## What is a short transmission line?

A short transmission line is a transmission line that has a length less than 80 kilometers, an operating voltage level of less than 20 kV, and zero capacitance effect.

## Transmission lines

Transmission lines are important components in electrical engineering. The transmission lines are specially designed cables or conductors used to conduct electromagnetic waves over large distances in a well-engineered manner with minimum losses. They are supported by long perpendicular poles. Specialized construction and impedance matching are done for the transmission lines to carry the electromagnetic signals. The sections of transmission cables are generally made uniform to obtain uniform impedance and reduce the losses during transmission.

The transmission lines are classified as long transmission lines, medium transmission lines, and short transmission lines based on the length and operating voltage they carry. The transmission lines that have a length of more than 250 kilometers and an operating voltage level of more than 100 kV are known as long transmission lines. The transmission lines that have a length of more than 80 kilometers but less than 250 kilometers and operating voltage levels of more than 20 kV but less than 100 kV are known as medium transmission lines.

For long transmission lines and medium transmission lines, all the three-line parameters, resistance, inductance, and capacitance are taken into consideration, whereas for the short transmission lines, only resistance and inductance line parameters are taken into consideration. The transmission lines are supposed to transfer the waves with minimum losses, hence with more efficiency. The transmission efficiency of a transmission line is given using the following formula,

$\%\eta =\frac{{V}_{R}{I}_{R}\mathrm{cos}{\phi}_{R}}{{V}_{S}{I}_{S}\mathrm{cos}{\phi}_{S}}$

where ${V}_{R}$ is the receiving end voltage, ${I}_{R}$ is the receiving end current, $\mathrm{cos}{\phi}_{R}$ is the receiving end power factor, ${V}_{S}$ is the sending end voltage, ${I}_{S}$ is the sending end current, and $\mathrm{cos}{\phi}_{S}$ is the sending end power factor.

The various types of transmission lines are coaxial cables, planar lines, microstrips, stripline, coplanar waveguide, balanced lines, twisted pair, star-quad, twin-lead, lecher lines, and single-wire lines. The transmission lines have a range of applications. The transmission lines are used for transmitting high-frequency signals over both short and long distances with maximum efficiency. The signal input is fed through one end, while the load is placed at the other end, known as the receiving end. The transmission lines are also used for generating pulses. For the generation of pulse, the transmission line is charged and then discharged into a resistive load.

## Short transmission line

As stated earlier, short transmission lines are the lines that have lengths less than 80 kilometers and operating voltage levels less than 20 kV. Due to such short distances and low voltage, the capacitive effect is negligible and the performance of these short transmission lines depends on the resistance effect and induction effect.

### Equivalent circuit and phasor diagram

To solve the circuits of short transmission lines, the equivalent circuit diagram is used, which simplifies the solving of the network. The resistance and induction are the only two parameters affecting transmission from the short transmission lines. The resistances and inductance are considered as lumped in the circuit. After solving the equivalent circuit, the series impedance is found in complex form using the following equation-

$Z=R+i.X$

where $Z$ is the series impedance, $R$ is the loop resistance, and $X$ is the loop reactance.

The phasor diagrams are necessary for calculating the voltage regulations of transmission lines. The phasor diagram is drawn using the phase lines and assuming the nature of the power factor to be lagging if the nature is not given. From the phasor diagram, the following equation is obtained-

${V}_{s}={V}_{R}+{I}_{R}R\mathrm{cos}{\phi}_{R}+{I}_{R}X\mathrm{sin}{\phi}_{R}$

where ${V}_{S}$ is the sending end voltage, ${V}_{R}$ is the receiving end voltage, ${I}_{R}$ is the receiving end current, ${\phi}_{R}$ is the angle made by the sending end voltage on the phasor diagram, $R$ is the loop resistance, and $X$ is the loop reactance.

In the phasor diagram of short transmission lines, it is assumed that ${\phi}_{R}={\phi}_{S}$, because the shunt capacitance of the network is neglected and the current at the sending end is the same as that of the current at the receiving end.

## Voltage regulation of transmission lines

The voltage regulation of transmission lines is an important parameter in the performance of power systems. The voltage regulation of transmission lines is defined as the ratio of the difference between the sending end voltage and receiving end voltage to the receiving end voltage. Mathematically, it can be expressed as,

$\%VoltageRegulation=\frac{{V}_{S}-{V}_{R}}{{V}_{R}}x100$

where ${V}_{S}$ is the sending end voltage and ${V}_{R}$ is the receiving end voltage.

The lagging loads and leading loads affect the voltage regulation of transmission lines.

For lagging load, the following equation is given for determining the voltage regulation of transmission lines-

$\%VoltageRegulation=\frac{I.R.\mathrm{cos}{\phi}_{R}+I.{X}_{L}.\mathrm{sin}{\phi}_{R}}{{V}_{R}}x100$

For leading load, the following equation is given for determining the voltage regulation of transmission lines-

$\%VoltageRegulation=\frac{I.R.\mathrm{cos}{\phi}_{R}-I.{X}_{L}.\mathrm{sin}{\phi}_{R}}{{V}_{R}}x100$

If the power factor is lagging, the voltage regulation increases and becomes positive, whereas, if the power factor is leading, the voltage regulation decreases and becomes negative. For a three-phase short transmission line, the following equation is used for obtaining the power at the receiving end-

${P}_{R}=3.{V}_{R}.I.\mathrm{cos}{\phi}_{R}$

where ${P}_{R}$ is the receiving end power, ${V}_{R}$ is the receiving end voltage, $I$ is the current flowing through the transmission line, and $\mathrm{cos}{\phi}_{R}$ is the receiving end power factor. As the sending end current and receiving end current are the same for the short transmission lines, $I={I}_{R}={I}_{S}$.

## Context and Applications

The short transmission line is taught in the following courses-

- Bachelors of Technology (Electrical Engineering)
- Masters of Technology (Power System and Power Electronics)

## Practice Problems

**Q1. **What is the length of a short transmission line?

a) Less than 80 kilometers

b) 80 kilometers to 250 kilometers

c) More than 250 kilometers

d) 80 kilometers to 200 kilometers

**Answer** - Option a

**Explanation–** The length of a short transmission line is less than 80 kilometers.

**Q2. **What is the operating voltage level of long transmission lines?

a) Less than 20 kV

b) 20 kV to 100 kV

c) More than 100 kV

d) 5 kV to 15 kV

**Answer** - Option c

**Explanation– **The operating voltage level of long transmission lines is more than 100 kV.

**Q3. **Which of the following is not a type of transmission line?

a) Coaxial cables

b) Planar lines

c) Magnetic line

d) Twisted pair

**Answer** - Option c

**Explanation- **Magnetic line is not a type of transmission line.

**Q4. **Which of the following is defined as the ratio of the difference between the sending end voltage and receiving end voltage to the receiving end voltage?

a) Voltage regulation of transmission lines

b) Admittance of transmission lines

c) Impedance regulation of transmission lines

d) Capacitance regulation of transmission lines

**Answer** - Option a

**Explanation– **Voltage regulation of transmission lines is defined as the ratio of the difference between the sending end voltage and receiving end voltage to the receiving end voltage.

**Q5. **Which of the following is not a line parameter considered for the medium transmission lines?

a) Resistance

b) Inductance

c) Capacitance

d) Power factor

**Answer** - Option d

**Explanation–** Power factor is not a line factor considered for the medium transmission lines.

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