Electrical Machines-I (PCEE 4203)
Lesson 02
Principle of Operation:
D.C generator is a machine that converts mechanical energy into DC electrical energy. It works
on the principle of dynamically induced emf i.e. whenever a conductor cuts flux, an emf is
induced in the conductor. The direction of the induced emf is given by Fleming’s right hand rule.
Simple Loop Generator:
Figure 2.1
Consider rectangular coil ABCD with coil sides AB and CD being rotated in the magnetic field.
The ends of the two coil sides are connected to two slip rings (S1 and S2). The two rings rotate
along with the conductors. Two brushes (B1 and B2) make contact to these two slip rings to
collect the current. When the coil starts rotating in anti-clockwise direction, conductor AB is
under the influence of North Pole and CD is under the influence of South Pole. By Fleming’s
right hand rule, the direction of the current through the load resistance is from M to N.
After the coil rotates through 1800, the conductor CD comes under the influence of North pole
and the conductor AB under the influence of South pole. Hence, again emf is induced in the coil
sides. As a result, the current flows through load resistance from N to M (reversed). This is
shown in figure.
Note that, e.m.f generated in the loop is an alternating emf hence the current also. The
alternating current in the load can be converted into direct current by commutator.
P K Nayak, Assistant Professor, Department of Electrical Engineering, SIET, Dhenkanal.
1
Electrical Machines-I (PCEE 4203)
Lesson 02
Generator E.M.F Equation
Let Φ = flux/pole in Weber
Z = total number of armature conductors = No. of slots x No. of conductors/slot
P = No. of generator poles
A = No. of parallel paths in armature
N = armature rotation in revolutions per minute (r.p.m)
E = e.m.f induced in any parallel path in armature
Generated e.m.f Eg = e.m.f generated in any one of the parallel paths i.e. E.
∅
Average e.m.f generated /conductor =
volt
Now, flux cut/conductor in one revolution ∅ = ∅ Weber
No. of revolutions/second = N/60 Time for one revolution,
=
second
Hence, according to Faraday's Laws of Electromagnetic Induction,
E.M.F generated/conductor is
∅
=
∅
60
For a simplex wave-wound generator
No. of parallel paths = 2
No. of conductors (in series) in one path =
E.M.F. generated/path is
∅
∅
× =
Volt
For a simplex lap-wound generator
No. of parallel paths = P
No. of conductors (in series) in one path =
E.M.F. Generated/path
∅
× =
∅
Volt
In general, generated e.m.f
Eg
=
∅
×( )
volt
Where, A = 2 - for simplex wave-winding
A = P - for simplex lap-winding
P K Nayak, Assistant Professor, Department of Electrical Engineering, SIET, Dhenkanal.
2
Electrical Machines-I (PCEE 4203)
Lesson 02
Numerical Problems
Example 01
A 6 pole DC machine has an armature connected as a wave winding having 48 slots with 4
conductors per slot. The machine is rotating at a speed of 600 rpm and flux per pole is 30 m Wb,
calculate the induced emf.
Example 02
The armature current of a machine is rated at 250 A. What is the current per path of the armature if
the armature winding is simplex wave or simplex lap wound? The machine has 12 poles.
Example 03
A 4 pole lap connected dc machine has an armature resistance of 0.15 ohm. Find the armature
resistance of the machine when rewound for wave connection.
Example 04
Calculate the voltage induced in the armature winding of a 4 pole, lap wound dc machine having 728
active conductors and running at 1800 rpm. The flux per pole is 30 m Wb.
Example 05
A 4 pole lap wound armature has 144 slots with two coil sides per slot, each coil has two turns. If the
flux per pole is 20 m Wb armature rotates at 720 rpm, what is the induced emf?
Example 06
A 4 pole dc generator has 51 slots and each slot contains 20 conductors. The machine has useful flux
of 0.007 wb and runs at 1500 rpm. Find the induced emf, if the machine is lap and wave connected.
Example 07
The armature of an 8 pole dc generator has 960 conductors and runs at 400 rpm. The flux per pole is
40 m wb. Calculate the induced emf, if the armature is lap wound. At what speed should it be driven
to generate 400 V, if the armature were wave connected?
Example 08
An 8 pole dc generator having lap wound armature is required to give the open circuit voltage of 220
V. The total number of armature conductors is 2000 and total flux is 120 m wb. Calculate the speed
at which the generator should be driven?
Example 09
A lap wound dc generator having 8 poles develops an emf of 500 V at 400 rpm. The armature has144
slots and each slot contain 6 conductors. Calculate the flux per pole?
Example 10
The armature of a 2 pole, 200 V generator has 400 conductors and runs at 300 rpm. Calculate the
useful flux per pole. If the number of turns in each field coil is 1200, what is the average induced emf
in each coil on breaking the field, if the flux dies away completely in 0.1 s?
P K Nayak, Assistant Professor, Department of Electrical Engineering, SIET, Dhenkanal.
3