# RMS Modeling and Control of a Grid-Forming E-STATCOM for Power System Stability in Isolated Grids
## 1 Introduction
According to their principle of operation, GFM converters can be classified into three categories: (a) droop control, (b) synchronous-machine-based control, and (c) other control methodologies such as virtual oscillator-based methods [16], virtual-flux orientation [17; 18], reactive power synchronization [19; 20], etc. An essential aspect of GFM operation is current limitation during sudden voltage drops or frequency changes. Several methods have been developed, including virtual impedances [21; 22], virtual admittances [23], and nested voltage-current controllers [24]. These techniques are now being widely studied to meet TSO-DSO requirements globally [25; 26; 27; 28; 29; 30]. Furthermore, some recent grid codes have started specifying explicit requirements for E-STATCOMs, ensuring their seamless integration into modern power networks [31]. Regarding GFM modeling, either electromagnetic transient (EMT) models or phasor-based RMS models can be used. EMT models provide time-variant instantaneous values of voltage and current, offering high accuracy but at a significant computational cost, making them impractical for large-scale power system simulations. In contrast, RMS models consider only the fundamental frequency components, providing a more computationally efficient alternative while maintaining sufficient accuracy for stability studies. Traditionally, power system analysis neglects transmission line dynamics, relying on algebraic modelsthat express the relationships between bus voltages and line currents. Reference [32] compares EMT and RMS phasor models for grid-forming converters, analyzing different control strategies and their effects on fast and slow synchronization dynamics. In [33], the suitability of phasor-approximation models for GFM converter simulations is examined, identifying specific conditions for outer-loop control gains that allow TSOs to effectively use RMS models in stability assessments. The choice of an RMS-based phasorial model over an EMT representation is motivated by the trade-off between computational efficiency and modeling precision. While EMT simulations capture fast-switching transients and harmonic interactions with high accuracy, they require extremely small time steps and high computational resources, making them impractical for large-scale system stability studies. In contrast, RMS models effectively capture the fundamental frequency dynamics of the power system while significantly reducing computational effort. Given that the focus of this study is on evaluating the system-wide stability impact of an E-STATCOM with grid-forming (GFM) control, rather than the detailed switching behavior of power electronic components, the RMS approach is the most suitable choice for this analysis. This paper proposes a GFM-RMS E-STATCOM model incorporating technical aspects not considered in the consulted bibliography:  
* It presents a governor model with an internal power system stabilizer (PSS), as proposed in [17], designed to suppress active power oscillations during setpoint changes or frequency disturbances, particularly when a high inertia constant is used. This model integrates an active current limiter (ACL) to prevent overcurrent excursions resulting from sudden frequency shifts or phase jumps, ensuring the stability of the RMS-based GFM converter. Additionally, an exciter model determines the GFM internal voltage magnitude based on DC-voltage dynamics, incorporating a nonlinear modulation function. Similar to the governor model, a reactive current limiter (RCL) is included for voltage magnitude regulation, enhancing the converter's response under grid disturbances. * It incorporates a conventional supercapacitor (SC) model, but introduces a novel control strategy that enables DC-voltage variations in response to active power exchanges between the E-STATCOM and the grid, a feature specifically developed in this work. Since RMS-based models focus on fundamental frequency dynamics, most grid-forming models in the literature assume a constant DC bus, typically modeled as an ideal DC source.