Electric Field Mitigation under Extra High Voltage Power ... - IEEE Xplore

54

R. M. Radwan et al.: Electric Field Mitigation under Extra High Voltage Power Lines

Electric Field Mitigation under Extra High Voltage Power Lines R. M. Radwan, A.M. Mahdy Cairo University, Faculty of engineering, Electrical Power Department, Giza, Egypt.

M. Abdel-Salam Assuit University, Faculty of engineering, Dept. of Electrical Engineering, Assuit, Egypt and M. M. Samy Beni Suief University, Faculty of Industrial Education, Dept. of Electrical Engineering, Beni Suief, Egypt.

ABSTRACT This paper deals with the mitigation of electric fields under extra high voltage transmission lines using active and passive shield wires. Two extra high voltage alternating current transmission lines are modeled and analyzed. One line is operating at 220 kV and the other is at 500 kV. The electric field is calculated at one meter above the ground level for the two transmission lines with and without active and passive shield wires using the charge simulation method (CSM). The effect of different shielding parameters on the ground level field is studied. These parameters include the spacing between shield wires and their number of these wires, and their height above ground as well as the value of the voltage applied to the shield wires. Also, the effects of passive and active shield wires on the magnetic field underneath the lines and the electric field on the conductor’s surface are highlighted. Index Terms — Charge simulation method, electric fields, electric field mitigation, shielding wires, transmission lines.

1 INTRODUCTION NOWADAYS extra high voltage alternating current (EHVAC) transmission lines are widely used for transmission of electrical energy. Consequently, the possible effects of electric fields underneath these lines received an increasing interest in research studies, e.g. electric field induction and short circuit currents through conducting objects (parallel metallic fences, pipelines and large vehicles). The electric field impact on environment and interaction with human beings are also of great interest [1]. Precise calculation of the electric field underneath overhead transmission lines is a very important aspect in transmission line design. Quantitative description of the electrostatic field around EHVAC overhead transmission lines has been presented in many papers [2-6]. The electric field effect on transmission lines’ maintenance crew is an important issue that electric utilities are most often required to respond to the potential health hazards. The effect of long term or chronic exposure to electric fields was studied in several countries [7-9]. Manuscript received on 2 February 2012, in final form 30 June 2012.

Several studies have reported that children living near high voltage transmission and distribution lines had a higher cancer and leukemia incidence than other children did [10]. However, limited studies have been reported regarding adults who live near high voltage transmission and distribution lines. Higher cancer incidences were observed for adults living near EHVAC lines [11]. In addition, various studies have suggested that exposure to electromagnetic fields could lead to DNA damages in cells under certain conditions [12]. These effects depend on factors such as mode of exposure, type of cell and intensity and duration of exposure. The analysis and reduction of electric fields at ground level is the most direct objective of efforts to minimize the field effects of EHVAC transmission lines. In fact, most electric field effects occur close to ground level and are function of the magnitude of the unperturbed electric field at one meter above ground. For the previous reasons, electric fields must be reduced to overcome their harmful effects on the people living or work nearby the transmission lines. One of the approaches is to use active and passive shield wires underneath the line conductors [13-22]. Most of the previous workers investigated the electric field reduction by using

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IEEE Transactions on Dielectrics and Electrical Insulation

Vol. 20, No. 1; February 2013

passive shield wires. The main purpose of this paper is to compare electric field mitigation using active and passive shield wires. Of course, the mitigation of the electric field will be only at key points, such as when the line crosses a communication building, railway stations, military building, etc. In practice the line towers can be used for supporting the shield wires at the required site for electric field mitigation. For a simple physical system, it is usually possible to find an analytical solution. However, in many problems the physical systems are so complex that it is extremely difficult, if not impossible, to find analytical solutions. Hence, in such cases numerical methods are employed for electric field calculations. The existing numerical methods include the Finite Difference Method, the Finite Element Method, the charge simulation Method, the Surface Charge Simulation Method. The CSM has many advantages when compared with the other numerical methods for calculating electric fields. CSM requires no or very little numerical integration in constructing the coefficient matrix for unknown charges and then in obtaining the field intensity. This makes the programming easier and the computation faster. CSM is very successful in most of the high voltage field problems, it is very simple and applicable to systems having more than one dielectric medium, and this method is also very suitable for 3– D fields with or without symmetry. Therefore, the charge simulation method is used in this paper for calculating electric fields underneath the transmission lines with and without active and passive shield wires.

