A comparative study of electric fields beneath compact and non-compact transmission lines

International Journal of Electrical Engineering Education, Jan 2007 by Dahab, A A, Abu-Elhaija, W S, Amoura, F K

Abstract This paper presents the charge simulation method (CSM) with complex charges for the computation of electric field distribution under Extra High Voltage (EHV) transmission lines (conventional and compact). Electric field at ground level is becoming one of the most important factors for proper design and safe operation of EHV lines because of its biological effects. The ground is taken into account by the method of images. A single tower transmission line carrying a single circuit with six different configurations is studied and analysed. All the cases have the same degree of compaction (i.e. the ratio of line-to-line voltage/space between the two phases is constant) for the purpose of comparison. It is found that the electric field is reduced by 30-70% for some of the compact designs compared with conventional ones.

Keywords electric field distribution; compact line, high voltage line, single tower transmission line; transmission line

(ProQuest-CSA LLC: ... denotes formulae omitted.)

Electric transmission lines are a common and necessary part of our life. The lines bring huge quantities of electric power from generating plants to our homes. Some of the largest lines carry up to 2000MW of power - enough to supply a large city with all of its electric energy needs. The transmission lines may take various forms - towers, single or double poles, and sometimes underground lines. Transmission lines are designed and constructed for safety to the general public, particularly with respect to the area surrounding the lines. This area, called the corridor, includes the spaces directly beneath and to each side of a transmission line. These corridors give the electric company the right to construct and maintain a transmission line. They also restrict the uses of the property within the boundary to protect the line from any construction that may pose a safety or reliability problem.

Any line that is energised and has an electric current produces an electric field. The electric field intensity varies directly with the line voltage and is also dependent on the configuration of the lines and the distance from the line. The predication of electric field in the vicinity of EHV lines at distances up to several tens of metres away from the line is a controversial issue regarding possible harmful biological effects. Therefore, the electric field distribution beneath the line and at the edge of the right-of-way has to be computed accurately. The main interest is in reducing the electric field. Compact designs have been suggested for this purpose. These lines allow transmission of equivalent amounts of power to that transmitted by conventionally designed lines and both operating at the same voltage, i.e. occupying less space than that of the conventionally designed ones.

Many studies have been developed for the calculation of electric field strength at ground level of EHV lines.1-7 These studies have simulated the conductors by infi- nitely long line charges. The ground is represented by a conducting plane. For a.c. transmission lines the charges are assumed to be complex.8 Therefore, the electric field at the ground level is a vector sum of the field strength due to the phase charges at the surfaces of the conductors and their images.

In this paper, the charge simulation method (CSM) with complex charges is used to compute the root mean square of the electric field intensity at the ground level for any configuration of transmission lines. Six transmission line configurations are studied (conventional, compact delta, compact inverted delta, sixphase, double 3-phase, and double 3-phase converted to 6-phase). The comparison between the lateral electric field intensity profiles for all cases is presented and discussed.

Method of calculation

The electric field intensity E due to a uniform line charge qo (C/m) is given in cylindrical coordinates by:

... (1)

where:

r is the distance between the line and the point in space.

ε^sub o^ is the permittivity of free space.

a^sub r^ is the unit vector in the direction of r.

The above expression for the electric field intensity E can be developed in Cartesian coordinates as:

... (2)

where:

x and x^sub o^ are the x-coordinates of the point at which E is to be measured and the charge carrying line respectively.

y and y^sub o^ are the y-coordinates of the point at which E is to be measured and the charge carrying line respectively.

a^sub x^ and a^sub y^ are the unit vectors in the x and y directions respectively.

The x- and y- components of the electric field at any point (x, y) induced from the simulated charges computed from (2) are given below.6

... (3)

... (4)

The magnitude of the total electric field Et is found using:

... (5)

The charge potential value, V between a line carrying conductor and a space point is given by:

... (6)

where:

R is the distance between the line charge and the space point.

In Cartesian coordinates, this is given by:

... (7)

A transmission line in practice is strung above ground plane and its effect can be taken into account by placing image charges. Therefore, the charge potential relations with n conductors on a tower for multi-conductor line (shown in Fig. 1) can be written in a matrix form as follows.6