Calculation of the Magnetic Field level in the Vicinity of ... · PDF fileCalculation of the Magnetic Field level in the Vicinity of a 400kV Transmission Line Page 3 Table of Graphs,

Bachelor of Engineering Electrical/Electronic Engineering (DT-021/4)

Calculation of the

Magnetic Field Level in

the Vicinity of a 400kV

Transmission Line

Power Systems Operations and Economics Daniel Greenan – D10119777

Calculation of the Magnetic Field level in the Vicinity of a 400kV Transmission Line

Page 2

Table of Contents

Introduction ............................................................................................................................... 4

Transmission Lines and the Public ............................................................................................. 6

400kV Overhead Line ................................................................................................................. 8

Magnetic Field ............................................................................................................................ 9

Attempts at Reducing Magnetic Field ..................................................................................... 11

Conclusion ................................................................................................................................ 13

Works Cited .............................................................................................................................. 14

Appendix .................................................................................................................................. 15


Page 3

Table of Graphs, Figures & Tables

Graph 1: Magnetic Field (Tesla) ............................................................................................................ 10

Graph 2: Magnetic Field (Gauss) ........................................................................................................... 10

Graph 3: Different Configurations for Analysis of Magnetic Fields ...................................................... 11

Graph 4: Magnetic Field with Conductors in Bundle 1 meter apart ..................................................... 12

Figure 1: Ireland’s National Grid (Designed in PowerPoint) ................................................................... 5

Figure 2: EirGrid’s Interconnector Plans (EirGrid, 2012) ......................................................................... 6

Figure 3: 400kV L12 Overhead Line Dimensions (Designed in PowerPoint) ........................................... 8

Figure 4: X and Y Values (PowerPoint) .................................................................................................... 9

Figure 5: EirGrid’s Future Plans for Expansion of Transmission Lines (Ivan Dudurych, 2011) .............. 13

Table 1: Surge Impedance Loading Table for Different Bundle Spacing (Nayak, 2006) ......................... 9


Page 4

Introduction

Electromagnetic Fields

Electric and magnetic fields (EMFs) are invisible lines of force that are created with the production of

electricity. Current is the flow of power. Therefore, if high units of power are required the voltage is

stepped up. The higher the current the stronger the electromagnetic forces will be. With higher

current and voltage (110-400kV) transmission, there is great concern for people who live in the

vicinity of these structures.

For Electric Fields the Force between two charges can be written as:

The Magnetic Fields are based on the application of Ampere’s Circuital Law which states that the

integral of the magnetic field intensity around a closed contour is equal to the current enclosed by

the contour, where (H) is the magnetic field intensity in amps per meter and (I) is the enclosed

current. (Conlon, 2012)


Page 5

Supply and Demand for Electricity

Electricity is “transported” from power stations (remote locations mostly) to the end users homes or

businesses. The transportation of energy is achieved by transmission and distribution lines. The

operational policy for these lines comes from the Commissioner for Energy Regulation (CER), which

is the regulator for the electricity and gas sectors in Ireland. Their job regarding the electricity sector

is to “keep the lights on” and ensure a safe and reasonably priced service to customers from

suppliers. Policy the CER make regarding the Transmission and Distribution Systems Infrastructure is

carried out by the systems operators. The CER therefore requires full control over any machine that

is generating power on to the system. The Transmission system in Ireland refers to the network of

cables that carry 400/220/110kV. EirGrid are the Transmission System Operator (TSO) and they have

control of every generator on their system. The Distribution System is the network of cables that

carries 38/20/10kV and even down to 230V, which is operated by ESB Networks. The Transmission

System is connected to the Distribution Network at connection points called nodes. The

Transmission views these nodes as if they were loads on their system. Theoretically there are 6

different stages at which a generator can connect to the Grid. However the 400kV line is not directly

connected to any generator. There are only two 400kV lines in the country. They run from

Moneypoint in Claire to Dublin. Moneypoint is the largest power plant in the country and Dublin has

by far the largest electrical load. Moneypoint produces power at 220kV and uses a step up

transformer to connect to the 440kV line. The reason the voltage is stepped up is to increase power

flow capacity and reduce transmission losses in the line from Claire to Dublin.

