RESEARCHON ELECTRIC FIELD ON HIGH VOLTAGE-TRANSMISSION

Research on electric field of High-Voltage transmission line power frequency 2011

RESEARCHON ELECTRIC FIELD ON HIGH VOLTAGE-TRANSMISSION

LINE POWER FREQUENCY

SEMINAR REPORT

BY

Roshan joy

DEPT OF ELECTRICAL AND ELECTRONICS ENGINEERINGST.JOSEPH’S COLLEGE OF ENGINEERING AND TECHNOLOGY, PALAI

2011

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ABSTRACT

This paper presents a model for computing Power frequency electromagnetic

field of over head high voltage transmission line based on Simulation Charge

Method. Based on this model, the electric field intensity under power line is

calculated and the distribution is analyzed in different conditions such as

different distant between phase line, different phase order for double circuit, and

different arrangement of line in single circuit or double circuit. According to the

simulation results, the electric fields under over head transmission line can be

forecast. This is no doubt important in environment protection and in the design

of transmission line.

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INTRODUCTION

Electric Power is the basic need for the economic development of any country.

Electricity is the most inevitable thing today The transmission system is to deliver bulk power

from power stations to the load centers and large industrial consumers. With the rapid

developing of economy and enlarging of the city, the electric power supply is faced a new

demand. In order to fulfill these requirements high voltage transmission is now used.

There are several advantages in adopting high voltage for transmission and distribution. They

include: increase in transmission efficiency, reduction in electrical losses, improvement of

voltage regulation, flexibility for future etc... There are many disadvantages like corona loss and

radio interference, need of heavy supporting structures, electromagnetic pollution etc. These

losses increase with a small increase in electric field intensity. The influence of electric field is

more than magnetic field. So electric field is concerned in this paper.

This paper presents a model for computing electromagnetic field of overhead high voltage

transmission line based on simulation charge method. Based on this model, the electric field

intensity under line is calculated and the distribution is analyzed in different condition such as

different distant between phase line, different phase order for double circuit and different

arrangement of line in single or double circuit Here we are not conducting the test actually. But,

we are simulating the system with actual factors. Simulation under power line is on the basis of

charge simulated method (C.S.M). According to the simulation results, the electric fields under

overhead transmission line can be forecast. This is no doubt important in environment

protection and available in the design of transmission line.

With the rapid developing of economy and enlarging of city, the electric power supply is faced a

new demand. At the same time, with the improving of living standard, the consciousness for

environment protection and health is increasing. So, the electromagnetic pollution is no doubt to

become a new and most concerned problem. With the increasing conflict to electromagnetic

environment, it is essential for electrical department to take action to decrease the

electromagnetic field level under the over head power line. To solve this problem, the first way

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is to simulate and analyze the electromagnetic field there. Here we are considering the electric

field. In this paper, a computation model is built up first, it contains actual factors, such as

bundle conductors, multicircuit, overhead ground wire and the phase order, And Then software

is developed. After this software is verified with field test results measured and the software is

used to study the electric field under over head high-voltage transmission line.

ELECTRIC AND MAGNETIC FIELD

Electromagnetic fields consist of electric (E) and magnetic (H) waves traveling together, as

shown in the diagram below. They travel at the speed of light and are characterized by a

frequency and a wavelength. The frequency is simply the number of oscillations in the wave per

unit time, measured in units of hertz (1 Hz = 1 cycle per second), and the wavelength is the

distance traveled by the wave in one oscillation (or cycle).

Sinusoidal electromagnetic wave

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Electric fields arise from electric charges. They govern the motion of other charges situated in

them. Their strength is measured in units of volt per meter, (V/m), or kilovolt per meter (kV/m).

When charges accumulate on an object they create a tendency for like or opposite charges to be

repelled or attracted, respectively. The strength of that tendency is characterized by

the voltage and is measured in units of volt, (V). Any device connected to an electrical outlet,

even if the device is not switched on, will have an associated electric field that is proportional to

the voltage of the source to which it is connected. Electric fields are strongest close the device

and diminish with distance. Common materials, such as wood and metal, shield against them.