The idea of CSM [23-25] is very simple. For the calculation of electric fields, the distributed charges on the surface of a conductor are replaced by N number of fictitious charges placed inside the conductor at a radius Rf as shown in Figure 1. In order to determine the magnitudes of the fictitious charges, some boundary points are selected on the surface of the conductor. The number of boundary point’s n is selected equal to the number of fictitious charges. Then, it is required that at any boundary point the potential resulting from superposition of all the fictitious charges effects is equal to the known conductor potential. Let, Qj is the jth fictitious charge and V is the known potential of the conductor. Then, according to the superposition principle, n

transmission line, it leads to the following system of N linear equations for N unknown fictitious charges, then: [P]NxN [Q]N = [V]N

(2)

Where [P] = potential coefficient matrix, [Q] = column vector of known potential of contour points, [V] is the applied voltage for boundary points on conductor surface, the stressed voltage for boundary points on active shield wires and zero voltage for boundary points on passive shield wires. Equation (2) can be solved for the unknown fictitious charges. As soon as the unknown charges are determined, the potential and the field intensity at any point, outside the line conductors and shield wires can be calculated. While the potential is found by equation (1), the electric field components are calculated by superposition of all the field vector components. For a Cartesian coordinate system, the x, y coordinate Ex and Ey for a number of N charges would be given by: N

Ex=

pij

 x j 1 N

Ey=

Qj

pij

 y Q j 1

N

=

f 

Qj

(3)

 

Qj

(4)

j 1 N

j

x ij

= f y j 1

ij

where (fx)ij, (fy)ij are "field intensity coefficients" in the x and y direction. rc Rf

Line charges Boundary points Figure 1. Charge representation for the line conductor and shield wires.

2 ELECTRIC FIELD CALCULATION METHODOLOGY

V =  Pij Q j

55

(1)

j 1

Where Pij is the potential coefficient, which can be evaluated analytically for different types of fictitious charges. When equation (1) is applied to N boundary points selected on the phase conductors and shield wires of an EHVAC

3 RESULTS AND DISCUSSIONS Case study 1: A 220 kV transmission line with and without active and passive shield wires: 3.1 WITHOUT SHIELD WIRES The charge simulation method is applied to the 220 kV transmission line shown in Figure 2. The number of subconductors per phase is two, the radius of a single conductor, rc is 0.0135 m, the sub-conductor spacing, D is 0.3 m, the heights H2, H3 are function of H1, where H2 = H1 + 9.2 m, H3= H1 + 19.4 m and the height H1 is the variable parameter. The tower arm lengths B1, B2 and B3 are 8.55, 4.5, 8.55 m respectively. The number of simulation line charges per subconductor is equal to six. The simulation charges are arranged around a cylinder of radius Rf equal to 0.05rc. The potential error at the selected contour points -midway between boundary points- did not exceed 0.001%. Figure 3 shows the electric field at 1m height above the ground level for the configuration shown in Figure 2. The maximum field strength at 220 kV applied voltage is found to be about 2.984 kVm-1 corresponding to minimum ground clearance H1=10 m.

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R. M. Radwan et al.: Electric Field Mitigation under Extra High Voltage Power Lines B3

A

A

B3

B2 B2

B

D

Figure 6 plots the relation between maximum electric field with different number of passive shield wires and different values of the spacings S and Hs=10.7 m.

