Multiple Fourier Series Analysis Method for PWM Amplitude and Frequency Characteristics of Grid Converters Under High-frequency Interference of Modulation Waves' Amplitude and Frequency

Yue CUI; Han PENG; Sicheng WANG

doi:10.13334/j.0258-8013.pcsee.241094

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Multiple Fourier Series Analysis Method for PWM Amplitude and Frequency Characteristics of Grid Converters Under High-frequency Interference of Modulation Waves' Amplitude and Frequency

Power Electronics | 更新时间：2026-02-05

- Multiple Fourier Series Analysis Method for PWM Amplitude and Frequency Characteristics of Grid Converters Under High-frequency Interference of Modulation Waves' Amplitude and Frequency
- Proceedings of the CSEE Vol. 45, Issue 11, Pages: 4447-4457(2025)
- 作者机构：
  
  强电磁工程与新技术国家重点实验室(华中科技大学电气与电子工程学院), 湖北省武汉市 430074
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(U23B6008);The Delta Power Electronics Science and Education Development Program of Delta Group
- DOI：10.13334/j.0258-8013.pcsee.241094
  CLC： TM46
- Received：14 May 2024，
  
  Published Online：05 November 2024，
  
  Published：05 June 2025
- 稿件说明：
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Yue CUI, Han PENG, Sicheng WANG. Multiple Fourier Series Analysis Method for PWM Amplitude and Frequency Characteristics of Grid Converters Under High-frequency Interference of Modulation Waves' Amplitude and Frequency[J]. Proceedings of the CSEE, 2025, 45(11): 4447-4457.
DOI：

Yue CUI, Han PENG, Sicheng WANG. Multiple Fourier Series Analysis Method for PWM Amplitude and Frequency Characteristics of Grid Converters Under High-frequency Interference of Modulation Waves' Amplitude and Frequency[J]. Proceedings of the CSEE, 2025, 45(11): 4447-4457. DOI： 10.13334/j.0258-8013.pcsee.241094.

摘要

随着新能源发电和电力电子设备在电力系统中的渗透率逐步提高，变换器开关频率附近的高频谐波和间谐波在电网中越发显著，由此产生的波形畸变和振荡问题会严重影响电网的电能质量和运行稳定性。并网变换器采用脉宽调制(pulse width modulation，PWM)控制是导致电网中出现复杂频率谐波和间谐波的重要原因。掌握并网变换器的PWM幅值和频率特性对于研究电网电压/电流在异常频率下的波形畸变和振荡问题以及形成对应的抑制方法具有重要意义。为此，开展调制波幅值和频率干扰下的变换器PWM幅值和频率特性研究。基于调制波的幅值和频率干扰特性以及多元周期函数多重傅里叶级数分解的原理，提出多重傅里叶级数PWM分析方法，实现对由复杂频率分量构成的调制波和载波调制生成的PWM信号的准确建模和频谱分析；揭示PWM中基频、干扰频率和载波频率之间的耦合关系，明确PWM信号中高频谐波和间谐波分量的产生原因及幅值和频率特性与调制波、载波和干扰之间的关联；以降低计算复杂性和增强多重傅里叶级数法在PWM分析中的适用性为目标，提出一种简便的多重傅里叶级数系数计算方法；最后，通过仿真和实验验证所提方法的有效性。

Abstract

With increases of new energy generation and power electronic equipment in power system

harmonics and inter-harmonics with frequencies approaching converter switching frequencies have become increasingly prominent in the power grid. The resulting waveform distortion and oscillation would affect power quality and operation stability of the power grid. Pulse width modulation (PWM) control used for grid converters is an important reason for the occurrence of complex-frequency harmonics and inter-harmonics in the power grid. Knowing PWM amplitude and frequency characteristics of grid converters are significant for analyzing the waveform distortion and oscillation of the power grid voltage/current at abnormal frequencies

as well as for establishing corresponding suppression methods. Therefore

in this paper

a study on PWM amplitude and frequency characteristics of grid converters is carried out under the modulation wave amplitude and frequency interference. Based on the analysis of modulation wave characteristics with amplitude and frequency interference

as well as the multiple Fourier series decomposition principle of multivariable periodic function

a multiple Fourier series PWM analysis method is proposed

which achieves accurate PWM signal modeling and spectral analysis under modulation wave composed of complex frequency components. Coupling relationship among fundamental frequency

interference frequency

and carrier frequency in the PWM process is revealed

and the cause of high-frequency harmonic and inter-harmonic components in PWM signals

as well as correlations between their amplitude and frequency characteristics and the modulation wave

carrier

and interference is clarified. In order to reduce calculation complexity and enhance applicability of multiple Fourier series method to PWM modeling and analysis

a simple multiple Fourier series coefficient calculation method is proposed. Finally

effectiveness of proposed method is verified by simulation and experiment.

