Investigation of Comparison on Optimal Structure of Five-Loop Simplified Scaling Model for Dry-Type Air-Core Reactors
Dai Lingjun1, Zou Liang1, Sun Yuxin1, Liu Qingsong2, Zhang Li1
1. School of Electrical Engineering Shandong University Jinan 250061 China; 2. Maintenance and Test Center CSG EHV Power Transmission Company Guangzhou 510663 China
Abstract The large dry hollow reactor has been widely used in HV and UHV power systems due to its high linearity, low loss, stable parameters, and low resistance. However, with the increase of the voltage level and size of the hollow reactor, the magnetic field will be generated in the surrounding space. It is necessary to establish a scale-down model for predicting the magnetic field distribution of the large hollow reactor in the design stage to provide the theoretical and technical basis for designing and manufacturing of the large hollow reactor. The three-ring simplified model can effectively predict the spatial magnetic field distribution of the hollow reactor, but the accuracy is limited. Therefore, a five-ring simplified scaled model of the dry hollow reactor is proposed, in which the number of turns and position of the coil can be adjusted. According to the structural parameters of the model, the formulas for calculating the spatial magnetic field distribution of the original model and two simplified scaled models are derived. Under the premise of constant coil turns, the influence of coil position on spatial magnetic field distribution is studied, and the function expression of the position parameters of the five rings and the height-to-diameter ratio H/D of the original model is fitted. Comparing the magnetic induction intensity in four specific directions between the original model and the optimal five-ring simplified model, the five-ring simplified model can well simulate the magnetic induction intensity of the original model without considering the effect of equivalent errors in the near-field region. The root means square error (RMSE) and absolute percentage error (MAPE) of the five-ring simplified scaled model were reduced by 18 % and 17 %, respectively, and the coefficient of determination (R2) was increased by 4 % compared with the three-ring simplified model. When the number of turns and the position of the coil can be adjusted, the optimal position and the number of turns of the five rings are determined based on the least square method and the minimum sum of the square losses in each direction. The function expression of the structure parameters of the simplified model of the optimal five rings and the height-to-diameter ratio H/D of the original model is fitted. The five-ring simplified model can not only reduce the magnetic flux leakage, but also reduce the error in the four monitoring directions at the same time. Compared with the three-ring simplified model, the corresponding RMSE and MAPE are reduced by 40 % and 21 %, respectively, and have higher equivalent accuracy. It is found that the RMSE and MAPE corresponding to the optimal structural parameters of the five-ring simplified scaling model are reduced by 21 % and 22 %, respectively, compared with the three-ring simplified scaling model. Therefore, it is proved that the five-ring simplified model has higher prediction accuracy than the three-ring simplified model in magnetic field prediction. The field test measurements are carried out in the converter station. Compared with the measurement data of two simplified scale models, it is also proved that the simplified scale model of five rings has a better equivalent effect of space magnetic field.
Dai Lingjun,Zou Liang,Sun Yuxin等. Investigation of Comparison on Optimal Structure of Five-Loop Simplified Scaling Model for Dry-Type Air-Core Reactors[J]. Transactions of China Electrotechnical Society, 2023, 38(4): 1088-1103.
[1] Wang Yu, Chen Xiaoyue, Pan Zhuohong, et al.Theoretical and experimental evaluation of the tempe-rature distribution in a dry type air core smoothing reactor of HVDC station[J]. Energies, 2017, 10(5): 623. [2] 汪泉弟, 张艳, 李永明, 等. 干式空心电抗器周围工频磁场分布[J]. 电工技术学报, 2009, 24(1): 8-13. Wang Quandi, Zhang Yan, Li Yongming, et al.The power frequency magnetic field distribution around dry-type air-core reactor[J]. Transactions of China Electrotechnical Society, 2009, 24(1): 8-13. [3] 姜志鹏, 周辉, 宋俊燕, 等. 干式空心电抗器温度场计算与试验分析[J]. 电工技术学报, 2017, 32(3): 218-224. Jiang Zhipeng, Zhou Hui, Song Junyan, et al.Tempe-rature field calculation and experimental analysis of dry-type air-core reactor[J]. Transactions of China Electrotechnical Society, 2017, 32(3): 218-224. [4] 宋晗, 邹亮, 张秀群, 等. 基于空间磁场分布的干式空心电抗器匝间短路检测方法[J]. 电工技术学报, 2019, 34(增刊1): 105-117. Song Han, Zou Liang, Zhang Xiuqun, et al.Inter-turn short-circuit detection of dry-type air-core reactor based on spatial magnetic field distribution[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 105-117. [5] 高树国, 汲胜昌, 孟令明, 等. 