## 4 Simulation Results
### Transient Stability Analysis in the Case with PV System Installed  
This section represents the simulation results for the power system model with the PV system installed instead of SG3. As described above, the PV system also has FRT capability, the same as the VSWG. The results of Case 3, the coordinated reactive power control with the VSWG and PV system, are also shown in this section. Figure 17 shows \(\Delta W_{total}\). It can be seen that the oscillations of \(\Delta W_{total}\) in Cases 2 and 3 are significantly restrained. In particular, the oscillation in Case 3 is greatly restrained and quickly converged. Figure 18 shows the power system frequency. It is clear that the frequency fluctuations are smaller in Cases 2 and 3. In these cases, each value of \(|\Delta f|\) is maintained less than or equal to 0.2 Hz after 10.0 and 6.8 s, respectively. Figure 19 shows the grid voltage at bus 7. It can be seen that the voltage fluctuations in Cases 2 and 3 are effectively restrained. In particular, the overshoot voltage in Case 3 is suppressed. Each value of \(|\Delta V|\) in Cases 2 and 3 is maintained less than or equal to 1% of pre-fault voltage after 11.1 and 8.3 s, respectively. Figure 17: \(\Delta W_{total}\): deviation of summation of kinetic energy of each SG (with PV system installed). Figure 18: Power system frequency (with PV system installed). Figures 20-22 show the active power, the reactive power and the apparent power of the VSWG, respectively. In Case 1, although the kinetic energy released from the rotor of the VSWG to the grid increases more than that in case with SG3 installed, both oscillations of \(\Delta W_{total}\) and \(\Delta f\) are not sufficiently restrained as shown in Figures 17 and 18. On the other hand, in Cases 2 and 3, both oscillations of \(\Delta W_{total}\) and \(\Delta f\) are sufficiently restrained in spite of the smaller release of the active power than that in Case 1. The kinetic energy released from the rotor of the VSWG to the grid in each case is depicted in Table 4. As can be seen from Figure 21, the amount of reactive power absorbed by the VSWG in Case 3 is less than that in Case 2. This is because the PV system also absorbs the reactive power to suppress the overshoot voltage after the fault clearing. Figures 25 and 26 show the active and reactive power outputs of the PV system. It can be seen that the reactive power in Case 3 is controlled based on the voltage-reactive power characteristic as shown in Figure 3. However, as described above, as the time constants of the control system of the PV system were set to larger values than those of the VSWG to avoid the hunting of the reactive power output, the response of the reactive power of the PV system in Case 3 is slower than that of the VSWG. Therefore, as can be seen from Figures 19 and 26, the reactive power control of the PV system mainly contributes to the suppression of the overshoot and the fluctuation of the voltage after the fault clearing. Finally, the results of the simulations performed under the various conditions are summarized. Table 5 shows the integrated value from 0 to 20 s of the absolute value of \(\Delta W_{total}\), divided by pre-fault value. A low value represents small oscillation and hence better transient stability [20]. It is clear that the transient stability can be enhanced in all of the simulation cases by using the proposed method. In particular, the control methods of Cases 2 and 3 effectively enhance the transient stability. Figure 26: Reactive PV power (with PV system installed).