## 4 Simulation Results  
### Transient Stability Analysis in the Case with SG3 Installed  
First, the simulation results for the power system model with SG3 installed, in which it is assumed that 3 LG fault occurs at F1, are presented. Figure 8 shows the deviation of the kinetic energy of each SG, \(\Delta W\), which is the per unit value on the summation of the steady state kinetic energy of each SG. It can be seen that the oscillations of all of SGs in Cases 1 and 2 are restrained compared with those of \"No control\". In particular, the oscillations in Case 2 are greatly restrained. Figure 9 shows the deviation of the summation of the kinetic energy of each SG, \(\Delta W_{total}\). As \(\Delta W_{total}\) is the collective dynamic response of all generators, we can evaluate the stability of the overall power system from the response of \(\Delta W_{total}\). It can be seen from the figure that the oscillation of \(\Delta W_{total}\) in Case 2 is restrained, hence the enhanced transient stability. Figure 8: \(\Delta W\): deviation of kinetic energy of each SG: (**a**) No control; (**b**) Case 1; (**c**) Case 2. Figure 10 shows the power system frequency. It can be seen from the figure that the frequency fluctuations are smaller in Cases 1 and 2, and hence the frequency fluctuations are restrained in these cases. In Case 2, \(|\Delta f|\) becomes less than or equal to 0.2 Hz after 6.13 s, and hence \(P_{\mathit{ref}}\) of the VSWG is equal to \(P_{\mathit{mpt}}\) after this time. In other words, the active power control of the VSWG is returned to the steady state mode at 6.13 s. The control mode in Case 1 is not returned to the steady state mode within 20 s.  
Figure 11 shows the grid voltage at bus 7. As the VSWG has FRT capability, the grid voltage is gradually returned to the pre-fault value after the fault clearing. It can be seen that the voltages in Cases 1 and 2 after the fault clearing rise up slightly faster than that in \"No control\". In Case 1, however, a larger overshoot occurs. The overshoot in Case 2 is suppressed more than that in Case 1, and the subsequent fluctuation is also suppressed more than those in other cases. In Case 2, \(|\Delta V|\) becomes less than or equal to 1% of pre-fault voltage after 11.2 s, and hence the reactive power control is also returned to the steady state mode at this time. Figure 11: Voltage at bus 7 (with SG3 installed). Figure 10: Power system frequency (with SG3 installed). Figure 9: \(\Delta W_{\mathit{total}}\): deviation of summation of kinetic energy of each SG (with SG3 installed). Figures 12-14 show the active power, the reactive power and the apparent power of the VSWG, respectively. As the power capacity of the VSWG is 0.5 pu (power system base), it can be seen from Figure 14 that the apparent power of the VSWG is controlled in the range of 0 to about 0.5 pu. As can be seen from Figure 12, the active power of the VSWG in Cases 1 and 2 decreases due to the increase in frequency when the fault occurs. As a result, in these cases, the power loads of SGs increase, and thus the accelerating power acting on rotors of SGs is decreased. On the other hand, when the frequency decreases, the decelerating powers acting on the rotors are decreased because the active power of the VSWG increases. Thus, as the power loads of the SGs are controlled by the active power of the VSWG, the rotor speed variations of the SGs can be restrained. Furthermore, the effect of the active power control on transient stability enhancement may be improved by the grid voltage control. This is because the voltage control changes the power demands in the grid loads. As can be seen from Figure 13, the reactive power in Case 2 rises up quickly more than that in Case 1 after the fault clearing. After that, the reactive power drops down significantly to suppress the overshoot voltage. As a result, as the power demand-supply balance in the grid is improved more than that in Case 1, and the kinetic energy released from the rotor of the VSWG becomes smaller than that in Case 1.