基于在线监测系统与声振特征预测模型的高压并联电抗器运行状态评估方法[J]. 电工技术学报, 2022, 37(9): 2179-2189. Gao Shuguo, Ji Shengchang, Meng Lingming, et al.Operation state evaluation method of high-voltage shunt reactor based on on-line monitoring system and vibro-acoustic characteristic prediction model[J]. Transactions of China Electrotechnical Society, 2022, 37(9): 2179-2189. [6] Lin Dingsheng, Zhou Ping, Fu Weinong, et al.A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis[J]. IEEE Transactions on Magnetics, 2004, 40(2): 1318-1321. [7] 王革鹏, 金文德, 曾向阳, 等. 特高压并联电抗器铁心振动的分析与控制研究[J]. 电工技术学报, 2022, 37(9): 2190-2198. Wang Gepeng, Jin Wende, Zeng Xiangyang, et al.Analysis and control research on core vibration of UHV shunt reactor[J]. Transactions of China Elec-trotechnical Society, 2022, 37(9): 2190-2198. [8] Cook R D, Malkus D S, Plesha M E, et al.Concepts and applications of finite element analysis[M]. River Street: John Wiley & Sons, 2007. [9] 郑涛, 刘校销. 磁控式并联电抗器容量调节暂态过程及其对匝间保护的影响[J]. 电工技术学报, 2021, 36(5): 1052-1063. Zheng Tao, Liu Xiaoxiao.Power regulation transient process of magnetically controlled shunt reactor and its impact on protection against turn-to-turn faults[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 1052-1063. [10] 毛启武, 曾庆赣. 空心与铁心电抗器工频磁场测量与分析[J]. 高电压技术, 2003, 29(4): 49-50. Mao Qiwu, Zeng Qinggan.Measurement and analysis of power frequency magnetic of air-core and iron-core reactors field[J]. High Voltage Engineering, 2003, 29(4): 49-50. [11] 袁发庭, 吕凯, 刘健犇, 等. 基于电磁-热-结构多物理场耦合的铁心电抗器线圈结构优化方法[J]. 电工技术学报, 2022, 37(24): 6431-6441. Yuan Fating, Lü Kai, Liu Jianben, et al.Coil structures optimization method of iron core reactor based on electromagnetic-thermal-structure multi-physical field coupling[J]. Transactions of China Electrotechnical Society, 2022, 37(24): 6431-6441. [12] Binns K J, Lawrenson P J.Analysis and computation of electric and magnetic field problems: pergamon international library of science, technology, engineering and social studies[M]. 2nd ed. Amsterdam, The Netherlands: Elsevier, 2013. [13] 张鹏宁, 李琳, 聂京凯, 等. 考虑铁心磁致伸缩与绕组受力的高压并联电抗器振动研究[J]. 电工技术学报, 2018, 33(13): 3130-3139. Zhang Pengning, Li Lin, Nie Jingkai, et al.Study on the vibration of high voltage shunt reactor considering of magnetostriction and winding force[J]. Transactions of China Electrotechnical Society, 2018, 33(13): 3130-3139. [14] 聂洪岩, 魏新劳, 姚远航, 等. 热老化对干式空心电力电抗器匝间绝缘操作过电压耐受特性的影响[J]. 电工技术学报, 2020, 35(24): 5096-5104. Nie Hongyan, Wei Xinlao, Yao Yuanhang, et al.Effect of thermal aging on the characteristic to with-stand switching overvoltage of interturn insulation of dry-type air core power reactor[J]. Transactions of China Electrotechnical Society, 2020, 35(24): 5096-5104. [15] Yan Xiuke, Dai Zhongbin, Yu Cunzhan, et al.Research on magnetic field and temperature field of air core power reactor[C]//2011 International Con-ference on Electrical Machines and Systems, Beijing, China, 2011: 1-4. [16] de Abreu Silveira C, da Costa C A, da Costa E Silva R, et al. Electromagnetic environment measurement under steady-state conditions in utility substations[C]//2006 IEEE/PES Transmission & Distribution Con-ference and Exposition, Caracas, Venezuela, 2007: 1-6. [17] Xu Gan, Zou Liang, Zhang Li, et al.Investigation on small-scale experiments of magnetic field around air-core reactors[J]. Applied Mechanics and Materials, 2014, 521: 389-393. [18] 邹亮, 宫攀, 张黎, 等. 干式空心电抗器空间磁场缩比试验与模型简化[J]. 高电压技术, 2014, 40(6): 1675-1682. Zou Liang, Gong Pan, Zhang Li, et al.Small-scale experiment and model simplification of space magnetic fields around air-core reactors[J]. High Voltage Engineering, 2014, 40(6): 1675-1682. [19] Yu Q, Sebo S A.Calculation accuracy of the planar filament current loop stack model of large air-core reactor coils[J]. IEEE Transactions on Magnetics, 1997, 33(5): 3313-3315. [20] Yu Q, Sebo S A.Simplified magnetic field modeling and calculation of large air-core reactor coils[J]. IEEE Transactions on Magnetics, 1996, 32(5): 4281-4283. [21] Han Zhiyun, Zou Liang, Song Han, et al.Study on optimal structure of three-loop simplified scaling model for dry-type air-core reactors[J]. IEEE Access, 2018, 6: 48259-48267. [22] 杜淑文, 宋春燕, 祝春捷, 等. 10kV空心电抗器周围工频磁场的简化计算及影响范围[J]. 高压电器, 2006, 42(3): 179-182. Du Shuwen, Song Chunyan, Zhu Chunjie, et al.Simplified calculation and coverage of power frequ-ency magnetic field around 10kV air-core reactors[J]. High Voltage Apparatus, 2006, 42(3): 179-182. [23] 陈彬, 秦小彬, 万妮娜, 等. 基于R-L型分数阶导数与损耗统计理论的铁磁材料高频损耗计算方法[J]. 电工技术学报, 2022, 37(2): 299-310. Chen Bin, Qin Xiaobin, Wan Nina, et al.Calculation method of high-frequency loss of ferromagnetic materials based on R-L type fractional derivative and loss statistical theory[J]. Transactions of China Elec-trotechnical Society, 2022, 37(2): 299-310. [24] 徐干. 基于缩比简化的干式空心电抗器空间磁场分析与预测[D]. 济南: 山东大学, 2016.
2023, Vol. 38 
