Long Transmission Line

Last Updated : 13 Mar, 2024

A long transmission line is an electrical transmission line that extends over a good-sized distance, typically carrying energy from one part of the grid to another. A long transmission line is an important part of the electrical system as it is made by using simple methods and is easy to understand.

In this article, we will be going through the long transmission line in a Power System, We will start our Article with the Definition of the Long Transmission Line, Then we will go through its Derivation and See its Different Types, At last, we will conclude our Article with its Advantages, Disadvantages and Some FAQs.

Table of Content

Long Transmission Line
Derivation
Characteristics
Types
Advantages and Disadvantages
Applications

What is a Long Transmission Line?

Long transmission lines are transmission lines with lengths greater than 150 km and voltages above 100V. It plays an important role in the transmission of energy and power over long distances supporting the functioning of modern electrical technologies. They are very long and stretched across so many regions.

To understand long transmission lines properly we need to understand the basics of some topics like voltage regulation, power stability, transfer capability, etc. If we want to learn more about the features of the long transmission line we could learn from areas like- power flow analysis, Characteristic impedance, and transmission line impedance. Long transmission lines are used in a wide range of applications which are including our day-to-day lifestyle and also for bigger purposes like industries, machinery, etc.

Some important points are

They typically operate at high voltage levels to minimize transmission losses and transport the power for long distances.
Voltage regulation is very important for maintaining the stability of long transmission lines.
Long transmission lines line has resistive losses due to corona losses and skin effect.
Long transmission lines require regular inspection and monitoring.

Derivation of Long Transmission Line

Given Below is the Diagram Which represents one Phase and Neutral Connection of the three phase, having Impedance and Shunt Admittance Uniformly Distributed.

Long Transmission Line

Within the transmission line, Let us take Small Element of length dx. This element is located at a distance x measured along the line from the receiving end towards the sending end.

Denotions

Z=Series impedance per unit length

Y=Shunt admittance per unit length

I=Total length of the line

Z=zl=total series impedance of line

y=yl=total shunt admittance of the line

[Tex]Z_c- characteristics impedance[/Tex]

[Tex]\gamma-propagation constant[/Tex]

Now we can show the network as,

[Tex]dV=Izdx[/Tex]

[Tex]dI=Vydx[/Tex]

[Tex]\frac{dV}{dx}=Iz……eq^n(1)[/Tex]

[Tex]\frac{dI}{dx}=Vy……eq^n(2)[/Tex]

Now we differentiate both the equations

[Tex]\frac{d^2V}{dx^2}=z\frac{dI}{dx}=z.y.V……eq^n(3)[/Tex]

[Tex]\frac{d^2V}{dx^2}-zyV=0…….eq^n(4)[/Tex]

[Tex]V=Ae^{(\sqrt{yz})x}+Be^{(-\sqrt{yz})x}……eq^n(5)[/Tex]

Now we will write this-

[Tex]Z_c=\sqrt{\frac{z}{y}} [/Tex] and [Tex]\gamma = \sqrt{yz} = \alpha+j\beta[/Tex]

Now we will write equation (5) as

[Tex]V=Ae^{\gamma x}+Be^{\gamma x}…..eq^n(6)[/Tex]

Above value is voltage value

Now we can find value of current also as-

[Tex]\frac{dV}{dx}=A.\sqrt{yz}.e^{\gamma x}-B.\sqrt{yz}.e^{-\gamma x}[/Tex]

Putting the value of [Tex]\frac{dV}{dx} in equation (1) [/Tex]we will find

[Tex]I=(\frac{dV}{dx})/z[/Tex]

[Tex]I=\frac{\sqrt{yz}}{z}[Ae^{\gamma x}-Be^{\gamma x}][/Tex]

[Tex]I=\frac{[Ae^{\gamma x}-Be^{\gamma x}]}{Z_c}……eq^n(7)[/Tex]

Now we know the voltage and current equations as equation (6) and equation (7)

But we need to find the value of A and B, that is

[Tex]A=\frac{V_R+I_RZ_C}{2}[/Tex]

[Tex]B = \frac{V_R-I_RZ_C}{2}[/Tex]

Therefore we get V and I as finally

[Tex]V=[\frac{V_R+I_RZ_C}{2}]e^{\gamma x} + [\frac{V_R-I_RZ_C}{2}]e^{-\gamma x}[/Tex]

[Tex]I=\frac{1}{Z_C}[\frac{V_R+I_RZ_C}{2}]e^{\gamma x} + [\frac{V_R-I_RZ_C}{2}]e^{-\gamma x}[/Tex]

Now we have to rearrange the both the equations such that

[Tex]V=V_R[\frac{e^{\gamma x + e^{-\gamma x}}}{2}]+I_RZ_C[\frac{e^{\gamma x + e^{-\gamma x}}}{2}][/Tex]

