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Ch 4: Transmission Line
Calculations
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Transmission lines physically integrate the output of generating plants and the
requirements of customers by providing pathways for the flow of energy
among the various circuits in an electric power system. For our purposes
here, we consider a transmission line to have a sending end and a receiving
end, and to have a series resistance and inductance and a shunt capacitance
and conductance as primary parameters. In addition, we classify transmission
lines as short, medium, and long. In a short line, the shunt effects
(conductance and capacitance) are neglected; this approximation is
considered valid for lines up to 80km long. In a medium line, the shunt
capacitances are lumped at a few predetermined locations along the line;
medium lines generally range from 80 to 240 km in length. Lines longer than
240 km are considered to be long lines and to have uniformly distributed
parameters.
In Chapter 3 we discussed the three most important parameters of
transmission lines. In this chapter we discuss the effect of those parameters
on the operation and performance of transmission lines. In particular, we
evaluate the losses, efficiency, and voltage regulation of transmission lines
and then determine the consequences of such performance characteristics on
the operation of a power system.
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4.1 TRANSMISSION.LINE REPRESENTATION
To facilitate performance calculations relating to a transmission line, the line
is approximated as a series-parallel interconnection of the relevant
parameters. A short transmission line, for which the shunt effects may be
neglected, is represented by a lumped resistance in series with a lumped
inductance. A medium-length line is represented by lumped shunt
capacitors located at predetermined points along an RL series circuit. (In
practice, the entire capacitive effect in a medium-length line may be
represented by only one or two lumped capacitors.) Finally, a long
transmission line is represented by uniformly distributed parameters.
Furthermore, the shunt branch of a long line consists of both capacitances
and conductances distributed uniformly along the line.
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4.2 SHORT TRANSMISSION L!NE
The short transmission line is represented by the lumped parameters R and
L, as shown in Fig. 4-1. Notice that R is the resistance (per phase) and L is
the inductance (per phase) of the entire line (even though we computed
transmission-line parameters per unit length of line in Chapter 3). The line
is shown to have two ends: the sending end (designated by the subscript S)
at the generator, and the receiving end (designated R) at the load.
Quantities of significance here are the voltage regulation and efficiency of
transmission. These quantities are defined as follows for lines of all lengths:
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Standing Wave vs Traveling Wave
http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html
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