Producing Rotating Fields
Principles
Mathematical Description
In the diagram above there are three coils, arranged around the stator of a machine such that the angle betweem each of the phases is 120°. Assuming that the steel in the rotor and stator is infintely permeable, the mmf produced in the airgap between the two sides of a coil will be constant. Each coil will produce a square wave mmf function, phase shifted by 120°. The mmf functions for each phase are:
Now, if the currents the phases are a sinusoidal balanced three-phase set
then the mmf functions will vary with both time and space
Although the above mmf functions may seem quite long, the mmfs simplify significantly when summed to find the total mmf.
It can be seen from the above equation that:
- the three pulsating mmf functions combine to create a rotating mmf function, with consant magnitude fundamental frequency component
- the magnitude of the rotating mmf is 1.5 times the magnitude of the pulsating mmf components
- all mulitples of the third harmonics are eliminated
- the magnitude of a higher space harmonic is inversely proportional to the harmonic number
- harmonic numbers 6n+1 where n is an integer rotate in the positive direction
- harmonic numbers 6n-1 where n is an integer rotate in the negative direction
The first three harmonics in the series are animated below:
Simplifications
For the rest of the course we will neglect higher space harmonics and assume that a simple three coil arrangement is capable of producing a sinusoidal air gap mmf. This assumption is aided by the fact that most real machines are constructed with distributed windings which have been designed to minimse space harmonic components.