Computation of the Capacitive Coupling in Conductors ... - IEEE Xplore

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Conductors Installed nearby AC Power Lines. A. H. Al-Badi, Member, IEEE, and M. A. Salam, Member, IEEE. Abstract-In this paper, a finite element computer ...
Computation of the Capacitive Coupling in Conductors Installed nearby AC Power Lines A. H. Al-Badi, Member, IEEE, and M. A. Salam, Member, IEEE

Abstract- In this paper, a finite element computer model was built to compute the capacitive coupling component produced on unburied pipeline installed nearby AC power transmission lines. Moreover, an experimental reduced-scale rig was also built to verify the computer modeling approach. A good correlation between the experimental and software based simulated results is obtained which validates the modeling approach of coupling between power transmission line and unburied pipeline. Index Terms--Capacitive, Coupling Interference, Element Analysis, Pipelines, Power Transmission Lines.

Finite

I. INTRODUCTION

A C interference caused by high voltage overhead power

fault conditions when the pipe is placed parallel with threephase overhead transmission lines. AC interference from high voltage ac power lines can be hazard for personal and public that may be in contact or in proximity with a pipeline which is within the right-of-way of high voltage power lines. Moreover, the integrity of the pipeline coating and corrosion mitigation effectiveness may be compromised if the levels of steady-state or fault interference are high. Excessive coating stress voltages (the difference between the pipe steel potential and local soil potential) can lead to degradation of the coating, resulting in an accelerated corrosion. To reduce the effects of the AC interference levels to acceptable limits according to NACE standard RP-01-77-95 [10] and ANSI/IEEE Standards 80 [11], mitigation system should be designed [5]. This paper presents a finite element computer model that can be used to find the capacitive coupling between an overhead transmission lines and nearby conductor such as pipeline. The results of the computer model were verified experimentally. Good correlation between the experimental and software based simulated results is obtained which validates the modeling approach of coupling between power transmission line and unburied pipeline.

transmission lines on non-energized conductors such as pipeline, communication line, railway or other metallic circuit sharing a common corridor with the electric lines is a serious concern because it can result in electric shock and can threaten the integrity of the utility lines [1-9]. The likelihood of interference increases with increasing overhead line current, with increasing quality of the coating on the pipeline, and with the length of pipeline parallel to and close to the transmission lines. The electromagnetic interference between a power system network and II. FINITE ELEMENT ANALYSIS neighboring gas pipeline has been traditionally [1] divided into three categories: capacitive (electrostatic), conductive SLIM is a finite element software package [12] which can (resistive) and inductive (magnetic) coupling. The first is the solve a wide range of electromagnetic field problems over a capacitive interference, which is generated by electric field spectrum of frequencies from DC to GHz. of any complex and occurs when the pipe is placed on a foundation that is geometries by considering boundary conditions and material well insulated from ground. The pipe picks up a voltage properties. SLIM is professional integrated software which relative to soil that is proportional to the transmission line provides the facilities for the generation of finite element voltage. The second is the conductive interference, which mesh, solution of electric, magnetic and thermal fields and the occurs during lightning strikes or a phase to ground fault. post processing of results of the geometry. In this software, When this is occurred, a large voltage cone is created around FEA is used and the whole domain of interest is divided into the grounding system as a result a voltage can get onto the smaller triangular elements which are shown in Fig. 1. Where pipeline through the pipe coating defects. The third is the 1, 2, 3, 4 and 5 are the node number; A, B, C, and D are the inductive interference, which is generated by the magnetic element code name. field and present during both normal operating conditions and 4

3

I

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The research was supported in part by Sultan Qaboos University (SQU), Sultanate of Oman, in 2005. A. H. Al-Badi is with Department of Electrical & Computer Engineering College of Engineering, Sultan Qaboos University P.O. Box 33, Muscat 123, Oman (e-mail: albadigsqu.edu.om ). M. A. Salam is with Department of Electrical & Communication Engineering, ITB, Brunei Darussalam.

