S2: Transmission Lines
10 EEE8044: Fundamentals
Section 2
Transmission Lines and Cables
Introduction
In a power system, power is transferred from one busbar to another via a
留学生论文网network oftransmission lines, usually in the form of three-phase overhead lines or, in denselypopulated urban areas, cables. In this section we will look at how transmission lines aremodelled, look at the factors that affect the physical parameters of the line and examine the
relationship between line voltages and the flow of power and reactive power along the line.
Learning Outcomes
On completion of this section you will be able to:
Model the behaviour of three-phase transmission overhead lines and cables using a simple per phase circuit representation.
Carry out circuit analysis for short and medium length transmission lines.
Describe the relationship between line voltages and line power and reactive power flows.
Calculate real and reactive power flows between two busbars with known voltages
Calculate busbar voltages from a knowledge of power and reactive power line
flows
Calculate line power losses
Time
You will need between 2 and 3 hours for this section.
Resources
Calculator, pen and paper.
S2: Transmission Lines
11 EEE8044: Fundamentals
2.1 Circuit Representation of Transmission Lines
Fig. 2.1 shows a single-phase line consisting of a conductor suspended above the ground.
The line is characterised by its resistance R, its series self-inductance L, its shunt
capacitance to earth C and its shunt leakage conductance G, which represents the leakage
current to earth.
I
V
R,L
G,C
Fig. 2.1 Single-phase line
A three-phase line includes mutual inductance and capacitance effects, but each of its’
three conductors can be modelled by an equivalent single-phase line with modified
parameters.
2.1.1 Distributed parameter model
All these parameters are of course distributed along the entire length of the line (Fig. 2.2)
and are usually expressed in Ohms per unit length (Ω/km), Henry per unit length (H/km),
Farad per unit length (F/km) and Siemens per unit length (S/km).
G .dx C .dx
R1 .dx L1 .dx
1 1 G .dx C .dx
R1 .dx L1 .dx
1 1
dx
Fig. 2.2 Distributed parameter model.
S2: Transmission Lines
12 EEE8044: Fundamentals
2.1.2 Nominal line models
It is usual practice to perform circuit calculations using lumped circuit elements obtained
simply by multiplying the distributed parameters by the length of the line. A line is usually
represented by either the T network or the π network shown in Fig. 2.3.
Is R L
Vs
G/2
C/2
G/2
C/2
IR
VR
Is
Vs
IR
VR
R/2 L/2 R/2 L/2
G
C
nominal-T
nominal-π
Fig. 2.3 Nominal line models
2.1.3 Short-line model
For fully-loaded lines less than 100km long, the current flow in the shunt elements is less
than 1% of the full-load current. In this case, the shunt elements may be neglected giving
the short line model shown in Fig. 2.4.
Is
Vs
IR
VR
R L
Fig. 2.4 Short line model
Normally the series reactance of the line is much bigger than the resistance and it may
sometimes be possible, especially for short urban lines, to disregard the resistance giving
the simplified line model shown in Fig. 2.5.
Vr
I
Vs
I L
Fig. 2.5 Simplified short lin
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