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Analysis of Frequency and Voltage Strength in Power Electronics-Dominated Power Systems Based on Eigen-subsystems

Huisheng Gao, Linbin Huang, Huanhai Xin, Zhiyi Li, Ping Ju

TL;DR

This paper presents a unified framework to analyze frequency and voltage strength in PE-dominated power systems by decomposing F/V responses into four eigen-subsystem modes: CM-F, DM-F, CM-V, and DM-V. Using a unified inertia-damper-spring device model and eigen-subsystem decoupling, it derives mode-specific strength metrics and links DM-V to gSCR while highlighting potential CM-V instabilities when IBRs approach voltage-support limits. The approach reconciles frequency and voltage analyses within one framework, revealing how device distribution and network topology jointly shape strength and stability. Through closed-form, numerical, and time-domain simulations, the work demonstrates the value of mode-resolved metrics for understanding and strengthening modern grids with inverter-based resources.

Abstract

The large-scale integration of inverter-based resources (IBRs) has deteriorated the frequency/voltage (F/V) responses of power systems, leading to a higher risk of instability. Consequently, evaluating the F/V strength has become an important task in power electronics (PE)-dominated power systems. Existing methods typically examine F/V strength separately, employing fundamentally different metrics, such as inertia (focusing on device dynamics) and short-circuit ratio (SCR, addressing network characteristics). These fragmented approaches have resulted in a lack of comprehensive understanding of the overall system strength, potentially overlooking critical aspects. To address this problem, this paper proposes a unified framework for analyzing F/V strength. First, a unified modeling of F/V regulations is introduced. Then, based on modal decoupling, the power systems are decomposed into several eigen-subsystems, where the F/V responses are both decomposed into common-mode (CM) and differential-mode (DM) components, namely, CM-F, DM-F, CM-V, and DM-V. The CM-F and CM-V represent the collective response of all devices to external active or reactive power disturbances, independent of the power network characteristics. In contrast, the DM-F and DM-V capture the redistribution of disturbance power within the system, which is strongly influenced by the network topology and the locations of devices. Notably, traditional strength analysis generally ignores the CM-V (global voltage response), which, as discovered in this paper, may also become unstable in PE-dominated power systems. Based on the proposed framework, new metrics are proposed to evaluate the strength of each modal component. Finally, the effectiveness of the proposed approach is validated through simulations.

Analysis of Frequency and Voltage Strength in Power Electronics-Dominated Power Systems Based on Eigen-subsystems

TL;DR

This paper presents a unified framework to analyze frequency and voltage strength in PE-dominated power systems by decomposing F/V responses into four eigen-subsystem modes: CM-F, DM-F, CM-V, and DM-V. Using a unified inertia-damper-spring device model and eigen-subsystem decoupling, it derives mode-specific strength metrics and links DM-V to gSCR while highlighting potential CM-V instabilities when IBRs approach voltage-support limits. The approach reconciles frequency and voltage analyses within one framework, revealing how device distribution and network topology jointly shape strength and stability. Through closed-form, numerical, and time-domain simulations, the work demonstrates the value of mode-resolved metrics for understanding and strengthening modern grids with inverter-based resources.

Abstract

The large-scale integration of inverter-based resources (IBRs) has deteriorated the frequency/voltage (F/V) responses of power systems, leading to a higher risk of instability. Consequently, evaluating the F/V strength has become an important task in power electronics (PE)-dominated power systems. Existing methods typically examine F/V strength separately, employing fundamentally different metrics, such as inertia (focusing on device dynamics) and short-circuit ratio (SCR, addressing network characteristics). These fragmented approaches have resulted in a lack of comprehensive understanding of the overall system strength, potentially overlooking critical aspects. To address this problem, this paper proposes a unified framework for analyzing F/V strength. First, a unified modeling of F/V regulations is introduced. Then, based on modal decoupling, the power systems are decomposed into several eigen-subsystems, where the F/V responses are both decomposed into common-mode (CM) and differential-mode (DM) components, namely, CM-F, DM-F, CM-V, and DM-V. The CM-F and CM-V represent the collective response of all devices to external active or reactive power disturbances, independent of the power network characteristics. In contrast, the DM-F and DM-V capture the redistribution of disturbance power within the system, which is strongly influenced by the network topology and the locations of devices. Notably, traditional strength analysis generally ignores the CM-V (global voltage response), which, as discovered in this paper, may also become unstable in PE-dominated power systems. Based on the proposed framework, new metrics are proposed to evaluate the strength of each modal component. Finally, the effectiveness of the proposed approach is validated through simulations.

Paper Structure

This paper contains 34 sections, 32 equations, 10 figures, 2 tables.

Table of Contents

  1. Abbreviations
  2. Notations
  3. Introduction
  4. System Modeling
  5. Modeling of Power Network
  6. Modeling of Generation Devices
  7. Unified Simplification of Devices
  8. Closed-loop System
  9. Eigen-subsystems of F/V Responses
  10. Decoupling Process
  11. Global/Local Characteristics of F/V Eigen-subsystems
  12. Corresponding Modal Power Components
  13. F/V Strength Quantification based on Eigen- subsystems
  14. Strength Quantification Approach
  15. Strength Quantification of CM-F
  16. ...and 19 more sections

Figures (10)

  • Figure 1: Framework of frequency and voltage strength evaluation.
  • Figure 2: Eigen-subsystems of (a) frequency (angle) and (b) voltage, where $\Delta P_{Ext}$ and $\Delta Q_{Ext}$ are the equivalent disturbances, $\Delta\theta$ and $V_e^{-1} \Delta V$ are the responses. Here, $V_{e,1} = V_{e,2} = 1$, and $\theta_{e,12} = 0$.
  • Figure 3: Demonstration of the two-device test system.
  • Figure 4: Frequency responses $\Delta\omega_i$ (a, b) and active power responses $\Delta P_i$ (e, f) along with their corresponding modal components (c, d and g, h) in Cases 1-a (left side) and 1-b (right side).
  • Figure 5: Frequency responses of G1 in Case 1-a, 1-c and 1-d.
  • ...and 5 more figures

Theorems & Definitions (4)

  • remark 1
  • remark 2
  • remark 3
  • remark 4