Abstract The windowed fast Fourier transform (WFFT) is widely used for harmonic analysis on rapidly changing time domain waveforms in power electronic distribution network, but WFFT is prone to errors so that the harmonic transient characteristics cannot be obtained accurately. In this paper, a dynamic phasor (DP) model of frequency-dependent transmission line is proposed for harmonic transient analysis in distribution network. The characteristic admittance and propagation coefficient are fitted in rational function by adopting vector fitting method, which exist in the model domain frequency-dependent transmission line model. The DP model of frequency-dependent transmission line is established based on state space equation, the DP model is also established for the thyristor controlled reactor (TCR) at receiving end of the transmission line, the harmonic dynamic coupling between TCR and power grid is described by the analytical formula with phasors of each order as state variables. The DP model of the simple test system is calculated based on Matlab, which can directly analyze harmonic transient characteristics for the voltage of each node and current in each branch in the system, and the instantaneous power quality parameters can also be obtained. The transient steady state results of the simulation system based on EMTP verify the effectiveness and accuracy of the model.
Xie Runsheng,Zhang Guorong,Gao Kai等. Modeling and Simulation of Dynamic Phasor Harmonic Analysis for Frequency-Dependent Transmission Line[J]. Transactions of China Electrotechnical Society, 2021, 36(15): 3200-3210.
[1] Bollen M H J, Das R, Djokic S, et al. Power quality concerns in implementing smart distribution-grid applications[J]. IEEE Transactions on Smart Grid, 2016, 8(1): 1-8. [2] 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(4): 707-720. Xiao Xiangning, Liao Kunyu, Tang Songhao, et al.Development of power-electronized distribution grids and the new supraharmonics issues[J]. Transactions of China Electrotechnical Society, 2018, 33(4): 707-720. [3] 陶顺, 罗超, 肖湘宁, 等. 电流物理分量理论改进方法及其在电能质量评估中的应用[J]. 电工技术学报, 2019, 34(9): 1960-1970. Tao Shun, Luo Chao, Xiao Xiangning, et al.A modified current physical components theory and its application in power quality assessment[J]. Transactions of China Electrotechnical Society, 2019, 34(9): 1960-1970. [4] 严静, 邵振国. 电能质量谐波监测与评估综述[J]. 电气技术, 2020, 21(7): 1-7. Yan Jing, Shao Zhenguo.Summary of harmonic monitoring and evaluation[J]. Electrical engineering, 2020, 21(7): 1-7. [5] 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. Xie Ning, Luo An, Chen Yandong, et al.Dynamic modeling and characteristic analysis on harmonics of photovoltaic power stations[J]. Proceedings of the CSEE, 2013, 33(36): 10-17. [6] Medina A, Segundo J, Ribeiro P, et al.Harmonic analysis in frequency and time domain[J]. IEEE Transactions on Power Delivery, 2013, 28(3): 1813-1821. [7] 程佩芬, 李崇涛, 傅闯, 等. 基于状态空间法的高压直流输电系统电磁暂态简化模型的解析算法[J]. 电工技术学报, 2019, 34(6): 1230-1239. Cheng Peifen, Li Chongtao, Fu Chuang, et al.An analytic solution for simplified electromagnetic transient model of HVDC transmission system based on state space method[J]. Transactions of China Electrotechnical Society, 2019, 34(6): 1230-1239. [8] 王保帅, 肖霞. 一种用于谐波分析的高精度多谱线插值算法[J]. 电工技术学报, 2018, 33(3): 553-562. Wang Baoshuai, Xiao Xia.A high accuracy Multi-spectrum-line interpolation algorithm for harmonic analysis[J]. Transactions of China Electrotechnical Society, 2018, 33(3): 553-562. [9] 李建闽, 林海军, 梁成斌, 等. 基于双分辨率S变换和学习向量量化神经网络的电能质量扰动检测方法[J]. 电工技术学报, 2019, 34(16): 3453-3463. Li Jianmin, Lin Haijun, Liang Chengbin, et al.Detection method of power quality disturbances based on double resolution s transform and learning vector quantization neural network[J]. Transactions of China Electrotechnical Society, 2019, 34(16): 3453-3463. [10] Gallo D, Langella R, Luiso M, et al.A new test procedure to measure power electronic devices frequency coupling admittance[J]. IEEE Transactions on Instrumentation & Measurement, 2018, 67(10), 2401-2409. [11] 谢桦, 任超宇, 郭志星, 等. 