Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 46

conductors, D m . This result assumes that each phase conductor is located in each of
the three possible positions for one third of the line length - a condition known as
equal transposition.

2.5.1.3 Typical line parameter values
The behaviour of transmission and distribution overhead lines is governed mainly
by their series resistance and inductance parameters. Shunt capacitance becomes a
significant issue for transmission lines longer than 100 km, and for cables of any
length. We will confine our attention to the distribution lines and shorter trans-
mission lines relevant to wind farm connection. Hence shunt capacitance will be
ignored in the following discussion.
It is clear from (2.19) that the resistance of a line is proportional to its length
and inversely proportional to its cross-sectional area. The cross-sectional area a
must be such as to enable the expected current to be carried without excessive
heating or sag. The cross-sectional area a will clearly be a much higher value for
transmission lines rated at several hundred MVA than for distribution lines
designed to carry a few MVA. Thus distribution line resistance tends to be higher
than transmission line resistance for a given length.
Line inductance per unit length was given in (2.20). The value of inductance is
governed by the ratio of the geometric average of the distances between con-
ductors, D m , and conductor radius r . D m will be greater for the higher voltage levels
found in transmission, to ensure adequate insulation between phases under extreme
conditions. However, conductor radius will also be greater in transmission to cope
with the higher power and current requirements. Hence the ratio of D m / r does not
vary greatly as we move from transmission to distribution. As the inductance per
unit length is the natural log of this ratio, the variation in the parameter is even less
marked than the D m / r ratio.
It is convenient to express the reactance X ¼w L of the line rather than its
inductance. It is found that the X / R ratio of transmission lines, with line voltages
greater than, say, 100 kV, are generally greater than 2.5. The same ratio for dis-
tribution lines (11, 20 and 33 kV) is often close to unity. The following analysis
should be interpreted in the light of these very different ratios.
Typical line resistance and reactance values are shown in Table 2.1 (Weedy
and Cory, 1998). It may be seen from these data that reactance values vary little
between voltage ranges and X / R ratios increase with voltage level .

Table 2.1 Overhead line parameters at 50 Hz

(per phase, per km)

Voltage (kV) 33 132 275

Number of conductors 1 1 2

Area of conductor (mm 2 )

100 113 258

Thermal rating, 5-18 C (MVA) 20 100 620

Resistance R ( W ) 0.30 0.16 0.034

Reactance X ( W ) 0.31 0.41 0.32