关键词

Keywords

references

肖先勇, 郑子萱 .. "双碳"目标下新能源为主体的新型电力系统: 贡献、关键技术与挑战 [J ] .. 工程科学与技术 ,, 2022 ,, 54 (( 1 ):): 47 -- 59 ..

XIAO Xianyong, ZHENG Zixuan .. New power systems dominated by renewable energy towards the goal of emission peak & carbon neutrality: contribution, key techniques, and challenges [J ] . Advanced Engineering Sciences , 2022 ,, 54 (( 1 ):): 47 -- 59 ..

侯延琦, 刘崇茹, 王宇, 等 .. 柔性直流输电系统高频振荡抑制策略研究 [J ] .. 中国电机工程学报 ,, 2021 ,, 41 (( 11 ):): 3741 -- 3750 .. DOI: 10.13334/j.0258-8013.pcsee.201084 http://doi.org/10.13334/j.0258-8013.pcsee.201084 .

HOU Yanqi, LIU Chongru, WANG Yu, et al .. Research on the suppression strategy of high-frequency resonance for MMC-HVDC [J ] . Proceedings of the CSEE , 2021 ,, 41 (( 11 ):): 3741 -- 3750 .. DOI: 10.13334/j.0258-8013.pcsee.201084 http://doi.org/10.13334/j.0258-8013.pcsee.201084 .

冯俊杰, 邹常跃, 杨双飞, 等 .. 针对中高频谐振问题的柔性直流输电系统阻抗精确建模与特性分析 [J ] .. 中国电机工程学报 ,, 2020 ,, 40 (( 15 ):): 4805 -- 4819 .. DOI: 10.13334/j.0258-8013.pcsee.200327 http://doi.org/10.13334/j.0258-8013.pcsee.200327 .

FENG Junjie, ZOU Changyue, YANG Shuangfei, et al .. Accurate impedance modeling and characteristic analysis of VSC-HVDC system for mid-and high-frequency resonance problems [J ] . Proceedings of the CSEE , 2020 ,, 40 (( 15 ):): 4805 -- 4819 .. DOI: 10.13334/j.0258-8013.pcsee.200327 http://doi.org/10.13334/j.0258-8013.pcsee.200327 .

郭贤珊, 刘斌, 梅红明, 等 .. 渝鄂直流背靠背联网工程交直流系统谐振分析与抑制 [J ] .. 电力系统自动化 ,, 2020 ,, 44 (( 20 ):): 157 -- 164 ..

GUO Xianshan, LIU Bin, MEI Hongming, et al .. Analysis and suppression of resonance between AC and DC systems in Chongqing-Hubei back-to-back HVDC project of China [J ] . Automation of Electric Power Systems , 2020 ,, 44 (( 20 ):): 157 -- 164 ..

杜镇宇, 阳岳希, 季柯, 等 .. 张北柔直工程高频谐波振荡机理与抑制方法研究 [J ] .. 电网技术 ,, 2022 ,, 46 (( 8 ):): 3066 -- 3075 ..

DU Zhenyu, YANG Yuexi, JI Ke, et al .. High frequency harmonic resonance and suppression in Zhangbei project [J ] . Power System Technology , 2022 ,, 46 (( 8 ):): 3066 -- 3075 ..

杨硕, 郭春义, 杜东冶, 等 .. 混合双馈入直流输电系统的高频振荡特征及机理研究 [J ] .. 中国电机工程学报 ,, 2024 ,, 44 (( 8 ):): 3059 -- 3071 .. DOI: 10.13334/j.0258-8013.pcsee.223090 http://doi.org/10.13334/j.0258-8013.pcsee.223090 .

YANG Shuo, GUO Chunyi, DU Dongye, et al .. Research on high-frequency oscillation characteristics and mechanism of the hybrid dual-infeed HVDC system [J ] . Proceedings of the CSEE , 2024 ,, 44 (( 8 ):): 3059 -- 3071 .. DOI: 10.13334/j.0258-8013.pcsee.223090 http://doi.org/10.13334/j.0258-8013.pcsee.223090 .