B1

B1

H3

B

Figure 5 shows the electric field at one meter height above the ground level for the configuration shown in Figure 4 at Hs=10.7 m with different numbers ns of shield wires at constant spacing S=5 m between shield wires.

rc

C

C H1

H2

B3

A

Figure 2. A 220 kV, transmission line.

3500

H1=10 H1=15.7 H1=20 H1=25 H1=30

3000

Electric field (V/m)

2500

H3

A

B1

B1 S

C

S

S

Hs

rc

D

B

C

H2

S

H1

Figure 4. A 220 kV transmission line with passive shield wires

From Figures 5 and 6, it is clear that the maximum electric field decreases with the increase of the number ns of passive shield wires and the spacing S. The percentage reduction of maximum electric field is 63.35 % for five shield wires spaced 5 m. 2000

2000

No shield ns=1 ns=2 ns=3 ns=4 ns=5

1800

1500 1600

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0

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Distance (m)

1400

Electric Field (V/m)

1000 500

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B2 B2

B

Increasing the line height is the most effective parameter in line design, which reduces the maximum field stress at the ground level. Figure 3 plots the field strength for different line heights of 10, 15.7, 20, 25 and 30 m. The maximum field strength values corresponding to these line heights are 2.984, 1.89, 1.488, 1.138 and 0.89 kVm-1 respectively. It is clear that as the line height increases, the maximum field decreases significantly within the transmission line corridor.

B3

1200 1000 800 600

Figure 3. Electric field distribution at 1m height above ground surface for 220 kV transmission line of Figure 2 with the height H1 as a parameter.

400 200 0 -80

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-40

-20

0

20

40

60

80

100

Distance (m)

Figure 5. Electric field distribution at 1m height above ground surface of the 220 kV transmission line with S=5 and Hs=10.7 m. 2000

S=1 S=2 S=3 S=4 S=5

1800

Maximum Electric Field (V/m)

3.2 WITH PASSIVE SHIELD WIRES The charge simulation method is applied to the transmission line and shield wires shown in Figure 4. The configuration of this transmission line is the same as that in Figure 2, but with passive shield wires positioned underneath the phase conductors. The shield wires are extended parallel to the phase sub-conductors and connected together at one end where they are grounded. The radius of passive shield wires rsh is 0.0039 m, the spacing between shield wires is S and the height from shield wires to ground is Hs. The number of simulation line charges for both phase sub-conductors and shield wires is equal to six. The simulation charges are arranged around a cylinder of radius 0.05rc for phase sub-conductors and 0.05rsh for shield wires. The potential error at selected contour points on the line conductors and grounded shield wires did not exceed 0.001%. Different number ns of shield wires, different spacings S between shield wires and different heights Hs from ground to shield wires are studied.

-100

1600 1400 1200 1000 800 600 400 200 0 0

1

2

3

Number of Passive Shield Wires

4

5

Figure 6. Maximum Electric field against of the number of passive shield wires of the 220 kV transmission line for different spacings S at Hs=10.7 m.


The mitigation of the electric field at the right of way (ROW) increase with the increase of the number of shield wires, being 53.07% and 10% for five and one shield wires respectively see Figure 7. 3.3 WITH ACTIVE SHIELD WIRES The charge simulation method is applied to the transmission line shown in Figure 8. The configuration is the same as in Figure 4. The phase sequence of the line conductors and active shield wires is the same ABC as shown in Figure 8. Again the shield wires are extended parallel to the phase sub-conductors and stressed by a voltage Vsh expressed as a percentage of the phase voltage Va. The shield wires are open-circuited with no current flowing through them. The number of active shield wires is fixed at three wires, but different spacings S between them and different heights Hs from ground are considered for this study.

increase of the voltage Vsh applied to the shield wires, Figure 9. The percentage reduction of the maximum electric field is 50.9 % for S=5 m and ns =3 for the same phase sequence ABC of both line conductors and shield wires. 2000

No shield 1800

Vsh=0.001Vc Vsh=0.01Vc

1600

Vsh=0.05Vc 1400

Vsh=0.1Vc

1200 1000 800 600 400 200

100

ns=1 ns=2 ns=3 ns=4 ns=5

ROW 80

0 -100

-80

-60

-40

-20

0

Distance (m)

20

40

60

80

100

Figure 9. Electric field distribution at 1m height above ground surface of the 220 kV transmission line with ns=3, S=5 and Hs=10.7 m.