Magnetic fields arise from the motion of electric charges, i.e. a current. They govern the motion

of moving charges. Their strength is measured in units of ampere per meter, (A/m) but is usually

expressed in terms of the corresponding magnetic induction measured in units of tesla, (T),

millitesla (mT) or microtesla (µT). In some countries another unit called the gauss, (G), is

commonly used for measuring magnetic induction (10,000 G = 1 T, 1 G = 100 µT, 1 mT = 10

G, 1 µT = 10 mG). Any device connected to an electrical outlet, when the device is switched on

and a current is flowing, will have an associated magnetic field that is proportional to the current

drawn from the source to which it is connected. Magnetic fields are strongest close to the device

and diminish with distance. They are not shielded by most common materials, and pass easily

through them.

ELECTROMAGNETIC POLLUTION

Electric and magnetic fields produced by electric power systems have

recently been added to the list of environmental agents that are a potential threat to public

health. This paper describes peoples’ exposures to fields from power systems and other sources

reviews existing scientific evidence on the biological effects of these fields presents a history of

research support and of regulatory activity and discusses problems and alternatives in regulatory

action.

The electric power that is used in our homes, offices and factories uses

AC or alternating current. This is in contrast to the DC or direct current that is produced by

batteries. An alternating current doesn’t flow steadily in one direction. It alternates back and

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forth. The power used in North America alternates back and forth 60 times each second. This is

called 60 hertz (Hz) power. In Europe and some other parts of the world the frequency of

electric power is 50 hertz rather than 60 Hz.

There are electric and magnetic fields wherever there is electric power.

This means that there are fields associated with large and small power lines, wiring and lighting

in homes and places of work, and all electrical appliances. These fields are created by the

electric charges that are pumped into the power system by electric power generating stations.

Electric fields arise from the amount of that charge and magnetic fields result from the motion

of that charge. Taken together, these fields are often referred to as electromagnetic fields. The

electric and magnetic fields created by power systems oscillate with the current. That is why

fields around power systems are called power-frequency or 60 hertz fields.

Public concerns about power-frequency fields first emerged in the late

1960s as power companies turned increasingly to extra high voltage (EHV) transmission lines to

handle large increases in electricity use. EHV lines carry electric power with lower energy

losses and with smaller land usage than multiple lower-voltage lines with the same power-

delivery capacity. Public attention to EHV transmission lines focused first on the aesthetic

impact of their large towers, on the aesthetic and ecological impacts of their rights-of-way, and

on various nuisance effects created by their strong electric fields. These nuisance effects include

audible noise, TV/radio interference, and induced shocks that can occur when a person standing

beneath an EHV line touches a large ungrounded metal object such as a truck or farm vehicle.

By the early 1970s, the American National Standards Institute had issued voluntary standards to

address nuisance effects. The first evidence that power-frequency fields might have a direct

effect on human health appeared in 1972 when Soviet investigators reported that workers in

Soviet EHV switchyards suffered from a number of nonspecific ailments. Although these

reports were greeted with much skepticism by western scientists, they served to stimulate public

concern. By the mid seventies, health effect There are two reasons why conventional wisdom

has until recently held that the fields associated with power systems could pose no threat to

human health. First, there is no significant transfer of energy from power-frequency fields to

biological systems. Unlike X-rays (i.e. ionizing radiation), power frequency fields do not break

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chemical bonds. Unlike microwaves (i.e. non-ionizing radiation), power frequency fields cannot

cause significant tissue heating. Second, all cells in the body maintain large natural electric

fields across their outer membranes. These naturally occurring fields are at least 100 times more

intense than those that can be induced by exposure to common power-frequency fields. It had

become a central issue in transmission line sitting hearings in several states.

However, despite the low energy of power-frequency fields and the very small

perturbations that they make to the natural fields within the body, studies over the last fifteen

years have demonstrated unequivocally that under certain circumstances, the membranes of

cells can be sensitive to even fairly weak externally imposed low frequency electromagnetic

fields. Extremely small signal changes can trigger major biochemical responses critical to the

functioning of the cell. This should perhaps have come as no surprise, as cells, especially those

in the nervous system, make use of complex electrochemical processes in their normal function.

The ability of some animals including eels, sharks, and pigeons to detect extremely weak ELF

fields and use them for homing and finding prey clearly demonstrates that at least some specialized

cells can be acquisitively sensitive to such fields. Among the responses demonstrated in laboratory

studies using animal cells and tissue are:

modulation of ion flows;

interference with DNA synthesis and RNA transcription;

interaction with the response of normal cells to various agents and biochemical such as

hormones, neurotransmitters, and growth factors;

Interaction with the biochemical kinetics of cancer cells.