Figure 1: Ireland’s National Grid (Designed in PowerPoint)


Page 6

Transmission Lines and the Public

As populations around the world increase, there is a never ending need to provide electricity to

maintain high standards of living and with the large expansion of wind on the system, there is a

requirement to upgrade the transmission and distribution lines. With plans to develop 10GW of

wind farm projects over the next 20 years, EirGrid are now setting up to export electricity to England

and Europe. EirGrid are working on the East-West Interconnector which is due for completion this

year and the North-South Interconnector which is still in planning. Both these projects are of huge

importance to Ireland’s plans for exportation of any excess power that will be produced on to the

Grid in the future. The East –West Interconnector project has been executed with little interruption

or protest from the public. Most of the cable will be laid on the seabed of the Irish Sea and will

connect to converter stations at Rush North Beach, Dublin. However the North-South Interconnector

project has been crippled with planning objections. This is due to local residence objecting due to

the overhead line will have a negative visual impact and health implications.

Figure 2: EirGrid’s Interconnector Plans (EirGrid, 2012)

As the North-South project is fundamental to Ireland’s future security of supply the idea that the

visual landscape should take preference does not make sense. If the construction of a motorway is

stopped due to a planned issue, a county council can overrule the decision if the project is deemed

of national strategic importance.


Page 7

Therefore the only objection remaining is the health concerns of the local residence. This should not

be overlooked regardless of the importance of any project. A website called power line facts claims

that,

“A major new study published in the British Medical Journal looked at cancer data in England and

Wales between 1962 and 1995, for children aged up to 15 years old. The study found that children

whose birth address was within 200 meters of an overhead power line had a 70% increased risk of

leukaemia.”

Case Study

There were two possible case studies that could be assigned to each student.

1. Calculation the electric field level in the vicinity of a transmission or distribution line.

Or

2. Calculation the magnetic field level in the vicinity of a transmission or distribution line.

The size (voltage) and location (overhead or underground) was also assigned to each student. This

report stayed away from commenting on the health implications of being exposed to Electric or

Magnetic Fields. Instead the report will display the steps required to measure the magnetic field at

any point of distance away from the overhead line. From the Graphs that will be produced, the

reader will gain a clear view of the exposure to magnetic fields in relation to the distance from a

transmission line.

The transmission line assigned for this report was a 400kV overhead line and the task was to

calculate the Magnetic Field Level its vicinity.


Page 8

400kV Overhead Line

There are different types of design for every overhead line. The overhead chosen for this report is

the 400kV version L12 (National Grid, 2011). The dimensions are displayed in Figure 3. To determine

the magnetic field at a given distance from the overhead line, the distances from a set point to all

twelve conductors need to be known. There are six pairs (twelve) conductors in L12. The pairs are

spaced 500mm apart.

Figure 3: 400kV L12 Overhead Line Dimensions (Designed in PowerPoint)

The measurement of the magnetic field will be based along the 1 meter above ground line shown in

Figure 3. This analysis will therefore show the magnetic fields exposure to anyone walking around

the area of the overhead lines. (mx), (bx) and (tx) are the labels assigned to the conductors in

MatLab.


Page 9

Magnetic Field

The following equations are used to calculate the magnetic field. The results for Equation 4 and 5

depend on the number of conductors on the line and the distance of all the conductors from a given

point along the one meter line.

As there are 12 conductors, there will therefore be 12 (Bx) and 12 (By) values. The value of the

current (I) following in the conductors must also be calculated.

Surge Impedance Loading (SIL) level.

SIL level of a typical uncompensated 400kV with a bundle spacing of 450mm is 623MW as seen in

Table 1. The SIL increases as spacing increases. The SIL that will be used is 630MW for a 500mm

bundle spacing.

