Electrical Power Systems

30 Electrical Power Systems
over the transposition cycle. Therefore, the inductance per phase can be obtained by finding the
average value of eqns. (2.66), (2.67) and (2.68).
( La + Lb + Lc)
\ L = ...(2.69)
3
or L = 0.4605 log D mI
mH/km ...(2.70)
D
where D m = (D ab D bc D ca) 1/3 and D s = r¢.
HG
s
Generally modern transmission lines are not transposed. However, for the purpose of
modeling, it is very much practical to treat the transmission line as transposed.
2.12 INDUCTANCE O THREE PHASE DOUBLE CIRCUIT LINES
KJ
A three phase double circuit line consists of two parallel conductors for each phase. It is common
practice to build double-circuit three phase lines for greater reliability and higher transmission
capacity. To enhance the maximum transmission capability, it is desirable to have a configuration
which results in minimum inductance per phase. This is possible if mutual GMD (D m ) is low and
self GMD (D s ) is high.
igure 2.10 shows the three sections of the transposition cycle of a double circuit three
phase line. This configuration gives high value of D s (Reader may try other configurations to
verify that these will lead to low D s ).
To calculate the inductance, it is necessary to determine D eq or Geometric Mean Distance
(GMD) and self GMD D s .
ig. 2.10: Arrangement of conductors in a double circuit three phase line.
Deq = (Dab · Dbc · Dca) 1/3
...(2.71)
where Dab = mutual GMD between phases a and b of section-I of the
transposition cycle
=(Dd2 Dd2) 1/4 = (Dd2) 1/2
Dbc = mutual GMD between phases b and c of section-I of the
transposition cycle
=(Dd2 Dd2 ) 1/4 = (Dd2 ) 1/2
Dca = mutual GMD between phases c and a of section-I of the
transposition cycle