陈思危(1998), 男, 硕士在读, 研究方向为柔性高压直流输电故障(E-mail:
李保宏(1986), 男, 博士, 副教授, 研究方向为电力系统稳定与控制、高压直流输电、直流电网和交直流混联电网稳定分析
刘天琪(1962), 女, 博士, 教授, 博士生导师, 研究方向为电力系统稳定与控制、高压直流输电、柔性直流电网
直流电网的故障特性可通过分析电网阻尼的方式获取,但传统电网阻抗建模往往忽略线路参数的频变特性,建模结果无法准确反映电网阻尼特性。为对比分析电缆和架空线直流电网故障电流特性的差异,文中首先基于矢量拟合提出一种考虑线路参数频变特性的直流电网阻抗模型。接着,基于此模型的幅频特性,对比分析电缆与架空线直流电网故障电流时延、初始上升率和幅值的差异,并研究改变电网关键参数对2种电网故障特性的影响。所提模型阻尼特性与依频模型直流电网扫频结果相比,均方根误差低于0.6,准确性高于简化模型。最后,基于对称单极双端系统极间短路故障进行仿真。结果表明:桥臂电感值增加时电缆直流电网故障电流上升率比架空线高24.96%,验证了电缆直流电网故障电流对感性关键参数变化更敏感的结论。
The fault characteristics of direct current (DC) grids can be analyzed by addressing the grid damping characteristics. However, the frequency-dependent characteristics of the transmission line parameters are usually ignored in the conventional grid impedance modeling methods, which cannot accurately reflect the grid damping characteristics. To compare and analyze the fault currents characteristics of the DC grids with cables and overhead lines, an impedance model of DC grid considering the frequency-dependent characteristics of the transmission line parameters based on vector fitting is proposed in this paper. Then, the proposed model is applied to compare and analyze the fault current features including time delays, initial rising rates and amplitudes of the DC grids with cables and overhead lines. Meanwhile, the impacts of the DC grids key parameters on the fault current characteristics of the two DC grids are investigated. Compared with the sweeping results of the frequency-dependent line model, the proposed model performs well in reflecting the damping characteristic of the DC grid, where the root square error is less than 0.6, informing that the proposed model is much more accurate than the simplified model. Finally, the simulation is conducted in a symmetrical monopolar two-terminal DC grid with pole-to-pole fault. The simulation results show that the fault current rising rate of the DC grid with cables is 24.96% higher than that of the DC grid with overhead lines when the arm inductance is increased, which validates that the fault currents of the DC grids with cables are more sensitive to the inductive key parameters than the DC grids with overhead lines.
随着环境问题的日益突出,世界各国加速了对可再生能源的开发和利用[
文献[
针对集中参数模型无法准确描述依频模型阻尼特性的问题,文中提出了一种可完整描述直流电网全频域阻尼特性的阻抗模型。首先,对比了电缆和架空线参数频变特性的不同;其次,通过矢量拟合得到依频模型单位阻抗频率响应的数学表达式,在此基础上对电缆与架空线直流电网分别进行了阻抗建模;然后,基于电网阻尼特性对比分析了2种电网故障电流特性的不同;最后,通过PSCAD/EMTDC仿真验证了电缆直流电网故障电流对感性关键参数变化更敏感的结论。
依频模型是目前最精确的输电线路电磁暂态模型。与集中参数模型相比,依频模型考虑了输电线路的分布特性和参数的频变特性[
基于依频模型的输电线路配置
