近年来，由无功补偿设备引起的配电网谐波谐振现象时有发生。谐波谐振会产生遍 及全网络的过电压和过激磁现象，导致变压器产生高频噪声和振动，严重时会击穿电缆绝缘薄弱点引发短路，甚至造成大面积停电事故，因此，配电网谐波谐振研究对提高配电网安全稳定运行具有重要意义。

谐波谐振的分析方法主要有频谱分析法和模态分析法。由于模态分析法既可以对配电网谐振频率进行分析，同时还可以研究各节点对谐振的贡献程度，因此在谐波谐振分析领域中得到了广泛应用。随着现代电力电子设备和新能源电源在配电网中大量投入，配电网的谐波特性发生了较大改变，呈现谐波频率点密集、广谱宽频的特性，与此同时配电网规模不断扩大，使得传统模态分析方法遇到了新的困难。

针对传统模态分析法存在误判配电网谐振频率和的谐振分析复杂度高问题，论文通过分析节点导纳矩阵行列式的特性及其随频率连续变化的规律，提出一种基于网络导纳矩阵奇异性的谐波谐振判别方法，该方法仅对网络导纳矩阵的行列式值进行分析，避免了传统模态分析法中伪模态出现所导致的配电网谐振误判，实现了对配电网是否存在谐振的准确判断，同时该方法在进行谐振分析过程中无需对网络导纳矩阵进行大规模模态分解与求逆，将谐振分析从多变量分析转换到单变量分析，显著降低了谐波谐振分析的复杂度。

针对谐振频率的传统识别方法存在计算效率低、工作量大的问题，论文建立了谐波谐振函数模型，研究大步长下谐振频率点附近网络导纳矩阵行列式值的变化规律，选用傅里叶函数模型拟合网络导纳矩阵行列式值的解析表达式，实现网络导纳矩阵行列式值与频率变化关系的量化，通过计算网络导纳矩阵解析表达式的极值点获取配电网的谐振频率，该方法具有低工作量和高计算效率的特点。

针对配电网谐波谐振抑制方法效果不理想的问题，通过计算特定网络导纳矩阵关键特征值及对应特征向量，量化各节点对谐振的贡献程度，根据本文提出的改进模态分析法所提供的准确信息，可计算出谐波谐振抑制装置的最佳安装位置和容量范围，在此基础上对谐振抑制装置的参数进行优化，实验效果表明可明显提高单调谐滤波器对谐波谐振的抑制效果。

将本文提出的改进方法分别应用在 IEEE14 节点系统、三节点测试系统中进行谐波谐振分析，并将本文方法分析结果与现有谐波谐振方法分析结果进行对比，验证了本文提出方法的优越性。为了进一步测试本文方法的先进性和应用效果，以陕西省某企业中压配电网为例，建立该企业配电网的等值电路，应用本文提出方法对该配电网进行谐波谐振分析和谐振抑制，综合验证本文方法的先进性。

In recent years, the phenomenon of harmonic resonance in distribution network caused by reactive power compensation equipment has occurred frequently. Harmonic resonance will produce overvoltage and overexcitation throughout the whole network, resulting in high-frequency noise and vibration of the transformer, which will break down the weak point of the cable insulation and lead to short circuit, and even cause a large area of power outage. Therefore, the study of harmonic resonance in the distribution network is of great significance to improve the safe and stable operation of the distribution network.

The analysis methods of harmonic resonance mainly include spectrum analysis and modal analysis. Because modal analysis can not only analyze the resonant frequency of distribution network, but also study the contribution degree of each node to the resonance, it has been widely used in the field of harmonic resonance analysis. With the large investment of modern power electronic equipment and new energy sources in the distribution network, the harmonic characteristics of the distribution network have changed greatly, showing the characteristics of dense harmonic frequency points and broad spectrum broadband. At the same time, the scale of the distribution network continues to expand, which makes the traditional mode analysis methods encounter new difficulties.

In view of the high complexity of resonance analysis due to the misjudgment of the harmonic frequency sum of the distribution network by traditional modal analysis method, this paper proposes a harmonic resonance discrimination method based on the singularity of the network admittance matrix by analyzing the characteristics of the determinant of the node admittance matrix and the law of its continuous change with frequency. It avoids the misjudgment of distribution network resonance caused by the appearance of pseudo-modes in the traditional modal analysis method, and realizes the accurate judgment of whether there isresonance in the distribution network. Meanwhile, in the process of resonance analysis, this method does not need to carry out large-scale mode decomposition and inversion of the network admitting matrix, and converts the resonance analysis from multivariate analysis to univariate analysis, significantly reducing the complexity of harmonic resonance analysis.

In view of the problems of low computational efficiency and heavy workload in traditional identification methods of resonant frequency, a harmonic resonance function model is established in this paper to study the change rule of the determinant value of the network admittance matrix near the resonant frequency point at a large length, and the analytical expression of the determinant value of the network admittance matrix is fitted with a Fourier function model. The resonant frequency of distribution network is obtained by calculating the extreme value of the analytic expression of the network admittance matrix. This method has the characteristics of low workload and high computational efficiency.

