# Overload Mitigation of Inertial Grid-Forming Inverters Under Frequency Excursions
## 1 Introduction  
Electrical grids are undergoing a significant transformation, with power electronics becoming more relevant at all stages of operation [1]. Inverter-based renewable energy resources are replacing conventional power plants based on synchronous generators (SGs). Additionally, flexible AC transmission systems (FACTS) are being deployed to increase grid efficiency and stability, while power-electronic loads, such as electric vehicles, are becoming prevalent [2]. Classical grid following (GFL)-operated inverters face stability challenges in power electronics-dominated grids, especially as their short circuit ratio decreases [3]. To address this issue, grid-forming (GFM) inverters have emerged as a promising solution to ensure the stability of future power grids [4]. GFM inverters behave as voltage sources, in a similar way to SGs, offering a range of ancillary services to the grid: primary frequency regulation, inertia contribution, voltage support, oscillation damping, blackstart capability and standalone operation, and more [5]. In GFM inverters, the synchronization with the grid is based on an active power balance rather than on a phase-locked loop (PLL). This synchronization mechanism contributesto the stability under weak grid conditions, but it changes the overloading limitation paradigm [6]. While the synchronization and frequency support are decoupled in GFL inverters, they are tightly coupled in GFM inverters [7]. Hence, preventing overloading GFM inverters while keeping grid synchronization might pose a challenge, and it is crucial to ensure the stability of this type of converters. Overloading protection and synchronization of GFM inverters are critical in low-voltage ride-through events, where the voltage source behavior of these inverters results in high reactive currents [8]. In fact, this topic was identified as a key challenge in the context of the MIGRATE project [9]. The simplest approach to prevent overcurrent-induced tripping in GFM inverters is to switch to GFL mode [10; 11]. However, this strategy compromises grid-forming capability. It also requires resynchronization mechanisms, extending recovery time when switching back to GFM mode [12]. The literature has proposed other fast current limiting strategies to address voltage sags, including current-based saturation, threshold virtual impedance, and/or voltage limiters, each with its own advantages and disadvantages [13; 14]. Since these current limiting strategies break the power balance of the GFM active power controller, they must also incorporate transient synchronization enhancing strategies to avoid phase angle windup and ensure post-fault recovery [15]. Despite being less studied in the literature, grid frequency excursions are another type of events that could lead to overload. In transmission systems with predominantly inductive lines, such overloading may be triggered by the active power transient of the GFM inverters. These transients depend on grid frequency deviation and rate of change of frequency (RoCoF), which depend on the system overall active power imbalance and inertia. Additionally, the power transient also depends on the frequency services requested to the GFM inverter, such as inertia and primary frequency regulation, which are currently being standardized by grid operators and organizations [16]. Consequently, frequency excursion-induced overloading must also be considered, particularly when inverters operate near their power limits or under source constraints, such as renewable energy systems operating at maximum power point tracking (MPPT) without reserves [17]. Frequency excursions differ from low voltage ride-through events in two aspects: (1) they involve slower dynamics and (2) the grid voltage amplitude is unaltered, having minor impact on reactive power. Due to these characteristics, the previously described fast current limiting strategies can be avoided, and both overloading and synchronization issues can be handled simultaneously by acting on the active power controller of the GFM inverter [18].