Even when effects are demonstrated consistently on the cellular

level in laboratory experiments, it is hard to predict whether and how they will affect the whole

organism. Processes at the individual cell level are integrated through complex mechanisms in

the animal. When a process in the cell is lightly perturbed by an external agent such as an ELF

field, other processes may compensate for it so that there is no overall disturbance to the

organism. Some perturbations may be within the ranges of disturbances that a system can

experience and still function properly. This difficulty in extrapolating cellular level effects to

predict the existence or severity of possible public health effects, together with the absence of

any large-scale and obvious public health effect associated with electrification, are two

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arguments advanced during the last decade in support of the claim that there is no need for

concern about possible public health effects from exposure to power-frequency fields.

Another problem in deducing possible health effects from cellular

level effects has been the lack of a theoretical model to explain and understand the detailed

mechanism of interaction. ELF fields affect the cell via the cell membrane. Cell membrane

biology is still in its infancy although this area of molecular biology has made great strides in

the past few years. Until recently, there was not enough understanding to even advance

hypotheses on the potential mechanisms by which ELF fields may cause significant

perturbations in cell and organ functions. Hypotheses are now being advanced but are still at a

speculative stage

As we discuss earlier, findings at the cellular level display considerable

complexity including resonant responses (or, “windows”) in frequency and field strength,

complex time dependencies, and dependence on the ambient DC magnetic field created by the

earth. For these reasons, ELF field appear to be an agent to which there is no known analog.

Many lessons learned from environmental hazards such as chemical agents (PCB, vinyl

chloride, benzene, etc.) or physical agents (ionizing radiation, asbestos etc.) may not directly

apply to ELF fields. This is because in the case of fields it is not yet clear what measures of

exposure or “dose” are relevant. In contrast to more familiar environmental agents where “if

some of it is bad, more of it is worse”, it may not be safe to assume that if ELF field

exposure leads to health risks, exposure to stronger fields or exposure for longer periods is

worse than exposure to weaker fields or brief periods. In addition to cellular studies, whole

animal and human experiments have examined five general categories of effects:

1. General effects such as detection, avoidance and behavior response and development and

learning of animals, and moods of humans

2. Effects on externally measured physical parameters such as growth and birth weight,

respiration, heartbeat rate, and temperature rhythms

3. Effects on specific biochemical such as hormones that are responsible for the maintenance,

regulation and control of general physiological and psychological functions ;for response to

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environmental stressors; for growth and development; and, for triggering special responses such

as sexual function, and fetal and newborn nourishment

4, Effects on circadian rhythms of animals and humans; and

5. Effects in the epidemiology of cancer, particularly leukemia and brain cancer.

In summary, the results are complex and inconclusive. There have been many “negative”

experiments, that is, experiments that have looked for effects but not found any difference

between biological systems that have been exposed to fields and those that have not. However,

the growing numbers of positive findings have now clearly demonstrated that under specific

circumstances even weak. Low-frequency electromagnetic fields can produce substantial

changes at the cellular level, and in a few experimental settings, effects have also been

demonstrated at the level of the whole animal. Epidemiological evidence, while controversial

and subject to a variety of criticisms, is beginning to provide basis for concern about risks from

chronic exposure. Some observers find this epidemiological evidence more persuasive in light

of the clear evidence of effects that is available at the cellular level, but others insist on treating

the evidence from these two areas as separate.

As recently as a few years ago, scientists were making categorical statements that on the basis of

all available evidence there are no health risks from human exposure to power-frequency fields.

In our view, the emerging evidence no longer allows one to categorically assert that there are no

risks. But it does not provide a basis for asserting that there is a significant risk. If exposure to

fields does turn out to pose a health risk, it is unlikely that high voltage transmission lines will

be the only sources of concern. Power-frequency fields are also produced by distribution lines,

Wall wiring, appliances, and lighting fixtures. These non-transmission sources are much more

common than transmission lines and could play a far greater role than transmission lines in any

public health problem.