60

2000

40

No shield Vsh=.001Vc Vsh=.01Vc Vsh=.05Vc Vsh=.1Vc Vsh=.2Vc

1800

20

1600

0

-100

-80

-60

-40

-20

0

20

40

60

80

100

-20

-40

1400


Electric Field mitigation %

57



1200 1000 800 600

-60 400

Distance (m)

Figure 7. Mitigation profiles for the 220 kV transmission line with the variation of the number of passive shield wires at S=5 and Hs=10.7 m.

200 0

B3

A

B2 B H3

A

B3

A Hs

B1

rc

-40

-20

0

20

40

60

80

100

Figure 10. Electric field distribution at 1m height above ground surface of the 220 kV transmission line with ns=3 S=5 and Hs=5.7 m.

C

S

S

B C

-60

Distance (m)

B B1

-80

D

B2

C S

-100

A

S

H2

B C

H1

Figure 8. A 220 kV transmission line with active shield wires.

Figures 9 and 10 show plots of the electric field at one meter height above the ground level for the configuration shown in Figure 8 at Hs=10.7, 5.7 m respectively with three active shield wires at spacing 5 m. It is noted that when using active shield wires, there is no noticeable change in the maximum electric field with the

When the height Hs changes as in Figure 10, it is noted that the maximum electric field increases with the increase of active voltage irrespective of the number of active shield wires and their spacing S, The percentage reduction of the maximum electric field reaches 9.7 % for S=5 m and ns =3 for the same phase sequence ABC with Vsh equals 20% of the conductor voltage. Case Study 2: A 500 kV transmission line with and without active and passive shield wires 3.4 WITHOUT SHIELD WIRES The charge simulation method is applied to the 500 kV transmission line shown in Figure 11. The number of subconductors per phase is three, the sub-conductor radius rc is 0.0153 m, the sub-conductor spacings, D1, D2 and D3 are 0.47, 0.45, 0.45 m respectively. The height H=19.1 m and the tower arm length B is 12 m. The number of simulation line charges

58


per sub-conductor is six. The simulation charges are arranged around a cylinder of radius 0.05rc. The potential error at selected contour points did not exceed 0.001%.

B

B

A

B

C

rc

D1

D3 B

B D1

A

B

C

S

rc

S

S

S

S

S

D2 H HS

D3

D2 H

Figure 13. A 500 kV transmission line with passive shield wires. 4500

S=1 S=2 S=3 S=4 S=5


4000

Figure 11. A 500 kV transmission Line.

Figure 12 plots the field strength for different line heights of 25, 19.1, 15, 12 and 10 m. The maximum field stress values corresponding to these line heights are 2.389, 3.856, 5.729, 8.016 and 10.3 kVm-1, respectively. It is clear that as the line height increases, the maximum electric field decreases with a significant increase within the transmission line corridor.

3500 3000 2500 2000 1500 1000 500

12000

H=25 H=19.1 H=15 H=12 H=10


10000

0 0

0 -20

0

20

Distance (m)

40

60

80

100

Figure 12. Electric field distributions at 1m height above ground surface for 500 kV transmission line of Figure 10 with the line height H as a parameter.

