隨著電力系統的發展，人們對於電力品質監控的需求日益增加。然而，以往架空線路電流的量測方法存在著操作複雜、高觸電風險等問題。此外，即使已經有新的無接觸式的電流量測方法被提出，但通常是假定電纜為理想的長直導體，並不能反應出真實現場量測情況。為了解決這些問題，本研究基於非接觸式感測器陣列量測技術，使用三顆三軸隧道磁阻(tunneling magnetoresistance, TMR)感測器組成的垂直陣列來量測空間磁場分布，並搭配設計的電流演算法即可實現非接觸式電流量測。而演算法中的磁場模型考慮了電纜垂降幅度參數的影響，可使電流量測技術可用於實際架空線現場量測。
本研究在MATLAB中建構了加拿大架空線系統，觀察實際架空線垂降幅度對地平面磁場分布的影響，來設計三相電流演算法與感測器擺放位置。為了進一步評估該技術的性能，本研究對多個實驗數據進行計算，以評估該技術在五種電流演算法方面的表現。實驗結果表明，該技術可以實現高準確度的電流量測，同時具有良好的穩定性和可靠性。量測誤差可以達到10 %以下，並且可以實現即時量測。
最終，本研究採用LabVIEW結合MATLAB來研製一智慧型電流量測平台。此平台可擷取三顆三軸TMR感測器量測到的架空線電流之空間磁場，並搭配演算法所建構的量測流程，即可準確檢測架空線三相電流有效值與相位。未來，可以進一步應用這種技術來進行線路故障檢測和預警，以及對電力系統進行智能化管理和控制。此外，該技術也將繼續進行改良和優化，以滿足不斷增長的電力監控需求。

With the development of the power system, the demand for monitoring the quality of electricity is increasing. However, the previous methods of measuring the current of overhead lines had problems such as complicated operation and high risk of electric shock. Additionally, even with new non-contact current measurement methods, they often assume the cable is an ideal long straight conductor and cannot reflect the actual measurement situation on site. To solve these problems, this study uses non-contact sensor array measurement technology based on a vertical array composed of three-axis tunneling magnetoresistance sensors to measure the spatial magnetic field distribution. Combined with the designed current algorithm, non-contact current measurement can be achieved. The magnetic field model in the algorithm considers the influence of the cable sag parameter, making the current measurement technology applicable to actual field measurement of overhead lines.
This study constructed a Canadian overhead line system in MATLAB to observe the effect of actual overhead line sag on the distribution of the magnetic field on the ground and design the three-phase current algorithm and sensor placement. To further evaluate the performance of this technology, multiple sets of experimental data were calculated to evaluate the performance of this technology in five current algorithm aspects. The experimental results show that this technology can achieve high accuracy current measurement, while also having good stability and reliability. The measurement error can be below 10%, and real-time measurement can be achieved.
Finally, this study used LabVIEW combined with MATLAB to develop an intelligent current measurement platform. This platform can capture the spatial magnetic field of overhead line current measured by three-axis TMR sensors, and combined with the measurement process constructed by the algorithm, accurately detect the effective value and phase of the three-phase current of overhead lines. In the future, this technology can be further applied to line fault detection and warning, as well as intelligent management and control of the power system. Additionally, this technology will continue to be improved and optimized to meet the growing demand for power monitoring.

參考文獻
[1] S. Xie, Y. Zhang, H. Yang, H. Yu, Z. Mu, C. Zhang, S. Cao, X. Chang, and R. Hua, “Application of integrated optical electric-field sensor on the measurements of transient voltages in AC high-voltage power grids,” Appl. science, vol. 9, no. 9, pp. 1951, May. 2019.
[2] H. Wang, C. Zhuang, R. Zeng, S. Xie, and J. He, “Transient voltage measurements for overhead transmission lines and substations by metal free and contactless integrated electro-optic field sensors,” IEEE Trans. Industrial Electronics, vol. 66, no. 1, pp. 571-579, Jan. 2019.
[3] H. Liang, B.X. Du, and L. Jin, “Non-intrusive measurement of transient electric field distribution under AC and impulse voltages,” IEEE Sensors Journal, vol. 20, no.18, Spet. 2020.
[4] B. Li, C. Li, B. Li, and W. Wen, “Real-time and contactless initial current traveling wave measurement for overhead transmission line fault detection based on tunnel magnetoresistive sensors,” Electric Power Systems Research, vol 187, Oct. 2020, art. no. 106508.
[5] Đ. Lekić, P. Mršić, B. Erceg, Č. Zeljković, N. Kitić, and P. Matić, “Laboratory setup for fault detection on overhead power lines based on magnetic field measurement,” in Proc. 2020 International Symposium on Industrial Electronics and Applications (INDEL), Banja Luka, Bosnia and Herzegovina, Nov. 2020.
[6] P. Yang, X. Wen, Z. Chu, X. Ni, and C. Peng, “AC/DC fields demodulation methods of resonant electric field microsensor,” Micromachines, vol. 11, no. 5, May 2020.