1-4244-0288-3/06/$20.00 (©2006 IEEE

Fig. 1. Simple finite element mesh.

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Finite element analysis, as applied to electromagnetic problems, is a numerical method of solving Maxwell's equations, which are the mathematical expressions of the laws of electromagnetism deduced from empirical observation by Gauss, Coulomb, Ampere and Faraday. Considering only static electric field, for simplicity, Gauss's law (that the total electric flux flowing through a surface is equal to the charge enclosed by the surface) can be written in differential form as: V.D = 0 (1) Where D is the electric flux density (C/M2). Electric scalar potential (voltage) can be introduced via its relationship with electric field strength E (Vlm):

(2)

E=-VV

Where V is the electric scalar potential (V). The relationship between D and E is defined as material permittivity:

D=

io E

(3)

Where: 8r is the material relative permittivity. £8 is the permittivity of free space (F/m). From equations (1), (2) and (3), the Laplace's equation in terms of electric scalar potential in Cartesian coordinates for three dimensional problems comes,

-82V 02V Fa2v V -o£r Lax2 + a2 _x y

02V- =0 DV + z2j oZ

(4)

Analytical solution of equation (4) is usually possible only for relatively simple problems in 1 or 2 dimensions. For example, in 2-dimenntional studies, equation (4) can be reduced to:

a2v a2v ax2

ay

=0

(5)

Let as assume that the potential (V) varies linearly across each element:

V = a+bx+cy

(6) element with nodes i , j and k , the nodal potential

For an can be written in terms of the nodal coordinates: In matrix format:

