Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Notes  >  Power Systems  >  Performance of Transmission Line & Travelling Wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE) PDF Download

Transmission Line

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.

Short Transmission Line

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

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

∴ A  =1, B=2,C=0, D=1

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Two part representation of transmission networkTwo part representation of transmission network

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Efficiency

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

where, P = Power received

Medium Transmission Line


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.

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

For Voltage Regulation

The no-load receiving end voltage

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Nomial-π circuit under no load condition


Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

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,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

For Voltage Regulation
The no-load receiving end voltage

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Note: Percentage regulation

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Here, |VS| = Sending end voltage |VR.r2| = Full load receiving end voltage.

Long Transmission Line

The length of long transmission line is more than 250 km.

The ABCD parameters of the long transmission line are,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

where,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

which is called the characteristic impedance

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

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

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

where,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

T-Representation of Long Transmission Line

Parameters are

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

and

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Power Flow Through a Transmission Line

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

The complex power VR IR at receiving end

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

The real active power at receiving end,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

The reactive power at the receiving end,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

For fixed value of VS and VR the receiving end real active power is maximum when

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Surge Impedance

This is also known as characteristic impedance. It is impedance offered by the system under surge impedance loading.

Characteristic impedance

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Here, Z = Series impedance per unit length

Y = Shunt admittance per unit length

For lossless line, R = 0, G = 0

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

It can be also given by

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

where, ZOC = Sending end impedance with receiving end open circuited

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

ZSC = Sending end impedance with receiving end short-circuited

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Propagation Constant

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

where, α = Attenuation constant

β = Phase constant

Surge Impedance Loading (SIL)

Surge Impedance Loading (SIL) of a line is the power delivered by a line to a purely resistive load equal to its surge impedance.

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

where, β = Phase shift in red/mile

Key Points

  • Surge impedance for the transmission line is 400Ω and for cable, it is 40 Ω.
  • The phase angle of surge impedance (ZC) of transmission lines is in range of 0o to -15o.
  • If loading of the = SIL, then the power factor will be unity. Hence, maximum power can be transferred and the line can be called as the flat line.
  • If loading of line < SIL, then power factor will be leading.
  • If loading of line > SIL, then power factor will be lagging.

Wave Phenomenon

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

Transmission Line Termination

Case (1) Open-Ended Line

  • Current becomes at load end zero. Due to this electromagnetic energy Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE) converted into electrostatic energy Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
  • The potential at the open end becomes 2V.
    Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)where, IT = Transmitted or refracted current wave
    IR = Reflected current wave

Case (2) Short Circuited Line

  • When line is short-circuited at load end, the voltage at load end becomes zero and electrostatic energy is converted into electromagnetic energy
  • The current becomes 2l at the short end.
    Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)VT = 0
    VR = -VR
    IT = 2 / F
    IR = IF

Case (3) Termination of Line with Resistor

Coefficient of refraction of voltage

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Coefficient of reflection of voltage wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Coefficient of refraction (transmit) of current wave
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Coefficient of refraction of current wave
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

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
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Reflected voltage wave
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Transmitted (refracted) current wave.
Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Reflected current wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)
Where, Zc = Surge impedance of the line.
Transmission line terminated by a inductor LTransmission line terminated by a inductor L

Case (5) Line Terminated by a Capacitor

Transmitted (refracted) voltage wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Reflected voltage wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Transmitted (refracted) current wave 

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Reflected current wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Case (6) Parallel Reactive Termination

Refracted (transmitted) voltage wave,

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Transmission Coefficient at T Junction (Forked Line)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE) 

Refraction coefficient

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Refracted (transmitted voltage wave)

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

Line Connected to Cable

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE) 

Refracted voltage wave

Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE)

The document Performance of Transmission Line & Travelling Wave | Power Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Power Systems.
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FAQs on Performance of Transmission Line & Travelling Wave - Power Systems - Electrical Engineering (EE)

1. What is the performance of a transmission line?
Ans. The performance of a transmission line refers to its ability to transmit electrical signals efficiently and effectively from one point to another without significant loss or distortion. It is usually evaluated based on parameters such as impedance, attenuation, reflection, and dispersion.
2. How is impedance important in the performance of a transmission line?
Ans. Impedance plays a crucial role in the performance of a transmission line as it determines the matching of the line with the connected devices or systems. A well-matched impedance ensures maximum power transfer and minimizes signal reflections, which can cause distortions or loss of signal integrity.
3. What is attenuation in the context of a transmission line?
Ans. Attenuation refers to the loss of signal strength or power as it propagates through a transmission line. It occurs due to various factors such as resistance, skin effect, and dielectric losses. Attenuation is undesirable as it can degrade the signal quality and limit the maximum distance over which the transmission line can effectively transmit signals.
4. How does reflection affect the performance of a transmission line?
Ans. Reflection occurs when a portion of the transmitted signal is reflected back towards the source due to impedance mismatch or discontinuities in the transmission line. These reflections can interfere with the original signal, causing distortions, signal degradation, and increased signal loss. Minimizing reflections is crucial to maintain signal integrity and maximize the performance of the transmission line.
5. What is meant by dispersion in a transmission line?
Ans. Dispersion refers to the phenomenon where different frequency components of a signal propagate at different speeds through a transmission line. This can cause distortion and signal degradation, especially in high-speed data transmission. Dispersion can be categorized into two types: chromatic dispersion, which occurs due to the wavelength-dependent refractive index of the transmission medium, and modal dispersion, which arises from different propagation modes within the transmission line.
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