Generalized Passivity Sensitivity Methodology for Small-Signal Stability Analysis

TL;DR

The paper addresses stability challenges in power systems with high penetration of power-electronic devices by moving beyond conventional eigenvalue-based sensitivity methods. It introduces a generalized passivity sensitivity methodology that uses the frequency-domain passivity index derived from the Hermitian matrix $ \mathcal{H}(j\omega)=\boldsymbol{G}(j\omega)+\boldsymbol{G}^\dagger(j\omega)$ and its minimum eigenvalue $\underline{\Lambda}\{\mathcal{H}\}$, avoiding explicit eigenvalues. The authors derive device-level and system-level sensitivities of this passivity index, enabling identification of the most effective mitigation actions without requiring full modal information. They validate the approach on grid-forming and grid-following VSCs and on larger networks via PSCAD/EMTDC simulations, showing that passivity-guided adjustments (e.g., PLL gains, filter inductances, passivation) can stabilize oscillations around tens of Hz without full-passivation. The work offers a practical, less conservative design tool for stability-aware control and system integration of PE-based devices.

Abstract

This paper proposes a generalized passivity sensitivity analysis for power system stability studies. The method uncovers the most effective instability mitigation actions for both device-level and system-level investigations. The particular structure of the admittance and nodal models is exploited in the detailed derivation of the passivity sensitivity expressions. These proposed sensitivities are validated for different parameters at device-level and at system-level. Compared to previous stability and sensitivity methods, it does not require detailed system information, such as exact system eigenvalues, while it provides valuable information for a less conservative stable system design. In addition, we demonstrate how to utilize the proposed method through case studies with different converter controls and system-wide insights showing its general applicability.

Figures (20)

• Figure 1: Summary of FD analysis methods.
• Figure 2: Frequency domain sensitivity analysis results for bust elements with full modal information and only frequency cases (a) $\lambda=-0.18\pm j0.29$, $\zeta$ = 1.89 (b) $\lambda=-0.64\pm j8.30$, $\zeta$ = 13.07 (c) $\lambda=-1.98\pm j7.81$, $\zeta$ = 4.06 (d) $\lambda=-40.32\pm j22774.20$, $\zeta$ = 564.84 (e) $\lambda=-31.19\pm j376.84$, $\zeta$ = 12.12 and (f) $\lambda=-1153.58\pm j769.07$, $\zeta$ = 1.2.
• Figure 3: GFL VSC scheme.
• Figure 4: Device parametric passivity sensitivity validation results (a) Converter interface inductance $L_{c}$ case, (b) Converter PLL proportional gain $K_{p,pll}$ case
• Figure 5: Impact of $K_{p,pll}$ on the GFL-VSC's passivity index.