Vi =a+bxi +cyi

-viLVk

vj [

xi

yi

xi

Yj

(7) a

b

~~~~~~(8)

where,

[P]

XjYk

XkYj

equation (8).

] I2A

V

(9)

XiYj-XjYi

Yk Yi xi -xi

Yi Yj xi -xi

Yj yk _Xk -x

and A is the area of the element, given by:

1

yi

xi

Xj y1

2A=1

Xk

1

Yk

Yk ) + Xj (Yk -Yi ) + Xk

xi Y

-YiYj

(10)

The equation (9) can be written more concisely as, a 1 a ori 6cx1°k a a

b

2 A

#iA Ak Vj

Yi

c

Yj

1

)k - Vk

Substituting equation (11) into equation (6) gives the potential at any point in the element in terms of the potential at the nodes and nodal coordinates: V = NiVi +N NV + Nk (2

V=N~J>N1V]+NkVk

(12)

Where the functions Ni etc. are called shape function for the elements and can be written as:

1

(13) ai + #, x + Y/i Y] 2A Assuming there is only one media in the problem area. The 2A Ni =~

equation describing the field is Laplace's equation would become:

a2v a2v 0 x2 + =y2

(14)

A numerical form of equation (14) can be derived via two convenient theorems. The first is Galarkin's theorem, which states that the solution of equation (14) can be found by setting the integral of the product of the same equation (14) with a suitable weighting function over an elemental area to zero. In this case the weighting function is, conveniently, the shape function:

fSNk

d2'

+

e

2

jds = 0

(15)

Equation (15) can be modified using Greens theorem to replace the 2nd order terms with 1St order terms, as following:

Xk Yk]C1 )J)

The coefficients a, b and c describe the potential variation across each element. It can be written in terms of the nodal coordinates and the nodal geometries by inversion of

XkYi-XiYk

(a2v + A-N

\

ax2

=-jNk KD-ND ex ol

02V)d ay 2

(16)

ds =

N

r b de From equation (I13), the following relations can be derived as,

F1

3

aNk

Jk aNk 2A' ay

ax

k

2A

(17)

From equation (12), the following expressions can be derived as,

av

2

ax

2Aullj- jfk

1

=

I

[V)/, + vV.)j + vjSk

(18) ( 19)

Substituting equations (18) and (19) into equation (16) and performing the integration which gives,

4A

[(IkAAi -YkYi )Vi + (IkIj

Ykj )Vj

(20)

+(,6k2 Yk))Vk]= 0

If we consider any element with boundary conditions and nodal coordinates then the unknown potential can be calculated from equations (10) and (20). III. SYSTEM MODEL PARAMETERS

Fig.2 shows the finite element model used to model the system together with contour of the electric flux lines. Energized wire

___

The following is a list of parameter settings of the computer models used in this study: Pipeline * Length: 2 m * Shunt resistance per unit length: 9*10912 / m * Outer Radius: 0.6385 cm * Inner Radius: 0.515 cm * Wall thickness: 0.24 cm * Vertical Separation between ground and pipeline, Z: 3 cm * Vertical Separation between ground and overhead wire, h: 50 cm * Relative Resistivity: 17 (with respect to annealed copper). * Relative permeability: 1(with respect to free space).

Transmission line * Length: 2.4 m * Conductor Outer Radius: 1mm. * Applied voltage to wire, Vw =40 kV IV. EXPERIENTIAL TEST RIG Fig. 3 shows the schematic diagram of the reduced scale test rig used to investigate the electromagnetic coupling between the energized wire and a steel pipeline. A copper conductor with radius of 1 mm was used and a steel pipe having 1.27cm/1.03cm (o.d./i.d.) and being 2 m long was used. In this test both the pipe height z and the wire height h are kept constant at 3 cm and 50 cm respectively. A single-phase AC voltage (Vw) is applied to the conductor and varied up to 40 kV. Moreover, the horizontal coordinate of the pipe from the center of symmetry underneath the conductor (lateral distance r) is fixed to zero. An aluminum plate was used to model the soil resistivity. To eliminate the end effects of the conductor, the aluminum plate was divided into three separate sections; the current signal is picked up from the middle section while the two other sections are earthed.

Simultaneous measuring and displaying of both the applied voltage to the conductor (Vw) and the pipe-induced voltage (Vp), and the corona current (Ij) are recorded. Energized wire

LAluminum plate

Isolated steel pipe Earth

Fig.2. Contour of the electric flux lines for the finite element model

Fig.3. Schematic diagram of the test rig

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V. DISCUSSIONS OF RESULTS

Fig.4 presents the relationship between the applied voltage and the relative pipeline voltage for both the test rig and the model. It is clear from the Figure 4 that increasing the applied voltage will increase the pipeline induced voltage due to the effect of capacitive coupling. For applied voltages less than the corona inception voltage, excellent correlation is achieved between the measured and simulated results. However, at voltages higher than corona inception voltage, the measured results are higher compared to the simulated results which indicate that the model did not consider the effects of corona and space charge. In fact under normal weather conditions, the rated voltage of overhead power lines is normally lower than the corona inception voltage. The latter can be reduced due to two different conditions, namely, changing the weather condition, i.e. by increasing the ambient temperature and/or decreasing the air pressure, and during the temporary overvoltages which can continue for few cycles and up to 140% of the peak phase voltage. Therefore, taking the corona effects into account in the simulation is insignificant from the practical point-ofview. Measured

