Small-signal Harmonic Voltage-Power Flow Stability Criterion of Converter-based Grid: Mathematic Modelling

Ke JI; Minxiao HAN; Chongru LIU; Yongqiang ZHU

doi:10.13334/j.0258-8013.pcsee.232597

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Small-signal Harmonic Voltage-Power Flow Stability Criterion of Converter-based Grid: Mathematic Modelling

Power Electronics | 更新时间：2026-02-05

- Small-signal Harmonic Voltage-Power Flow Stability Criterion of Converter-based Grid: Mathematic Modelling
- Proceedings of the CSEE Vol. 45, Issue 11, Pages: 4430-4446(2025)
- 作者机构：
  
  新能源电力系统国家重点实验室(华北电力大学), 北京市昌平区 102206
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (Young Scientistic Program)(52207099)
- DOI：10.13334/j.0258-8013.pcsee.232597
  CLC： TM72
- Received：01 December 2023，
  
  Published：05 June 2025
- 稿件说明：
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Ke JI, Minxiao HAN, Chongru LIU, et al. Small-signal Harmonic Voltage-Power Flow Stability Criterion of Converter-based Grid: Mathematic Modelling[J]. Proceedings of the CSEE, 2025, 45(11): 4430-4446.
DOI：

Ke JI, Minxiao HAN, Chongru LIU, et al. Small-signal Harmonic Voltage-Power Flow Stability Criterion of Converter-based Grid: Mathematic Modelling[J]. Proceedings of the CSEE, 2025, 45(11): 4430-4446. DOI： 10.13334/j.0258-8013.pcsee.232597.

摘要

随着双碳目标的迅速推进，电力系统中的换流器占比显著提升并导致系统对扰动的灵敏度增加。该特性一方面使电力系统具备更强的扰动处理和控制能力，另一方面也意味着如果系统的控制设计不当更加容易被扰动所影响并诱发谐振失稳的问题。目前，研究电力系统抗(小)扰动能力的主流方法是阻抗网络/节点导纳矩阵法，通过系统节点导纳矩阵的特征根即可辨识系统的谐振模式。然而，换流器引入的非线性频率耦合效应导致系统电压/电流在扰动激励下出现非同频分量，使得传统基于同频电压-电流关系的阻抗/导纳矩阵难以完整揭示系统的动态特性。通过进一步研究发现，换流器端口电压幅值/相位和有功/无功功率的扰动始终为同频关系。该文从电压-功率关系的视角出发，首先类比工频潮流给出电网电压-功率小扰动谐波潮流的定义和概念；接着，分别给出集总电路元件(电阻、电感、电容)和典型电力电子换流器的电压-功率谐波模型构建方法；然后，推导并构建高占比换流器电网电压-功率小扰动谐波潮流模型，用以揭示系统电压-功率之间的小扰动动力学作用关系；其次，给出电网电压-功率谐波潮流模型的电磁仿真测量方法，并以IEEE 9节点系统为例，在Matlab/Simulink仿真软件中对所提模型进行仿真验证。

Abstract

The transition to carbon-free targets rapidly increases the proportion of power converters in the power system

which makes the power system more sensitive to the perturbation. This feature not only enhances the power system's ability to handle and control perturbations

but also means that if the control design of the system is improper

the power system is more likely to be affected by disturbances and induce resonance instability. At present

the main method for investigating the anti-perturbation ability of the power system is impedance network/node admittance matrix method

which can identify the system resonance modes by the characteristic values of the node admittance matrix. However

the frequency coupling effect introduced by the power converters will lead to coupling between small-signal perturbations at different frequencies in voltages/currents

which makes it difficult to directly apply the traditional impedance/admittance matrices to fully reveal the power system dynamics. After further research

it was found that the disturbance of the voltage amplitude/phase and active/reactive power at the converter port is always in the same frequency relationship. Therefore

from the perspective of voltage-power relationship

this article first provides the definition and concept of small-signal voltage-power harmonic power flow model by comparing with the traditional power flow model at fundamental frequency. Subsequently

methods for constructing voltage-power harmonic models of lumped circuit components (resistors

inductors

capacitors) and typical power converters are presented. Then

the small-signal voltage-power harmonic power flow model of a high proportion converter-based grid is derived and constructed to reveal the dynamic relationship between system voltage and power. Moreover

an electromagnetic simulation measurement method for the small-signal voltage-power harmonic flow model is presented

and the proposed model is verified through simulation using the IEEE 9-node system as an example in Matlab/Simulink simulation software.

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Keywords

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Frequency/Voltage Regulation and Power Sharing Strategy of Converter-based Grid With Improved Autonomous Decentralized Control

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