Extending the Generalized Bode Criterion to Black-Box Power Systems: A Practical Approach for Stability Evaluation

Impedance-based stability analysis techniques are increasingly used to assess the stability of power converter-dominated power systems. Among these techniques, the Generalized Bode Criterion (GBC) has emerged as a robust method, combining the strengths of the Nyquist Stability Criterion (NSC) with the ease of application of the Bode criterion. However, the GBC requires knowledge of the phase derivative at 0 Hz, which can be challenging to obtain when the system transfer function is analytically unknown. This paper proposes and proves a mathematical relation to eliminate the need for the phase derivative in the GBC. Consequently, all necessary information required for the GBC can be directly obtained from the system Bode plot, enabling the application of the GBC to power systems represented by black-box models with no detailed internal information. The proposed approach is validated by analyzing the stability of a DC-DC converter connected to a DC grid and comparing the results with time-domain simulations.