EMF Induced in a DC Generator

EMF INDUCED IN A DC GENERATOR

Let

Ɵ = Flux/pole in Weber

z = Total number of armature conductors

= No of slots ×No of conductors/slots

P = No of poles

A = No of parallel paths in armature

N = Speed of rotation in revolutions per minute (rpm)

E = EMF induced in any parallel path in armature.

E_g = EMF generated in any one of the parallel paths (ie) E.

Average emf generated/conductor = dϕ/dt ( n = 1)

Flux cut/conductor in one revolution

dϕ = ϕ P weber

No of revolutions/second = N/60

Time for one revolution, dt = 60/ N second

According to faraday's law of electromagnetic induction.

EMF generated/conductor = dϕ/dt = ϕΡ/ (60/Ν)

ϕΡN/60 volt

For a wave wound generator

No fo parallel paths (A) = 2

No of conductors in one path = Z/2

EMF generated/path = 

For a lap wound generator

No of parallel paths (A) = P

No of conductors in one path = Z/2 = Z/A

EMF generated/path = 

Example: 1

A 4 pole, wave wound generator has 40 slots and 10 conductors are placed per slot. Find the generated emf when the generator is driven at 1200 rpm and ϕ = 0.02 wb.

Given data

No of poles P = 4

Total number of conductors Z = No of slots > conductors/slot.

Z = 40 × 10 = 400

Flux/pole ϕ = 0.02 wb

Speed N = 1200 rpm

Solution:

Generated emf E_g = ϕPNZ / 60 A

For a wave wound A = 2

Eg = 0.02 x 400 x 4 × 1200 / 60 × 2

= 320 V

Example: 2

A 6 pole, Lap wound armature rotated at 350 rpm is required to generate 300V. the useful flux per pole is 0.05 ωb. If the armature has 120 slots, calculate the number of conductors per slot.

Given data

No of poles, P = 6

Speed, N = 350 rpm

Generated emf, E_g = 300 V

No of slots = 120

Flux/pole, ϕ = 0.05 ωb

For lap wound generator, A = P=6

To find

No of conductors/slot.

Solution:

Generated emf, E_g = 

No of conductors Z = 

No of conductors/slot =  1029/120 = 8.575

Conductors/slot = 9