# Virtual Flux Control Methods for Grid-Forming Converters: A Four-Method Comparison
## 1 Introduction
Finally, a pulse width modulation (PWM) algorithm, which sets a switching frequency, is used to generate the switching pattern of the converter. Another approach for controlling a converter is to apply the flatness property of differential algebra. This property enables the complete characterization of a system's dynamics through a specific set of flat outputs once the system is identified as flat. Consequently, by imposing a desired trajectory on these outputs, it is possible to ensure full control over all system variables, both in steady-state and during transient conditions [34; 35; 36]. Theoretically, this technique shows better performance than PI regulators for transitions between equilibrium points, especially in a nonlinear system [37]. In addition, the simple implementation and parameterization of this type of technique are two of its benefits. Like vector control, this type of technique also needs to use PWM to generate the switching pattern. Alternatively, DC is an approach that regulates a key variable of the converter without relying on conventional internal control loops. Instead of using PWM, it operates based on switching tables and hysteresis regulators [38; 39; 40]. This method provides a fast dynamic response and high robustness; however, due to its variable switching frequency, it can introduce resonances in the system. Another control method widely explored in the literature is MPC. This technique relies on a mathematical model of the system to predict the future behavior of the converter's variables and determine the optimal control action through a defined cost function [41; 42; 43; 44; 45]. Additionally, it does not require a PWM, as it directly selects the optimal switching states of the converter. Therefore, as well as the DC, MPC operates with a variable switching frequency, although this can be addressed through the cost function [46; 47]. Finally, an essential aspect in the design of GFM is the implementation of current limitation mechanisms, as these converters can withstand significantly lower overcurrents compared to SGs [48]. The literature presents various strategies to mitigate overcurrents during critical disturbances, such as voltage sags. One proposed approach involves switching the converter to GFL mode during disturbances. However, as previously discussed, this method can lead to stability issues [49; 50]. Another widely implemented technique is saturating the current regulators, but this can adversely affect the control angle, potentially compromising the converter's stability [51; 52; 53]. The use of virtual impedances is also a common solution [54; 55]; however, its design and parameterization remain a complex challenge [56]. More recently, a novel control architecture has been proposed to limit current in a straightforward manner. This approach is a synchronous machine-based controller and is based on virtual flux-oriented control (VFOC), eliminating conventional current control loops, which enhances system robustness and stability [57]. Additionally, by incorporating two control blocks that influence both the control angle and the magnitude of the reference flux, this method effectively limits both active and reactive currents, demonstrating strong performance even in commercial converters [58].