Types of armature winding of an AC machine

3. Concentrated and Distributed Winding- In three-phase alternators, we have seen that there are three different sets of windings, each for a phase. So depending upon the total number of slots and number of poles, we have certain slots per phase available under each pole. This is denoted as'

m = Slots per pole per phase = n/number of phases
    = n/3 (generally number of phases is 3)

For example in 18 slots, 2 pole alternator we have

n= 18/2 = 9

and m =9/3=3

So we have 3 slots per pole per phase available. Now let 'x' number of conductors per phase are to be placed under one pole. And we have 3 slots per pole per phase available. But if all 'x' conductors per phase are placed in one slot keeping remaining 2 slots per pole per phase empty then the winding is called concentrated winding.

Note:-  So in the concentrated winding, all conductors or coils belonging to a phase are placed in one slot under every pole.

But in practice, an attempt is always made to use all the' slots per pole per phase available for distribution of the winding. So if 'x' conductors per phase are distributed amongst the 3 slots per phase available under every pole, the winding is called Distributed winding. So in a distributed type of winding all the coils belonging to a phase are well distributed over the' slots per phase, under every pole. Distributed winding makes the waveform of the induced emf more sinusoidal in nature. Also in concentrated winding due to a large number of conductors per slot, heat dissipation is poor.

Note:- So in practice, double layer, short-pitched and distributed type of armature winding is preferred for the alternators.

Example- Write the scheme of connections for a 3 phase, 1 layer stator lap winding of a synchronous machine having 6 poles and 36 slots.


Solution- P=6, 36 slots, n= Slots/pole =6

m= slots/pole/phase = n/3 =2, β= 180 degree/n = 30 degree

For full pitch coils if phase 1 say R starts in slot 1 then it must be connected in slot 7 so that coil span is 6 slots i.e. 6β degree i.e. 180 degrees. Thus the coils are full pitch coils.

  For distributed winding, both slots per pole per phase available are to be used. And all coils of one phase are to be in series. So from slot 7, connect it to coil in slot 2 for lap winding and the second end of slot 2 to coil in slot 8 and so on. After finishing all slots per pole per phase available under the first pair of poles connect the coil to slot 13 under next pole and the winding will be repeated thereon in a similar fashion. The starting end Rs and final end Rf for R phase is taken out finally. The connections for the R phase are shown in figure-

There must be a phase difference of 120 degrees between R and Y. Each slot contributes 30 degrees so the start of Y phase should be 120 degrees apart from Rs i.e. 4 slots away from Rs i.e. in slot 5. Similarly, the start of the B phase is further 120 degrees away from the Y phase i.e. 4 slots away from Ys i.e. in slot 9. Finally, all six ends Rs, Rf, Ys, Yf and Bs, Bf is brought out which are connected in star or delta to complete the winding.

EMF equation of DC generator

As the armature turns, a voltage is created in its loops. On account of a generator, the emf of the pivot is known as the Generated emf or Armature emf and is indicated as Er = Eg. On account of an engine, the emf of the pivot is known as Back emf or Counter emf and spoke to as Er = Eb. The articulation for emf is same for both the tasks. I.e., for Generator just as for Motor.

Derivation of EMF Equation of a DC Machine – Generator and Motor

Let,

• P – Number of poles of the machine
• ϕ – Flux per pole in Weber.
• Z – Total number of armature conductors.
• N – Speed of armature in revolution per minute (r.p.m).
• A – number of parallel paths in the armature winding.

In one revolution of the armature, the flux cut by one conductor is given as

Time taken to complete one revolution is given as

Therefore, the average induced e.m.f in one conductor will be

Putting the value of (t) from Equation (2) in the equation (3) we will get

The number of conductors connected in series in each parallel path = Z/A.

Therefore, the average induced e.m.f across each parallel path or the armature terminals is given by the equation shown below.

Where n is the speed in revolution per second (r.p.s) and given as

For a given machine, the number of poles and the number of conductors per parallel path (Z/A) are constant. Hence, equation (5) can be written as

Where, K is a constant and given as

Therefore, the average induced emf equation can also be written as

Where K1 is another constant and hence induced emf equation can be written as

Where ω is the angular velocity in radians/second is represented as

Along these lines, plainly the instigated emf is straightforwardly relative to the speed and motion per shaft. The extremity of instigated emf relies on the bearing of the attractive field and the heading of revolution. If both of the two is turn around the extremity changes, however, if two are switched the extremity stays unaltered. 

This initiated emf is an essential wonder for all the DC Machines whether they are filling in as a generator or engine. 

If the machine DC Machine is filling in as a Generator, the instigated emf is given by the condition demonstrated as follows.

Where Eg is the Generated Emf

If the machine DC Machine is working as a Motor, the induced emf is given by the equation shown below.

In a motor, the induced emf is called Back Emf (Eb) because it acts opposite to the supply voltage.