3.5 WITH PASSIVE SHIELD WIRES The charge simulation method is applied to the transmission line shown in Figure 13. The configuration of the transmission line is the same as in Figure 11, but with passive shield wires positioned underneath the phase conductors. The radius of shield wires rsh is 0.0039 m, the spacing between shield wires is S and the height from shield wires to ground is Hs. The number of simulation line charges for both phase subconductors and shield wires is equal to six. The simulation charges are arranged around a cylinder of radius 0.05rc for phase sub-conductors and 0.05rsh for shield wires. The potential error at selected contour points on the line subconductor and shield wires did not exceed 0.0001%. Different number of passive shield wires, different spacings S between shield wires and different heights Hs from ground to shield wires are studied. Figures 14 and 15 show plots of the maximum electric field for the configuration shown in Figure 13 at constant height Hs=15 m for different number ns of shield wires and different spacings S between shield wires.


4000

-40

4

5

3000

6000

-60

3

Figure 14. Maximum Electric field versus the number of passive shield wires of the 500 kV transmission line at different spacings S with Hs=15 m.

8000

-80

2

Number of Passive Shield Wires

2000

-100

1

2500

2000

1500

n=2 n=3 n=4 n=5

1000

500

0 1

2

3

4

spacing between Passive shield wires S

5

Figure 15. Maximum Electric field with the variation of the spacing S between passive shield wires of the 500 kV transmission line with different number ns and Hs=15 m.

From Figures 14 and 15, it is clear that the maximum electric field decreases with the increase of the number ns of passive shield wires at constant values of the spacing S and height Hs. The maximum electric field decreases with the increase of the spacing S up to two meters approximately, beyond which there is no noticeable change of the maximum electric field. Figure 16 shows plots of the electric field at 1 m height above the ground level for the configuration shown in Figure 13 at Hs=15 m for different numbers ns of shield wires at spacing S of 5 m between shield wires. From Figure 16, it is clear that the maximum electric field decreases with the increase of the number ns of passive shield wires. The percentage reduction of maximum electric field reach 55.5% for S=5 m and ns =5.


Vol. 20, No. 1; February 2013 5000

4500

No shield n=1 n=2 n=3 n=4 n=5

4000

3000

2500

2000

No shield Vsh=.001 Vsh=.01 Vsh=.05 Vsh=0.1 Vsh=0.2

4500 4000 3500


3500


59

3000 2500 2000 1500

1500

1000

1000

500 500

0 -100

0 -100

-80

-60

-40

-20

0

20

40

60

80

100

Distance (m)

Figure 16. Electric field distribution at 1m height above ground surface of the 500 kV transmission line with S=5 and Hs=15 m.

3.6 WITH ACTIVE SHIELD WIRES: PHASE SEQUANCE ABC FOR BOTH PHASE CONDUCTORS AND SHIELD WIRES The charge simulation method is applied to the transmission line shown in Figure 13. The voltage of active shied wires is a percentage of the phase voltage. Different numbers of shield wires, different spacings S between shield wires and different heights Hs from ground to shield wires are studied. 4500

No shield Vsh=0.001

4000

Vsh=0.01 Vsh=0.05 Vsh=0.1 Vsh=0.2

3500


3000

-80

-60

-40

-20

0

20

Distance (m)

40

60

This is because the voltage applied to the shield wires results an additional electric field which is added to the original field provided they have the same phase sequence. The percentage reduction of maximum electric field reaches 21.5% when ns =1 with Vsh equals 0.1% of the phase voltage Va and becomes 8.3% when Vsh reaches 20% Va. Also, the percentage reduction of maximum electric field reaches 44.8% when ns =3 at Vsh=0.1%Va and S=4 m, but the maximum electric field exceeds the original value by 13.47% when Vsh=20%Va. Figure 19 shows the percentage reduction of electric field at ground level for the transmission line shown in Figure 13 with different values of Vsh for three shield wires spaced 5 m at height Hs of 15 m. The phase sequence for both phase conductors and shield wires is the same (ABC sequence). From Figure 19, it is clear that the mitigation profile of the electric field reduces at the edge of ROW with the increase of Vsh. The percentage reduction of electric field at the edge of ROW is 9.5% for Vsh=0.1%Va and 2.317% for Vsh=10%Va. 50

ROW

Vsh=.001Vc Vsh=.01Vc Vsh=.05Vc Vsh=.1Vc Vsh=.2Vc

2000

40 1500

0 -100

-80

-60

-40

-20

0

20

Distance (m)

40

60

80

100

Figure 17. Electric field distribution at 1m height above ground surface of the 500 kV Transmission line with active shield wires (ns=1) at S=1 m, Hs=15 m and same phase sequence for both line conductors and shield wires.

