent single-bus model of the power system is created in the PSCAD environment. RES plants are represented as a unique VSC, and the conventional SGs is represented as a unique equivalent SG. The internal control model of the equivalent VSC considers the grid impedance and two different options for calculating the reference current, starting from a steady-state condition and evaluating the effects due to a phase-to-phase short-circuit simulated at the PCC. Simulations are done for different values of the control parameters, energy scenarios, system inertia and provided virtual inertia, and for two values of the short circuit ratio (SCR) to represent both a strong and a weak grid [22]. The rest of the paper is organized as follows: Section 2 presents the structure of the system under study and the mathematical representation of VSM with VCC. Section 3 reports the initial data for the simulations. Section 4 provides the results of the simulations and, finally, Section 5 reports the conclusions of the study.