Abstract:The hybrid DC transmission system, which gives full play to the advantages of conventional DC and flexible DC, has become a research hotspot in the fields of long-distance transmission and renewable-energy grid connection. However, HVDC transmission lines are long and the working environment is complex, resulting in high fault probability. Once a short-circuit fault occurs on the DC line, it will generate fault current several times the rated current within 10ms, exposing the whole system to a serious overcurrent risk and threatening the sTab.operation of the system. In addition, the highly nonlinear characteristics of the converter station make the existing short-circuit current solutions ignore the response process of the control system and rely on the modeling and simulation results. It is impossible to obtain the specific analytical formula of the short-circuit current to realize the quantitative analysis and calculation of the fault characteristics, which brings difficulties to the protection and design of DC control systems and restricts the development of hybrid DC transmission technologies. Therefore, considering control response, an approximate calculation method for short-circuit current of multi-terminal hybrid DC transmission systems is proposed. First, three system model simplification measures are proposed, which take into account both accuracy and computational complexity, including port processing, non-fault-pole discharging-loop processing and AC system processing. Second, the system topology model and control model are modeled. Based on the fault-component network, the short-circuit current is obtained regardless of the action of the control system, and then the corrected current under the control action is obtained by using this calculation result. The two are superimposed to obtain the final complex frequency domain analytical formula for the short-circuit current, and the inverse Laplace transform is used to obtain the time-domain solution for the short-circuit current. The proposed method corrects the trigger angle of the LCC side, using Pade approximation and piecewise linearization method to reasonably reduce the order of short-circuit current model, which takes into account the calculation accuracy and efficiency, to effectively avoid the problem that the inverse Laplace transform cannot be solved due to the high order of complex frequency domain expression. Finally, based on PSCAD/EMTDC, the simulation analysis on different fault distances, transition resistance and fault types is carried out. It can be concluded that, the proposed method can accurately describe the transient characteristics and trend of the fault current at the outlet of each converter station before the blocking of the MMC station, obtaining the analytical expression of the fault current which provides a quantitative calculation method of fault current for power grid planning, equipment parameter selection and protection setting. In addition, the transient current increment considering the control characteristics of the converter station is less than that without considering the control characteristics. Therefore, the fault transient characteristics can be quickly analyzed and judged by using the fault current calculation results without considering the control. Finally, it can be concluded that, in terms of calculation efficiency, the proposed method does not have the problem of excessive computational complexity due to the order reduction. The calculation error is mainly related to the factors neglected or simplified in the calculation process, including the approximate equivalent processing of the model, the approximate fitting process of the waveform and the accuracy reserved when the intermediate variables are obtained, but the overall relative error is still controlled within 10% to meet the accuracy requirements of fault current calculation.
