Question

A balanced delta connected load takes 20 KVA at 0.8 power factor when connected to a 415 v, 3 sigma system.Calculate the resistance of each branch of balanced star connected non reactive load which when connected to same supply coil takes the same power?

Answer 1

The active power per each phase (since the load is balanced, it means that all branches have the same impedance) can be calculated as

$$P=\frac{S\space\text{cos}\phi}{\sqrt{3}}.$$

With non-reactive load each phase of the star-connected load has power of

$$P=\frac{U^2_\text{phase}}{R_\text{branch}},$$

and therefore

$$R_\text{branch}=\frac{U^2_\text{phase}}{P}=\frac{\sqrt{3}\cdot U^2_\text{phase}}{S\space\text{cos}\phi}=\frac{\sqrt{3}\cdot [U^2_\text{line}/3]}{S\space\text{cos}\phi},$$

$$R_\text{branch}=\frac{\sqrt{3}\cdot 415^2/3}{20000\cdot0.8}=6.21\space\Omega.$$