From Figures 17 and 18, it is clear that the maximum electric field decreases with the increase of the number ns of shield wires and the spacing S for the same voltage applied to shield wires. Increasing the voltage applied to the shield wires affects the maximum electric field and sometimes it exceeds its value in absence of shield wires.

Electric Field Mitigation%

30

500

100

Figure 18. Electric field distribution at 1m height above ground surface of the 500 kV Transmission line with active shield wires (ns=3) at S=4 m, Hs=15 m and same phase sequence for both phase conductors and shield wires.

2500

1000

80

-100

20 10 0 -80

-60

-40

-20

0

20

40

60

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-10 -20 -30 -40

Distance (m)

Figure 19. Mitigation profiles for the 500 kV transmission line at different values of Vsh, ns=3, S=5 and Hs=15 m.

60


3.7 WITH ACTIVE SHIELD WIRES: PHASE SEQUENCE ABC FOR PHASE CONDUCTORS AND ACB FOR ACTIVE SHIELD WIRES Figures 20 and 21 show plots of the electric field at 1 m height above the ground level for the configuration shown in Figure 13 at Hs=15 m with different numbers ns and different values of Vsh at S=1 m and 4 m. The phase sequence of line conductors, ACB is different from that for shield wires. 4500

No shield Vsh=.001 Vsh=.01 Vsh=.02 Vsh=.05 Vsh=.1 Vsh=.2

4000 3500


3000 2500 2000 1500

The percentage reduction of the maximum electric field underneath the right phase reaches 21.5% and 19.87% at ns =1 and Vsh of 0.1% and 20% of Va respectively, and remains almost the same underneath the left phase at Vsh=0.1%Va but increases with 10.04% when Vsh is Vsh=20%Va . For S=4 m, ns =3 and Vsh=0.1% and 20% of Va, Figure 21, the percentage reduction underneath the right phase reaches 44.9% and 23.23% respectively to the left of the outer phase. These values become 10.69% for Vsh=20% of Va and remains constant for Vsh=0.1% of Va Figure 22 shows the percentage reduction of electric field at lateral distribution of the transmission line shown in Figure 13 for different values of Vsh, ns=3, S=3 m and Hs = 15 m. The phase sequence for line conductors is ABC where that for shield wires is ACB. From Figure 22, it is shown from the mitigation profiles that the percentage reduction of electric fields reduces at the edge of ROW with the increase of Vsh. Changing the phase sequence for phase conductor and shield wires changes the mitigation profiles underneath the right and left phases at the edge of ROW.

1000

80

500

Vsh=.001Vc Vsh=.01Vc Vsh=.05Vc Vsh=.1Vc Vsh=.2Vc

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0 -80

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Figure 20. Electric field distribution at 1m height above ground surface of the 500 kV transmission line with active shield wires (ns=1) at S=1, Hs=15 m and different phase sequence for phase conductors and shield wires. 4500 No shield Vsh=.001 Vsh=.01 Vsh=.05 Vsh=.1 Vsh=.2

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3500


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40

Electric Field Mirigation %

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2500

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Distance (m)

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Figure 22. Mitigation profiles for the 500 kV transmission line with the variation of the active voltage, variation of the phase sequence, ns=3 at S=3 and Hs=15 m.

