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# Three Phase AC Circuits

Three Phase AC Circuits

Contents

Explain Generation of Three-Phase EMF with Phasor diagram 1

Describe Three-Phase Star & Delta Connections 5

List advantages of Three-Phase systems 6

Derive the expression for Line and Phase voltages in Delta Connection 7

Explain Power in Star Connection 8

Explain the relationship between Line and Phase Voltages Connection and Currents in Delta Connection 9

Explain Power in Delta Connection 10

Explain Two-Wattmeter method for Balanced Three-Phase load for measurement of Power and Power factor 10

Describe Unbalanced Delta connected load 11

Describe Unbalanced Star connected load with 3-wire and 4-wire system 12

# Explain Generation of Three-Phase EMF with Phasor diagram

In a three-phase system, three identical voltages or EMFs with the same frequency are generated, each having a phase difference of 120 degrees. These voltages can be created by a three-phase AC generator that incorporates three identical windings positioned 120 degrees apart from each other electrically.

When the windings are fixed in place, and the magnetic field is rotated, as illustrated in figure A, or when the windings remain stationary while the magnetic field is rotated, as depicted in figure B, an EMF is induced in each winding. The magnitude and frequency of these EMFs are identical, but they are phase-shifted by an angle of 120 degrees relative to one another.

Figure A

Consider the above figure, which displays three identical coils labeled as a1a2, b1b2, and c1c2. In this configuration, a1, b1, and c1 represent the starting terminals, while a2, b2, and c2 represent the finishing terminals of the coils. It is crucial to maintain a phase difference of 120 degrees between the starting terminals a1, b1, and c1.

Now, suppose the three coils are aligned on the same axis and are rotated either by keeping the coils stationary and moving the magnetic field or by rotating the coils while keeping the magnetic field fixed in an anticlockwise direction at a rate of (Ï‰) radians per second. As a result of this rotation, three electromotive forces (EMFs) are induced in the respective coils.