[7] H. Wang, R. Zeng, C. Zhuang, G. Lyu, J. Yu, B. Niu, and C. Li, “Measuring AC/DC hybrid electric field using an integrated optical electric field sensor,” Electric Power Systems Research, vol. 179, Feb. 2020, art. no. 106087.
[8] F. A. Viawan, J. Wang, Z. Wang, and W. Y. Yang, “Effect of current sensor technology on distance protection,” in Proc. IEEE/PES Power Systems Conference and Exposition, Seattle, WA, USA, Mar. 2009.
[9] J. Li and J. Liang, “A new method for current measurement of overhead lines,” in Proc. 2011 International Conference on Advanced Power System Automation and Protection, Beijing, China, Oct. 2011.
[10] Y. Yang, D. Divan, R. G. Harley, and T. G. Habetler, “Design and implementation of power line sensornet for overhead transmission lines,” in Proc. IEEE Power & Energy Society General Meeting, Calgary, AB, Canada, Jul. 2009.
[11] R. Moghe, Y. Yang, F. Lambert, and D. Divan, “Design of a low cost self powered “stick-on” current and temperature wireless sensor for utility assets,” in Proc. 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, USA, Sept. 2010.
[12] R. Moghe, F. Lambert, and D. Divan, “A novel low-cost smart current sensor for utility conductors,” IEEE Trans. Smart Grid, vol. 3, no. 2, pp. 653–663, Jun. 2012.
[13] X. Liu, W. He, and Z. Xu, “Non-contact current measurement method for multiconductor systems based on tunnel magnetoresistance sensor array,” in Proc. 2022 IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control ( SDPC), Chongqing, China, Oct. 2022.
[14] 江昭皚，劉志文，梁瑜庭，陳家榜，莊欽龍，王景儀，「感測裝置及應用該感測裝置之輸電線路監測系統」，中華民國專利，TW I542105，2016。
[15] 江昭皚，鄭翔耀，王健豪，楊育誠，曾靖雅，「感測裝置及應用該感測裝置之輸電線路監測系統」，中華民國專利，TW I612314，2018。
[16] W. Z. Fan, “A novel transducer to replace current and voltage transformers in high-voltage measurements,” IEEE Trans. Instrumentation and Measurement, vol. 45, no. 1, pp. 190–194, Jan. 1996.
[17] L. D. Rienzo, R. Bazzocchi, and A. Manara, “Circular arrays of magnetic sensors for current measurement,” IEEE Trans. Instrumentation and Measurement, vol. 50, no. 5, pp. 1093–1096, Oct. 2001.
[18] T. Sorensen, Current measurement device, U.S. Patent 6717397 B2, Apr. 6, 2004.
[19] M. Blagojević, U. Jovanović, I. Jovanović, D. Mančić, and R. S. Popović, “Realization and optimization of bus bar current transducers based on Hall effect sensors,” Meas. Sci. Technol., vol. 27, no. 6, May 2016, art. no. 065102.
[20] R. Weiss, R. Makuch, A. Itzke, and R. Weigel, “Crosstalk in circular arrays of magnetic sensors for current measurement,” IEEE Trans. Industrial Electronics, vol. 64, no. 6, pp. 4903–4909, Feb. 2017.
[21] M. Chiampi, G. Crotti, and A. Morando, “Evaluation of flexible Rogowski coil performances in power frequency applications,” IEEE Trans. Instrumentation and Measurement, vol. 60, no.3, pp. 854–862, Aug. 2010.
[22] R. F. Brooks and T. J. Miller, Flexible circuit Rogowski coil, U.S. Patent 9408298 B2, Aug. 2, 2016.
[23] P. R. Watekar, S. Ju, S. A. Kim, S. Jeong, Y. Kim, and W. T. Han, “Development of a highly sensitive compact sized optical fiber current sensor,” Opt. Exp., vol. 18, pp. 17096–17105, Aug. 2010.
[24] G. M. Muller, W. Quan, M. Lenner, L. Yang, A. Frank, and K. Bohnert, “Fiber-optic current sensor with self-compensation of source wavelength changes,” Opt. Lett., vol. 41, no. 12, pp. 287–2870, 2016.
[25] B. Niu, L. Yao, J. R. Li, S. Wang, and Jin Wang, “Development of monitoring system for lightning current waveforms of transmission lines based on flexible Rogowski coil,” in Proc. 2014 International Conference on in High Voltage Engineering and Application (ICHVE), Poznan, Poland, Sept. 2014.
[26] Y. Jun, G. Li, H. Liu, G. Yang, and G. Ling, “Design of a flexible rogowski coil with active integrator applied in lightning current collection,” in Proc. 2016 International Conference on Lightning Protection (ICLP), Estoril, Portugal, Dec. 2016.
[27] L. Cui, Y. Cao, H. Guo, C. Wang, and Q. Guo, “A flexible self–integrating lightning current sensor based on a Rogowski coil,” Revista de la Facultad de Ingeniería, vol. 32, no. 10, pp. 332–339, Nov. 2017.