[Tex]V=V_R cosh(\gamma x)+I_RZ_C sinh(\gamma x)[/Tex]……….eq(8)

[Tex]I=\frac{V_R}{Z_C}sing\gamma x + I_R cosh(\gamma x)[/Tex]

Therefore after watching both equations we get A , B , C , D

[Tex]A=cosh(\gamma l)[/Tex]

[Tex]B=Z_Csinh\gamma l[/Tex]

[Tex]C=\frac{sinh\gamma l}{Z_C}[/Tex]

[Tex]D=cosh\gamma l[/Tex]

Here , we find out that important points are

[Tex]A=D=cosh\gamma l[/Tex]

[Tex]AD-BC=1[/Tex]

Key Characteristics of Long Transmission Lines

Given below are the Key Characteristics of Long Transmission Lines :

High voltage: Long transmission lines operate at high voltages to minimize power losses.
High Capacitance: Long transmission has high capacitance due to parallel arrangement of the conductors.
Inductive Effects: The inductive effects in the conductors increase due to magnetic fields generated by the conductor.
Line Charging Currents: Because of the capacitance the line charging currents generates.
Voltage Regulation Challenges: Voltage drop increases with the length of the line and the magnitude of the current flowing through it.
Power Losses: Long transmission line increases power loss due to resistance of the conductors. These losses increase with the square of the current flowing through the lines and the resistance of the conductors.
Corona Discharge: Corona Discharge causes power loss and make noise and radio interference.

Types of Long Transmission lines

There are many types of long transmission lines based on many factors :

HVDC Transmission Lines
AC Transmission Lines
Overhead Transmission Lines
HVAC Transmission Lines
EHV Transmission Lines

HVDC (High Voltage Direct Current) Transmission Lines

HVDC transmission lines works on direct current(DC current),from them the power losses also reduces. Some important points are

It has low transmission losses
It increases power transfer capacity
It helps in voltage stability and control
It helps in reducing environmental impact
It has a Bi-Directional power flow

AC (Alternating Current) Transmission Lines

As per the name they mainly work on Alternating current(AC current) to make electric power. Some important points are:

It operates at high voltage levels to minimize losses
They work on three-phase system
They require a reactive power compensation to maintain voltage stability
They may experience corona losses and also radio interference
They require long transformer substations at both step up and step down voltage levels for long transmission line

Overhead Transmission Lines

They are the oldest method of transmitting electricity from long distances. Some important points are

They have different conductor configuration.
The conductor material used here is made of aluminum or aluminum alloy.
Their tower design are made from steel and lattice towers.
Insulators are used to support the conductors.
They need regular inspection and maintenance.

HVAC (High Voltage Alternating Current) Transmission Lines

HVAC transmission lines carry high voltage alternating current. Some Important points are

They operate using alternating current where the current flow periodically reverses.
They operate at high voltage levels to minimize transmission losses.
They work on three-phase system.
They require transformer substations at both ends to step up voltage and step down voltage.

EHV (Extra High Voltage) Transmission Lines

They operate above 345 KV. They are used for highest voltage level power transmission in electrical field . Some important points are

They are designed to lower the transmission losses.
They can transmit large amounts of power for long distances.
They may have environmental impacts like nature harm and more generation of electromagnetic fields.
They require more safety measurements due to high voltage levels.

Advantages and Disadvantages of Long Transmission Lines

Given Below are the Some Advantages and Disadvantages of Long Transmission Lines

Advantages of Long Transmission lines

Efficient Power Transfer: Long transmission lines enable the efficient transfer of electricity.
Grid Stability and Reliability: Long transmission lines increase the stability and reliability of the power grid.
Scalability and Flexibility :Long transmission lines offer scalability and flexibility.
Environmental Considerations: long transmission lines contribute to reducing greenhouse gas emissions.

Disadvantages of Long Transmission lines

High Initial Cost:For building a long transmission line the cost is very high.
Transmission Losses: Long transmission lines experience higher resistive losses.
Voltage Drop: Voltage drop occurs due to the resistance, inductance, and capacitance of the conductors.
Electromagnetic Fields (EMF): Long transmission lines produce electromagnetic fields (EMF) that increases potential health risks for living beings.

Applications of Long Transmission lines

There are many applications of long transmission line some of them are as follows:

Industrial and Commercial Applications
Electric Vehicle Charging Infrastructure
Renewable Energy Integration
Used in renewable energy sources like hydroelectric dams and also wind farms.
Used in long distance communication cables that are underwater.
They are used in microwaves for making design of their components.

Conclusion

In conclusion we can conclude that long transmission play a very vital role in electrical field and modern world. It is very efficient in transmission of electricity. It does has its own advantages and disadvantages with a wide range of applications in today’s world. As the society is growing so is the technology in long transmission lines.