Electromag

netic fields and public health

Everyone is exposed to a complex mix of electromagnetic fields

(EMF) of different frequencies that permeate our environment. Exposures too many EMF

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frequencies are increasing significantly as technology advances unabated and new applications

are found.

While the enormous benefits of using electricity in everyday life

and health care are unquestioned, during the past 20 years the general public has become

increasingly concerned about potential adverse health effects of exposure to electric and

magnetic fields at extremely low frequencies (ELF). Such exposures arise mainly from the

transmission and use of electrical energy at the power frequencies of 50/60 Hz.

The World Health Organization (WHO) is addressing the associated

health issues through the International Electromagnetic Fields Project. Any health consequence

needs to be clearly identified and appropriate mitigation steps taken if deemed necessary.

Present research results are often contradictory. This adds to public concern, confusion and lack

of confidence that supportable conclusions about safety can be reached.

The purpose of this Fact Sheet is to provide information about ELF

field exposure and its possible impacts on health within the community and the workplace.

Information comes from a WHO review of this subject and other recent reviews by eminent

authorities.

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SOURSES

Naturally occurring 50/60 Hz electric and magnetic field levels are extremely low; of the order of

0.0001 V/m, and 0.00001 µT respectively. Human exposure to ELF fields is primarily associated

with the generation, transmission and use of electrical energy. Sources and typical upper limits of

ELF fields found in the community, home and workplace are given below.

Community: Electrical energy from generating stations is distributed to communities via high

voltage transmission lines. Transformers are used to lower the voltage for connections to residential

distribution lines that deliver the energy to homes. Electric and magnetic fields underneath overhead

transmission lines may be as high as 12 kV/m and 30 µT respectively. Around generating stations

and substations, electric fields up to 16 kV/m and magnetic fields up to 270 µT may be found.

Home: Electric and magnetic fields in homes depend on many factors, including the distance from

local power lines, the number and type of electrical appliances in use in the home, and the

configuration and position of household electrical wiring. Electric fields around most household

appliances and equipment typically do not exceed 500 V/m and magnetic fields typically do not

exceed 150 µT. In both cases, field levels may be substantially greater at small distances but they do

decrease rapidly with distance.

Workplace: Electric and magnetic fields exist around electrical equipment and wiring throughout

industry. Workers who maintain transmission and distribution lines may be exposed to very large

electric and magnetic fields. Within generating stations and substations electric fields in excess of 25

kV/m and magnetic fields in excess of 2 mT may be found. Welders can be subjected to magnetic

field exposures as high as 130 mT. Near induction furnaces and industrial electrolytic cells magnetic

fields can be as high as 50 mT. Office workers are exposed to very much smaller fields when using

equipment such as photocopying machines and video display terminals.

HEALTH EFFECTS

The only practical way that ELF fields interact with living tissues is by inducing electric fields and

currents in them. However, the magnitude of these induced currents from exposure to ELF fields at

levels normally found in our environment is less than the currents occurring naturally in the body.

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Electric Field Studies: Available evidence suggests that, apart from stimulation arising from

electric charge induced on the surface of the body, the effects of exposures of up to 20 kV/m are few

and innocuous. Electric fields have not been shown to have any effect on reproduction or

development in animals at strengths over 100 kV/m.

Magnetic Field Studies: There is little confirmed experimental evidence that ELF magnetic fields

can affect human physiology and behavior at field strengths found in the home or environment.

Exposure of volunteers for several hours to ELF fields up to 5 mT had little effect on a number of

clinical and physiological tests, including blood changes, ECG, heart rate, blood pressure, and body

temperature.

Melatonin: Some investigators have reported that ELF field exposure may suppress secretion of

melatonin, a hormone connected with our day-night rhythms. It has been suggested that melatonin

might be protective against breast cancer so that such suppression might contribute to an increased

incidence of breast cancer already initiated by other agents. While there is some evidence for

melatonin effects in laboratory animals, volunteer studies have not confirmed such changes in

humans.

Cancer: There is no convincing evidence that exposure to ELF fields causes direct damage to

biological molecules, including DNA. It is thus unlikely that they could initiate the process of

carcinogenesis. However, studies are still underway to determine if ELF exposure can influence

cancer promotion or co-promotion. Recent animal studies have not found evidence that ELF field

exposure affects cancer incidence.