[28] Y. R. Chen, K. L. Chen, Y. P. Tsai, and N. Chen, “The wireless transmission design of a novel electronic current transformer,” in Proc. 2013 12th International Conference on Environment and Electrical Engineering, Wroclaw, Poland, May 2013.
[29] S. Lin, P. Gao, and W. Xu, “Zero sequence power line current measurement by using magnetic field sensor array,” International Transactions on Electrical Energy Systems, Apr. 2014.
[30] P. Gao, “Power system current measurement using sensor array techniques,” University of Alberta, Doctoral Thesis, 2018.
[31] A. Z. E. Dein, “Magnetic-field calculation under EHV transmission lines for more realistic Cases,” IEEE Trans. Power Delivery, vol. 24, no. 4, pp. 2214–2222, Oct. 2009.
[32] K. Yamabuki, N. Nagaoka, and A. Ametani, “Contactless surge sensor using a distributed closed loop detector,” IEE Proceedings - Generation, Transmission and Distribution, vol. 146, no. 2, pp. 101–106, Mar. 1999.
[33] N. P. Tobin, M. McCormack, E. O'Loughlin, and K. Tobin, “Remote current sensing on overhead power lines,” in Proc. 2001 International Conference and Exhibition on Electricity Distribution, Amsterdam, Netherlands, Jun. 2001.
[34] N. P. Tobin, Apparatus and method for remote current sensing, U.S. Patent 6727682 B1, Apr. 27, 2004.
[35] K. T. Selvaa, O. A. Forsbergb, D. Merkoulovab, F. Ghasemifardb, N. Taylorb, and M. Norgrenb, “Non-contact current measurement in power transmission lines,” Procedia Technology, vol. 21, pp. 498–506, 2015.
[36] X. Sun, Q. Huang, Y. Hou, L. J. Jiang, and P. W. T. Pong, “Noncontact operation-state monitoring technology based on magnetic-field sensing for overhead high-voltage transmission lines,” IEEE Trans. Power Delivery, vol. 28, no. 4, pp. 2145–2153, Oct. 2013.
[37] X. Sun, Q. Huang, L. J. Jiang, and P. W. T. Pong, “Overhead high-voltage transmission-line current monitoring by magnetoresistive sensors and current source reconstruction at transmission tower,” IEEE Trans. Magnetics, vol. 50, no. 1, Oct. 2014, art. no. 4000405.
[38] X. Sun, K. S. Lui, K. K. Y. Wong, W. K. Lee, Y. Hou, Q. Huang, and P. W. T. Pong, “Novel application of magnetoresistive sensors for high-voltage transmission-line monitoring,” IEEE Trans. Magnetics, vol. 47, no. 10, pp. 2608–2611, Oct. 2011.
[39] A. H. Khawaja, Q. Huang, J. Li, and Z. Zhang, “Estimation of current and sag in overhead power transmission lines with optimized magnetic field sensor array placement,” IEEE Trans. Magnetics, vol. 53, no. 5, May 2017, art. no. 6100210.
[40] A. H. Khawaja and Q. Huang, “Estimating sag and wind-induced motion of overhead power lines with current and magnetic-flux density measurements,” IEEE Trans. Instrumentation and Measurement, vol. 66, no. 5, pp. 897–909, May 2017.
[41] J. Wu, Z. Chen, C. Wang, and L. Hao, “A novel low-cost multicoil-based smart current sensor for three-phase currents sensing of overhead conductors,” IEEE Trans. Power Delivery, vol. 31, no. 6, pp. 2443–2452, Dec. 2016.
[42] 馬嘯宇，「架空線電流非接觸式量測方法研究」，中國福州大學碩士論文，2020。
[43] M. Mukherjee, R. G. Olsen, and Z. Li, “Non-contact monitoring of overhead transmission lines using space potential phasor measurements,” IEEE Trans. Instrumentation and Measurement, vol. 69, no. 10, pp.7494–7504, Oct. 2020.
[44] S. Z. Malik, A. H. Khawaja, A. K. Janjua, and M. Kazim, “A contactless method for unbalanced loading detection in power distribution lines by magnetic measurements,” IEEE Trans. Instrumentation and Measurement, vol. 69, no. 10, pp. 7472–7483, Oct. 2020.
[45] X. Wang, H. Du, Z. Liang, L. Guo, J. Gao, M. Kheshti, and W. Liu, “Single phase to ground fault location method of overhead line based on magnetic field detection and multicriteria fusion,” International Journal of Electrical Power & Energy Systems, vol. 145, Feb. 2023, art. no. 108699.
[46] A. Hatibovic, P. Kádár, and G. Morva, “Comparison of the length of the catenary curve and its parabolic approximation in the span of an overhead line,” in Proc.2020 IEEE 3rd International Conference and Workshop in Óbuda on Electrical and Power Engineering (CANDO-EPE), Budapest, Hungary, Nov. 2020.
[47] 王家倫，「架空線之智慧型電流量測平台研製」，國立臺灣海洋大學電機工程學系碩士論文，2021。
[48] J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proc. International Conference on Neural Networks, Perth, WA, Australia, Nov. 1995.