In view of the unsatisfactory effect of the harmonic resonance suppression method in the distribution network, the contribution degree of each node to the resonance can be quantified by calculating the key eigenvalues and corresponding eigenvectors of the admittance matrix of a specific network. According to the accurate information provided by the improved modal analysis method proposed in this paper, the optimal installation position and capacity range of the harmonic resonance suppression device can be calculated. On this basis, the parameters of the resonant suppression device are optimized, and the experimental results show that the suppression effect of the single tuned filter on harmonic resonance can be significantly improved.

The improved method proposed in this paper is applied to IEEE14-node system and three-node test system respectively for harmonic resonance analysis, and the analysis results of the proposed method are compared with the existing harmonic resonance analysis results, and the superiority of the proposed method is verified. In order to further test the advanced nature and application effect of the proposed method, taking the medium voltage distribution network of an enterprise in Shaanxi Province as an example, the equivalent circuit of the distribution network of the enterprise is established, and the harmonic resonance analysis and resonance suppression of the distribution network are carried out by the proposed method, and the advanced nature of the proposed method is comprehensively verified.

[1]韦明杰. 基于宽频同步测量的配电网高阻故障诊断技术与应用[D]. 山东大学, 2022.

[2]徐丙垠. 配电网继电保护与自动化[M]. 北京:中国电力出版社, 2017.

[3]国家能源局. 20116-2020年全国电力可靠性年度报告[R/OL]. 2021.https://prpq.nea.gov,cn/ndbg

[4]张海鹏, 林舜江, 刘明波. 考虑光伏不确定性的低压配电网分散无功补偿鲁棒优化配置[J]. 电网技术, 2016,40(12):8.

[5]刘晋武, 王红伟. 无功补偿技术在配电网中的应用分析[J]. 中国电业(技术版), 2015,No.848(03):21-23.

[6]闵阳. 复杂有源配电网的综合性无功优化研究[D]. 南昌大学, 2022.

[7]程从智, 徐晨, 戴珂.基于PSC-PWM的MMC-SAPF中压配电网谐振阻尼技术[J]. 高电压技术, 2023,49(01):258-268.

[8]国家电网有限公司．国家电网有限公司服务新能源发展报告2021[R]. 2021.

[9]李朝阳. 电力系统谐波谐振概率评估方法研究[D]. 西南交通大学, 2020.

[10]周孝信, 鲁宗相, 刘应梅, 等. 中国未来电网的发展模式和关键技术[J]. 中国电机工程学报, 2014, 34(29): 4999-5008.

[11]刘吉臻. 大规模新能源电力安全高效利用基础问题[J]. 中国电机工程学报, 2013, 33(16): 1-8.

[12]肖湘宁, 廖坤玉, 唐松浩, 等. 配电网电力电子化的发展和超高次谐波新问题[J]. 电工技术学报, 2018, 33(04): 707-720.

[13]谢宁, 罗安, 陈燕东, 等. 大型光伏电站动态建模及谐波特性分析[J]. 中国电机工程学报, 2013, 33(36): 10-17.

[14]谢宁, 罗安, 马伏军, 等. 大型光伏电站与电网谐波交互影响[J]. 中国电机工程学报, 2013, 33(34): 9-16.

[15]Sainz L, Caro M, Caro E. Analytical study of the series resonance in power systems with the steinmetz circuit[J]. IEEE Transaction on Power Delivery, 2009, 24(4): 2090-2098.

[16]殷洪海, 章立, 王凯. 配电物联网架构下基于云边协同的有源配电网故障定位方法[J]. 电气自动化, 2022,44(06):74-76.

[17]吴璐子, 缪希仁, 庄胜斌, 等. 含分布式电源配电网故障检测与定位研究综述[J]. 福州大学学报(自然科学版), 2022,50(06):751-759.

[18]王艳松, 李强, 李习武. 油田配电网的谐波分析与集中治理[J]. 中国石油大学学报(自然科学版), 2008, No.168(04):148-151+160.

[19]李建文, 杨瑞卿, 李戎, 等. “双高”配电网下变电站并联电容器灵活投切[J]. 电力系统及其自动化学报, 2023,35(02):132-139.

[20]孙媛媛, 李树荣, 石访, 等. 含分布式谐波源的配电网多谐波源责任划分[J]. 中国电机工程学报, 2019,39(18):5389-5398+5586.

[21]孔祥兴, 盛军, 王燕英, 等. 基于改进小波变换法的风电场谐波检测[J]. 南华大学学报(自然科学版), 2019,33(02):55-60.

[22]赵庆亮, 袁正勇, 陈宗祥, 等. 大功率高频微波发生器的PWM整流器研究与应用[J]. 真空电子技术, 2021,No.352(03):71-75.

