Power from Generating
Station to the Load Center is transmitted by 3 phase 3 wire system. The comparison between 3 phase Power Transmission and 1 phase Power Transmission is
done assuming the Power to be transmitted, Voltage, Distance and loss to be
same.

From the economy point of view the weight of
conductor required for both the cases are important to be considered. The
weight of conductor required is directly proportional to the distance and
inversely proportional to the resistance of conductor.

Let P

_{1}= Power Transmitted using 1 phase
P

_{2}= Power Transmitted using 3 phase
Therefore,

P

_{1}= VI_{1}CosØ
Where V = RMS Voltage at
which Power is transmitted

I

_{1}= RMS Current flowing in 1 phase
CosØ = Power factor

We will assume power factor
for 1 phase and 3 phase to be same for comparison purpose.

P

_{2}= Power Transmitted using 3 phase
= 1.732VI

_{2}CosØ
I

_{2}= RMS Current flowing in 3 phase
As power transmitted in 1
phase and 3 phase are assumed same,

P

_{1}= P_{2}_{}

VI

_{1}CosØ = 1.732VI_{2}CosØ
So, I

_{1}= 1.732I2 ………………………(1)
From equation (1), it is
quite clear that current flowing in the single phase system is 1.732 times that
of current flowing in 3 phase system for transmitting the same power.

Again, Loss in 1 phase
system = 2xI

_{1}^{2}R_{1}(As there are two conductors)
Loss in 3 phase system = 3xI

_{2}^{2}R_{2}(As there are three conductors)
Where R

_{1}= Resistance per conductor in 1 phase system
R

_{2}= Resistance per conductor in 3 phase system
Assuming loss to be same,

Loss in 1 phase system = Loss
in 3 phase system

So, 2xI1

^{2}R_{1}= 3xI2^{2}R_{2}_{}

R

_{1}/R_{2}= 3I_{2}^{2}/2I_{1}^{2}^{}

From equation (1),

R

_{1}/R_{2}= 1/2 …………………….(2)
From the above expression,
we see that Resistance in case of 3 phase system is more which means less cross
sectional area of the conductor needed to transmit power from Generating
Station to Load Center when compared with 1 phase system.

So,

Weight of Conductor in 3
phase / Weight of Conductor in 1 phase

= (No. of conductor in 3
phase / No. of conductor in 3 phase) x (R

_{1}/ R_{2})
= 3R

_{1}/2R_{2}_{}

From equation (2),

*Weight of Conductor in 3 phase / Weight of Conductor in 1 phase*

*= 3 / 4*

Therefore, we observe that
for transmitting the same amount of Power over a fixed distance with a fixed
line loss, we need only 75% amount of conductor that would be required for a
single phase in 3 phase system. Thus 25% conductor material is saved by using 3
phase system for transmitting power.

## 1 comment:

Thanks

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