It is defined as the ratio of EMF PRODUCED PER PHASE in Distributed winding to that of Concentrated winding. It is denoted by Kd.
Let us derive the equation for kd.
Let us consider a 2 Pole synchronous machine with 12 slots in stator and with full pitch winding(i.e coil span is equal to 180°electrical. The total electrical angle is equal to 360° (180*2).
Electrical angle is calculated by formula
Electrical angle=(number of poles*180°)
Number of slots per pole is equal to 6 ((12/(2)).
[Formula:
Number of slots per pole is given by the ratio of number of slots to that of number of poles.]
Number of slots per pole per phase is equal to 2 (6/3).
[Formula:
Number of slots per pole per phase is given by the ratio of number of slots per pole to that of number of phases.]
Slot angle is equal to 30° ((180*2)/12)
[Formula:
Slot angle=
((No of poles*180)/(total no of slots))]
Let us draw armature winding(only for one phase).
It is shown clearly in the photographs.
The emfs E1 and E2 in the coil side 1 and 2 will be in same phase.
And the emfs E3 and E4 are in the same phase and their resultant will be lagging by an angle with the resultant of E1 and E2.
Their vectors are shown in the figure 2.
Let us assume that their are n turns and'Q' (some times represented as alpha during explanation)be the slot angle then the vector diagram is shown in the figure. Let us draw perpendicular bisectors of all the vectors.Perpendicular bisectors meet at a point O as shown in the figure 3.
Let Er be the total emf induced in the distributed winding per phase and From Fig3
Er=ci=2yc=2*oc*sin(nQ/2)[from fig 3]
In case of concentrated winding the they use only two slots and hence emf induced in the coil sides are equal(coil span=180°).
Let ct is the emf induced in each coil side
Hence each phase has 2 coil sides and n turns, So total emf induce is given by
E=2*n*ct=2*n*oc*sin(Q/2).[from fig3]
Distribution factor(Kd)=((emf induced per phase in case of distributed winding)/(emf induced in case of concentrated winding))
Kd=[(2*oc*sin(nQ/2))]/[2*oc*n*sin(Q/2)]
=[sin(nQ/2)]/[n*sin(Q/2)]
By using above formula we can calculate distribution factor where
n = the number of slots per pole per phase.
Q=slot angle.
Let us derive the equation for kd.
Let us consider a 2 Pole synchronous machine with 12 slots in stator and with full pitch winding(i.e coil span is equal to 180°electrical. The total electrical angle is equal to 360° (180*2).
Electrical angle is calculated by formula
Electrical angle=(number of poles*180°)
Number of slots per pole is equal to 6 ((12/(2)).
[Formula:
Number of slots per pole is given by the ratio of number of slots to that of number of poles.]
Number of slots per pole per phase is equal to 2 (6/3).
[Formula:
Number of slots per pole per phase is given by the ratio of number of slots per pole to that of number of phases.]
Slot angle is equal to 30° ((180*2)/12)
[Formula:
Slot angle=
((No of poles*180)/(total no of slots))]
Let us draw armature winding(only for one phase).
It is shown clearly in the photographs.
The emfs E1 and E2 in the coil side 1 and 2 will be in same phase.
And the emfs E3 and E4 are in the same phase and their resultant will be lagging by an angle with the resultant of E1 and E2.
Their vectors are shown in the figure 2.
Let us assume that their are n turns and'Q' (some times represented as alpha during explanation)be the slot angle then the vector diagram is shown in the figure. Let us draw perpendicular bisectors of all the vectors.Perpendicular bisectors meet at a point O as shown in the figure 3.
Let Er be the total emf induced in the distributed winding per phase and From Fig3
Er=ci=2yc=2*oc*sin(nQ/2)[from fig 3]
In case of concentrated winding the they use only two slots and hence emf induced in the coil sides are equal(coil span=180°).
Let ct is the emf induced in each coil side
Hence each phase has 2 coil sides and n turns, So total emf induce is given by
E=2*n*ct=2*n*oc*sin(Q/2).[from fig3]
Distribution factor(Kd)=((emf induced per phase in case of distributed winding)/(emf induced in case of concentrated winding))
Kd=[(2*oc*sin(nQ/2))]/[2*oc*n*sin(Q/2)]
=[sin(nQ/2)]/[n*sin(Q/2)]
By using above formula we can calculate distribution factor where
n = the number of slots per pole per phase.
Q=slot angle.
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