Three Phase Circuits

Generation, transmission, and heavy-power utilization of ac electric energy almost invariably involve a type of system or circuit called apolyphase system or polyphase circuit. In such a system, each voltage source consists of a group of voltages having related magnitudes and phase angles. Thus, an n-phase system employs voltage sources which typically consist of n voltages substantially equal in magnitude and successively displaced by a phase angle of 360°/n. A three-phase system employs voltage sources which typically consist of three voltages substantially equal in magnitude and displaced by phase angles of 120 ° . Because it possesses definite economic and operating advantages, the three-phase system is by far the most common, and consequently emphasis is placed on three-phase circuits in this appendix.

The three individual voltages of a three-phase source may each be connected to its own independent circuit. We would then have three separate single-phase systems. Alternatively, as will be shown in Section A. 1, symmetrical electric connections can be made between the three voltages and the associated circuitry to form a three-phase system. It is the latter alternative that we are concerned with in this appendix. Note that the word phase now has two distinct meanings. It may refer to a portion of a polyphase system or circuit, or, as in the familiar steady-state circuit theory, it may be used in reference to the angular displacement between voltage or current phasors. There is very little possibility of confusing the two.




1 Magnetic Circuits and Magnetic Materials
2 Transformers
3 Electromechanical Energy Conversion Principles
4 Introduction to Rotating Machines
5 Synchronous Machines
6 Polyphase Induction Machines
7 DC Machines
8 Variable-Reluctance Machines and Stepping Motors
9 Single- and Two-Phase Motors
10 Introduction to Power Electronics
11 Speed and Torque Control
Appendix A Three phase circuits
Appendix B Voltages, Magnetic Fields, and Inductances of Distributed AC Windings
Appendix C The dq0 Transformation
Appendix D Engineering Aspects of Practical Electric Machine Performance and Operation
Appendix E Table of Constants and Conversion