Calculation of sequence impedance of an overhead line
The Positive Sequence Impedance of 3-Phase 3-Wire Short Transmission Lines (i.e. Without Overhead Earth Wires)
Figure below shows a general arrangement of 3-phase 3-wire overhead line conductors. The insulators, cross arm and the pole supporting the conductors are not shown
General arrangement of a 3 phase 3 wire transmission line
Positive Sequence Resistance
For an overhead line it can be assumed that the positive sequence AC resistance of the conductor is equal to the DC resistance of the conductor. This is similar to the cable analysis at power frequency (i.e. 50Hz).
Positive Sequence Reactance
The positive sequence reactance of the 3 phase 3 wire line can be calculated from the following equation:
where:
ƒ - frequency Hz
GMD - Geometric Mean (mm). For an equilateral triangle disposition of the conductors, GMD = S - or the separation of the conductors. For any other arrangements of the 3-phase 3-wire line, it can be calculated with the following equation:
dab, dbcand dcaare the spacing (mm) between the phase conductors as shown in the figure above. GMR - Geometric Mean Radius of one conductor (mm). It is calculated by equation
We get the positive sequence impedance of a 3-phase 3-wire short transmission line combining R1and X1as follows:
The Negative Sequence Impedance of a Short 3-Phase 3-Wire Transmission Line
The negative sequence impedance of the line is equal to the positive sequence impedance.
The Zero Sequence Impedance of a Short 3-Phase 3-Wire Transmission Line
To calculate the zero sequence impedance of a short 3-Phase 3-Wire transmission line, the 3 conductors must be considered as a group and therefore the equivalent GMR for the group of conductors must be calculated. The equation to calculate the zero sequence impedance is given below.
where Rcond - Resistance of one conductor Ω/km
ƒ - frequency Hz
ρ- deep layer soil resistivity Ω-m
GMR1cond - Geometric Mean radius of one conductor (mm)
dab, dbc, and dcaare the spacing (mm) between the phase conductors as shown in the figure above.
Prepared by: zone4info.com
Reference: Fundamental of calculation of earth potential rise in the underground rise by Ashok