基于聚类抽样的随机潮流计算[J]. 电工技术学报, 2020, 35(23): 120-128. Xie Hua, Ren Chaoyu, Guo Zhixing, et al.Stochastic load flow calculation method based on clustering and sampling[J]. Transactions of China Electrotechnical Society, 2020, 35(23): 120-128. [12] Shu Dewu, Xie Xiaorong, Dinavahi V, et al.Dynamic phasor based interface model for EMT and transient stability hybrid simulations[J]. IEEE Transactions on Power Systems, 2017, 33(4): 3930-3939. [13] 姜宽, 王慧芳, 林达, 等. 面向逆变器型分布式电源的快速建模与仿真方法[J]. 电力系统自动化, 2017, 41(12): 13-19. Jiang Kuan, Wang Huifang, Lin Da, et al.Rapid modeling and simulation method for inverter interfaced distributed generators[J]. Automation of Electric Power System, 2017, 41(12): 13-19. [14] E Zhijun, Fang D Z, Chan K W, et al. Hybrid simulation of power systems with SVC dynamic phasor model[J]. International Journal of Electrical Power & Energy Systems, 2009, 31(5): 175-180. [15] 王童辉, 贾科, 毕天姝, 等. 基于动态相量理论的高压直流系统换相失败暂态特性[J]. 电力系统自动化, 2018, 42(23): 78-86. Wang Tonghui, Jia Ke, Bi Tianshu, et al.Transient characteristics of commutation failure of HVDC system based on dynamic phasor theory[J]. Automation of Electric Power System, 2018, 42(23): 78-86. [16] 许汉平, 杨炜晨, 张东寅, 等. 考虑换相失败相互影响的多馈入高压直流系统换相失败判断方法[J]. 电工技术学报, 2020, 35(8): 178-188. Xu Hanping, Yang Weichen, Zhang Dongyin, et al.Commutation failure judgment method for multi-infeed HVDC systems considering the interaction of commutation failures[J]. Transactions of China Electrotechnical Society, 2020, 35(8): 178-188. [17] 刘洁波, 黄纯, 江亚群, 等. 基于强跟踪泰勒-卡尔曼滤波器的动态相量估计算法[J]. 电工技术学报, 2018, 33(2): 433-441. Liu Jiebo, Huang Chun, Jiang Yaqun, et al.Dynamic phasor estimator based on strong tracking Taylor-Kalman filter[J]. Transactions of China Electrotechnical Society, 2018, 33(2): 433-441. [18] 应迪生, 张明, 陈家荣. 三相分布参数线路动态相量法的建模与仿真[J]. 中国电机工程学报, 2007, 27(34): 46-51. Ying Disheng, Zhang Ming, Chan K W.Modeling and simulation of 3-phase distribution parameter line using dynamic phasor[J]. Proceedings of the CSEE, 2007, 27(34): 46-51. [19] 邱丽萍, 张彦涛, 王蒙, 等. 适用于交流长线路的动态相量时域短路电流计算方法研究[J]. 中国电机工程学报, 2019, 39(13): 3736-3744. Qiu Liping, Zhang Yantao, Wang Meng, et al.Dynamic phasor time domain short-circuit current calculation method for power systems with long ac transmission lines[J]. Proceedings of the CSEE, 2019, 39(13): 3736-3744. [20] 张彦涛, 秦晓辉, 汤涌, 等. 输电线路工频动态相量模型在半波长交流输电系统机电暂态仿真中的应用研究[J]. 中国电机工程学报, 2017, 37(18): 5294-5302. Zhang Yantao, Qin Xiaohui, Tang Yong, et al.Half-wavelength system transients stability simulation using dynamic phasor model of AC transmission line[J]. Proceedings of the CSEE, 2017, 37(18): 5294-5302. [21] Marti J, Tavighi A.Frequency dependent multiconductor transmission line model with collocated voltage and current propagation[J]. IEEE Transactions on Power Delivery, 2017, 33(1): 71-81. [22] Gustavsen B.Improving the pole relocating properties of vector fitting[J]. IEEE Transactions on Power Delivery, 2006, 21(3): 1587-1592. [23] Semlyen A, Gustavsen B.Phase-domain transmission-line modeling with enforcement of symmetry via the propagated characteristic admittance matrix[J]. IEEE Transactions on Power Delivery, 2012, 27(2): 626-631. [24] Zhang Shao, Jiang Shuai, Lu Xi, et al.Resonance issues and damping techniques for grid-connected inverters with long transmission cable[J]. IEEE Transactions on Power Electronics, 2014, 29(1): 110-120. [25] Mercado M A C, Orillaza J R. Harmonic state space model of a closed-loop balanced thyristor controlled series compensator[C]//2016 17th International Conference on Harmonics and Quality of Power (ICHQP), Belo Horizonte, Brazil, 2016: 1-6. [26] 刘博宁, 姚蜀军, 张慧媛, 等. 多频段-动态相量法电磁暂态仿真研究[J]. 中国电机工程学报, 2019, 39(19): 5772-5781. Liu Boning, Yao Shujun, Zhang Huiyuan, et al.A research on multi-frequency band dynamic phasor for electromagnetic transients simulation[J]. Proceedings of the CSEE, 2019, 39(19): 5772-5781.
2021, Vol. 36 