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500

0 -100

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0

20

Distance (m)

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Figure 21. Electric field distribution at 1m height above ground surface of the 500 kV transmission line with active shield wires (ns=3) at S=4 m, Hs=15 m and the different phase sequence for phase conductors and shield wires.

From Figures 20 and 21, it is clear that the maximum electric field decreases at the right side of the middle phase and increases at the left side with the increase of the number ns and the spacing S. Also increasing the voltage Vsh increases the maximum electric field underneath both left and right line phases.

The percentage reduction of electric field at the edge of ROW underneath the right phase is 8.9% for Vsh=0.1%Va and 10.46% for Vsh=10%Va. The corresponding values underneath the left phase are 8.84% and 2.16% for the same values of Vsh. 3.8 EFFECT OF PASSIVE SHIELD WIRES ON THE MAGNETIC FIELD PROFILE Figure 23 shows plot of the magnetic field at one meter height above the ground level for the configuration shown in Figure 13 at Hs=15 m with ns=3 and spacing S=1 m between shield wires and load current of 2000A. From this Figure it is clear that the magnetic field profile is not affected by the existence of passive shield wires. For example at a radial distance of 20 m the reduction is 0.24% for passive shielding.



20

35

No shield

18

Surfuce Electric Field (kV/cm)

ns=3 passive

Magnetic field density (µT)

61

16 14 12 10 8 6 4

30 25 20 15

Etheatnoshield Etheatpassive

10

Etheatactive Onset Field

5

2 0

0 0

10

20

30

40

50

Radial distance (m)

Figure 23. Magnetic field distribution at 1 m height above ground surface of the 500 kV transmission line with S=1, Hs=15m and ns=3.

3.9 EFFECT OF SHIELD WIRES ON THE ELECTRIC FIELD AT THE CONDUCTOR'S SURFACE Figure 24 shows a plot of the surface electric field distribution around the periphery of the lowest sub-conductors of the outer and center phases. The corona onset field at natural temperature and pressure, according to Peek’s formula is about 37.5 kVpeak/cm, for smooth clean sub-conductors of Figure 13. The onset field is 30 kVpeak/cm for 0.8 conductor surface factor. This means that the line configuration of Figure 13 is not producing corona at the operating 500 kV. Also the electric field around the conductor’s surface decreases with the angle as shown in Figure 24. This can be explained from the equation given by [26, 27]: 2r (5) E  E [1  ( n  1 ) cos  ] 

a

D

Where Ea is the average field, r is the sub-conductor radius and n is the number of sub-conductors. 30

Eouter Ecenter

Surfuce Electric field (kV/cm)

25

20

15

10

0

60

20

40

60

80

100

120

140

160

180

angle

Figure 25. Electric field distribution around the periphery lowest subconductors o f center phases with and without shield wires.

4 CONCLUSIONS 1. The maximum electric field at the ground level underneath EHVAC transmission lines decreases with the increase of the spacing S between passive shield wires irrespective of the height Hs and the number ns of passive wires. Also it decreases with the increase of the number ns of passive shield wires whatever the spacing S or the height Hs of the passive shield wires. 2. The maximum electric field at the ground level underneath EHVAC transmission line decreases with the increase of the spacing S between active shield wires irrespective of the height Hs and the number ns of active wires with the same phase sequence for both phase conductors and active shield wires. 3. The maximum electric field at the ground level underneath EHVAC transmission lines decreases with the increase number ns of active wires irrespective of the height Hs and of the spacing S between active shield wires with the same phase sequence for both phase conductors and active shield wires. 4. The spatial distribution of the electric field at the ground level underneath EHVAC flat configuration transmission lines is no longer symmetrical being larger under one side phase and smaller under the other side phase when the phase sequence of phase conductors is different from that of the shield wires.

D

5 REFERENCES

5

[1]

 0 0

20

40

60

80

100

angle

120

140

160

180

Figure 24. Electric field distribution around the periphery lowest subconductors o f outer and center phases without shield wires.

