## 5 Simulation Result Analysis and Discussion
### Stability Analysis  
Stability analysis, regarding both symmetrical and asymmetrical fault conditions, was undertaken with the proposed control scheme. The LVRT capability of the SPV system has a positive effect on the transient stability of power systems, since the disconnection of a large amount of SPVs would stress the power system even more. The performance of the proposed control scheme is examined when the test system (Figure 7) is subjected to a three-phase short-circuit fault (3 LG). The fault is considered to occur at 0.5 s, and is cleared after 150 ms. Figure 15 illustrates the rotor speed of the synchronous generator (SG) during fault conditions, with and without the proposed control embedded with the SPV grid-connected system. The simulation results clearly show synchronous generator (SG) speed oscillations (Figure 15) over a wide range of 1.0 pu to 1.012 pu, with no control during the fault. However, the SG speed oscillation is significantly reduced with the proposed control, which is a positive indicator of the increased transient stability margin of the power system. The rotor-angle variation of the SG connected with the SPV system, with and without the proposed control, is shown in Figure 16. The results show that the system does not lose its rigidity, and remains robust to the faults. The simulation results illustrate that, with the proposed control system, the peak rotor angle of the synchronous machine is significantly reduced, leading to a much longer critical clearing time (CCT) and a positive impact of the stability enhancement of the system. For a clearer perspective, the stability of the system was evaluated using several performance indices, such as the speed deviation of the SG and the rotor angle deviation \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{5}{c}{**Values of Indices**} \\ \cline{2-7}  & \multicolumn{2}{c}{**3-LG**} & \multicolumn{2}{c}{**1-LG**} & \multicolumn{2}{c}{**2-LG**} \\ \hline \multirow{2}{*}{**Control Type**} & **MPPT** & **Proposed** & **MPPT** & **Proposed** & **MPPT** & **Proposed** \\  & **Control** & **Control** & **Control** & **Control** & **Control** & **Control** \\ \hline \(\mathrm{DCL_{vol}}\) & 5.4 & 3.7 & 3.2 & 1.9 & 6.2 & 3.5 \\ PVpower & 4.3 & 2.8 & 3.1 & 2.2 & 5.1 & 4.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance index enhancement with the proposed control scheme for symmetrical and asymmetrical faults. of the SG. A lower value of the indices indicates an enhanced system performance. Mathematical representations of the performance indices of the SG can be defined as follows:  
\[\text{SG}_{\text{speed}}=\frac{\int_{0}^{\text{T}}\lvert\Delta\omega\rvert\text { dt}}{\omega_{\text{SG}_{\text{rated}}}} \tag{22}\]  
\[\text{SG}_{\text{angle}}=\frac{\int_{0}^{\text{T}}\lvert\Delta\delta\rvert\text { dt}}{\delta_{\text{SG}_{\text{rated}}}} \tag{23}\]  
It is evident from Table 2 that the system performance on stability is weak without the proposed control scheme. Notable improvement is observed with the proposed control scheme. The consistency of the above results with other previous studies can be clearly seen when comparing with the work in [32]. Similar results were achieved in this work; however, a parallel-resonance bridge-type fault current limiter (PRBFCL) was used, and additional hardware devices increase the cost of the system. Alternatively, the proposed control scheme obtains these better results with lower costs. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Index Parameters (\%)**} & \multicolumn{2}{c}{**Value of Indices**} \\ \cline{2-3}  & **MPPT Control** & **Proposed Control** \\ \hline \(\text{SG}_{\text{angle}}\) & 1.8050 & 0.9722 \\ \(\text{SG}_{\text{speed}}\) & 0.0500 & 0.0300 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of indices for performance comparison during a 3 LG fault. Figure 16: Synchronous generator (SG) rotor angle: no control (MPPT control) and proposed control.