Meshless Methods for Computation of Overhead Transmission Lines Electromagnetic Fields

Ribeiro, G. C.; Coppoli, E. H. R.; Paganotti, A. L.; Ortiz, L. A. G.

doi:10.1590/2179-10742021v20i21094

G. C. Ribeiro

Department of Electrical Engineering, Centro Federal de Educação Tecnológica de Minas Gerais – CEFET-MG, Belo Horizonte, Brazil, gustavociroribeiro@hotmail.com, coppoli@cefetmg.br, paganotti@cefetmg.br

https://orcid.org/0000-0002-5138-4337

E. H. R. Coppoli

Department of Electrical Engineering, Centro Federal de Educação Tecnológica de Minas Gerais – CEFET-MG, Belo Horizonte, Brazil, gustavociroribeiro@hotmail.com, coppoli@cefetmg.br, paganotti@cefetmg.br

https://orcid.org/0000-0002-2846-4523

A. L. Paganotti

Department of Electrical Engineering, Centro Federal de Educação Tecnológica de Minas Gerais – CEFET-MG, Belo Horizonte, Brazil, gustavociroribeiro@hotmail.com, coppoli@cefetmg.br, paganotti@cefetmg.br

https://orcid.org/0000-0002-7318-749X

L. A. G. Ortiz

Department of Electrical Engineering, Universidade Federal de Minas Gerais - UFMG, Belo Horizonte, Brazil, luillyalejandrogo@ufps.edu.co

https://orcid.org/0000-0001-5167-2585

Data	TL Hydro-Québec
Average Current	4.68 kA
Operating Voltage	500 kV
Number of Phases	3
Number of Conductors per Phase	5
Geometric Mean Radius (GMR)	0.40 m
Conductors Radius	25.16 mm
Conductors Type	CAA Grosbeak
Phase Distance	5.84 m
Height of Measurement Point Above Ground Level	1 m
Vertical Spacing Between Center of Phase A and Ground	10.848 m
Vertical Spacing Between Center of Phase B and Ground	12.891 m
Vertical Spacing Between Center of Phase C and Ground	10.848 m

Magnetic Flux Density		Error Calculation
Analytical	EFGM	Global Error	Relative Error
71.2 μT	68.38 μT	1.47 %	4.2 %

Electric Field		Error Calculation
Analytical	EFGM	Global Error	Relative Error
10.0 kV/m	10.5 kV/m	0.9 %	1.3 %

Magnetic Field			Error Calculation
Analytical	2 points EFGM	4 points EFGM	Relative Error 2 Gauss point	Relative Error 4 Gauss points
71.2 μT	68.38 μT	65.72 μT	7.7 %	4.2 %

Data	TL Furnas
Average Current	675.23 A
Operating Voltage	525 kV
Number of Phases	3
Number of Conductors per Phase	4
Geometric Mean Radius (GMR)	0.35 m
Conductors Radius	31.96 mm
Conductors Type	CAA Ruddy
Phase Distance	7.5 m
Height of Measurement Point Above Ground Level	1 m
Vertical Spacing Between Center of Phase A and Ground	17.975 m
Vertical Spacing Between Center of Phase B and Ground	25.475 m
Vertical Spacing Between Center of Phase C and Ground	17.975 m

Electric Field		Error Calculation
Analytical	EFGM	Global Error	Relative Error
4.42 kV/m	4.14 kV/m	4.79 %	6.3 %

Item	FEM	EFGM
Configuration	Mesh Generation	Node Generation
Shape function	Pre-defined elements	Local support domains
Discretized system	Banded, symmetric	Banded, symmetric
Imposition of essential Boundary condition	Standard and easy	Standard and easy
Adaptive analysis	Difficult for 3D cases	Easier
Commercial software packages availability	Many	Few
Accuracy	Accurate compared to Finite Difference Method (FDM)	More accurate than FEM in some cases
Computation speed	Fast	Slower (not optimized)
Stage of development	Well developed	With many challenging problems

\sum_{i = 1}^{n} {ωi}_{} {\sum_{j = 1}^{n} [\int_{Ω}^{} (\nabla Φ_{j} \nabla Φ_{i} A_{j}) \partial Ω + \int_{Γ_{t}}^{} (Φ_{i} \overset{ˇ}{t}) \partial Γ - {\int_{Ω}^{} J_{s} (t) Φ}_{i} \partial Ω]} = 0.

\sum_{i = 1}^{n} ω_{i} {\sum_{j = 1}^{n} [\int_{Ω}^{} (\nabla Φ_{j} β \nabla Φ_{i} U_{j}) \partial Ω + \int_{Γ_{t}}^{} (Φ_{i} \overset{ˇ}{t}) \partial Γ]} = 0 \forall ω \in H^{1}

Meshless Methods for Computation of Overhead Transmission Lines Electromagnetic Fields

Abstract