# Electric Field Calculation Methodology

The voltage V on a point charge is closely related to the capacitance C and charge Q (in Coulombs). Assuming that this charge applies to a section of transmission line, it is possible to define the contained charge and voltage relationship by using a circular integral. This is known as Gauss’ Law. However, it is not possible to directly calculate the charge on each conductor of a multi-phase line without also considering the matrix of Maxwell potential coefficients for each conductor and the interactions between each conductor. Consequently, for a three phase circuit, the charges Q on the conductors are determined from the known phase voltages V and the Maxwell potential matrix P. where, PAA , PBB,and PCC are the potential cooefficients for the individal phases, while PAB , PAC, PBC , PBA , PCA and PCB are the potential coefficients that arise between the relevant phase conductors.

The electric fields are assumed to be tangential to the surface of the earth as the earth can be considered as a conductive plane as power frequencies. Therefore, it is possible to apply the ‘method of images’  to calculate the electric field at, or near, the ground level.

Since, the line voltage phasors are known, it is then possible to calculate the charge on each conductor, at each point in the power cycle. The method of images is then used to derive the horizontal and vertical components of the electric field at each location under the line, for each of the points in the power cycle. The root-mean square of these values are then derived to produce an rms value for the electric field at this location.

These matrix calculations can be validated by comparing the results with the electric fields obtained from a 525 kV transmission line in . These documented results include high and low reactance phasing of double circuit lines, as well as the electric field produced by a single circuit line with a horizontal conductor arrangement.  This computation is particularly complex when there is more than one three-phase circuits. For this reason, overhead earth wires are often not included within the calculations. Moreover, these calculations also assume that the power frequency voltages are balanced and that the conductors are parallel to the ground. Interestingly, the inclusion of shielding earth wire contributions affects the field at ground level by no more than 1-2% because the wires are above the phase conductors and a further from the ground .

## References

 EPRI, “Transmission Line Reference Book 345kV and Above” revised 2nd edition, EL-2500 1987, pp329-419
 AS 1531—1991, Conductors—Bare overhead—Aluminium and aluminium alloy
 AS 1746—1991, Conductors—Bare overhead— Hard-drawn copper
 AS 3607—1989, Conductors—Bare overhead,aluminium and aluminium alloy—Steel reinforced