[23]李亚辉, 孙媛媛, 李可军, 等. 不平衡供电条件下多脉动整流器的谐波特性分析[J]. 电力系统自动化, 2021,45(23):152-161.

[24]陈瑶, 童亦斌, 金新民. 基于PWM整流器的SVPWM谐波分析新算法[J]. 中国电机工程学报, 2007,No.240(13):76-80.

[25]杨廷林.双PWM变频器的交流调速技术研究[J]. 现代工业经济和信息化, 2022,12(11):126-128.

[26]王艳松, 李强, 李习武. 油田配电网的谐波分析与集中治理[J]. 中国石油大学学报(自然科学版), 2008,No.168(04):148-151+160.

[27]张军梁, 马皓. 大型石化配电系统谐波分析与治理[J]. 机电工程, 2007, No.149(07):11-13+56.

[28]龚华麟, 肖先勇. 非线性度法在配电网谐波源探测中的应用[J]. 电力系统保护与控制, 2010,38(08):30-34.

[29]董国震, 和敬涵. 电力系统局部电路谐波谐振产生原因分析及对策[J]. 电力系统保护与控制, 2007,35(1):77-80.

[30]李书应, 刘奇, 康忠健, 等. 页岩气田电网谐波谐振影响分析及对策研究[J]. 电气应用, 2022,41(10):81-88.

[31]薛福成. 变配电所异常过电压分析与治理[D]. 北京：北京交通大学, 2010.

[32]杜林, 李欣, 司马文霞, 等.110kV变电站过电压在线监测系统及其波形分析[J]. 高电压技术, 2012,38(3) :535-543.

[33]王彦东, 李群湛. 电力系统谐波阻抗特性及测量方法的探讨[J]. 电工技术杂志, 2004, 35 (2) :64-67．

[34]徐文远, 张大海. 基于模态分析的谐波谐振评估方法[J]. 中国电机工程学报, 2005(22):92-96.

[35]唐振东, 杨洪耕. 基于模态分析的风电场并网谐波谐振研究[J]. 电力自动化设备, 2017,37(3):87-92.

[36]刘洋, 帅智康,李杨, 等. 多逆变器并网系统谐波谐振模态分析[J]. 中国电机工程学报, 2016,36(0):1-9.

[37]文周辉, 吴耀武, 娄素华, 等. 基于模态分析法和虚拟支路法的串联谐波谐振分析[J]. 中国电机工程学报, 2007,27(28)：84-89.

[38]刘书铭, 李陈莹, 李琼林, 等. 电力系统串联谐波谐振的特性分析与灵敏度计算[J]. 电力系统保护与控制, 2015,43(09):21-27.

[39]XU W, HUANG Z, CUI Y, et al. Harmonic resonance mode analysis[J]. IEEE Transactions on Power Delivery, 2005, 20(2): 1182-1190．

[40]师立涛. 电力系统谐波谐振及防治措施的研究[D]. 天津：天津大学, 2010.

[41]贾莉. 基于模态分析法的无源滤波器优化配置[D]. 青岛：中国石油大学, 2010．

[42]李发才. 配电网的滤波器优化配置的研究[D]. 青岛：中国石油大学, 2010.

[43]吴国禄. 油田配电网的谐波分析与滤波器的优化配置[D]. 青岛：中国石油大学, 2011.

[44]郭明明. 有源电力滤波器在低压配电网中的应用研究[D]. 洛阳：河南科技大学, 2015.

[45]Qasim M, Kanjiya P, Khadkikar V. Artificial-Neural-Network-Based Phase-Locking Scheme for Active Power Filters[J]. IEEE Transactions on Industrial Electronics, 2014, 61(8):3857-3866.

[46]Yu-long, Hong, WANG, et al. Simulation and reliability analysis of shunt active power filter based on instantaneous reactive power theory[J]. Journal of Zhejiang University-SCIENCE A, 2007,8(3):416-421.

[47]Huang Z, Cui Y, Xu W. Application of Modal Sensitivity for Power System Harmonic Resonance Analysis[J]. IEEE Transactions on Power Systems, 2007,22(1):222-231.

[48]何彩霞. 基于模态分析法的电力系统谐波谐振问题研究及其灵敏度分析[D]. 武汉：武汉大学, 2010.

[49](奥地利)George J.Wakileh, 徐政译. 电力系统谐波—基本原理、分析方法和滤波器设计[M]. 北京机械工业出版社, 2005.

[50]丘凌, 丘扬. 谐波谐振的模态分析法及其应用[J]. 浙江电力,2014,(2)：14-17.

[51]IEEE Harmonics Model and Simulation Task Force. Test systems for harmonics modeling and simulation[J]. IEEE Transactions on Power Delivery, 1999,14(2)：579-587.

[52]李欣, 蒋平, 徐杏桃. 模态分析法在无源滤波参数设计校核中的应用[J]. 江苏工程, 2008,27(04):48-51.