李杭泽, 戴志辉, 石旭, 杨明玉. 计及控制响应的多端混合直流输电系统短路电流近似计算方法[J]. 电工技术学报, 2024, 39(9): 2810-2824.
Li Hangze, Dai Zhihui, Shi Xu, Yang Mingyu. Approximate Calculation Method of Short-Circuit Current of Multi-Terminal Hybrid DC Transmission System Considering Control Strategy. Transactions of China Electrotechnical Society, 2024, 39(9): 2810-2824.
[1] 贺永杰, 向往, 周家培, 等. LCC-MMC串联型混合直流输电系统小信号建模[J]. 电工技术学报, 2021, 36(7): 1492-1506. He Yongjie, Xiang Wang, Zhou Jiapei, et al.Small-signal modelling of LCC-MMC series hybrid HVDC transmission system[J]. Transactions of China Electrotechnical Society, 2021, 36(7): 1492-1506. [2] Dai Zhihui, Liu Ningning, Zhang Cheng, et al.State-space analysis based pole-to-ground line fault isolation strategy for LCC-HVDC systems[J]. IET Generation, Transmission & Distribution, 2019, 13(10): 1933-1941. [3] 苏见燊, 郭敬东, 金涛. 柔性直流电网中直流故障特性分析及线路故障重启策略[J]. 电工技术学报, 2019, 34(增刊1): 352-359. Su Jianshen, Guo Jingdong, Jin Tao.DC fault characteristics and line fault recovery strategy in flexible DC power network[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 352-359. [4] 郝亮亮, 李伟杰, 王卓雅, 等. MMC-HVDC电网输电线路双极短路故障电流的实用计算[J]. 电力系统自动化, 2020, 44(5): 68-76. Hao Liangliang, Li Weijie, Wang Zhuoya, et al.Practical calculation for bipolar short-circuit fault current of transmission line in MMC-HVDC grid[J]. Automation of Electric Power Systems, 2020, 44(5): 68-76. [5] 王子文, 张英敏, 刘天琪, 等. 基于伴随网络的直流电网短路电流计算方法[J]. 中国电力, 2021, 54(10): 2-10, 27. Wang Ziwen, Zhang Yingmin, Liu Tianqi, et al.A short-circuit current calculation method based on adjoint network for DC grid[J]. Electric Power, 2021, 54(10): 2-10, 27. [6] 彭宇锋, 张英敏, 李俊松, 等. 考虑线路电容的MMC-HVDC系统直流接地故障电流计算方法[J]. 电力系统保护与控制, 2020, 48(23): 57-63. Peng Yufeng, Zhang Yingmin, Li Junsong, et al.Ground fault current calculation method for an MMC-HVDC system considering line capacitance[J]. Power System Protection and Control, 2020, 48(23): 57-63. [7] 袁敏, 茆美琴, 程德健, 等. 主电路参数对MMC-HVDC电网直流短路故障电流综合影响分析[J]. 中国电力, 2021, 54(10): 11-19. Yuan Min, Mao Meiqin, Cheng Dejian, et al.Analysis of comprehensive influence of main circuit parameters on DC short circuit fault current of MMC-HVDC grid[J]. Electric Power, 2021, 54(10): 11-19. [8] Langwasser M, De Carne G, Liserre M, et al.Improved fault current calculation method for pole-to-pole faults in MMC multi-terminal HVDC grids considering control dynamics[C]//2018 IEEE Energy Conversion Congress and Exposition (ECCE), Portland, OR, USA, 2018: 5529-5535. [9] 王彤, 孙奕, 裴林, 等. 考虑控制系统的LCC-HVDC直流电流暂态特性分析与交流短路电流近似解析方法[J]. 中国电机工程学报, 2022, 42(23): 8509-8523. Wang Tong, Sun Yi, Pei Lin, et al.Analysis of DC current transient characteristics of LCC-HVDC considering control system and approximate analytical method of AC short-circuit current[J]. Proceedings of the CSEE, 2022, 42(23): 8509-8523. [10] 尹太元, 王跃, 段国朝, 等. 基于零直流电压控制的混合型MMC-HVDC直流短路故障穿越策略[J]. 电工技术学报, 2019, 34(增刊1): 343-351. Yin Taiyuan, Wang Yue, Duan Guozhao, et al.Zero DC voltage control based DC fault ride-through strategy for hybrid modular multilevel converter in HVDC[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 343-351. [11] 辛业春, 刘熠, 江守其, 等. 计及零直流电压控制的混合型MMC-HVDC输电系统短路电流计算方法[J]. 电网技术, 2023, 47(7): 2820-2828. Xin Yechun, Liu Yi, Jiang Shouqi, et al.Short-circuit current calculation method for FHMMC-HVDC transmission systems with zero DC voltage control[J]. Power System Technology, 2023, 47(7): 2820-2828. [12] 李海锋, 许灿雄, 梁远升, 等. 计及换流站控制特性的多端混合直流输电系统故障暂态计算方法[J]. 中国电机工程学报, 2023, 43(4): 1426-1438. Li Haifeng, Xu Canxiong, Liang Yuansheng, et al.Fault transient calculation method for multi-terminal hybrid HVDC systems considering control characteristics of converter station[J]. Proceedings of the CSEE, 2023, 43(4): 1426-1438. [13] Rao Hong, Zhou Yuebin, Xu Shukai, et al.Key technologies of ultra-high voltage hybrid LCC-VSC MTDC systems[J]. CSEE Journal of Power and Energy Systems, 2019, 5(3): 365-373. [14] 耿学锋, 何赟泽, 王广鑫, 等. IGBT关断时刻的应力波测量优化及影响因素分析[J]. 