7/24/2019 05630410

1/4

Analysis of the Line-frequency Electric Field

Intensity around EHV Transmission

Fei WANG1*

, Weijie WANG1, Zhichao JIANG

1, Xuezeng ZHAO

1

1School of Mechanical Engineering,Harbin Institute of Technology,Harbin, P. R. China

* matagraphics@gmail.com

AbstractWith the increase of the applications of EHV

transmission lines operation, electromagnetic pollutions caused

by power lines attract more peoples attention. So researching on

the electric field intensity at operating frequency of EHV

transmission lines is very meaningful for the EHV transmission

lines design and the measurement of the surrounding

electromagnetic environment. Firstly, this paper sets up a

computational modeling of the electric field intensity around the

EHV transmission lines based on the charge simulation method

and method of mirror. It calculates the electric field intensity

around EHV transmission lines by Matlab, and analyses the

regularity of the electric field intensity when lack of phrase

happens. Then it analyses the distributions and regularities of the

electric field intensity under the influences of several actual

conditions. In the end, it draws some helpful conclusions on the

reduction of electric field intensity of EHV transmission lines and

the estimation of the EHV transmission lines status according to

the distributions of electric field.

Keywords- EHV transmission lines, frequency electric field,

frequency magnetic field, non-contact measurement

I. INTRODUCTION

Since put into operation, the EHV transmission lines havegradually become the backbone network in electric powersystem in China. Thereupon the influence on residents andequipment nearby from the electromagnetic pollution produced

by the EHV transmission lines has attracted the attention ofvarious circles of society and more and more studies indicate

perniciousness of the pollution. So the transmission linesshould be designed to minimize electromagnetic pollution andreduce the transmission lines corridor area. Studying theelectromagnetic field surrounding the transmission lines hasimportant significance for transmission line design. In addition,maintainers must check whether the lines are still running

before overhauling the lines to ensure personal safety in thespring inspection or power failure. With the voltage levels of

power network in operation increase, the distance between

transmission line and ground higher and higher, traditionalcontacting electroscope has struggled to adapt to actual needs,thus developing electric equipment for non-contactexamination is an important research direction. When the EHVtransmission lines are running, frequency electric field

permeate the space around, we can judge the running state ofthe lines from the distribution rule under different conditions.To establish modeling and simulation of electric field aroundthe EHV transmission lines, some necessary hypothesis andsimplified handling charge are carried out, and themathematical model of two-dimensional electric field around

the EHV transmission lines is established based on the chargesimulation method, and the model is suitable for open field. Isummarize the basic distribution rule of the frequency electricfield through doing simulation analysis of examples by Matlab..Then I analyzed the electric field distributions around the EHVtransmission lines without part of three phases and summarizedthe characteristics and proposed a method to complete analysisfor the state of transmission lines according to the

characteristics. According to the characteristics of large currentabout EHV transmission lines in some simplified conditions,the mathematical model of two-dimensional magnetic fieldaround the EHV transmission lines is established on the basisof current simulation method. Through Matlab simulationanalysis, I arrived at the basic law of frequency magnetic fieldand analyzed frequency magnetic field distribution rule aroundEHV transmission lines on the influence of different conditions.

II. MODELING FOR THE LINE-FREQUENCY ELECTRIC FIELD

AROUND EHVTRANSMISSION

A. Theory Basis

We begin by discussing the general assumptions and

approximation supplemented in the present theoretical mode,and it is assumed that the EHV transmission line satisfies thefollowing criterion: (a) Taking the frequency alternatingelectric field as a quasi-static field. (b) Take the earth as a zero-electric potential, set the simulation charge on the image

position corresponds to the earth as the mirror. (c) Ignore theeffect of lightning line on the surrounding electric fieldintensity. (d) Treat the three-dimensional electric field as atwo-dimensional electric field.

Under normal circumstances, EHV transmission lines arerelatively long, to simplify the calculation, ignore the sag andthe end effect, and take the transmission lines as infinitely longstraight parallel conductors, and take the lowest point of the

power lines sag as the ground clearance and take the cross-

section of the wire as the calculating plane.

Figure 1. Calculation diagram for the equivalent radius

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 2010 IEEE

DOI 10.1109/iCECE.2010.815

3343

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 2010 IEEE

DOI 10.1109/iCECE.2010.815

3343

7/24/2019 05630410

2/4

(5) Treatment for the bundled conductors

Bundled conductors are often used as the EHVtransmission lines in practice. The lines are commonlysimplified as cylindrical wires in order to simplify thecalculation, as shown in Figure 1. The wire radius can bereplaced by the equivalent radius whose formula is as follows:

nn R nr R R = , 1

where nR is the equivalent radius,Ris the radius of the bundled

conductor, n is the quantity of minor wires and r is the radiusof the wire.

