Dynamic Evaluation of Frequency Support Requirements for Grid-Forming Converters Based on the Brent Iteration Algorithm

[Objective] To enhance frequency stability in systems with a high penetration of converters，this paper investigates a dynamic evaluation and quantification method for determining the frequency support requirements of grid-forming（GFM）converters. [Methods] First，a multi-machine system frequency response model is developed by incorporating the power-frequency characteristics of coupled GFM converters. Second，considering both the rate of change of frequency（RoCoF）and the maximum transient frequency deviation under anticipated disturbances，a comprehensive assessment method is constructed to evaluate the frequency support requirements of GFM converters. Finally，based on the Brent iterative algorithm，the critical thresholds of virtual inertia and primary frequency regulation gain for GFM converters are dynamically assessed under various operating conditions. Based on the modified IEEE-39 bus system，multiple scenario-based case studies were conducted. [Conclusions] The results show that the introduction of GFM converters can raise the minimum system frequency to 49.5 Hz，significantly enhancing system stability and highlighting the necessity of deploying GFM converters in highly power-electronic systems. Furthermore，a performance comparison of three algorithms demonstrates that the proposed iterative method requires only 11 iterations on average，reducing the iteration count by over 20% compared to traditional approaches，thereby validating the effectiveness of the proposed assessment method and iterative algorithm. [Conclusions] The proposed assessment method clarifies，from a system-level perspective，the frequency support requirements imposed by the grid on GFM converters，providing a theoretical foundation for their optimal allocation and parameter tuning.