Epidemiological Studies: In 1979 Wertheimer and Leeper reported an association between

childhood leukemia and certain features of the wiring connecting their homes to the electrical

distribution lines. Since then, a large number of studies have been conducted to follow up this

important result. Analysis of these papers by the US National Academy of Sciences in 1996

suggested that residence near power lines was associated with an elevated risk of childhood

leukemia (relative risk RR=1.5), but not with other cancers. A similar association between cancer

and residential exposure of adults was not seen from these studies.

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Many studies published during the last decade on occupational exposure to ELF fields have

exhibited a number of inconsistencies. They suggest there may be a small elevation in the risk of

leukemia among electrical workers. However, confounding factors, such as possible exposures to

chemicals in the work environment, have not been adequately taken into account in many of them.

Assessment of ELF field exposure has not correlated well with the cancer risk among exposed

subjects. Therefore, a cause-and-effect link between ELF field exposure and cancer has not been

confirmed.

PROTECTIVE MEASURES

Large conducting objects such as metal fences, barriers or similar metallic structures permanently

installed near high voltage electrical transmission lines should be grounded. If such objects are not

grounded, the power line can charge them to a sufficiently high voltage that a person who comes into

close proximity or contact with the object can receive a startling and uncomfortable shock. A person

may also receive such a shock when touching a car or bus parked under or very near high voltage

power lines.

General public: Since current scientific information is only weakly suggestive and does not

establish that exposure to ELF fields at levels normally encountered in our living environment might

cause adverse health effects, there is no need for any specific protective measures for members of

the general public. Where there are sources of high ELF field exposure, access by the public will

generally be restricted by fences or barriers, so that no additional protective measures will be

needed.

Workers: Protection from 50/60 Hz electric field exposure can be relatively easily achieved using

shielding materials. This is only necessary for workers in very high field areas. More commonly,

where electric fields are very large, access of personnel is restricted. There is no practical,

economical way to shield against ELF magnetic fields. Where magnetic fields are very strong the

only practical protective method available is to limit of personnel.

EMF INTERFERENCE

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Strong ELF fields cause electromagnetic interference (EMI) in cardiac pacemakers or other

implanted electro medical devices. Individuals using these devices should contact their doctor to

determine their susceptibility to these effects. WHO urges manufacturers of these devices to make

them much less susceptible to EMI.

Office workers may see image movement on the screen of their computer terminal. If ELF magnetic

fields around the terminal are greater than about 1 µT (10 mG) this can cause interference with the

electrons producing the image on the screen. A simple solution to this problem is to relocate the

computer to another part of the room where the magnetic fields are below 1 µT. These magnetic

fields are found near cables that provide electric power to office or apartment buildings, or around

transformers associated with power supplies to buildings. The fields from these sources are generally

well below the levels that cause any health concern.

Block diagram for EMI measurement

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NOISE, OZONE AND CORONA

Noise in the form of a buzzing or humming sound may be heard around electrical transformers or

high voltage power lines producing corona (see below). While the noise may be annoying, there are

no EMF health consequences associated with these sounds.

Electrical devices such as photocopiers or any device using a high voltage to function may produce

ozone, a colorless gas having a pungent smell. Electrical discharges in the air convert oxygen

molecules into ozone. While people may easily smell the ozone, the concentrations produced around

photocopiers and similar devices are well below health standards.

Corona or electrical discharges into the air are produced around high voltage power lines. It is

sometimes visible on a humid night or during rainfall and can produce noise and ozone. Both the

noise levels and ozone concentrations around power lines have no health consequence.

CHARGE SIMULATION METHOD

For the rather complicated and time-consuming three dimensional electric field calculations in the

vicinity of transmission lines and substations, this paper proposes an effective numerical calculation

method based on Charge Simulation Method (CSM).

In order to represent non-uniform charge distribution on an electrode

better, it is subdivided into small segments with linear charge density. Each segment with linear

charge density can be easily represented by a generalized finite line type of charge whose

expressions for potential and electric field were analytically derived and which was named "finite

slant line charge" in this paper. As for the arrangement of small segments of a subdivided electrode,

it has been found that unequally spaced arrangement method is superior to equally spaced one. In

order to arrange segments fast and effectively, effective formulas were derived from multiple

regression analysis of many simulations. The proposed method is applied to the electric field

calculation around the transmission lines with significant change in direction to the design of

transmission lines and substations bus bars.

