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e representation
S2: Transmission Lines
13 EEE8044: Fundamentals
2.2 Relationships between Line Parameters and Physical Layout
2.2.1 Line inductance
Fig. 2.6 shows the relationship between physical layout of a three phase overhead line and
its’ series line inductance.
a
b
c
dab
dca
dbc
L
D
R
H m
where
permeability of space H m
R effective conductor radius
D geometric mean dis ce d d d ab bc ca
=
⎧⎨⎩
⎫⎬⎭
= = ×
=
= = × ×
−
− −
μ
π
μ π
0 1
0
7 1
3
2
4 10
.ln .
:
.
tan
Fig. 2.6 Line inductance
To simplify operation of the power system it is desirable to have low values of inductance,
i.e. small D and large R.
Decreasing D reduces the insulation between lines and is therefore limited by the working
voltage.
Increasing R causes an increase in conductor weight and therefore cost.
One method employed to increase the effective radius is the use of bundle conductors, as
shown in Fig. 2.7.
Cross-section of line for one-phase in the UK transmission system:
275kV
approx 30cms
400kV
approx 30cms
Fig. 2.7 Bundle conductors
S2: Transmission Lines
14 EEE8044: Fundamentals
In comparison to a single solid conductor, bundle conductors:
􀂃 increase effective radius and therefore reduce inductance
􀂃 reduce skin effect
􀂃 have a larger surface area and therefore better cooling
􀂃 are easier to handle during construction
2.2.2 Line resistance
The resistance of a line varies between 0.5Ω/km for an 11kV distribution line and
0.015Ω/km for a 400kV overhead line or a 33kV underground cable.
Resistance includes skin effect, which causes an increase in resistance of about 5% (in
comparison to dc) in a 2.5cm diameter copper conductor operating at 50 Hz.
2.2.3 Line capacitance
The capacitance per unit length of the line shown in Fig. 2.6 above is given by the
equation:
(D R)
C
ln /
2 0 πε
=
for a given working voltage and frequency, dv/dt is fixed, so to minimise charging current,
i (i = C dv/dt), the line capacitance should be as small as possible. A low value of C
implies large D and small R conflicting with the requirements for small L.
Typical values for capacitive reactance (1/ωC) are 200kΩ/km for a transmission line and
4kΩ/km for an underground cable. The capacitive charging current in an underground
cable is thus much higher than in an overhead transmission line.
2.2.4 Line conductance
Line shunt conductance G models losses due to corona (discharge through air) and leakage
currents across insulator surfaces. Typical losses on a 400KV line are 600 W/km in fine
weather and 90 kW/km in snow or fog.
S2: Transmission Lines
15 EEE8044: Fundamentals
2.3 Underground Cables vs. Overhead Lines
Cables are 15-20 times more expensive than overhead lines, because:
􀂃 insulation cost (overhead lines uses air insulation, which is free)
􀂃 the maximum operating temperature for a cable is typically 70 or 90°C, so more copper
must be used to reduce losses and give a reasonable operating temperature
􀂃 installation cost: trench, continuous path across the ground
Plus, the large capacitive charging current limits useful lengths of cables to 15-20 km. For
longer lengths of cable (e.g. under th