马宁宁, 谢小荣, 贺静波, 等 .. 高比例新能源和电力电子设备电力系统的宽频振荡研究综述 [J ] .. 中国电机工程学报 ,, 2020 ,, 40 (( 15 ):): 4720 -- 4731 .. DOI: 10.13334/j.0258-8013.pcsee.191968 http://doi.org/10.13334/j.0258-8013.pcsee.191968 .

MA Ningning, XIE Xiaorong, HE Jingbo, et al .. Review of wide-band oscillation in renewable and power electronics highly integrated power systems [J ] . Proceedings of the CSEE , 2020 ,, 40 (( 15 ):): 4720 -- 4731 .. DOI: 10.13334/j.0258-8013.pcsee.191968 http://doi.org/10.13334/j.0258-8013.pcsee.191968 .

徐少博, 徐永海, 陶顺, 等 .. 并网换流器采样和PWM边带次生谐波特性研究 [J ] .. 中国电机工程学报 ,, 2023 ,, 43 (( 11 ):): 4340 -- 4354 .. DOI: 10.13334/j.0258-8013.pcsee.222738 http://doi.org/10.13334/j.0258-8013.pcsee.222738 .

XU Shaobo, XU Yonghai, TAO Shun, et al .. Research on sampling and PWM sideband secondary harmonic characteristics of grid connected converter [J ] . Proceedings of the CSEE , 2023 ,, 43 (( 11 ):): 4340 -- 4354 .. DOI: 10.13334/j.0258-8013.pcsee.222738 http://doi.org/10.13334/j.0258-8013.pcsee.222738 .

WANG Xiongfei, BLAABJERG F .. Harmonic stability in power electronic-based power systems: concept, modeling, and analysis [J ] .. IEEE Transactions on Smart Grid ,, 2019 ,, 10 (( 3 ):): 2858 -- 2870 .. DOI: 10.1109/TSG.2018.2812712 http://doi.org/10.1109/TSG.2018.2812712 .

YANG Dongsheng, WANG Xiongfei, BLAABJERG F .. Sideband harmonic instability of paralleled inverters with asynchronous carriers [J ] .. IEEE Transactions on Power Electronics ,, 2018 ,, 33 (( 6 ):): 4571 -- 4577 .. DOI: 10.1109/TPEL.2017.2731313 http://doi.org/10.1109/TPEL.2017.2731313 .

徐少博, 徐永海, 陶顺, 等 .. 谐波扰动下PWM边带谐波特性分析 [J ] .. 电测与仪表 ,, 2024 ,, 61 (( 9 ):): 172 -- 181 ..

XU Shaobo, XU Yonghai, TAO Shun, et al .. Analysis of PWM sideband harmonic characteristics with harmonic disturbance [J ] . Electrical Measurement & Instrumentation , 2024 ,, 61 (( 9 ):): 172 -- 181 ..

YUAN Xiaoming, WANG Sicheng .. Operating-point identification from dimensions of alternating signal based on the incremental iterative mapping mechanism for analyzing dynamics of AC systems [J ] .. CSEE Journal of Power and Energy Systems, Early Access Article ,, DOI: 10.17775/CSEEJPES.2022.01270 http://doi.org/10.17775/CSEEJPES.2022.01270 .

陶顺, 刘云博, 赵蕾, 等 .. 基于脉宽调制的DFIG并网谐波/间谐波幅频特性分析 [J ] .. 电力系统自动化 ,, 2019 ,, 43 (( 20 ):): 153 -- 161 ..

TAO Shun, LIU Yunbo, ZHAO Lei, et al .. Amplitude-frequency characteristic analysis of harmonic/inter-harmonic of grid-connected DFIG based on pulse width modulation [J ] . Automation of Electric Power Systems , 2019 ,, 43 (( 20 ):): 153 -- 161 ..

汪颖, 罗代军, 肖先勇, 等 .. 多逆变器并网下的超高次谐振特性分析 [J ] .. 电力系统自动化 ,, 2020 ,, 44 (( 1 ):): 192 -- 199 ..

WANG Ying, LUO Daijun, XIAO Xianyong, et al .. Analysis on supraharmonic resonance characteristics with integration of multiple inverters [J ] . Automation of Electric Power Systems , 2020 ,, 44 (( 1 ):): 192 -- 199 ..