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In case of transmission lines, analytical or numeric computations have been

mainly handled as two-dimensional problems. It has been shown that the computed values compared

researches. However, two-dimensional methods are not applicable to transmission lines that have a

significant change in direction. Scale model approach where the entire transmission lines are

modeled according to a linear factor would be used to deal with a problem like this. The method

proved quite effective but the construction of the scaled-down model is a painstaking exercise.

As for the electric fields in substations, the calculation is very complicated

due to the high degree of complexity of electrodes and large number of components. In 1979,

energized scale model studies of substation electric fields were carried out. Field measurements

would also be a possible way but this is time-consuming. J.E.T. Villas tried to calculate the three-

dimensional electric field in substation using ground grid performance equations. In each

electrode(substation busbar) was represented by a segment with uniform charge density. Hence the

non uniform charge distribution could not be represented properly. Finite element techniques were

also applied to the electric field calculation in substations. This method required many variables, a

large computer storage capacity and it is very time-consuming. In this paper, for the rather

complicated and time-consuming three-dimensional electric field calculation in the vicinity of

transmission lines and substations, an effective numerical calculation method based on CSM is

proposed. For a better representation of non-uniform charge distribution, the electrodes would be

subdivided into small segments with linear charge density. In order to represent a segment with

linear charge density, the expressions for potential and electric field produced by a generalized finite

line type of charge which was named "finite slant line charge" were analytically derived. Due to the

generality of the finite slant line charge. it can be easily used without any coordinate transform.

As for the arrangement method for small segments of a subdivided

electrode, the following four cases would be considered according to the segment length and charge

density.

1. Equally spaced segment with constant charge density.

2. Equally spaced segment with linear charge density

3. Unequally spaced segment with constant charge density

4. Unequally spaced segment with linear charge density

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Case 4 turned out to be the best charge arrangement method among

the four choices due to the comparison of potential errors. In case 4, potential errors strongly depend

on how unequally spaced segments are arranged. Thus a method to arrange these segments was dealt

with in terms of minimizing the mean value of relative potential errors without resorting to the

experience of computation. Moreover, in order to arrange segments fast and effectively regardless of

the geometric factors of an electrode, useful formulas for charge arrangement were derived from

multiple regression analysis of many simulations. The proposed method is applied to practical

examples.

THE METHOD

The simulation under power line is on the basis of Charge Simulation Method (CSM). According to

the Unique Theory, the continued free charges on the surface of electrode or the tied charge on the

dielectric material are substituted equivalently by discrete simulated charges, the electric fields in the

space are calculated on the base of these charges by using superposition principle, and these electric

fields are the electric field of power line.

If φ is the electric potential function, then

The boundary conditions are

Because of not knowing the distribution of actual charges, some dispersion charges, Q, the

equivalent charges are set to substitute these unknown charges outside the computation domain.

Then, the relationship between the equivalent charges and electric potentials of matching points are

described by the matrix [p]. [Q]= [φ] . Solve the matrix, the equivalent charges will be obtained, and

the potential or electric field in the space will also be gotten.

The model for the computation of electric field under power line is simplified as

below

a) Take the power frequency problem as quasi-static field;

b) The problem is simplified as two-dimension one;

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c) The earth is taking as a good conductor which electric potential is zero;

d) The computation voltage is 1.05 times of that the rating voltage.

On the basis of the above simplification, a soft developed. By using this software, the

electromagnetic field under power line is simulated; the result is very close to measured one as

shown in the graph below.

EFFECTIVE FORMULA FOR THE UNEQUALLY SPACED

ARRANGEMENT OF SEGMENTS WITH LINEAR CHARGE DENSITY

Optimal unequally spaced arrangement of segments with linear charge density for an electrode

In the case of unequally spaced arrangement of segments, the wrong initial

arrangement of segments does not give a more accurate answer with an increase in the number of

segments. This paper presents an optimal unequally spaced arrangement method through the analysis

of potential errors. Suppose an electrode parallel to x-axis whose length is L, radius is R and height

from the ground is H and that φb kV is applied to the electrode. Fig. shows the charge distribution on

the electrode and illustrates subdivision of an electrode into small segments according to the charge

distribution. Once the geometric factors and the number of segments are set, the mean value of the

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relative potential errors depends on how the electrode is subdivided. Thus, it is a function of the xi .

