Abstract：The node admittance/impedance matrix has become a common resonance analysis tool because of its clear physical meaning and intuitive presence of interaction. However, the node admittance/impedance matrix couldn′t fully describe system resonance since it neglects the disturbance source characteristics. For the scenario where the power supply is connected through converters, the node injection current is an equivalent current source, and the corresponding disturbance source on the input side might be a voltage source or other types of controlled source. Analyzing resonance merely by the node admittance/impedance matrix ignores the influence of the disturbance source output characteristics, which may lead to deviation in the analysis results, even the omission of resonance points. In this paper, the disturbance source transfer function is defined as the corresponding relationship between the source at the input side and the equivalent current source at the output side of the converter, taking the source at the input side as independent variables, the equivalent impedance model of the converter is established and the system impedance matrix is also modified. A modified impedance model considering the disturbance source transfer function is proposed from the system scale, and the influence mechanism of the disturbance source output characteristics on the resonance is revealed: the disturbance source transfer function acts on the impedance matrix array vector of the node in which it is located, which may introduce new resonance points to the system, and affects the accuracy of the resonance analysis. In addition, the source transfer function is homologous to the equivalent impedance of the converter, that is, the way the converter acts on the system resonance is not unique. Therefore, it is difficult to explain the resonance mechanism and influence degree of the converter by system-level resonant analysis, further research on the parameter scale is also needed. As one of the influencing factor analysis methods, modal sensitivity can quantify the influence of parameters and guide resonance suppression, which has been widely applied in mechanical and electrical fields. However, application scenarios of the existing methods are merely limited to the traditional AC systems, corresponding calculation methods for converters and control parameters inside are not discussed. Therefore, based on the modified system impedance model, from the component parameter scale, this paper proposes a modal sensitivity calculation method for converters, which quantifies the influence of the disturbance source output characteristics on resonance, expands the application field of modal sensitivity to the DC distribution network with converters. The proposed modal sensitivity calculation method is not affected by the scale of parameter changes, which could quantify the resonance influence degree of global influencing factors, providing guidance for resonance suppression. In practical applications, when there are multiple converters connected to the system, in order to reduce the amount of calculation, sensitivity analysis only needs to be carried out on the internal parameters of the high-sensitivity converter, so as to narrow the scope of analysis. Finally, the simulation model of a DC distribution network is built through PSCAD/EMTDC to analyze the resonance characteristics of the disturbance source transfer function, quantify the influence of converter parameters on the system resonance characteristics, and verify the effectiveness of the two scales proposed analysis method.
王莹鑫, 徐永海, 陶顺, 徐少博, 秦本双. 计及扰动源输出原副边特性的直流配电网谐振分析方法[J]. 电工技术学报, 2023, 38(7): 1723-1736.
Wang Yingxin, Xu Yonghai, Tao Shun, Xu Shaobo, Qin Benshuang. DC Distribution System Resonance Characteristics Analysis Method Considering the Output Characteristics of the Perturbation Source. Transactions of China Electrotechnical Society, 2023, 38(7): 1723-1736.
