# RMS Modeling and Control of a Grid-Forming E-STATCOM for Power System Stability in Isolated Grids
## 5 Results and Discussion  
Simulations are conducted on the power system of the Fuerteventura and Lanzarote islands in the Canary Archipelago, Spain, as shown in Figure 12a. The transmission grid operates at two voltage levels, 132 kV and 66 kV, interconnected by submarine cables linking both islands (shown by dashed lines in Figure 12b). It comprises 17 nodes: 6 at 132 kV, 6 at 66 kV, and 5 generation nodes at 20 kV. The conventional generation includes two synchronous power plants: 265 MVA at Punta Grande on Lanzarote Island, and 187 MVA at Las Salinas on Fuerteventura Island (see Figure 12b). The IBR is aggregated at three transmission nodes, with rated powers of 52 MW (wind and PV at Lanzarote Island), 60 MW (wind generation at Fuerteventura Island), and 44 MW (PV at Lanzarote Island). Table 1 presents the technical parameters of the Lanzarote-Fuerteventura power grid, including bus connections, the transmission line, and transformer parameters. All parameters are expressed in per unit (p.u.) on a 100 MVA system base. The power grid model is based on the 2026 planning horizon, incorporating two submarine interconnections (66 kV and 132 kV cables) and a 132 kV double-circuit corridor [36]. The dynamic simulations were performed using MATLAB/Simulink to analyze the transient response of the Lanzarote-Fuerteventura power system with the proposed E-STATCOM model. Both the Lanzarote-Fuerteventura power system and the E-STATCOM model were developed within MATLAB/Simulink, ensuring a precise and comprehensive representation of grid dynamics, including inverter-based resources, synchronous condensers, and load interactions. The solver used was ode4 (Runge-Kutta), a solver suitable for power system simulations, with a fixed time step of 100 us to accurately capture system dynamics while ensuring numerical stability. The total simulation times were set to 20 and 10 s to cover both the transient and steady-state responses of the system. The model parameters were initialized according to the grid conditions described in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**From Bus** & **To Bus** & **r** & **x** & **b** \\ \hline
1 & 2 & 0.0  
Two different reference contingencies in the system are simulated to evaluate the response of the E-STATCOM: a synchronous power plant outage and a direct three-phase short circuit. These simulations are conducted across the following three distinct scenarios:  
* Case study 1: This scenario represents the base case, the system operates without any compensation device. Figure 12: Power grid of Lanzarote and Fuetreventura Islands. **(a)** Geographical representation of the Lanzarote–Fuetreventura power grid. **(b)** Single-line diagram of the Lanzarote–Fuetreventura power system. Case study 2: The second scenario involves the connection of a 25 MVA synchronous condenser (SynCon) to the 66 kV Macher bus (see Figure 12). The SynCon is modeled using the standard \"genrou\" model [37] with an inertia constant \(H\) = 8 s.
* Case study 3: The third scenario involves connecting a 25 MVA E-STATCOM with a supercapacitor of 300 MWs to the 66 kV Macher bus. The E-STATCOM is represented using the proposed model in this work. The parameters of the model are \(H\) = 8 s, \(D\) = 50 p.u. (2% droop), \(T_{w}\) = 0.5 s, and \(K_{w}\) = 0.05 p.u. The selection of the parameters \(H\) = 8 s, \(D\) = 50 p.u., \(T_{w}\) = 0.5 s, and \(K_{w}\) = 0.05 p.u. was based on established practices for power system stability enhancement. The inertia constant \(H\) = 8 s was chosen to emulate the response of a synchronous generator, ensuring appropriate frequency stability in the absence of traditional inertia sources [34]. The damping coefficient \(D\) = 50 p.u. is within the recommended range for isolated grids with high renewable penetration, helping suppress frequency oscillations [2; 15]. The washout filter time constant \(T_{w}\) = 0.5 s allows effective transient control while preventing steady-state drift [38]. Finally, the power system stabilizer gain \(K_{w}\) = 0.05 p.u.