To find the solution which minimizes this function, consider an optimization problem involving

inequality constraints:~

Fig. Illustration of subdividing an electrode into small segments according to the charge density distribution

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Using symmetrical arrangement of segments, the number of optimization

variables can be reduced to by approximately 50 %. It is very difficult to find the solution for this

problem using the gradient based method. Hence, direct search method is used. When an electrode is

not parallel to the ground or is interconnected with other one. The charge distribution is no longer

symmetrical. However, the results of many simulations of the situation with an electrode angled to

the ground or with another shows that the symmetrical arrangement of segments gives an accuracy

of less than desired. It should be noted that the height of the electrode was treated as the average

height from the ground of both end points.

Effective formulas for unequally spaced arrangement method of segments

It is very difficult to find the optimal solution using the direct search method

whenever the geometric parameters of an electrode have changed. Fortunately, it has been found that

the ratios a(= length height) and p (=radius/length) are strongly correlated to the solution. For

instance, consider unequally spaced arrangement of 10 segments for the same electrode used in the

fig below. Due to the symmetric arrangement all that has to be done is to determine x1 to X6 in Fig.

It is obvious that It is obvious that x1 and x6 are -L/2(m) and O (m) respectively regardless of the

geometric factors. From many simulations using various geometric factors, it has been found that xi

(i=2, 3, 4, 5) formed their own surfaces which can be approximated by planes as shown in Fig.

These planes can be represented by parametric forms of α and β. In practice, using the multiple regression

analysis based on the least square method, the effective formulas for unequally spaced where C, n, xr and F;]

are as follows: arrangement of segments were obtained similar to = correction factor of line length (=Ll20)

These formulas make the arrangement of segments fast and = the number of segments X, = x-coordinates

subdividing an electrode effective. When the number of segments is even from 6 to 14, the effective formulas can

be expressed as matrix similar to equation given below.

Where c= correction factor of line length (L/20)

N= number of segments+1

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xt=x coordinate sub dividing an electrode

[K]= Coefficient matrix for the arrangement of electrode

Surfaces for xi according to the parameters a and β

SIMULATION STUDY OF ELECTRIC FIELD OF POWER

FREQUENCY UNDER POWER LINE

A. The comparison of power frequency electric field between double circuit and single circuit

The mode of double circuit on one tower is now commonly used. It is known that the

electromagnetic field under line has something with the order of phase. For double circuit, the

electric field intensity in athwart phase order is smaller than that of in alike phase order. In addition,

for the single circuit with same height and parameters, the maximum of electric field is intervenient,

as shown in gra.2.

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Graph. 2 Comparison of electric field for single circuit and double circuit in alike and athwart phase order. Curve 1 for double circuit in alike phase order; curve 2 for single circuit; curve 3 for double circuit in athwart phase order

B. The relationship between electric field and the line arrangement

At present, there are four kind of line arrangement for single circuit:

uprightness (erectness); deltoid; horizontal; V-shape. On the conditions of same voltage, same height

(the middle point) to the ground and same line parameters, the power frequency electric fields under

different line arrangement are show in Gra. 3. It is clearly for us to known that the best line

arrangement for less electric field is the V-shape.

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Graph. 3 Comparison of electric field in different line arrangement for single circuit. Curve 1 for uprightness arrangement, curve 2 for deltoid arrangement, curve 3 for horizontal arrangement, and 4 for V-Shaped arrangement.

C. The relationship between electric field and spacing of adjacent lines

No matter single circuit or double circuit even multi circuit, the spacing of two adjacent

phase line will affect the electric field under transmission line. This affection will be analyzed

below.

The relationship between phase spacing and electric field for single circuit in

horizontal mode

For single circuit in horizontal mode, the electric field under line is shown in Gra.4 when the spacing

of two adjacent lines is 6, 8, 10, 15, 20 meters, respectively. From the results we know that the closer

the two lines are, the smaller the electric field is.

