Electromagnetic Field Assessment of Indonesian 500-kV Double-Circuit Transmission Lines Using Charge Simulation and Biot-Savart Methods: Validation, Benchmarking, and Configuration Evaluation
DOI:
https://doi.org/10.59247/jfsc.v4i3.424Keywords:
Biot-Savart Law, Charge Simulation Method, Double-Circuit Conductor Configuration, Electromagnetic Field Assessment, Extra-High-Voltage Transmission LinesAbstract
This paper presents a mesh-free computational framework for assessing power-frequency electric and magnetic fields generated by 500-kV, 50-Hz overhead transmission lines in Indonesia. The framework integrates the Charge Simulation Method (CSM) for electric-field calculation and the Biot-Savart (BS) formulation for magnetic-field prediction within a GNU Octave environment. The proposed approach was validated against field measurements and benchmarked against Finite Element Method Magnetics (FEMM) using root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Validation results demonstrated good agreement with measurements, achieving MAPE values of 3.00% and 7.24% for electric-field and magnetic-field predictions, respectively, outperforming FEMM in both cases. Computational benchmarking revealed substantial efficiency improvements, with execution-time reductions of approximately 29-31 times for electric-field calculations and 83-86 times for magnetic-field calculations relative to FEMM. The validated framework was subsequently applied to evaluate three 500-kV double-circuit transmission-line configurations commonly used in Indonesia, namely the super-bundle, low-reactance, and double-delta arrangements. Although all configurations satisfied the exposure limits specified by SNI 04-6950-2003, WHO, and ICNIRP guidelines, significant differences were observed in their electromagnetic-field performance. The double-delta configuration consistently produced the lowest electric-field and magnetic-field levels, reducing peak field exposure by up to 61% and 72%, respectively, compared with the super-bundle arrangement. The proposed CSM-BS framework provides an accurate and computationally efficient tool for transmission-line electromagnetic-field assessment, conductor arrangement assessment, and compliance verification.
References
P. S. R. Murty, Power Systems Analysis, 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall, 2017. https://doi.org/10.1016/B978-0-08-101111-9.00014-8.
M. Iqbal, “Reliability analysis of 20 kV electric power distribution system based on SAIFI, SAIDI, CAIDI, MAIFI, ASAI and ASUI at PT. PLN Rayon Samalanga,” Journal Geuthee of Engineering and Energy (JOGE), vol. 3, no. 2, pp. 71–83, 2024, https://doi.org/10.52626/joge.v3i2.42.
J. Ma, “Growing the power system: Expansions on transmission and distribution systems for deep electrification,” iScience, vol. 28, no. 6, p. 112662, 2025, https://doi.org/10.1016/j.isci.2025.112662.
T. Gönen and Y. Hou, Electrical Power Transmission System Engineering: Analysis and Design, Fourth Edition, 4th ed. CRC Press, 2024, https://doi.org/10.1201/9781003129752.
M. Freire-Gormaly and A. M. Bilton, “Optimization of Renewable Energy Power Systems for Remote Communities,” in Volume 2A: 41st Design Automation Conference, American Society of Mechanical Engineers, 2015, https://doi.org/10.1115/DETC2015-47509.
S. Sikumbang and I. Garniwa, “Optimizing generation costs in electricity supply business plan for electricity companies in Indonesia: A reliability-based approach for the Sumatra power system,” International Journal of Electrical, Computer, and Biomedical Engineering, vol. 3, no. 2, 2025, https://doi.org/10.62146/ijecbe.v3i2.111.
H. Atma, F. Ruzzenenti, and M. A. van den Broek, “Exploring the evolution of long-term electricity demand and load curves in emerging economies: A case study of Indonesia’s energy transition,” Energy Strategy Reviews, vol. 60, p. 101805, 2025, https://doi.org/10.1016/j.esr.2025.101805.
M. Abedin Khan and M. Ghassemi, “Novel designs with optimally placed subconductors to enhance transmission line loadability at 230 kV and 345 kV voltage levels,” Electric Power Systems Research, vol. 253, p. 112583, 2026, https://doi.org/10.1016/j.epsr.2025.112583.
WHO, Extremely Low Frequency Fields, in Environmental Health Criteria Monograph No. 238, Geneva, Switzerland: WHO, 2007, http://www.who.int/peh-emf/publications/Complet_DEC_2007.pdf
International Commission on Non-Ionizing Radiation Protection, “Guidelines for limiting exposure to time-varying electric and magnetic fields (1 Hz TO 100 kHz),” Health Physics, vol. 99, no. 6, pp. 818–836, 2010, https://doi.org/10.1097/HP.0b013e3181f06c86.
P. E. Bubu, V. H. U. Eze, A. E. Adie, M. M. Mustafa, K. J. Ukagwu, and L. K. Alamu, “Simulation and analysis of magnetic fields around High-Voltage power lines using Python for enhanced safety and design insights,” Scientific Reports, vol. 15, no. 1, p. 33975, 2025, https://doi.org/10.1038/s41598-025-11464-2.
K. Karipidis, “Static electric and magnetic field guidelines,” in Non‐ionizing Radiation Protection, Wiley, pp. 357–362, 2017, https://doi.org/10.1002/9781119284673.ch23.
China Electric Power Research Institute, “UHV Transmission Technology,” in UHV Transmission Technology, Amsterdam, Netherlands: Academic Press, pp. 237–293, 2018, https://doi.org/10.1016/c2013-0-15562-6.