Table 1: Surge Impedance Loading Table for Different Bundle Spacing (Nayak, 2006)

Figure 4: X and Y Values (PowerPoint)


Page 10

Matlab was used to calculate the magnetic Field at any point for 100ms either side of the conductor

at 1m off the ground. As can be seen in Graph 1 the Magnetic field is 3.45 (μT) at the center of the

structure one meter above the ground. Graph 2 represents the magnetic field in Gauss (3.45 mG)

Graph 1: Magnetic Field (Tesla)

Graph 2: Magnetic Field (Gauss)

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

3.5x 10

-5

Magnetic f

lux (

T)

Meters

Magnetic Field Graph

Original 400/L12 Design

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

3.5x 10

-3

Magnetic f

lux (

G)

Meters




Page 11

Attempts at Reducing Magnetic Field

In an attempt to reduce the magnetic field along a range of points, 1 meter from the ground, the

distances of the conductors were changed in three different ways from the original design.

1. Original Design: This plot was calculated in Matlab using the dimensions from Figure 3 and

using Equations 4-6.

2. Compact Conductors: For this plot the bundles were brought closer together by a factor of

20% but the lowest conductor remained at 12 meters from the ground. However this change

is purely theoretical as to bring the conductors closer together could cause other

instabilities, (i.e. Structural, arcing, ect…)

3. Swapped Phases: As the angle of the current for the phase closest to the ground was zero for

the original Design, its magnitude was different to the other two phases as shown in the

Matlab code in the Appendix. The top and bottom phase were switched position and the

heights of the conductors were kept at the same as the Original Design. This design showed

the best improvement in the reduction of the magnetic field as shown in the Graph.

4. Minimum Height: The Minimum height allowed for the lowest conductor on a 400kV in 7.6

meters (National Grid, 2011). This simulation plotted the nearest conductor from the ground

at the minimum height but kept the distances between the phases the same as the Original

design. This resulted in a large increase in the magnetic field.

Graph 3: Different Configurations for Analysis of Magnetic Fields

-100 -80 -60 -40 -20 0 20 40 60 80 1000

1

2

3

4

5

6

7x 10

-5

Mag

netic

flu

x (T

)

Meters


Original Design

Compact Conductors

Swapped Phases

Minimum Height


Page 12

Table 1 and Equation 7 from page 9 of this report, displayed that a change in the spacing of the

conductors from a bundle causes a change in the Surge Impedance Loading, a change in the current

that flows in each conductor and therefore a change in the Magnetic Field. The original design

spaced the conductors in a bundle 500mm apart. Graph 4 displays the Magnetic field of the Original

design with all twelve conductors spaced 500mm apart against the conductors spaced 1 meter apart.

Graph 4: Magnetic Field with Conductors in Bundle 1 meter apart

This change to the parameters of the overhead line bundles displayed the highest level of magnetic

field at 1 meter from the ground and therefore shows that the closer the conductor bundles can be

together the lower the magnetic field.

-100 -80 -60 -40 -20 0 20 40 60 80 1000

1

2

3

4

5

6x 10

-5

Magnetic f

lux (

T)

Meters



1m Spaced Conductors


Page 13

Conclusion

The line assigned for this report was the 400kV overhead line. This line operates at the transmission

level of electricity supply system. In Ireland the transmission range of voltage operation is 110-

400kV. The parameters for this design were sourced from the National Grid, UK website.

400kV is the highest operational voltage rating in Ireland which made this a very interesting case

study as this is the overhead line that EirGrid will be looking to roll out in the future, as shown is

Figure 5. The reason for this potential rollout is to facilitate Irelands best wind resource in the West

of Ireland to provide electricity (and to export it) to the whole country but mostly Dublin in the east

of Ireland which is by far the largest load on the Nation Grid.

Figure 5: EirGrid’s Future Plans for Expansion of Transmission Lines (Ivan Dudurych, 2011)

The equations used to calculate the magnetic field is this case study were shown and can be

implemented for any sized overhead line if the structure parameters are known.

When attempting to reduce the magnetic filed in different scenarios the only reduction made was

when the phases were brought closer together. As stated, this would probably have caused a breach

of some other regulations regarding safety of operation. One other possibility would be to make the

structure taller and increase the height of all the phases. However this would not be financially or

operationally feasible. Therefore, this report can conclude that the National Grid plc UK designed

this overhead line structure to the safest operational magnetic field level as feasibly possible.


Page 14

Works Cited Conlon, M., 2012. Technical aspects of Electromagnetic Fields and Shielding, Dublin: D.I.T.

