Synchronous machines



Synchronous machines are extensively employed as generators in three phase AC power systems. Hence this article is focussed more on synchronous generator. As it has been told in basics of electromagnetic power conversion, synchronous generator or alternator as it is called uses the Faraday's law of electromagnetic induction to develop an emf across the windings. Three phase power is used due to its advantage of constant instantaneous power. Hence three phase generators are most common.

Basics and construction

There must be a field winding and an armature in which the emf will be induced. Typical construction has field winding on the rotor and armature winding on the stator. Note that this is opposite to that of a DC machine. High speed turbo-generators have non-salient or cylindrical rotor construction. Ususally they are driven by steam turbines. Whereas the alternators driven by hydro-turbines have salient pole alternators. Field winding is excited by a DC voltage and has same number of poles as that on stator. Each phase of armature winding on stator is displaced in space by 120o electrical from other (for three phase construction which is the most commonly deployed). The analysis assumes that the flux produced by the field winding is sinusoidally distributed in the air gap. When the field rotates at constant speed, flux which links the stationary armature winding varies sinsoidally with time. This produces the three phase emfs in the armature which are displaced in time by 120o electrical from each other.
The rotor has windings which carry DC current. These field windings are excited via slip-ring and brush assembly. Note that this is not the same as the commutator and brush assembly in DC machine. The slip-rings have no "segments"; they are two full rings connected to the DC supply. This can be seen from photo given below.


Governing equations

The voltage induced in the armature winding undergoes a complete cycle when one pole pair sweeps by. Thus in one mechanical revolution it undergoes cycles, where is number of poles. Hence if is the speed of prime mover in rpm then the frequency of induced voltages is



We assume that the flux is distributed sinusoidally in space in the air gap. If is the flux linkage per pole per phase then



Here is the flux per pole linking the winding. Hence emf induced in each phase winding having turns is



From which;



Note that is mechanical frequency of rotation of the rotor.

The induced emf in each of the phases has same magnitude but they are displaced in phase from each other by 120o.


Rotating Magnetic Field

Now, if we connect a balanced load across the three phases, balanced three phase currents will flow through armature. Lets look at the field produced in the air gap by these currents. Consider three coils A, B and C of turns each, displaced in space by 120o degrees and connected to a balanced 3 phase system as shown in figure. The coils are depicted to be single turn coils. Further this diagram shows only two pole machine. This is just to simplify the analysis. Similar analysis can be done for more complicated cases.



Let A phase current lags A phase voltage by an angle . Then instantenous armature currents are



Each coil produces a pulsating magnetic field whose amplitude and direction depend on the instantaneous value of the current flowing through the coil. Each phase winding produces a similar magnetic field displaced by 120o degrees in space from each other. The steps involved in determining the magnitude and position of the resultant field produced by these coils are as follows:
  1. Resolve the field produced by individual coil along X and Y axes
  2. Determine X and Y components
  3. Find the magnitude and angle of the resultant magnetic field with respect to the axis of coil-A
The sum of the X component of the field produced by the three coils is given by



And sum of Y axis component will be then



Hence the resultant of the two will be the



Table gives the X and Y components of the field produced by each coil and the magnitude and angle of the resultant magnetic field for various instantaneous values of the input current. It can be observed that the resultant of the three mmf (magneto-motive force or field) vectors is a vector whose magnitude remains constant (1.5 times the amplitude of mmf produced by the individual phases alone) and its position depends on the instantaneous value of input currents.



It can be seen from the table that when the instantaneous value of phase-A current is zero the resultant field is aligned along the y-axis. When the input cycle completes 90o the resultant field also rotates by the same amount. In other words, the result of displacing the three windings by 120o in space phase and displacing the winding currents by 120o in time phase is a single positive revolving field of constant magnitude.