Electric Circuits and Networks

9.3 ANALYSIS OF BALANCED THREE-PHASE CIRCUITS

Balanced three-phase circuits comprising a balanced three-phase source and a balanced three-phase load can be of four varieties, viz., Y–Y, Y–∆, ∆–Y or ∆–∆. We develop a common analysis procedure for all the possible configurations.

9.3.1 Equivalence Between a Y-connected Source and a ∆-connected Source

Let V_RY = V_L∠0°, V_YB = V_L∠–120° and V_BR = V_L∠120° be the three line voltages observed in a three-phase circuit and let I_R = I_L∠–(θ + 30°), I_Y = I_L∠–(θ + 150°) and I_B = I_L∠–(θ – 90°) be the observed line currents where the observed phase lag of first line current is expressed as 30° plus some angle designated by 6. If the source is within a black box and we are to guess whether it is a Y-connected source ...