The maximum electric field at the conductor’s surface decreases when the active shield wire voltage increases, but it increases in the case of passive shielding see Figure 25. The percentage increase of the maximum electric field in the presence of passive wires is about 7 %. This increase in the surface field is not high enough to produce appreciable corona on the line.

[2] [3] [4]

[5]

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[25] T. Takuma, T. Kawamoto and H. Fujinami, "Charge simulation method with complex fictitious charges for calculating capacitive-resistive fields", IEEE Trans. Power App. Syst., Vol. 100, pp. 4665-4672,1981. [26] M.G. Comber and L.E. Zaffanella, "The Use of Single-Phase Overhead Test Lines and Test Cages to Evaluate the Corona Effects of EHV and UHV Transmission Lines", IEEE Trans. Power App. Syst., Vol. 93, pp. 81-90. 1974. [27] A.S. Timascheff, "Fast calculation of gradients of a three-phase bundle conductor line with any number of subconductors Part II: Gradients calculation for the side-phase", IEEE Trans. Power App. Syst., Vol. 94, pp. 104-107. 1975. R. M. Radwan was born in 1936. He received the B.Sc. degree in electrical engineering from Cairo University, Egypt, and the Ph.D. in electrical engineering from the University of Manchester Institute of Science and Technology, England, in 1959, and 1965 respectively. He received the Egyptian State Prize in Engineering Sciences and Cairo University Prize in 1992, and 2004 respectively. Professor Radwan is a Distinguished Member of the International Council on Large High Voltage Electric Systems, CIGRE, Paris, France. Currently, he is a full time professor in the Faculty of Engineering, Cairo University. His research interests are in the area of Gas Insulated Systems, Electric and Magnetic Fields, Partial Discharge, and Insulation Systems. M. Abdel-Salam (F’92) was born in Egypt. He received the B.S. and Ph.D. degrees in electrical engineering from the University of Cairo, Cairo, Egypt, in 1970 and 1973, respectively. He is a Fellow of IEE, Institution of Electrical Engineers, in 1992, England, United Kingdom and Alexander-von-Humboldt Fellow in 1977, Germany, Fellow of IOP, Institute of Physics in 2002, Bristol, U.K., Fellow of JSPS, Japanese Society for Promotion of Science, Tokyo, Japan in 1996. He is also a member of the Electrostatics Processes Committee, IEEE Industrial Applications Society. He received the following prizes and awards, National Prize in Engineering Sciences in 1986, 1992, 2000, 2001 and 2004 from the Egyptian Academy of Science and Technology, Assuit University Prize for Best Research Paper in Electrical Engineering in 2000, 2001, 2004, 2008 and 2009. Currently, he is professor in the Faculty of Engineering, Assuit University. His research activities include corona studies, digital calculation of electric field and renewable energy. A. M. Mahdy was born in El-Sharkia, Egypt in 1956. He received the B.Sc., M.Sc. and Ph.D. degrees from Cairo University, Faculty of Engineering, Dept. of Electrical Engineering, Giza, Egypt in 1979, 1983 and 1988, respectively. He is a staff member of Dept. of electrical engineering of Cairo University from 1979 until now. He is an associate professor of dept of electrical Engineering, Cairo University. His researches interests are high voltage engineering, insulation co-ordination, high voltage application, and electric field. M. M. Samy was born in Egypt in 1972. He received the B.S. degree in electrical engineering from High Institute of Technology, Benha, Egypt, M.S. degree in electrical power and machines from Zagazig University, Zagazig, Egypt, and Ph.D. degree in electrical power and machines from Cairo University, Giza, Egypt, in 1995, 2007 and 2011, respectively. Currently he is an assistant Prof. in electrical engineering department at the faculty of Industrial Education, Beni Suief University, Beni Suief, Egypt. His research activities include digital calculation of electric and magnetic fields, mitigation of electromagnetic fields underneath high voltage transmission lines.