Transmission line configuration based on frequency-dependent line model
文献[
输电线路依频模型单位导纳
Unit admittance of frequency-dependent transmission line model
输电线路类型 | 电导/(μS·km-1) | 电容/(μF·km-1) |
电缆 | 0.1 | 0.257 |
架空线 | 0.01 | 0.009 938 |
输电线路电阻和电感的频率响应
Frequency dependence of transmission line resistance and transmission line inductance
文献[
由式(1)和式(2)可以得到经过长线修正后的π型等效模型线路参数。
式中:
搭建π型等效模型须考虑式(1)和式(2)中线路参数的频变特性。使用PSCAD/EMTDC中的线路常量程序(line constant program, LCP)可以计算依频模型指定频率下的稳态参数值[
原则上,若不考虑阶数,有理函数可以逼近任何频率响应。有理函数逼近的表达式为:
式中:
设置未知的修正辅助函数
式中:
对于电缆,可直接使用式(3)进行拟合。从
式中:
基于矢量拟合算法拟合电缆单位阻抗
Fitting cable unit impedance based on vector fitting
对于架空线,如果直接使用式(3)进行拟合,拟合阶数
式中:
架空线参数拟合结果见
基于矢量拟合算法拟合架空线单位阻抗
Fitting overhead line unit impedance based on vector fitting
基于2.2节输电线路单位阻抗的频率响应拟合结果进行直流电网阻抗建模,以MMC端口处接入双极线路为例进行模型验证,系统结构如
MMC端口接入双极线路
Connecting bipolar transmission line at MMC port
从
式中:Δ
分别将电缆和架空线直流电网阻抗建模与依频模型直流电网扫频结果进行对比,结果如
电缆直流电网阻抗建模与扫频结果的比较
Comparison of impedance modeling and frequency sweeping results of the DC grid with cables
架空线直流电网阻抗建模与扫频结果的比较
Comparison of impedance modeling and frequency sweeping results of the DC grid with overhead lines
将采用文中模型、π型等效模型、串联π节模型(10π节)的直流电网幅频特性与依频模型直流电网扫频结果进行对比,如
不同阻抗模型幅频特性与扫频结果的比较
Comparison of the amplitude-frequency characteristics of different impedance models and frequency sweeping results
由文献[
极间短路故障时,与线路电压相位相反的高频电压波从故障点向两端前进,在到达换流站后使换流站子模块电容放电产生故障电流[
故障电流的时延取决于故障行波的波速。使用均匀无损单导线波速公式可得故障电流的时延计算公式,如式(9)所示。
式中:
将
电缆和架空线直流电网幅频特性比较
Comparison of the amplitude-frequency characteristics of the DC grid with cables and overhead lines
以MMC桥臂电感为例,对比分析直流电网关键参数的变化对电缆和架空线直流电网幅频特性的影响,进一步验证模型的正确性,并以此为基础研究关键参数的变化对2种电网故障电流的影响。
基于2.3节的直流电网阻抗建模可以得到桥臂电感对幅频特性的影响结果,如
桥臂电感对幅频特性的影响
Influence of arm inductance on amplitude-frequency characteristics
由理论分析可知,中频段幅频特性影响的是故障电流的整体上升率,因此随着桥臂电感值的增加,电网端口故障电流将会下降;与架空线直流电网相比,电缆直流电网故障电流对桥臂电感的变化会更敏感。
文献[28]指出故障电流的上升率仅与故障回路电感有关,且成反比关系。例如桥臂电感、平波电抗器等关键参数会直接影响直流电网的等效等值电感。由
高压直流系统中常见故障类型包括单极接地短路、极间短路和单极断线,其中极间短路最严重。文中基于PSCAD/EMTDC中MMC对称单极双端系统的极间短路故障进行仿真验证,系统参数如
对称单极双端直流电网参数
Parameters of the symmetrical monopolar two-terminal DC grid
换流站编号 | 控制方式 |
|
|
|
|
|
|
1 |
|
50 | 10 000 | 1.361 | 200 | 2 | 200 |
2 |
|
50 | 10 000 | 1.361 | 200 | 2 | 200 |
电缆与架空线直流电网故障电流仿真结果比较
Simulation results comparison of fault currents of the DC grid with cables and overhead lines
采用式(9)计算不同长度线路的时延,并与仿真结果对比,结果如
计算时延与仿真时延的对比
Comparison of calculation delay and simulation delay
线路长度/km | 电缆 | 架空线 | |||||
计算时延/ms | 仿真时延/ms | 误差/% | 计算时延/ms | 仿真时延/ms | 误差/% | ||
100 | 0.523 | 0.510 | 2.549 | 0.357 | 0.340 | 5.000 | |