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Graph. 4 The distributions of electric field in different adjacent distant for a 500kV single circuit in horizontal arrangement. 6 stands for the adjacent distance is 6 meters, 8 stands for the adjacent distance is 8 meters, 10 stands for the adjacent distance is 10 meters, 15 stands for the adjacent distance is 15 meters, 20 stands for the adjacent distance is 20 meters

The relationship between electric field and spacing of two adjacent lines in upright

double circuit

When the lines of double circuit are in upright mode, the electric field will be affected by

the spacing of line and the phase order. Fig. 5 shows the results of electric field when the space

between the two circuits is 12,16,28 meter respectively in alike phase order. And Fig.6 shows the

results in athwart phase order. From the results shown in Fig.5, we know that in alike phase order the

wider the space is, the weaker the electric field is. On the contrary, for athwart phase order, smaller

the space is, the weaker the electric field is. We know that no matter the middle line or the lowest

line be fixed, the electric field under transmission line will be weaker with the space's decrease of

two adjacent lines.

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Fig. 5 The electric field distribution for a 500kV vertical double circuit in alike phase order. 12 stands for the space between the two circuits is 12 meters, 16 stands for the space between the two circuits line is 16 meters, and 28 stands for the space between the two circuits is 28 meters.

Fig. 6 The electric field distribution for a 500kV vertical double circuit in athwart phase order. 12 stands for the space between the two circuits is 12 meters, 20 stands for the space between the two circuits is 20 meters, and 28 stands for the space between the two circuits is 28 meters.

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The influence of space on the electric field for single circuit in upright mode

We now study the relationship between the electric field and space in upright mode for single circuit.

First, let the middle line be fixed at 25 meters high, if the distances of two adjacent lines are 5,6,7,8

meters respectively, their electric fields are shown in Fig.7. Then, let the lowest line be fixed at 20

meters high, the distances of two adjacent lines are still 5,6,7,8 meters respectively, the results are

shown in Fig.8. From these results we know that no matter the middle line or the lowest line be

fixed, the electric field under transmission line will be weaker with the space’s decrease of two

adjacent lines.

Fig.7.the electric field for the upright single circuit when the middle line is fixed at 25 meters, curve 5 stands

for s meters, curve 6 for 6 meters and so on.

D. The electric field of power frequency vary with the change of line's height

The height of transmission line affects the strength of electric field under line

directly. With the increase of line's height, the electric field under line will decrease. For a

500kVsingle circuit, which is arrangement as deltoid mode, the distance between lines is 9.16

meters, the relationship between height H of line and the electric field is shown in Fig.9. From Fig.

9, meters to 20 meters, the decrease of electric field is 10.5 kV/m.It is a steep gradient. If the height

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increases from 20 meters to 40 meters, the decrease of electric field is 2.3 kV/m. It is a flat gradient.

If the height increases from 40 meters to 50 meters, the decrease of electric field is 0.3 kVMm. It is

almost the same. So, in order to depress the electric field under line, it is significant within specified

height of the transmission line. Otherwise, exceed the range, there is no obvious effect and it will

increase the cost greatly. We can adjust the height of transmission line according to different demand

to give attention to environment protection or decreasing of engineering cost.

Fig. 8 the electric field for the upright single circuit when the lowest line is fixed at 20 meters, curve 5 stands for the distance of two adjacent line is 5 meters, curve 6 for 6 meters and so on.

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CONCLUSION

From the simulations above, we can get some conclusion.

1) The electric field under super-high voltage transmission line is lower when the lines are in athwart

phase order for double circuits;

2) The electric field under super-high voltage transmission line is less when the lines are put in V-

shape for a single-loop on a tower;

3) In order to reduce the electric field under super-high voltage transmission line in particular area,

the distant between lines or the distant between two circuits of double circuit should be lessen as

more as possible;

4) It is possible to balance the demand of environment protection and the engineer cost reducing in

some area by adjusting the height of tower;

5) For multi-circuit transmission line, the electric field under line can also be predicted reduced to a

less level by adjusting the phase order. It is beneficial in environment protection.

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[2] Al-Arainy A.A, Malik N.H, Abdul-Aal L.N. Electromagnetic interference from transmission

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Issue. 1:532-538.

[3] Working group 36.01 CIGRE, Electric and magnetic fields produced by transmission systems.

Description of phenomena practical guide for calculation, Paris, 1980.

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RESEARCHON ELECTRIC FIELD ON HIGH VOLTAGE-TRANSMISSION

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