[1] 李海波, 赵宇明, 刘国伟, 等. 基于时序仿真的商业楼宇交流与直流配电系统能效对比[J]. 电工技术学报, 2020, 35(19): 4194-4206. Li Haibo, Zhao Yuming, Liu Guowei, et al.The time sequential simulation based energy efficiency comparison of AC and DC distribution power system in commercial buildings[J]. Transactions of China Electrotechnical Society, 2020, 35(19): 4194-4206. [2] 郑重, 苗世洪, 李超, 等. 面向微型能源互联网接入的交直流配电网协同优化调度策略[J]. 电工技术学报, 2022, 37(1): 192-207. Zheng Zhong, Miao Shihong, Li Chao, et al.Coordinated optimal dispatching strategy of AC/DC distribution network for the integration of micro energy Internet[J]. Transactions of China Electrotechnical Society, 2022, 37(1): 192-207. [3] 马钰, 韦钢, 李扬, 等. 考虑孤岛源-荷不确定性的直流配电网可靠性评估[J]. 电工技术学报, 2021, 36(22): 4726-4738. Ma Yu, Wei Gang, Li Yang, et al.Reliability evaluation of DC distribution network considering islanding source-load uncertainty[J]. Transactions of China Electrotechnical Society, 2021, 36(22): 4726-4738. [4] 郑凯元, 杜文娟, 王海风. 动态单元间交互作用对直流微电网稳定性影响的分析[J]. 中国电机工程学报, 2021, 41(23): 7963-7979. Zheng Kaiyuan, Du Wenjuan, Wang Haifeng.Analysis on the stability of DC microgrid affected by interactions among dynamic components[J]. Proceedings of the CSEE, 2021, 41(23): 7963-7979. [5] 程林, 万宇翔, 齐宁, 等. 含多种分布式资源的配用电系统运行可靠性研究评述及展望[J]. 电力系统自动化, 2021, 45(22): 191-207. Cheng Lin, Wan Yuxiang, Qi Ning, et al.Review and prospect of research on operation reliability of power distribution and consumption system considering various distributed energy resources[J]. Automation of Electric Power Systems, 2021, 45(22): 191-207. [6] Mohamad A M I, Mohamed Y A R I. Investigation and enhancement of stability in grid-connected active DC distribution systems with high penetration level of dynamic loads[J]. IEEE Transactions on Power Electronics, 2019, 34(9): 9170-9190. [7] 游逍遥, 刘和平, 苗轶如, 等. 带恒功率负载的双极性直流系统稳定性分析及其有源阻尼方法[J]. 电工技术学报, 2022, 37(4): 918-930. You Xiaoyao, Liu Heping, Miao Yiru, et al.Stability analysis and active damping method of the bipolar DC system with constant power loads[J]. Transactions of China Electrotechnical Society, 2022, 37(4): 918-930. [8] 张美清, 袁小明, 胡家兵. 基于自稳/致稳性的路径级数展开方法及其在含多样化电力电子装备电力系统稳定性分析中的应用[J]. 中国电机工程学报, 2021, 41(5): 1637-1654. Zhang Meiqing, Yuan Xiaoming, Hu Jiabing.Path series expansion method based on self-/ en-stabilizing properties and its application in the stability analysis of power systems with diversified power electronic devices[J]. Proceedings of the CSEE, 2021, 41(5): 1637-1654. [9] 谢小荣, 贺静波, 毛航银, 等. “双高”电力系统稳定性的新问题及分类探讨[J]. 中国电机工程学报, 2021, 41(2): 461-474. Xie Xiaorong, He Jingbo, Mao Hangyin, et al.New issues and classification of power system stability with high shares of renewables and power electronics[J]. Proceedings of the CSEE, 2021, 41(2): 461-474. [10] 姜涛, 李雪, 李国庆, 等. 含多端柔性直流的交直流电力系统静态电压稳定域构建方法[J]. 电工技术学报, 2022, 37(7): 1746-1759. Jiang Tao, Li Xue, Li Guoqing, et al.A predictor-corrector algorithm for forming voltage stability region of hybrid AC/DC power grid with inclusion of VSC-MTDC[J]. Transactions of China Electrotechnical Society, 2022, 37(7): 1746-1759. [11] 蒋海玮, 徐永海, 何志轩, 等. 考虑系统参数不确定性的谐波谐振监测点优化配置方法[J]. 电力系统自动化, 2021, 45(23): 141-151. Jiang Haiwei, Xu Yonghai, He Zhixuan, et al.Optimal placement method for harmonic resonance monitoring points considering uncertainties of system parameters[J]. Automation of Electric Power Systems, 2021, 45(23): 141-151. [12] 黄旭程, 何志兴, 刘亚丽, 等. 考虑光伏发电单元孤岛检测影响的直流电网稳定性分析与阻尼控制[J]. 中国电机工程学报, 2021, 41(1): 109-122. Huang Xucheng, He Zhixing, Liu Yali, et al.Stability analysis and damping control of DC grid considering PV generators with island detection[J]. Proceedings of the CSEE, 2021, 41(1): 109-122. [13] 秦垚, 王晗, 庄圣伦, 等. 海上风电场集电网的高频谐振分析[J]. 中国电机工程学报, 2022, 42(14): 5169-5181. Qin Yao, Wang Han, Zhuang Shenglun, et al.Analysis on high frequency resonance of collector network in offshore wind farm[J]. Proceedings of the CSEE, 2022, 42(14): 5169-5181. [14] 曾志杰, 肖华锋, 高博, 等. 结合阻抗比与振荡阻尼特征的并网系统谐波谐振稳定性分析方法[J]. 中国电机工程学报, 2020, 40(22): 7201-7211. Zeng Zhijie, Xiao Huafeng, Gao Bo, et al.Stability analysis method of harmonic resonance of grid-connected generation system based on impedance ratios and oscillation damping[J]. Proceedings of the CSEE, 2020, 40(22): 7201-7211. [15] Markovic U, Stanojev O, Aristidou P, et al.Understanding small-signal stability of low-inertia systems[J]. IEEE Transactions on Power Systems, 2021, 36(5): 3997-4017. [16] 陈鹏伟, 姜文伟, 阮新波, 等. 