电工技术学报, 2022, 37(21): 5503-5512. Geng Xuefeng, He Yunze, Wang Guangxin, et al.Measurement optimization and analysis of influencing factors of IGBT’s turn-off stress wave[J]. Transactions of China Electrotechnical Society, 2022, 37(21): 5503-5512. [15] Beddard A, Sheridan C E, Barnes M, et al.Improved accuracy average value models of modular multilevel converters[J]. IEEE Transactions on Power Delivery, 2016, 31(5): 2260-2269. [16] 樊强, 俞永杰, 夏嘉航, 等. 低容值半桥型模块化多电平变换器直流故障辅助清除策略[J]. 电工技术学报, 2022, 37(14): 3713-3722. Fan Qiang, Yu Yongjie, Xia Jiahang, et al.Auxiliary strategy for DC fault clearing of low capacitance half-bridge modular multilevel converter[J]. Transactions of China Electrotechnical Society, 2022, 37(14): 3713-3722. [17] 辛业春, 罗鑫, 王拓, 等. 计及过渡电阻影响的直流电网不同拓扑结构故障电流简化计算方法[J]. 电网技术, 2023, 47(2): 804-817. Xin Yechun, Luo Xin, Wang Tuo, et al.Simplified calculation method of fault current in different topological structures of DC grid considering the influence of transition resistance[J]. Power System Technology, 2023, 47(2): 804-817. [18] 高本锋, 王刚, 刘毅, 等. LCC-HVDC送端电网等值方案研究[J]. 电工技术学报, 2021, 36(15): 3250-3263, 3271. Gao Benfeng, Wang Gang, Liu Yi, et al.Study on equivalence method of AC system in sending-end of LCC-HVDC[J]. Transactions of China Electrotechnical Society, 2021, 36(15): 3250-3263, 3271. [19] 姚骏, 谭义, 裴金鑫, 等. 模块化多电平变流器高压直流输电系统直流故障改进控制策略[J]. 电工技术学报, 2018, 33(14): 3306-3318. Yao Jun, Tan Yi, Pei Jinxin, et al.Improved control strategy for DC fault in modular multi-level converter-HVDC system[J]. Transactions of China Electrotechnical Society, 2018, 33(14): 3306-3318. [20] Langwasser M, De Carne G, Liserre M, et al.Fault Current estimation in multi-terminal HVDC grids considering MMC control[J]. IEEE Transactions on Power Systems, 2019, 34(3): 2179-2189. [21] 余修勇, 顾菊平, 张新松, 等. 多端柔性直流电网线路故障暂态等值电路及暂态特征分析[J]. 中国电机工程学报, 2023, 43(24): 9546-9557. Yu Xiuyong, Gu Juping, Zhang Xinsong, et al.Study on the transient equivalent circuits and the transient characteristics of multi-terminal flexible DC grids after line faults[J]. Proceedings of the CSEE, 2023, 43(24): 9546-9557. [22] 汤兰西, 董新洲. MMC直流输电网线路短路故障电流的近似计算方法[J]. 中国电机工程学报, 2019, 39(2): 490-498, 646. Tang Lanxi, Dong Xinzhou.An approximate method for the calculation of transmission line fault current in MMC-HVDC grid[J]. Proceedings of the CSEE, 2019, 39(2): 490-498, 646. [23] 邓文军, 刘麒麟, 张英敏, 等. 张北柔直电网单极接地故障短路电流计算方法及接地策略[J]. 高电压技术, 2022, 48(10): 4050-4059. Deng Wenjun, Liu Qilin, Zhang Yingmin, et al.Short circuit current calculation method and grounding strategy of pole-to-ground fault in Zhangbei flexible DC power grid[J]. High Voltage Engineering, 2022, 48(10): 4050-4059. [24] Li Chengyu, Zhao Chengyong, Xu Jianzhong, et al.A pole-to-pole short-circuit fault current calculation method for DC grids[J]. IEEE Transactions on Power Systems, 2017, 32(6): 4943-4953. [25] 高飘, 郑晓冬, 晁晨栩, 等. 基于控制特征量响应的多端柔性直流输电线路保护[J]. 电力系统自动化, 2022, 46(5): 122-131. Gao Piao, Zheng Xiaodong, Chao Chenxu, et al.Protection for multi-terminal flexible DC transmission lines based on response of control characteristics[J]. Automation of Electric Power Systems, 2022, 46(5): 122-131. [26] 吴通华, 戴魏, 李新东, 等. 基于数值拉普拉斯逆变换的MMC-HVDC故障电流计算[J]. 电力工程技术, 2022, 41(5): 40-49. Wu Tonghua, Dai Wei, Li Xindong, et al.Calculation of fault current in MMC-HVDC based on numerical inverse Laplace transform[J]. Jiangsu Electrical Engineering, 2022, 41(5): 40-49. [27] 陈玉林, 张杰, 黄涛, 等. 高压直流输电线路行波色散及行波测距研究[J]. 电气技术, 2021, 22(12): 8-13. Chen Yulin, Zhang Jie, Huang Tao, et al.Research on traveling wave dispersion and fault location for high voltage direct current transmission lines[J]. Electrical Engineering, 2021, 22(12): 8-13. [28] Xie Zhongrun, Li Bin, He Jiawei, et al.Hybrid HVDC system fault transient analysis considering traveling wave propagation and converter control response[J]. International Journal of Electrical Power & Energy Systems, 2023, 147: 108794.