# RMS Modeling and Control of a Grid-Forming E-STATCOM for Power System Stability in Isolated Grids
## 1 Introduction
However, this assumption does not accurately represent real-world conditions, where energy storage systems (ESSs) cannot instantaneously supply power. By dynamically adjusting the DC voltage according to power exchanges, the proposed RMS-based control strategy ensures a more accurate representation of energy storage behavior in E-STATCOM applications, while maintaining computational efficiency for large-scale stability studies. The main contributions of this work are as follows:
* Development of a complete RMS-based GFM E-STATCOM model specifically designed for power system stability studies. The key innovation of this work lies in the integration of the governor with an internal power system stabilizer (PSS) and an energy storage system (ESS), all within a control architecture tailored for an RMS framework. This model provides a computationally efficient yet accurate representation of grid-forming dynamics, making it well suited for large-scale stability analyses in weak and isolated grids. * Integration of a nonlinear modulation function in the exciter model, enhancing the representation of real-world modulation techniques used in power electronic converters. While electromagnetic transient (EMT) models explicitly capture high-frequencyswitching harmonics, this study employs an RMS phasorial model, focusing on fundamental frequency dynamics relevant to power system stability studies. The inclusion of nonlinear modulation in the RMS framework is justified as it captures the nonlinear relationship between internal voltage magnitude and DC-link voltage, ensuring a realistic dynamic response without requiring high-resolution EMT simulations. Since RMS models inherently do not capture harmonics, any potential distortion effects introduced by modulation do not manifest in this formulation, making harmonic concerns irrelevant in the context of RMS-based stability studies. * Enhanced damping of power oscillations is achieved through the integration of a power system stabilizer (PSS) within the governor model, even in systems with a high damping coefficient. This approach effectively suppresses oscillatory power modes, a challenge often underestimated in low-inertia grids, thereby improving frequency stability during sudden disturbances. Additionally, an active current limiter (ACL) is incorporated to independently regulate active and reactive current, ensuring robust performance and preventing excessive phase shifts even under large disturbances. * A comprehensive stability assessment of an isolated power system, using the Fuerteventura-Lanzarote grid (Canary Islands) as a case study. The system's size, topology, and low inertia make it highly susceptible to large frequency deviations and system instabilities under disturbances. A comparative study is conducted, analyzing the responses of an RMS-based GFM E-STATCOM and a SynCon, demonstrating their respective impacts on frequency regulation, voltage support, and fault response. The paper is organized as follows: Section 2 presents the description of the E-STATCOM system, including the algebraic equations governing the GFM currents and voltage components in different reference frames. Section 3 outlines the governor and exciter models of the GFM converter, incorporating active and reactive current limiters to ensure stable operation. Section 4 develops the dynamic equations of the synchronous condenser (SynCon) using power and energy parameters for a clearer representation of its behavior. Section 5 presents the simulation results, analyzing the impact of the proposed E-STATCOM model on the stability of the Fuerteventura-Lanzarote (Canary Islands, Spain) power system, including comparisons with a SynCon under different operating scenarios. Finally, Section 6 summarizes the conclusions and outlines potential future research directions.