12.1 Introduction

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12.1 Introduction

So far in this text, we have dealt with single-phase circuits. A singlephase ac power system consists of a generator connected through a pair of wires (a transmission line) to a load. Figure 12.1(a) depicts a singlephase two-wire system, where Vp is the rms magnitude of the source voltage and ϕ is the phase. What is more common in practice is a singlephase three-wire system, shown in Fig. 12.1(b). It contains two identical sources (equal magnitude and the same phase) that are connected to two loads by two outer wires and the neutral. For example, the normal household system is a single-phase three-wire system because the terminal voltages have the same magnitude and the same phase. Such a system allows the connection of both 120- and 240-V appliances.

Historical note: Thomas Edison invented a three-wire system, using three wires instead of four.

Circuits or systems in which the ac sources operate at the same fre quency but different phases are known as polyphase. Figure 12.2 shows a two-phase three-wire system, and Fig. 12.3 sho ws a three-phase fourwire system. As distinct from a single-phase system, a two-phase system is produced by a generator consisting of tw o coils placed perpendicular to each other so that the voltage generated by one lags the other by 90°. By the same token, a three-phase system is produced by a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120°. Because the three-phase system is by far the most pre valent and most economical polyphase system, discus sion in this chapter is mainly on three-phase systems.

Figure 12.2 Two-phase three-wire system.

Three-phase systems are important for at least three reasons. First, nearly all electric po wer is generated and distrib uted in three-phase,

Historical

Nikola Tesla (1856–1943) was a Croatian-American engineer whose inventions—among them the induction motor and the first polyphase ac power system—greatly influenced the settlement of the ac versus dc debate in favor of ac. He was also responsible for the adoption of 60 Hz as the standard for ac power systems in the United States.

Born in Austria-Hungary (now Croatia), to a clergyman, Tesla had an incredible memory and a keen affinity for mathematics. He moved to the United States in 1884 and first worked for Thomas Edison. At that time, the country was in the “battle of the currents” with George Westinghouse (1846–1914) promoting ac and Thomas Edison rigidly leading the dc forces. Tesla left Edison and joined Westinghouse be cause of his interest in ac. Through Westinghouse, Tesla gained the reputation and acceptance of his polyphase ac generation, transmission, and distribution system. He held 700 patents in his lifetime. His other inventions include high-voltage apparatus (the tesla coil) and a wireless transmission system. The unit of magnetic flux density, the tesla, was named in honor of him.

Library of Congress [LC-USZ62-61761]

at the operating frequenc y of 60 Hz (or ω = 377 rad/s) in the United States or 50 Hz (or ω = 314 rad/s) in some other parts of the w orld. When one-phase or tw o-phase inputs are required, the y are taken from the three-phase system rather than generated independently. Even when more than three phases are needed—such as in the aluminum industry , where 48 phases are required for melting purposes—the y can be pro vided by manipulating the three phases supplied. Second, the instanta neous power in a three-phase system can be constant (not pulsating), as we will see in Section 12.7. This results in uniform power transmission and less vibration of three-phase machines. Third, for the same amount of power, the three-phase system is more economical than the singlephase. The amount of wire required for a three-phase system is less than that required for an equivalent single-phase system.

We begin with a discussion of balanced three-phase v oltages. Then we analyze each of the four possible configurations of balanced threephase systems. We also discuss the analysis of unbalanced three-phase systems. We learn how to use PSpice for Windows to analyze a balanced or unbalanced three-phase system. Finally, we apply the concepts developed in this chapter to three-phase po wer measurement and residential electrical wiring.