Question

A single phase ac system comprising of two overhead conductors is to be converted into a 3-phase, 3-wire system by providing an additional conductor of same size. If the operating line voltage, percentage line losses and power factor of load remains same in both systems. The percentage of additional load that can be transmitted by the three phase phase system is

• A. 86.6%
• B. 173.2%
• C. 50%
• D. 100%

Answer 1

The correct option is D 100%

Let the operating voltage and power factor in both the systems be V volts and cos $\varphi$ respectively.

If $I_1$is single phase current, $I_2$ is the three phase current and R is the resistance of each conductor, then
Single phase system:

$P_1=V{I}_{1}cos\varphi$ Watts
Losses $=2I_1^2$R Watts

Percentage line losses $=\frac{W_1}{P_1}\times 100=\frac{2I_1^{2}R}{V{I}_{1}cos\varphi }\times 100$

3-$\varphi$ system
$P_2=\sqrt{3}V{I}_{2}cos\varphi$
Percentage line losses $=\frac{3I_2^2}{\sqrt{3}V{I}_{2}cos\varphi }\times 100$

For the same percentage line losses in both the cases, we have

$=\frac{2I_1^{2}R}{V{I}_{1}cos\varphi }\times 100=\frac{3I_2^2}{\sqrt{3}V{I}_{2}cos\varphi }\times 100$

$2I_1=\sqrt{3}{I}_2$
$I_2=\frac{2}{\sqrt{3}}{I}_1$

$\therefore$ Power transmitted in 3-$\varphi$ system,

$P_2=\sqrt{3}V\times \frac{2}{\sqrt{3}}{I}_{1}cos\varphi =2V{I}_{1}cos\varphi =2P_1$

$\therefore$ Percentage of additional load $=\frac{P_2-P_1}{P_1}\times 100$

$=\frac{P_1}{P_1}\times 100=100\%$