Three Phase Short Transmission Lines

Three Phase Short Transmission Lines

By Aman KKBBM

As a matter of convenience, we generally analyse 3- phase system by considering one phase only. Therefore, expression for regulation, efficiency etc. derived for a single phase line can also be applied to a 3-phase system.

For reasons associated with economy, transmission of electric power is done by 3-phase system. This system may be regarded as consisting of three single phase units, each wire transmitting one-third of the total power.

Three-Phase Short Transmission Lines

Figure 10 (i) shows a Y-connected generator supplying a balanced Y-connected load through a transmission line. Each conductor has a resistance of R Ω and inductive reactance of XL Ω.

Since only one phase is considered, phase values of 3- phase system should be taken. Thus, VS and VR are the phase voltages, whereas R and XL are the resistance and inductive reactance per phase respectively.

Three-Phase Short Transmission Lines

Figure 10 (ii) shows one phase separately. The calculations can now be made in the same way as for a single phase line.

​

The relationship between magnitudes of the line-to-line (LL) voltage or current and the line-to-neutral (phase, Ф) voltage or current in Y-connected generator or load is :

​

​Some text here about the topic of discussion.

​Voltages and Currents in the wye (Y) Connection.

The real power (W) input and output to a 3-phase transmission line can be computed as :

​

​VS or VR= magnitude of source (input/output) line-to-neutral voltage VLL,S or VLL,R = magnitude of source (input/output) line-to-line voltage

​Power Flow in Transmission Lines

The reactive power (VAR) input and output to a 3-phase transmission line can be computed as :

​

​Power Flow in Transmission Lines

The apparent power (VA) input to a 3-phase transmission line can be computed as :

​

Power Flow in Transmission Lines

Transmission line efficiency :

​The power lost in transmission line is :

​Power Flow in Transmission Lines

Example 1

An overhead 3-phase transmission line delivers 5000kW at 22 kV at 0.8 p.f lagging. The resistance and reactance of each conductor is 4 Ω and 6 Ω respectively.

​Determine : (i) sending end voltage (ii) percent regulation (iii) transmission efficiency

Answer

Answer.... Cont..

Answer.... Cont..

Answer.... Cont..

EXERCISE 1

Some text here about the topic of discussion

Open Ended

An 11 kV , 3-phase transmission line has a resistance of 1.5 Ω and reactance of 4 Ω per-phase. Calculate the percentage regulation and efficiency of the line when apparent power of 5000 kVA at 0.8 lagging power factor is supplied at 11kV at the distance end.

​ANSWER

​

EXERCISE 2

Some text here about the topic of discussion

Open Ended

A load of 1000kW at 0.8 p.f lagging is received at the end of a 3-phase line 20km long. The resistance and reactance of each conductor are 0.25 Ω and 0.28 Ω per km. If the receiving end line voltage is maintained at 11 kV, calculate :

i) Sending end voltage (line-to-line)

ii) Percentage regulation

iii) Transmission efficiency

EXERCISE 3

Some text here about the topic of discussion

Open Ended

A three-phase, 60Hz overhead short transmission line has a line-to-line voltage of 23kV at the receiving end, a total impedance of 2.48 + j6.57 Ω/phase , and a load of 9MW with a receiving-end lagging power factor of 0.85, calculate:

i) Line-to-neutral (VS(L-N)) & line-to-line (VS(L-L)) at sending end.

ii) Calculate load angle, ɗ

iii) Percentage of voltage regulation