200 | 1.046 | 1.030 | 1.553 | 0.714 | 0.685 | 4.234 | |
300 | 1.569 | 1.545 | 1.553 | 1.070 | 1.030 | 3.883 | |
400 | 2.091 | 2.075 | 1.063 | 1.426 | 1.375 | 3.709 |
不同桥臂电感下的故障电流
Fault currents under different arm inductances
由
文中以依频模型阻尼特性为基础,提出了一种考虑输电线路参数频变特性的直流电网阻抗模型。通过PSCAD/EMTDC仿真验证了所提模型的正确性。同时,基于该模型的幅频特性,对比分析了电缆和架空线直流电网故障电流特性的不同,明确了在直流电网中,对于长度相同、稳态幅频特性接近的电缆和架空线,故障电流特性有如下不同:
(1) 输电线路故障电流存在时延现象,时延时间与线路长度成正比。电缆故障电流的时延时间大于架空线;
(2) 电缆直流电网故障电流的初始上升率和整体幅值高于架空线直流电网;
(3) 与架空线直流电网相比,电缆直流电网故障电流对桥臂电感、平波电抗器等感性关键参数的变化更为敏感。
文中所提模型可准确描述输电线路阻抗特性。基于文中模型,下一步研究将在频域对直流电网故障电流进行定量计算,由此进一步对电缆和架空线的故障电流特性进行定量分析。
陆晶晶, 贺之渊, 赵成勇, 等. 直流输电网规划关键技术与展望[J]. 电力系统自动化, 2019, 43(2): 182-191.
LU Jingjing, HE Zhiyuan, ZHAO Chengyong, et al. Key technologies and prospects for DC power grid planning[J]. Automation of Electric Power Systems, 2019, 43(2): 182-191.
贺之渊, 陆晶晶, 刘天琪, 等. 柔性直流电网故障电流抑制关键技术与展望[J]. 电力系统自动化, 2021, 45(2): 173-183.
HE Zhiyuan, LU Jingjing, LIU Tianqi, et al. Key technologies and prospect of fault current suppression in flexible DC power grid[J]. Automation of Electric Power Systems, 2021, 45(2): 173-183.
叶敏芝, 喻哲扬, 徐政. 欧洲柔性直流电网的规划及其仿真研究[J]. 电力工程技术, 2020, 39(6): 66-75.
YE Minzhi, YU Zheyang, XU Zheng. Planning and simulation research of European VSC-HVDC grid[J]. Electric Power Engineering Technology, 2020, 39(6): 66-75.
陈宗正, 张旭航, 申亚, 等. 基于500 kV长距离电缆线路的合闸过电压研究[J]. 电瓷避雷器, 2021(6): 108-112.
CHEN Zongzheng, ZHANG Xuhang, SHEN Ya, et al. Closing overvoltage based on EHV long-distance cable line[J]. Insulators and Surge Arresters, 2021(6): 108-112.
周远翔, 赵健康, 刘睿, 等. 高压/超高压电力电缆关键技术分析及展望[J]. 高电压技术, 2014, 40(9): 2593-2612.
ZHOU Yuanxiang, ZHAO Jiankang, LIU Rui, et al. Key technical analysis and prospect of high voltage and extra-high voltage power cable[J]. High Voltage Engineering, 2014, 40(9): 2593-2612.
刘伟, 陈皓. 基于分布参数模型的混合线路故障测距新算法[J]. 电力系统保护与控制, 2009, 37(24): 76-80, 132.
LIU Wei, CHEN Hao. A new fault location algorithm for hybrid transmission line based on distributed parameter model[J]. Power System Protection and Control, 2009, 37(24): 76-80, 132.
LI Y J, LI J P, XIONG L S, et al. DC fault detection in meshed MTDC systems based on transient average value of current[J]. IEEE Transactions on Industrial Electronics, 2020, 67(3): 1932-1943.
吕敬, 蔡旭, 张占奎, 等. 海上风电场经MMC-HVDC并网的阻抗建模及稳定性分析[J]. 中国电机工程学报, 2016, 36(14): 3771-3781.
LYU Jing, CAI Xu, ZHANG Zhankui, et al. Impedance modeling and stability analysis of MMC-based HVDC for offshore wind farms[J]. Proceedings of the CSEE, 2016, 36(14): 3771-3781.
