# RMS Modeling and Control of a Grid-Forming E-STATCOM for Power System Stability in Isolated Grids
## 6 Conclusions  
The increasing penetration of renewable energy sources in modern power systems, particularly in weak grids, presents significant stability challenges. This study introduces an RMS-based phasorial model of an E-STATCOM with grid-forming (GFM) control, providing a computationally efficient and accurate tool for power system stability analysis. Unlike conventional approaches, the proposed model dynamically adjusts DC voltage in response to active power exchange, capturing energy storage dynamics with greater precision. Additionally, the integration of a power system stabilizer (PSS) enhances frequency stability by mitigating low-frequency oscillations, while the active current limiter (ACL) ensures robust synchronization under large disturbances. Furthermore, the nonlinear modulation function in the exciter improves voltage regulation without introducing harmonic concerns in the RMS framework. The simulation results on the Lanzarote-Fuerteventura power system confirm that the proposed RMS-based E-STATCOM model significantly enhances frequency stability, voltage control, and fault response. Specifically, the E-STATCOM improves the frequency nadir from 49.35 Hz to 49.55 Hz, compared to the base case, and reduces the settling time by 3.2 s. However, despite these advantages, the E-STATCOM has limitations compared to the synchronous condenser (SynCon). The E-STATCOM delivers approximately 230 MJ to stabilize the grid, while the SynCon supplies around 185 MJ to achieve a similar performance. This energy exchange occurs in both transient and steady-state conditions, emphasizing the longer energy injection period of the E-STATCOM, as it keeps the DC-link voltage relatively constant for an extended duration. Additionally, during short-circuit faults, the E-STATCOM's current injection is limited to 1.2 p.u., whereas the SynCon can provide up to 5 p.u., demonstrating a significantly superior fault ride-through capability. The findings demonstrate that E-STATCOM with GFM can effectively replace synchronous condensers in scenarios where fast dynamic response and frequency support are required. However, for applications demanding strong fault current injection, SynCons remain a superior choice. As power grids continue their transition toward inverter-dominated architectures, the proposed RMS modeling framework serves as a valuable tool for evaluating and optimizing grid resilience, ensuring stable and reliable system operation in the evolving energy landscape. Future research will focus on experimental validation and the extension of the model to hybrid energy storage applications, further enhancing its practical applicability. Conceptualization, J.L.R.-A., M.E.M.-D., S.A. and F.A. ; methodology, J.L.R.-A., M.E.M.-D., S.A. and F.A. ; software, J.L.R.-A. and M.E.M.-D.; validation, J.L.R.-A., S.A. and F.A. ; formal analysis, J.L.R.-A., S.A., F.A. and M.E.M.-D.; investigation, J.L.R.-A. and M.E.M.-D.; resources, J.L.R.-A. and M.E.M.-D.; data curation, S.A. and F.A. ; writing--original draft preparation, J.L.R.-A. and M.E.M.-D.; writing--review and editing, M.E.M.-D., S.A., F.A. and J.L.R.-A. ; visualization, J.L.R.-A. and S.A. and M.E.M.-D.; supervision, J.L.R.-A. and S.A.; project administration, J.L.R.-A. and S.A. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Spanish Research Agency (AEI) under Grant TED2021-130468B-I00 MCHN/AEI/MCIN/AEI/10.13039/501100011033. NextGenerationEU/PRTR: Contribution of grid forming converters to power system stability and operability with high penetration of renewable energy sources(GFM-RES), Grant PDC2022-133349-I00 funded by MCIN/AEI/10.13039/501100011033 and by the European Union \"NextGenerationEU/PRTR\". \"Proof of Concept of Grid-Forming Converters providing Power System Restoration Services (PdC-GFM)\". **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.