THREE PHASE SYSTEMS

In a single-phase ac circuit, instantaneous power to a load is of a pulsating nature. Even at the unity power factor (i.e., when the voltage and the current are in phase with respect to each other), the instantaneous power is less than unity (i.e., when the voltage and the current are not in phase). The instantaneous power is not only zero four times in each cycle but it is also negative twice in each cycle. Therefore, because of economy and performance, almost all electrical power is produced by polyphase sources (i.e., by those generating voltages with more than one phase.

A polyphase generator has two or more single phases connected so that they provide loads with voltages of equal magnitudes and equal phase differences. For example, in a balanced n-phase system, there are n voltage sources connected together. Each phase voltage (or source) alternates sinusoidally, has the same magnitudes, and has a phase difference of 360/n° (where n is the number of phases) from its adjacent voltage phasors, except in the case of two-phase systems. Generators of 6, 12, or even 24 phases are sometimes used with polyphase rectifiers to supply power with low levels of ripples in voltage on the do side in the range of kilowatts. Today, virtually all the power produced in the world is three-phase power with a frequency of 50 or 60 Hz. In the United States, 60 Hz is the standard frequency. Recently, six-phase power transmission lines have been proposed because of their ability to increase power transfer over existing lines and reduce electrical environmental impact. Even though other polyphase systems are feasible, the power utility industry has adopted the use of three-phase systems as the standard. Consequently, most of the generation, transmission, distribution, and heavy-power utilization of electrical energy are done using three-phase systems. A three-phase system is supplied by a three-phase generator (i.e., alternator), which consists essentially of three single-phase systems displaced in time phase from each other by one-third of a period, or 120 electrical degrees. The advantages of three-phase systems over single-phase systems are as follows:

• Less conductor material is required in the three-phase transmission of power and therefore it is more economical.

• Constant rotor torque and therefore steady machine output can be achieved.

• Three-phase machines (generators or motors) have higher efficiencies.

• Three-phase generators may be connected in parallel to supply greater power more easily than single-phase generators.

Figure 1(a) shows the structure of an elementary three-phase and two-pole ac generator (also called an alternator). Its structure has basically two parts: the stationary outside part which is called the stator and the rotating inside part which is called the rotor. The field winding is located on the rotor and is excited by a direct current source through slip rings located on the common shaft. Thus, an alternator has a rotating electromagnetic field; however, its stator windings are stationary. The elementary generator is shown in Figure (1)a has three identical stator coils (aa’, bb’, and cc’), of one or more turns, displaced by 120° in space with respect to each other. If the rotor is driven counterclockwise at a constant speed, voltages will be generated in the three phases according to Faraday’s law, as shown in Figure (1)b. Notice that the stator windings constitute the armature of the generator (unlike dc machines where the armature is the rotor). Thus, the field rotates inside the armature. Each of the three stator coils makes up one phase in this single generator. Figure (1)b shows the generated voltage waveforms in the time domain, while Figure (1)c shows the corresponding phasors of the three voltages. The stator phase windings can be connected in either wye or delta. In wye configuration, if a neutral conductor is brought out, the system is defined as a four-wire three-phase system; otherwise, it is a three-wire, three-phase system. In a delta connection, no neutral exists and therefore it is a three-wire three-phase system.