The simplification of the transmission line systempresented above is the basis to establish the electric fieldcalculation model for EHV transmission line, which may causea certain deviation between the simulation results andmeasured values. Even though, the simulation is still able tomeet the demands of precision in engineering calculation.

B.

Modeling

(1) The Cartesian coordinates for the analysis have beenestablished in the plane perpendicular to the wire as shown inFigure 2.

(2) Selection and configuration of the simulation chargeand match points we select infinitely long straight wires assimulation charges, which are placed in the center of thecylindrical transmission lines. The matching points are set upin near the boundaries of the cylindrical transmission lines, asshown in Figure 2.

Figure 2. Configuration of the simulation charge and match points for the

Single-back three-phase power transmission lines

(3) Simulation charge equations

Here, as shown in figure 2, 4Q 5Q 6Q are the image

charges for 1Q 2Q 3Q respectivelywhose quantity ofelectricity are identity but the directions are onsite to their

corresponding points therefore there are only there

unknown varies in the model shown in figure 2. as a result,only three formulae are needed for solution of the model.Because the electric potential of A1, A2 and A3 are alreadyknow, it is easily to obtain following formulae based on the

principle of superposition.

11 1 12 2 13 3 A1

21 1 22 2 23 3 A2

31 1 32 2 33 3 A3

P Q P Q P Q

P Q P Q P Q

P Q P Q P Q

+ + =

+ + = + + =

, 2

where ijP is the potential coefficient and we have

ij

ij

ij

D1P ln2 d

=

is the dielectric coefficient of air which

can be obtained through91 10 /

36F m

= ijd is the

distance between the simulation charge i and j; ijD the

distance between the simulation i and the image of simulationcharge j.

After the solving of Equation 2we have obtained value of

the simulation charges,

[ ] [ ] [ ]1

Q P

= . 4

(4) Verification for the accuracy of the simulation

However the accuracy of the simulation charges obtainedby the method presented above should be verified later as

followsFirstly, select a several verification points on the

boundaries labeled 1, 2, 3, , n, whose electrical potential canbe calculated by:

( )3

1

Ai ij j

j

P Q=

= . i=1, 2, ...,

Secondly, compare the calculated values to the boundary

conditions and calculate the relative error which can indicatethe accuracy of the simulationIf the accuracy does not meet

the requirements, the positions and quantity of simulationcharges should be changed and the simulation procedureshould be re processed.

Figure 3. Diagram for the potential distribution of three-phase

(5) Calculation of electric field intensity

Considering that the currents passing through the lines arethree-phase symmetrical sinusoidal currentswe can use the

RMS value to characterize the value of their potentials andcurrent. See fig 3, the phase voltage of each line of thetransmission lines can be determined as the following

33443344

7/24/2019 05630410

3/4

1 3( )

2 2

1 3( )

2 2

A

B

C

U U

U j U

U j U

=

= +

==

. 4

We can calculate the electrical field within the calculationregion though the simulation charges calculated by Equation 2.

Note that, the electrical field of any point should be in the formof phasor because the electrical potential as well as thesimulation charges are phasors.

The sum electrical field intensity of a random point P(x,y)generated by a number of n wires can be obtained through theGauss theorem and the superposition theorem.

ii

1 ip ip

Q 1 1E = ( )

2 d D

N

i = . 5

In the rectangular coordinate system we have establishedthe x-axis parallels to the earth and the y-axis perpendiculars

to the earththerefore, the horizontal and vertical components

of the electrical field intensity is as follows:

ix 2 2

1 ip ip

QE = ( )

2 d D

Ni i

i

x x x x

=

, 6

iy 2 2

1 ip ip

QE = ( )

2 d D

Ni i

i

y y y y

=

+ , 7

where,i iy

the coordinated for the line are number i.

As the charges in the wire are written in the form ofcomplex, the components should be given in complex form

either.

1

( )n

x xR xI ixR ixI

i

E E jE E jE=

= + = + , 8

1

( )n

yR yI iyR iyI

i

E E jE E jE=

= + = + , 9

where the foot scripts R and I indicates the real part andimaginary part.