R. Sardaro, F. Bozzo, and V. Fucilli, “High-voltage overhead transmission lines and farmland value: Evidences from the real estate market in Apulia, southern Italy,” Energy Policy, vol. 119, pp. 449–457, 2018, https://doi.org/10.1016/j.enpol.2018.05.005.
L. Imbachi and M. Rodriguez, “Strategy to reduce the electric field in transmission lines, modifying the geometry of the tower and its bundle configuration,” in Proceedings of the World Congress on Electrical Engineering and Computer Systems and Science, Barcelona, Spain, 2024 https://doi.org/10.11159/eee24.125.
C. Li et al., “IronPython-Based Automated Computational Platform for 3-D Finite Element Modeling and Electric/Magnetic Field Analysis of Overhead Transmission Lines,” Energies, vol. 19, no. 6, p. 1565, 2026, https://doi.org/10.3390/en19061565.
M. Ren, F. Yin, Y. Fang, J. Chen, and Z. Qin, “Electromagnetic Studies of AC Transmission Lines and Off-Line Personnel,” in 2024 4th International Conference on Energy Engineering and Power Systems, EEPS 2024, pp. 815–820, 2024, https://doi.org/10.1109/EEPS63402.2024.10804338.
P. E. Bubu, V. H. U. Eze, A. E. Adie, M. M. Mustafa, K. J. Ukagwu, and L. K. Alamu, “Simulation and analysis of magnetic fields around High-Voltage power lines using Python for enhanced safety and design insights,” Scientific Reports, vol. 15, no. 1, Sep. 2025, https://doi.org/10.1038/s41598-025-11464-2.
C. Li et al., “3D Finite Element Analysis of Electromagnetic Fields in Transmission Line Crossing Areas Under Different Operating Conditions,” Applied Sciences (Switzerland), vol. 16, no. 7, p. 3425, 2026, https://doi.org/10.3390/app16073425.
X. Spahiu and S. Orhani, “Applications of numerical analysis in computer simulations,” Multidisciplinary Science Journal, vol. 7, no. 8, p. 2025387, 2025, https://doi.org/10.31893/multiscience.2025387.
A. Allal, A. Boubakeur, and A. Mujezinović, “Improved Optimization of the Charge Simulation Method for the Calculatiosn of the Electric Field Around Overhead Transmission Lines Using Statistical Methods,” Engineering, Technology and Applied Science Research, vol. 12, no. 4, pp. 8910–8915, 2022, https://doi.org/10.48084/etasr.5004.
R. Djekidel, S. A. Bessedik, A. Cavallini, B. Bentouati, and R. A. El-Sehiemy, “Optimization of electric field screening effect under EHV overhead transmission lines using hybrid computing CSM-GOA paradigm,” Electrical Engineering, vol. 107, no. 1, pp. 363–381, 2025, https://doi.org/10.1007/s00202-024-02509-2.
M. Abdel-Salam, H. Anis, A. El-Morshedy, and R. Radwan, High-Voltage Engineering, 3rd ed. Boca Raton, FL, USA: CRC Press, 2018. https://doi.org/10.1201/9781482290035.
A. K. Sallabi, J. A. Khaliel, and A. S. Mohamed, “Method of Images to Study the Charge Distribution in Cases of Potentials Deviating from Coulomb’s Law,” Journal of Electromagnetic Analysis and Applications, vol. 06, no. 04, pp. 51–56, 2014, https://doi.org/10.4236/jemaa.2014.64008.
J. R. Riba and M. Moreno-Eguilaz, “Analyzing the effect of corona losses on dynamic line rating models for overhead transmission lines,” International Journal of Electrical Power and Energy Systems, vol. 166, p. 110546, 2025, https://doi.org/10.1016/j.ijepes.2025.110546.
IEEE, “IEEE Recommended Practice for Overhead Transmission Line Design,” IEEE Std 2954-2023, no. IEEE Std 1863-2019. pp. 1–43, 2024. https://doi.org/10.1109/IEEESTD.2020.9086170.
R. S. Widagdo, I. M. Kastiawan, I. S. Tauladan, and I. B. Hermawan, “Voltage Regulation and Power Loss Analysis on 500 kV EHV Transmission Line Krian-Grati,” International Journal of Electrical, Energy and Power System Engineering, vol. 8, no. 1, pp. 40–54, 2025, https://doi.org/10.31258/ijeepse.8.1.40-54.
J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, “GNU Octave Manual, version 11.1.0.” 2026. https://doi.org/10.5555/1502028.
W. Watson, Extra High Voltage AC Transmission Engineering, 4th ed., vol. 33, no. 1. New Delhi, India: New Age International, 1987. https://doi.org/10.1049/ep.1987.0042.
D. Meeker, “Finite Element Method Magnetics, Version 4.2, User’s Manual.” 2006, http://femm.info
S. A. Hanna, Y. Motai, W. Varhue, and S. Titcomb, “Measurement evaluations of static and low frequency magnetic fields in the near field region,” Measurement: Journal of the International Measurement Confederation, vol. 44, no. 8, pp. 1412–1421, 2011, https://doi.org/10.1016/j.measurement.2011.05.008.
D. Baaken, D. Wollschläger, T. Samaras, J. Schüz, and I. Deltour, “Exposure to extremely low-frequency magnetic fields in low- and middle-income countries: an overview,” Radiation Protection Dosimetry, vol. 191, no. 4, pp. 487–500, 2020, https://doi.org/10.1093/rpd/ncaa172.
A.-S. H. Hamza, “Evaluation and measurement of magnetic field exposure over human body near EHV transmission lines,” Electric Power Systems Research, vol. 74, no. 1, pp. 105–118, 2005, https://doi.org/10.1016/j.epsr.2004.10.003.
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