10 9 8 Q Q 0)

>

0

1 Applied Voltage (kV)

Fig.4. relative pipeline voltage versus applied voltage

VI. CONCLUSIONS Capacitive coupling caused by high voltage overhead transmission lines on neighboring, parallel pipeline has been analyzed using finite element computer model. The developed model can predict the level of the voltage on the pipeline. An experimental reduced-scale rig was also built to verify the simulation results. A good correlation between the experimental and software based simulated results is obtained which validates the modeling approach of coupling between power transmission line and unburied pipeline. VII. REFERENCES [1]

[2]

[5] [7]

[8] [9] [10]

[11] [12]

VIII. BIOGRAPHIES

6 5 4 3 2

0

[4]

R. D. Southey, F. P. Dawalibi, and W. Vukonich, "Recent Advances in the Mitigation of AC Voltages Occurring in Pipelines Located Close to Electric Transmission Lines," IEEE Transactions on Power Delivery, Vol. 9, No. 2, April 1994, pp. 1090-1097. F. P. Dawalibi, R. D. Southey, J. Ma, and Y. Li, "On the Mechanisms of Electromagnetic Interference between Electrical Power Systems and Neighboring Pipelines," NACE 2000, T1OB Symposium on DC &AC Interference, Orlando, March 26-31, 2000. A. H. Al-Badi, I.A. Metwally, " Induced Voltages on Pipelines Installed in Corridors of AC power Lines," Journal of Electric Power components & Systems, to be publish. A. H. Al-Badi, H. Al-Rizzo," Simulation of Electromagnetic Coupling on Pipelines close to Overhead Transmission Lines: A Parametric Study," Journal of Communications Software and Systems, to be publish. Y. Baba, M. Ishii, "Numerical electromagnetic field analysis on lighting surge response of tower with shield wire," IEEE Transactions on Power Delivery, Vol. 15, No. 3, July 2000, pp. 1010- 1015. R. D. Southey, W. Ruan, and F. P. Dawalibi, "AC Mitigation Requirements: A Parametric Analysis," The Corrosion/2001 NACE International Conference, Texas, March 11- 16, 2001. Mitigation of Alternating Current and Lightning Effects on Metallic Structures and Corrosion Control Systems, NACE Standard RPO 177-95. IEEE guide for safety in alternating current substation grounding (ANSI), Publication 80,193. L. Egiziano, V. Tucci, C. Petrarca, M. Vitelli, "A Galerkin Model to Study the Field Distribution in Electrical Components Employing Nonlinear Stress Grading Materials" IEEE Trans. On Dielectrics and Electrical Insulation, Vol. 6, No. 6, pp. 765-773, December 1999.

-....Simulated

7

S

.

[3]

Y. Li, F. P. Dawalibi, and J. Ma, "Electromagnetic Interference Caused by a Power System Network and a Neighboring Pipeline," Proceedings of the 62nd Annual Meeting of the American Power Conference, Chicago, April 10-12, 2000, pp. 311-316. CIGRE Working Group 36.02, " Guide On The Interference of High Voltage AC Power Systems On Metallic Pipelines," 1995.

Abdullah Al-Badi (M' 1994) was born in Oman, on Sept 19, 1969. He obtained the degree of B.Sc. in Electrical Engineering from Sultan Qaboos University, Oman, in 1991. He received the degree of M.Sc. and Ph.D from UMIST, UK, in 1993 and 1998 respectively. In September 199 1, he joined the Sultan Qaboos University as demonstrator and, in 1998, he became an A sistant professor. His areas of interest include modeling and simulation of electrical machines, drives and interferences. He has published several papers in International Journals and Conferences in the filed of electrical machines, drives, interference and high voltage. He carried out several projects on electrical machines and the effect of AC interferences on pipelines. He is a Member of the Institute of Electrical Engineering and Electronics, IEEE, USA. Md. Abdus Salam was born in Chuadanga,

Bangladesh, on February 2, 1965. He obtained his B.Sc., M.Sc. and PhD, all in Electrical

Engineering, respectively in 1990 (Bangladesh Institute of Technology, Chittagong), 1994

(Bangladesh University of Engineering & Technology, Dhaka) and 2000 (University

Teknologi Malaysia). He was in the faculty of Department of Electrical & Electronic Engineering of Bangladesh Institute of Technology, Chittagong from April 1994 to January 2002. He also served as an Assistant Professor, Department of Electrical and Computer Engineering College of Engineering, Sultan Qaboos University, Oman from January 16, 2002 to Aprill, 2006. Currently, he is working as a faculty in the Dept. of Electrical & Communication Engineering, ITB, Brunei Darussalam. His research interests include power system modelling for on-line control, insulator contamination studies and renewable energy. He has published two text books on the title "Fundamentals of Electrical Machines" Alpha Science UK International Ltd, September 2005 and other title "Basic Electrical Circuits" with Shroff Publishers & Distributors Pvt. Ltd, Mumbai, India. He is a member of IEEE and a fellow of the Institution of Engineers, Bangladesh.