The total electrical field intensity of point P can be givenby:

( ) ( )xR yR x yR yI y

E E jE e E jE e

= + + + , 10

where xe

ye

are the unit vectors.

Equation (10) is the model for the relationship between theelectrical field intensity and the potential of the EHVtransmission lines.

C. Case study for 500KV EHV

We set the conditions according to the distribution oftransmission lines in practice. The average overhead height isset to 12m, Level spacing is 8m, Each phase conductor isequivalent to a radius of 0.0136mwe simulated the electric

field under the transmission lines arranged horizontally throughthe method established above. Diagram for the field intensitycan be obtained as shown in Figure 4.

Figure 4. Diagram for electric field intensity under wires arrangedhorizontally

We study the electric field intensity of the points within

30m distance from the center of the wire (1m space) and 1.5mheight from the ground (approximately the height of the

human heart). The distribution curve is shown in Figure 4.We can know from Figure 4, in the situations where the

lines array horizontally, the ground electric field intensitydistribution is symmetrical, the electric field intensity near

ground depend on the vertical component mainly and thecombined field strength distribution is saddle-shaped. The

field strength peaks around the bottom of center of thetransmission lines, whereas the electric field shows clearly a

downward trend away from the two sides of the wires.According to the 4kV/m limitation of electric field intensitynear EHV transmission lines given by SEPA , we can see that

regions about 25m away from the center conductor can meetthe requirement.

33453345

7/24/2019 05630410

4/4

D. electrical indensity changes of EHV transmission lineslack of phases

Practically, the electrical intensity of EHV wires would

change effectively when one or more lines turn offThis

change can be utilize to develop the equipments to detectwhether there is one or more wires of EHV are tuned off forsafety applications. Or, we can detect the electric field

distributed through a professional field strength meter andjudge the status of the EHV wires, which is especially

important for protection of the maintenance persons.

Figure 5. Field indensity distibution under 2 phases on and 1 phase off

Figure 6. field intensity distribution under 2 phases off and 1 phase on

The field distribution diagram under the situations where 1phase is off and 2 phases are on is shown in figure 5, whereasthe field distribution diagram under the situations where 1

phase is on and 2 phases are off is shown in figure 6. We cansee from the figure that the field strength distribution iscontinuous at the same height and the horizontal electric fieldchanges much more effectively than the vertical electric field.Further more, the vertical component is main factor which canaffects the overall field strength

If we measure several points from left to right in turn, thenthe status of the EHV wires can be determined through themeasured electric field distribution. This non-contactmeasurement is of great importance for the protection of

personal safety. Finally, because the changes in the horizontaldirection are much more obvious, we can select the fieldstrength in the horizontal direction to determine power states ofthe wires.

III. CONCLUSION

A model for simulation of electric field around the EHVtransmission lines has been established. Basic distribution rule

of the frequency electric field through the presented model hasbeen summarized. A detailed analysis has been done to studythe electric field distributions around the EHV transmissionlines without part of three phases and a method to detect the

state of transmission lines based on the analysis has beenpresented which is of importance for researches on EHV and

can be easily extended for the designing of the non contactequipment for s EHV wires power status detection.

REFERENCES

[1] Yinbiao SHU. Current situation and development of state grid. Beijin.

Proceeding of the fifth international conference on transmission anddistribution technology.

[2] Qichun ZHANG, Hongjun RUAN, Jianhui YU. Mathematical modelsfor electric field under high voltage overhead line. High VoltageEngineering. 2000, 26(1).

[3] Peng SUN, Xiaodong ZHANG. Mathematical model and simulation ofelectric field of high-voltage line under working frequency. ElectricPower Construction. 2005, 26(4).

[4] Shijiang CHEN. Study on distribution and control of 500kV EHVtransmission line power frequency. Master's thesis of Fuzhou University.2006.

[5] Yanyan FENG. Study on simulation of electromagnetic field caused bysuper high voltage transmission lines. Master's thesis of ChongqinUniversity. 2004.

[6] Linhua LIU, Quandi WANG, Jihui YU, Xinzhe HOU, Huaiqin ZHANG.Measurement result and analysis of electromagnetic environment of 500

kV extra high voltage power lines. Journal of ChongqingUniversity(Natural Science Edition). 2006, 29(5): 0028-04.

[7] Lee B.Y.Park J.K.Myung S. H. etc. An Effective Modeling toAnalyze Electric Field around Transmission Lines and SubstationsUsing a Generalized Finite line Charge. IEEE Transactions on PowerDelivery, 1997, 12(3).

33463346