Modeling of Induction and Synchronous Machines

Induction Machine Theory

Induction motor is the most widely used ac motor in the industry. An induction motor like any other rotating machine consists of a stator (the fixed part) and a rotor (the moving part) separated by air gap. The stator contains electrical windings housed in axial slots. The induction machines used in industries are mainly three-phase, except for small power where single phase machines are common. Each phase on the stator has distributed winding, consisting of several coils distributed in number of slots. The distributed winding results in MMF due to the current in the winding to be stepped waveform similar to a sine wave. The MMF wave has its maximum value at the center of the winding. In three-phase machine the three windings have spatial displacement of 120 degrees between them. When balanced three phase currents are applied to these windings, the resultant MMF in the air gap has constant magnitude equal to ${{3}\over{2}}$ times the magnitude of one phase, and rotates at an angular speed of ω electrical radians per second. Here ω is the angular frequency of the supply current. The actual speed of rotation of magnetic field depends on the number of poles in the motor. This speed is known as synchronous speed of the motor and is given by

$$ \omega _{s} = \mbox{2}{\rm \pi \mbox{f/p} rad/sec}~~~ (2.1) $$

Where p is number of pole pairs. It can also be expressed as f/p rev/sec or 60f/p rev/min.

If the rotor of an induction motor has a winding similar to the stator it is known as wound rotor machine. These windings are connected to slip rings mounted on the rotor. There are stationary brushes touching the slip rings through which external electrical connected. The wound rotor machines are used with external resistances connected to their rotor circuit at the time of starting to get higher starting torque. After the motor is started the slip are short circuited.