Three-Phase A.C. Circuits
This chapter introduces the concepts and principles of the three-phase electrical supply, and the corresponding circuits. On completion you should be able to:
1 Describe the reasons for, and the generation of the three-phase supply.
2 Distinguish between star (3 and 4-wire) and delta connections.
3 State the relative advantages of three-phase systems compared with single-phase-systems.
4 Solve three-phase circuits in terms of phase and line quantities, and the power developed in three-phase balanced loads.
5 Measure power dissipation in both balanced and unbalanced three-phase loads, using the
1, 2 and 3-wattmeter methods, and hence determine load power factor.
6 Calculate the neutral current in a simple unbalanced 4-wire system.
3.1 Generation of a Three-Phase Supply
In order to understand the reasons for, and the method of generating a three-phase supply, let us ﬁrstly consider the generation of a singlephase supply. Alternating voltage is provided by an a.c. generator, more commonly called an alternator. The basic principle was outlined in Fundamental Electrical and Electronic Principles, Chapter 5.
It was shown that when a coil of wire, wound on to a rectangular former, is rotated in a magnetic ﬁeld, an alternating (sinusoidal) voltage is induced into the coil. You should also be aware that for electromagnetic induction to take place, it is the relative movement between conductor and magnetic ﬂux that matters. Thus, it matters not whether the ﬁeld is static and the conductor moves, or vice versa.
For a practical alternator it is found to be more convenient to rotate the magnetic ﬁeld, and to keep the conductors (coil or winding) stationary.
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Further Electrical and Electronic Principles
In any rotating a.c. machine, the rotating part is called the rotor, and the stationary part is called the stator. Thus, in an