EirGrid, 2012. EirGrid's East-West Twitter Page. [Online]

Available at: http://twitter.com/#!/ewicIreland/

[Accessed 2nd April 2012].

Ivan Dudurych, 2011. EirGrid plc. [Online]

Available at: www.eirgrid.com

[Accessed 2 april 2012].

National Grid, 2011. EMFs Information. [Online]

Available at:

http://www.emfs.info/Sources+of+EMFs/Overhead+power+lines/Calculating/geometries/

[Accessed 02 April 2012].

Nayak, R., 2006. EHV Transmission Line Capacity Enhancement through Increase in Serge Impedance

Loading Level. IEEE xplore, p. 3.


Page 15

Appendix This is the main body of code that was used for this analysis. To plot different scenarios in the same

graph this code was copied, altered accordingly and then simulated.

%% Code for Magnetic Plots %% Fixed u = 4*pi*10^(-7); u1 = u/(2*pi);

y1 = 12; y2 = 20.7; y3 = 30; %% Defining each conductor from point (0,1) bx11 = -2.25 +100; bx12 = -1.75 +100;

bx21 = 1.75 +100; bx22 = 2.25 +100;

mx11 = -9.37 +100; mx12 = -8.87 +100;

mx21 = 9.37 +100; mx22 = 8.87 +100;

tx11 = -6.55 +100; tx12 = -6.05 +100;

tx21 = 6.55 +100; tx22 = 6.05 +100;

%%%Phase Currents I1 = complex(909,0); %(Convert from Polar to Rectangular) I2 = complex(-455,-787); %(909,<-120); I3 = complex(-455,787); %(909,<-240);

B =[]; %%%%Working out magnetic field starting at 100m to the left

for i =0:200

Bx = (-u1*I1*y1)/(bx11^2+y1^2) + (-u1*I1*y1)/(bx12^2+y1^2) + (-

u1*I1*y1)/(bx21^2+y1^2)+ (-u1*I1*y1)/(bx22^2+y1^2) + (-

u1*I2*y2)/(mx11^2+y2^2) + (-u1*I2*y2)/(mx12^2+y2^2) + (-

u1*I2*y2)/(mx21^2+y2^2)+ (-u1*I2*y2)/(mx22^2+y2^2) + (-

u1*I3*y3)/(tx11^2+y3^2) + (-u1*I3*y3)/(tx12^2+y3^2) + (-

u1*I3*y3)/(tx21^2+y3^2)+ (-u1*I3*y3)/(tx22^2+y3^2);

By = (u1*I1*bx11)/(bx11^2+y1^2) + (u1*I1*bx12)/(bx12^2+y1^2) +

(u1*I1*bx21)/(bx21^2+y1^2)+ (u1*I1*bx22)/(bx22^2+y1^2) +

(u1*I2*mx11)/(mx11^2+y2^2) + (u1*I2*mx12)/(mx12^2+y2^2) +

(u1*I2*mx21)/(mx21^2+y2^2)+ (u1*I2*mx22)/(mx22^2+y2^2) +

(u1*I3*tx11)/(tx11^2+y3^2) + (u1*I3*tx12)/(tx12^2+y3^2) +

(u1*I3*tx21)/(tx21^2+y3^2)+ (u1*I3*tx22)/(tx22^2+y3^2);

B = [B abs(sqrt((abs(Bx)^2)+(abs(By)^2)))];


Page 16

%% Defining X values along the 1 meter line

bx11 = bx11-1; bx12 = bx12-1; bx21 = bx21-1; bx22 = bx22-1; mx11 = mx11-1; mx12 = mx12-1; mx21 = mx21-1; mx22 = mx22-1; tx11 = tx11-1; tx12 = tx12-1; tx21 = tx21-1; tx22 = tx22-1; end figure X = [-100:1:100]; plot(X,B) ylabel 'Magnetic flux (uT)' xlabel 'Meters' title 'Magnetic Field Graph'

%%%Only used for plotting multiple scenarios

hold on;

Documents

Calculation of the Magnetic Field level in the Vicinity of ... · PDF fileCalculation of the Magnetic Field level in the Vicinity of a 400kV Transmission Line Page 3 Table of Graphs,