# RMS Modeling and Control of a Grid-Forming E-STATCOM for Power System Stability in Isolated Grids
## 5 Results and Discussion
### Synchronous Power Plant Outage  
This subsection analyzes the outage of the synchronous power plant at Las Salinas on Fuerteventura Island, Figure 12. At the time of the incident, it was generating 81 MW. Figure 13 shows and compares the evolution of various variables in the system across the three case studies. Figure 13a depicts the system frequency measured at the Punta Grande bus, while Figure 13b shows the active power delivered by the synchronous power plant connected to this bus for the three case studies. In the initial moments after the outage, an inertial response is observed. As shown in Figure 13a, the response during the first second is similar across the three case studies, although slightly better when compensation devices are connected. After the first second, the compensation devices improve the system response,  
Figure 13: Response to a synchronous power plant outage. (**a**) Frequency measured at Punta Grande bus. (**b**) Active power delivered by the Punta Grande power plant. (**c**) Active power delivered by the synchronous condenser and the E-STATCOM. (**d**) DC voltage and current at the E-STATCOM DC link. and help dampen the frequency nadir to higher values. The inertial response is crucial as it temporarily stabilizes the system while the primary frequency regulation takes effect. In all cases, the Punta Grande synchronous power plant responds by supplying power to the grid in order to compensate the imbalance caused by the incident, as illustrated in Figure 13b. When the SynCon is connected (case study 2), the inertial response improves, and the system stabilizes after reaching a frequency nadir of approximately 49.35 Hz, slightly higher than the base case (49.25 Hz), as shown in Figure 13a. In Figure 13b, it is evident that the initial active power delivered by the Punta Grande SG is lower compared to the base case. To further quantify the system response, key stability metrics were analyzed. The rate of change of frequency (RoCoF) was computed as the initial frequency slope following the outage. The base case exhibited an RoCoF of 0.26 Hz/s, while the inclusion of a SynCon reduced this to 0.20 Hz/s. The E-STATCOM with GFM demonstrated the best performance, limiting the RoCoF to 0.15 Hz/s, thereby improving the transient frequency stability. The frequency recovery time, defined as the time taken for the frequency to return to within \(\pm\)0.1 Hz of nominal, was 10 s for the base case, 8 s for the SynCon, and 6 s for the E-STATCOM, highlighting the faster dynamic response enabled by synthetic inertia and active power injection. Figure 13c shows the active power delivered by the SynCon, which initially peaks at 15 MW. This power response is dictated by the swing equation of a synchronous machine without a coupled turbine governor, meaning that its power injection is inherently tied to the rate of change of frequency at its connection bus. The fundamental difference in dynamic response between the E-STATCOM with GFM and the SynCon stems from their distinct control mechanisms. The SynCon, governed by its physical inertia, follows the natural swing equation, providing frequency support that is inherently constrained by its mechanical properties. In contrast, the E-STATCOM with GFM actively regulates frequency through synthetic inertia control, enabling a more rapid and sustained injection of active power in response to grid disturbances. This contrast is clearly observed in Figure 13c, where the E-STATCOM maintains active power injection well beyond the initial transient, whereas the SynCon's contribution gradually declines as its inertial effect dissipates. Upon connecting the E-STATCOM (case study 3), the inertial response improves, and the system stabilizes after it reaches a frequency nadir of 49.48 Hz, which is significantly better than in the other case studies. Another advantage of the E-STATCOM over the SynCon solution is its capacity to maintain primary regulation, as depicted in Figure 13c, as long as the supercapacitor retains energy.