# Overload Mitigation of Inertial Grid-Forming Inverters Under Frequency Excursions
## 1 Introduction
An extended strategy to prevent overloading is to modify the active power setpoint of the power controller. Strategies such as virtual power [19] or power matching [20] limit the primary frequency regulation contribution of droop-based GFM inverters. However, the slow active power dynamics of inertial GFM inverters makes this approach ineffective. To prevent the transient overloading in the latter case, inertial contribution should also be reduced accordingly [21]. GFM inverters which adapt their inertia based on the voltage amplitude at the point of common coupling (PCC) have proven effective during fault scenarios [22; 23]. However, in frequency excursions, the voltage amplitude is constant, requiring a different approach: a GFM inverter should exhibit two inertial behaviors, one for normal operation and another for overloading conditions, with the latter being significantly lower than the former. This work presents a comprehensive analysis and comparison of three overload mitigation strategies that can be implemented within the active power control loop of grid-forming (GFM) inverters to prevent overloading during frequency excursions: (1) parallel PI, (2) angle limiter (AL), and (3) external frequency support (EFS). Although these strategies have been previously applied to GFM inverters without inertia [24; 25] and to protect them against fault-induced voltage sags [26; 27; 28], this study is, to the best of the authors' knowledge, the first to adapt and systematically evaluate them for inertial GFM inverters operating under frequency disturbances. To address the risk of overloading during frequency excursions, the three proposed active power control strategies actively reshape the GFM inverter response to frequency events. During such disturbances, these devices tend to exceed their power limits due to combined inertial and primary frequency regulation contributions. Each strategy mitigates this risk through a different mechanism: the parallel PI limits power by overriding frequency support when power thresholds are exceeded; the AL constrains the phase shift between inverter and grid voltages, bounding the active power exchange; and the EFS decouples synchronization from frequency support through a cascaded control structure that saturates the frequency support command during overloading. These strategies ensure safe operation of inertial GFM inverters while preserving synchronization with the grid. The main contribution of this study lies in the unified framework it provides for analyzing, tuning, and benchmarking the overload mitigation strategies for inertial GFM inverters. The formal analysis characterizes each strategy and its effectiveness to reshape both inertial and primary frequency response. This work also identifies key trade-offs between performance, robustness, and implementation complexity of the proposed strategies. The rest of the paper is organized as follows. Section 2 introduces the GFM inverter model and explains how frequency regulation and inertia contribute to overloading during frequency excursions. Section 3 presents three overloading mitigation strategies and develops their small-signal models, providing a tuning criteria for each strategy. Section 4 evaluates and compares the strategies under grid frequency excursions and oscillations using a simulation model. Simulation results are then validated experimentally in Section 5. Finally, Sections 6 and 7 present the discussion and conclusions, respectively.