A transmission line is a set of conductors being run from one place to another supported on transmission towers. Therefore, such lines have four distributed parameters, series resistance, inductance shunt capacitance and conductance.
The effect of capacitance is ignored in these lines, length of short transmission line is less than 80 km.
where, Vs = Sending end voltage
ls = Sending end current
VR = Receiving end voltage
IR = Receiving end current
IS = IR
VR +l(R+ jX) = Vs
∴ A =1, B=2,C=0, D=1
Two part representation of transmission network
Efficiency
where, P = Power received
The range of length of this transmission line is 80 km to 250 km. Medium transmission lines are modeled with lumped shunt admittance.
Nomial-π Representation
The lumped series impedance is placed in the middle while the shunt admittance is divided into equal parts and placed at the two ends.
For Voltage Regulation
The no-load receiving end voltage
Nomial-π circuit under no load condition
Nominal-T Representation
The shunt admittance is placed in the middle and the series impedance is divided into equal parts and these parts are placed on either side of the shunt admittance.
Here,
For Voltage Regulation
The no-load receiving end voltage
Note: Percentage regulation
Here, |VS| = Sending end voltage |VR.r2| = Full load receiving end voltage.
The length of long transmission line is more than 250 km.
The ABCD parameters of the long transmission line are,
where,
which is called the characteristic impedance
π-Representation of a Long Transmission Line
In this, the series impedance is denoted by Zj while the shunt admittance is denoted by Y’
ABCD, parameters are
where,
T-Representation of Long Transmission Line
Parameters are
and
Power Flow Through a Transmission Line
The complex power VR IR at receiving end
The real active power at receiving end,
The reactive power at the receiving end,
For fixed value of VS and VR the receiving end real active power is maximum when
This is also known as characteristic impedance. It is impedance offered by the system under surge impedance loading.
Characteristic impedance
Here, Z = Series impedance per unit length
Y = Shunt admittance per unit length
For lossless line, R = 0, G = 0
It can be also given by
where, ZOC = Sending end impedance with receiving end open circuited
ZSC = Sending end impedance with receiving end short-circuited
where, α = Attenuation constant
β = Phase constant
Surge Impedance Loading (SIL) of a line is the power delivered by a line to a purely resistive load equal to its surge impedance.
where, β = Phase shift in red/mile
Refracted (transmitted) wave = Incident (forward) wave + Reflected wave
VT = VF + VR
where, VT = Refracted (transmitted) voltage wave
VF = Incident or forward voltage wave
VR = Reflected voltage
Case (1) Open-Ended Line
Case (2) Short Circuited Line
Case (3) Termination of Line with Resistor
Coefficient of refraction of voltage
Coefficient of reflection of voltage wave
Coefficient of refraction (transmit) of current wave
Coefficient of refraction of current wave
Note: When the terminated by a resistor equal to surge impedance
VT =VF; VR = IT = IF; IR = 0
The incident wave continuous as it is and there is no reflection.
Case (4) Line Terminated by an Inductor
Transmitted (refracted) voltage
Reflected voltage wave
Transmitted (refracted) current wave.
Reflected current wave
Where, Zc = Surge impedance of the line.
Transmission line terminated by a inductor L
Case (5) Line Terminated by a Capacitor
Transmitted (refracted) voltage wave
Reflected voltage wave
Transmitted (refracted) current wave
Reflected current wave
Case (6) Parallel Reactive Termination
Refracted (transmitted) voltage wave,
Transmission Coefficient at T Junction (Forked Line)
Refraction coefficient
Refracted (transmitted voltage wave)
Line Connected to Cable
Refracted voltage wave
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2. How is impedance important in the performance of a transmission line? |
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