# Comparison between 3 Phase and 1 Phase Power Transmission

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.

Thanks