When the three-phase voltage system is applied to an induction motor, the phase currents are phase-shifted from the phase voltages in the lagging direction by the power factor angle, φ, which appears to be close to a value of 30º for the classes of 2-hp and 5- hp motors studied in this thesis, as shown by the phasor diagram in Fig. 2.6, where V ab , V bc , and V ca are the line-to-line voltages and V a , Vb , and V c are the phase voltages.
The speed of the magnetic rotating field is the synchronous speed. For a induction motor with P poles, the synchronous speed is given in r/min as (2.9).
where, nasyn is the asynchronous speed in r/min, and ns is the slip speed in r/min. Moreover, the slip speed can also be defined in a per unit system as the slip, spu, as given in (2.11).
As aforementioned, the synchronous speed of an induction motor connected to a constant frequency sinusoidal ac power supply depends on the frequency and number of poles. The number of poles is an inherent characteristic of an induction motor, which can be typically two, four, six, or eight, etc. On the other hand, the asynchronous rotor speed depends not only on the frequency and number of poles, but also depends of the load torque. Thus, higher torque results in a higher slip and a slower asynchronous rotor speed. Accordingly, an induction motor connected to a constant frequency sinusoidal power supply runs only at one asynchronous speed and thus provides no means of speed variation/control. In this case, an induction motor can be run only at a constant speed, and thus be used in fixed speed applications, such as pumps with constant flow, fans, air compressors, conveyor belts with constant speed, mixers, and drills.