# Performance of Transmission Line & Travelling Wave Analysis For Electrical Engineering

By Yash Bansal|Updated : May 20th, 2021

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.

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.

### 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      Reglation % Regulation  Efficiency 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.  Here,  For Voltage Regulation  ∴ % regulation % efficiency 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 % regulation % efficiency  Note: Percentage regulation 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, where, which is called the characteristic impedance For lossless line R = 0; G = 0 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

Ss = Ps + jθs = VsIs*

SR = PR + jθR Let A = D = |A|<α°

B = |B| β°

∴ Vs = AVR + BIR  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 Surge Impedance

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 Propagation Constant 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. Wavelength 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 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 converted into electrostatic energy • 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

IR = IF

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

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 Reflected voltage wave Transmitted (refracted) current wave. Reflected current wave 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 Refracted (transmitted voltage wave) Line Connected to Cable Refracted voltage wave If you are preparing for GATE and ESE, avail of BYJU'S Exam Prep Online Classroom Program to get unlimited access to all the live structured courses and mock tests from the following link :

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write a comment Shravan SankatiDec 8, 2016  Shravan SankatiDec 8, 2016  Thakkar JayOct 16, 2019

Why capacitor bank or synchronous condensor delivers reactive power to transmission line? What is the need of kvar? Please explain.. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com