直流配电系统有源阻尼控制的阻抗释义与谐振点灵敏度参数调节方法[J]. 中国电机工程学报, 2021, 41(19): 6616-6629. Chen Pengwei, Jiang Wenwei, Ruan Xinbo, et al.Impedance explanation and resonance point sensitivity-based parameter design method of active damping applied to DC distribution system[J]. Proceedings of the CSEE, 2021, 41(19): 6616-6629. [17] Xu W, Huang Zhenyu, Cui Yu, et al.Harmonic resonance mode analysis[J]. IEEE Transactions on Power Delivery, 2005, 20(2): 1182-1190. [18] 钟庆, 冯俊杰, 王钢, 等. 基于节点阻抗矩阵的直流配电网谐振特性分析[J]. 中国电机工程学报, 2019, 39(5): 1323-1334. Zhong Qing, Feng Junjie, Wang Gang, et al.Analysis of resonance characteristics of DC distribution network based on node impedance matrix[J]. Proceedings of the CSEE, 2019, 39(5): 1323-1334. [19] Liu Qunfeng, Ai Yongle, Li Shuai.Recognition of branch series resonance based on port equivalent method[J]. CPSS Transactions on Power Electronics and Applications, 2019, 4(3): 197-203. [20] 唐力, 胡海涛, 李朝阳, 等. 考虑谐波源支路类型的谐波谐振分析方法[J]. 电力系统自动化, 2019, 43(16): 132-147. Tang Li, Hu Haitao, Li Zhaoyang, et al.Harmonic resonance analysis method considering branch type of harmonic source[J]. Automation of Electric Power Systems, 2019, 43(16): 132-147. [21] 李云丰, 汤广福, 吴亚楠, 等. 直流电网建模分析与阻尼控制研究[J]. 中国电机工程学报, 2017, 37(12): 3372-3382, 3664. Li Yunfeng, Tang Guangfu, Wu Yanan, et al.Modeling, analysis and damping control of DC grid[J]. Proceedings of the CSEE, 2017, 37(12): 3372-3382, 3664. [22] 陈新, 张旸, 王赟程. 基于阻抗分析法研究光伏并网逆变器与电网的动态交互影响[J]. 中国电机工程学报, 2014, 34(27): 4559-4567. Chen Xin, Zhang Yang, Wang Yuncheng.A study of dynamic interaction between PV grid-connected inverters and grid based on the impedance analysis method[J]. Proceedings of the CSEE, 2014, 34(27): 4559-4567. [23] 林刚, 李勇, 王姿雅, 等. 低压直流配电系统谐振机理分析与有源抑制方法[J]. 电网技术, 2017, 41(10): 3358-3364. Lin Gang, Li Yong, Wang Ziya, et al.Resonance mechanism analysis and its active damping suppression of LVDC distribution system[J]. Power System Technology, 2017, 41(10): 3358-3364. [24] Huang Zhenyu, Cui Yu, Xu W.Application of modal sensitivity for power system harmonic resonance analysis[J]. IEEE Transactions on Power Systems, 2007, 22(1): 222-231. [25] 王彤, 马静, 王增平, 等. 采用多参数2阶摄动灵敏度的电力系统低频振荡模态分析方法[J]. 中国电机工程学报, 2013, 33(34): 205-213, 30. Wang Tong, Ma Jing, Wang Zengping, et al.Multiple parameter modal analysis of power system low-frequency oscillation based on the 2nd order sensitivity matrix[J]. Proceedings of the CSEE, 2013, 33(34): 205-213, 30. [26] 杨洁, 刘开培, 王东旭, 等. 向无源网络供电的双端柔性直流输电系统小信号稳定性分析[J]. 中国电机工程学报, 2015, 35(10): 2400-2408. Yang Jie, Liu Kaipei, Wang Dongxu, et al.Small signal stability analysis of VSC-HVSC applied to passive network[J]. Proceedings of the CSEE, 2015, 35(10): 2400-2408. [27] Luo Jianqiang, Bu Siqi, Zhu Jiebei, et al.Modal shift evaluation and optimization for resonance mechanism investigation and mitigation of power systems integrated with FCWG[J]. IEEE Transactions on Power Systems, 2020, 35: 4046-4055. [28] Gao Fei, Zheng Xiancheng, Bozhko S, et al.Modal analysis of a PMSG-based DC electrical power system in the more electric aircraft using eigenvalues sensitivity[J]. IEEE Transactions on Transportation Electrification, 2015, 1(1): 65-76. [29] 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, 2017, 37(14): 4156-4164, 4295. Liu Yang, Shuai Zhikang, Li Yang, et al.Harmonic resonance modal analysis of multi-inverter grid-connected systems[J]. Proceedings of the CSEE, 2017, 37(14): 4156-4164, 4295. [30] 秦本双, 徐永海. 多虚拟同步机并网系统功频振荡模态分析[J]. 中国电机工程学报, 2021, 41(19): 6570-6580. Qin Benshuang, Xu Yonghai.Modal analysis of multi-virtual synchronous machine grid-connected power-frequency oscillation[J]. Proceedings of the CSEE, 2021, 41(19): 6570-6580. [31] Li Zebiao, Hu Haitao, Tang Li, et al.Quantitative severity assessment and sensitivity analysis under uncertainty for harmonic resonance amplification in power systems[J]. IEEE Transactions on Power Delivery, 2020, 35: 809-818.
2023, Vol. 38 
