Grid-forming (GFM) inverters play a critical role in stabilizing future power grids. However, their synchronization is inherently coupled with frequency support, which poses a challenge to prevent overloading while maintaining synchronization. While existing literature has proposed strategies to mitigate the overload of GFM inverters during frequency excursions, these typically focus on limiting primary frequency regulation and overlook their inertial contribution, limiting their effectiveness. The present work addresses this gap by analyzing three overload mitigation strategies that dynamically adjust both primary frequency regulation and inertia. The main contribution of this work is formal analysis of the control structures, providing insight into the tuning process, dynamic behavior, and inherent trade-offs. The performance of these strategies is evaluated under grid frequency excursions and oscillations, focusing on their ability to limit overloads and ensure seamless recovery. Simulation results are validated through experimental testing.

The increasing penetration of power electronic converters into the grid demands advanced control strategies that ensure a high performance and stability, while avoiding undesired interactions with other grid components. Designing these converter controllers with traditional methods is becoming impractical, caused by the difficulties to simultaneously consider and balance diverse and conflicting objectives and to concurrently evaluate converter- and system-level objectives. This paper presents a multi-objective optimization (MOO) methodology aimed at multi-converter scenarios, which employs symbolic state-space representations to systematically explore optimal configurations across diverse performance measures. The methodology is first validated experimentally on a current-controlled grid-connected inverter, demonstrating that the objectives are handled better than with a conventional tuning approach. Additionally, the methodology is applied to a CIGRE benchmark system and compared to a traditional control tuning method to show the potential applications at more complex scenarios. The results demonstrate that the proposed MOO methodology effectively considers multiple converter- and system-level performance criteria simultaneously, leading to configurations that outperform the solutions obtained with conventional approaches.