吕敬, 蔡旭, 张建文. 模块化多电平换流器的交直流侧阻抗模型[J]. 电力自动化设备, 2017, 37(1): 131-136, 143.
LYU Jing, CAI Xu, ZHANG Jianwen. AC and DC-side impedance models of modular multilevel converter[J]. Electric Power Automation Equipment, 2017, 37(1): 131-136, 143.
SEMLYEN A, DABULEANU A. Fast and accurate switching transient calculations on transmission lines with ground return using recursive convolutions[J]. IEEE Transactions on Power Apparatus and Systems, 1975, 94(2): 561-571.
MARTI J R. Accurate modelling of frequency-dependent transmission lines in electromagnetic transient simulations[J]. IEEE Transactions on Power Apparatus and Systems, 1982, PAS-101(1): 147-157.
GUSTAVSEN B, IRWIN G, MANGELRØD R, et al. Transmission line models for the simulation of interaction phenomena between parallel AC and DC overhead lines[C]//Proceedings of International Conference on Power Systems Transients (IPST 1999), June 20-24, 1999, Budapest, Hungary: 61-67.
GUSTAVSEN B, SEMLYEN A. Rational approximation of frequency domain responses by vector fitting[J]. IEEE Transactions on Power Delivery, 1999, 14(3): 1052-1061.
BEERTEN J, D'ARCO S, SUUL J A. Cable model order reduction for HVDC systems interoperability analysis[C]//11th IET International Conference on AC and DC Power Transmission. Birmingham, UK. Institution of Engineering and Technology, 2015: 1-10.
WEDEPOHL L M, NGUYEN H V, IRWIN G D. Frequency-dependent transformation matrices for untransposed transmission lines using Newton-Raphson method[J]. IEEE Transactions on Power Systems, 1996, 11(3): 1538-1546.
PINTO R T, RODRIGUES S, BAUER P, et al. Operation and control of a multi-terminal DC network[C]//2013 IEEE ECCE Asia Downunder. Melbourne, VIC, Australia. IEEE, 2013: 474-480.
PINARES G, TJERNBERG L B, TUAN L A, et al. On the analysis of the DC dynamics of multi-terminal VSC-HVDC systems using small signal modeling[C]//2013 IEEE Grenoble Conference. Grenoble, France. IEEE, 2013: 1-6.
CHAUDHURI N R, MAJUMDER R, CHAUDHURI B. Stability analysis of VSC MTDC grids connected to multimachine AC systems[C]//2012 IEEE Power and Energy Society General Meeting. San Diego, CA, USA. IEEE, 2012.
KALCON G O, ADAM G P, ANAYA-LARA O, et al. Small-signal stability analysis of multi-terminal VSC-based DC transmission systems[J]. IEEE Transactions on Power Systems, 2012, 27(4): 1818-1830.
BEERTEN J, D'ARCO S, SUUL J A. Frequency-dependent cable modelling for small-signal stability analysis of VSC-HVDC systems[J]. IET Generation, Transmission & Distribution, 2016, 10(6): 1370-1381.
MORCHED A, GUSTAVSEN B, TARTIBI M. A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables[J]. IEEE Transactions on Power Delivery, 1999, 14(3): 1032-1038.
MARTINEZ-VELASCO J A. Power system transients: parameter determination[M]. Boca Raton, FL: CRC Press, 2010.
WIGINGTON R L, NAHMAN N S. Transient analysis of coaxial cables considering skin effect[J]. Proceedings of the IRE, 1957, 45(2): 166-174.
URIBE F A. Calculating mutual ground impedances between overhead and buried cables[J]. IEEE Transactions on Electromagnetic Compatibility, 2008, 50(1): 198-203.
林圣, 武骁, 何正友, 等. 基于行波固有频率的电网故障定位方法[J]. 电网技术, 2013, 37(1): 270-275.
LIN Sheng, WU Xiao, HE Zhengyou, et al. A power system fault location method based on natural frequencies of traveling waves[J]. Power System Technology, 2013, 37(1): 270-275.
TAO Y, LI B H, DRAGICEVIC T, et al. HVDC grid fault current limiting method through topology optimization based on genetic algorithm[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(6): 7045-7055.