DOLGUNTSEVA I, KRISHNA R, SOMAN D E, et al .. Contour-based dead-time harmonic analysis in a three-level neutral-point-clamped inverter [J ] .. IEEE Transactions on Industrial Electronics ,, 2015 ,, 62 (( 1 ):): 203 -- 210 .. DOI: 10.1109/TIE.2014.2327579 http://doi.org/10.1109/TIE.2014.2327579 .

MOUTON H, PUTZEYS B .. Understanding the PWM nonlinearity: single-sided modulation [J ] .. IEEE Transactions on Power Electronics ,, 2012 ,, 27 (( 4 ):): 2116 -- 2128 .. DOI: 10.1109/TPEL.2011.2169283 http://doi.org/10.1109/TPEL.2011.2169283 .

DU TOIT MOUTON H, MCGRATH B, HOLMES D G, et al .. One-dimensional spectral analysis of complex PWM waveforms using superposition [J ] .. IEEE Transactions on Power Electronics ,, 2014 ,, 29 (( 12 ):): 6762 -- 6778 .. DOI: 10.1109/TPEL.2014.2304677 http://doi.org/10.1109/TPEL.2014.2304677 .

高云辉, 谢小英, 牛益国, 等 .. 基于FFT的电力系统谐波检测方法综述 [J ] .. 科技资讯 ,, 2017 ,, 15 (( 5 ):): 49-53, 55 . .

GAO Yunhui, XIE Xiaoying, NIU Yiguo, et al .. Review of FFT based harmonic detection methods in power systems [J ] . Science & Technology Information , 2017 ,, 15 (( 5 ):): 49-53, 55 . .

YAN Shaomin, CUI Yue, LI Chengmin, et al .. An improved FCS-MPC based on novel sector optimization and capacitor charge balance algorithm for T-type 3P-3L converters [J ] .. IEEE Transactions on Power Electronics ,, 2023 ,, 38 (( 4 ):): 4559 -- 4571 .. DOI: 10.1109/TPEL.2023.3233996 http://doi.org/10.1109/TPEL.2023.3233996 .

季子杰, 胡家兵, 王思成, 等 .. 电力系统振荡信号瞬时幅值/频率的调制特征分析 [J ] .. 电网技术 ,, 2021 ,, 45 (( 11 ):): 4577 -- 4584 ..

JI Zijie, HU Jiabing, WANG Sicheng, et al .. Modulation characteristics analysis for instantaneous amplitude/ frequency of power systems oscillation signals [J ] . Power System Technology , 2021 ,, 45 (( 11 ):): 4577 -- 4584 ..

季子杰. 基于幅频视角的电力系统振荡信号的调制规律分析[D]. 武汉: 华中科技大学, 2021.

JI Zijie. Modulation characteristics analysis of power system oscillation signal based on amplitude-frequency perspective[D]. Wuhan: Huazhong University of Science and Technology, 2021(in Chinese).

王思成, 袁小明 .. 基于内电势幅值/频率和网络有功/无功电流工作点的变换器并网交流系统小扰动线性化方法 [J ] .. 中国电机工程学报 ,, 2024 ,, 44 (( 3 ):): 1081 -- 1093 .. DOI: 10.13334/j.0258-8013.pcsee.222491 http://doi.org/10.13334/j.0258-8013.pcsee.222491 .

WANG Sicheng, YUAN Xiaoming .. Small-disturbance linearization method for converter interfaced AC power systems based on operating points of internal-voltage amplitude/frequency and networks' active/reactive current [J ] . Proceedings of the CSEE , 2024 ,, 44 (( 3 ):): 1081 -- 1093 .. DOI: 10.13334/j.0258-8013.pcsee.222491 http://doi.org/10.13334/j.0258-8013.pcsee.222491 .

袁小明, 李胜 .. 电力系统中变换器电流时间尺度动态过程分析的幅值/频率调制方法 [J ] .. 中国电机工程学报 ,, 2020 ,, 40 (( 15 ):): 4732 -- 4743 .. DOI: 10.13334/j.0258-8013.pcsee.200474 http://doi.org/10.13334/j.0258-8013.pcsee.200474 .

YUAN Xiaoming, LI Sheng .. An amplitude/frequency modulation based method of voltage source converter for power systems dynamic analysis in current control timescale [J ] . Proceedings of the CSEE , 2020 ,, 40 (( 15 ):): 4732 -- 4743 .. DOI: 10.13334/j.0258-8013.pcsee.200474 http://doi.org/10.13334/j.0258-8013.pcsee.200474 .

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