Performance of Transmission Line & Travelling Wave Analysis For Electrical Engineering

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In this article, you will find the study notes on Performance of Transmission Line & Travelling Wave Analysis, which will cover the topics such as Transmission Line, Short Transmission Line, Regulation & Efficiency of Short Transmission Line, Medium Transmission Line, regulation & Efficiency of Medium Transmission Line, Long Transmission Line, Regulation & Efficiency Of Medium transmission Line, Surge Impedance Loading, Termination of Transmission; Line with Open-Ended, Short Circuited Line, Termination of Line With Resistance, Line Terminated by an Inductor, Line terminated by a Capacitor, Parallel reactive Termination, Transmission Coefficient at T Junction & Line connected to a Cable.

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 energ

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.

Transmission lines are typically made of conductive materials, such as copper or aluminum, that have low resistance to allow for efficient power transmission. They are used in both overhead and underground applications, depending on the specific requirements and environmental factors.

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


VR +l(R+ jX) = Vs

03-Models-and-performance (1)%

03-Models-and-performance (2)

03-Models-and-performance (3)

03-Models-and-performance (4)

03-Models-and-performance (5)

03-Models-and-performance (6)

Reglation % Regulation 03-Models-and-performance (7)

03-Models-and-performance (8)

Efficiency 03-Models-and-performance (9)

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.

03-Models-and-performance (10)

03-Models-and-performance (11)

Here, 03-Models-and-performance (12)

03-Models-and-performance (13)

For Voltage Regulation

The no-load receiving end voltage

03-Models-and-performance (14)

03-Models-and-performance (15)

∴ % regulation 03-Models-and-performance (16)

% efficiency 03-Models-and-performance (17)

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.


03-Models-and-performance (18)

For Voltage Regulation

The no-load receiving end voltage

03-Models-and-performance (19)% regulation 03-Models-and-performance (20)

% efficiency 03-Models-and-performance (21)

03-Models-and-performance (22)

Note: Percentage regulation 03-Models-and-performance (23)

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,

03-Models-and-performance (24)

where, 03-Models-and-performance (25) which is called the characteristic impedance 03-Models-and-performance (26)

For lossless line R = 0; G = 0

03-Models-and-performance (27)

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

03-Models-and-performance (28)

03-Models-and-performance (29)

where, 03-Models-and-performance (30)

03-Models-and-performance (31)

03-Models-and-performance (32)

03-Models-and-performance (33)

T-Representation of Long Transmission Line

Parameters are 03-Models-and-performance (34)

03-Models-and-performance (35)

03-Models-and-performance (36)

and 03-Models-and-performance (37)

03-Models-and-performance (38)


Power Flow Through a Transmission Line

Ss = Ps + jθs = VsIs*

SR = PR + jθR

03-Models-and-performance (39)

Let A = D = |A|<α°

B = |B| β°

∴ Vs = AVR + BIR

03-Models-and-performance (40)

03-Models-and-performance (41)

The complex power VR IR at receiving end

03-Models-and-performance (42)

The real active power at receiving end,

03-Models-and-performance (43)

The reactive power at the receiving end,

03-Models-and-performance (44)

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

03-Models-and-performance (45)

Surge Impedance

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

Characteristic impedance

03-Models-and-performance (46)

Here, Z = Series impedance per unit length

Y = Shunt admittance per unit length

For lossless line, R = 0, G = 0

03-Models-and-performance (47)

It can be also given by 03-Models-and-performance (48)

where, ZOC = Sending end impedance with receiving end open circuited 03-Models-and-performance (49)

ZSC = Sending end impedance with receiving end short-circuited 03-Models-and-performance (50)

Propagation Constant

03-Models-and-performance (51)

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.

03-Models-and-performance (52)

Wavelength 03-Models-and-performance (53)

  • y image078 converted into electrostatic energy image079
  • The potential at the open end becomes 2V.


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.



VT = 0

VR = -VR

IT = 2/F


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 image084

Coefficient of refraction of current wave image085


Note: When the terminated by a resistor equal to surge impedance

V=VF; V= I= IF; I= 0

The incident wave continuous as it is and there is no reflection.

Case (4) Line Terminated by an Inductor

Transmitted (refracted) voltage image087

Reflected voltage wave image088

Transmitted (refracted) current wave. image089

Reflected current wave image090

Where, Zc = Surge impedance of the line.


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 image099

Refracted (transmitted voltage wave)



Line Connected to Cable


Refracted voltage wave


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