Mumbai University > FE > Sem 1 > Basic Electrical and Electronics Engineering

Marks: 6 M

Year: DEC 2012, MAY 2012

The above fig. shows a balanced star connected load.

Let VRN, VYN and VBN be the three phase voltages.

Let IR, IV, IB be the phase currents.

The phase currents will lag behind their respective phase voltages by angle Ф

Current through coil of W1 =IR

Voltage across voltage coil

W1= VRB

= VRN + VNB

= VRN – VBN

From phase diagram, it is clear that the phase angle between VRB and IR is (30o – ф)

∴ W1 = VRB IR cos (30- ф)

Current through coil W2 = IY

Voltage across voltage coil

W2 = VYB

=VYN + VNB

= VYN – VBN

From phase diagram, it is clear that the phase angle between VYB & IY is (30o + ф)

∴ W2 = VYB IY is (30o + ф)

But, IR =IY = IL

VRB = VYB = VL

W1= VLIL cos (30o - ф)

W2 = VLIL cos (30o + ф)

∴ W1 + W2 = VLIL [cos (30 + ф) + cos (30 – ф)]

= VLIL (2cos 30o cos ф)

= √3 VLIL cos ф

Therefore W1 + W2 = √3 VLIL cos ф