Losses in the DC Machines

The various losses occurring in DC machines can be given as follows.

Iron loss (Magnetic or Core Loss) : Hysteresis Loss and Eddy Current Loss
Copper Losses : Armature Copper Loss, Shunt Field copper loss and Series field copper loss
Mechanical Losses : Friction Loss and Windage Loss

Iron Loss

The iron losses are taking place continuously in the core of the armature due to rotation of the core under the magnetic flux of the main field poles.

Hysteresis Loss

This loss is due to rapid reversal of the magnetization of the armature core under the influence of main poles.
When the armature rotates, it comes under the N – pole and S – pole of the main field winding thereby attaining S – pole and N – pole respectively.
The armature core undergoes a complete cycle of magnetization reversal after passing through a pair of poles.
The losses in the core of armature occur due to reversal of magnetization is known as hysteresis loss.
The hysteresis loss according to the Steinmetz formula is given by W_h = hB_max^1.6fV watt

Where h = Steinmetz constant, depend upon the core material B_max = Maximum flux-density in the core ( Weber / meter²) f = Frequency of the magnetization reversal V = Volume of the core material ( Meter³ )

As we know that h and V are constant W_hα B_max^1.6f

It means that the hysteresis loss depends upon ( i ) Maximum flux density ( B_max ) and ( ii ) Frequency of magnetization reversal ( f )
( According to Weber’s molecular theory of magnetization when core (magnetic) material is magnetized its molecules are forced along a straight path.
Therefore some energy is spent during this process.
If the core material does not possess any retentivity, the energy spent during straightening the molecules could be completely recovered by reducing magnetizing force to zero.
It means that if the magnetic material possesses high retentivity, all the energy spent during straightening the molecules is not completely recovered when magnetizing force reduces to zero.
The retentivity is responsible for hysteresis loss in this sense. )

Eddy Current Loss

It is fact that an emf is induced in the rotating armature according to the Faraday's law of electromagnetic induction when it cuts the magnetic flux sets up by the main poles.
This induced emf sets up current in the iron core.
This current is responsible for eddy current loss. The flow of eddy current in the armature core is shown in the figure A.
The Eddy current flows through the core resistance and thus produce power loss in the form of heat.
The armature core is made up of one solid piece as shown in the Figure A.
As the cross – section area of the core is very large, its resistance ( R α 1/a ) is very small resulting eddy current loss is very large.
The armature core is built up of thin laminations as shown in the Figure B.
These laminations are insulated from each other by a thin layer of paper or varnish or oxide layer.
As the cross sectional area of each path is very small, its resistance is very large thereby reducing the eddy current loss.

The eddy current loss is given by following equation

W_e = K B_max²f²t²V² Watt

Where

B_max = Maximum flux-density in the core ( Weber / meter² )

t = Thickness of lamination ( mm )

f = Frequency of magnetic reversal ( Cycle / second )

V = Volume of the core material ( Meter³ )

K = Constant depend upon resistivity of the material.

= 1 / ρ

Therefore, the eddy current loss W_e a B_max²f²

Factors affecting the eddy current loss

Frequency	The eddy current loss is directly proportional to the square of the supply frequency.
Volume of the core	The eddy current loss is directly proportional to the square of the volume of the core.
Maximum flux density	The eddy current loss is directly proportional to the square of the maximum flux density.
Thickness of lamination	The eddy current loss is directly proportional to the square of thickness of lamination. Lower the eddy current loss for thinner the lamination thickness.
Resistivity of the material	As the resistivity of material increases, the eddy current loss decreases.

How to reduce Iron Losses?

The magnetic circuit particularly at low frequency will reduce the hysteresis loss as well as eddy current loss.
Use of laminated cores reduces the eddy current loss.
The silicon steel has narrow hysteresis loop and very high resistivity therefore it reduces the eddy current loss and also hysteresis loss.
The core loss is reduced by reducing maximum flux density in the core material.

Copper Losses

It depends upon the amount of current passing through winding and resistance of the winding.

W_cu = I² R

( 1 ) Armature copper loss

The armature copper loss is given by

W_cu = I_a² R_a

Where I_a = Armature current

R_a = Armature resistance

As the armature copper loss is directly proportion to the square of the armature current it becomes four times for twice the armature current.

( 2 ) Shunt field copper loss

The shunt field copper loss is given by

W_cu = V I_sh = I_sh² R_sh

Where V = Supply voltage

I_sh = Shunt field current

R_sh = Shunt field resistance

This loss is practically constant due to shunt field current is almost constant in the DC Shunt machines.

( 3 ) Series field copper loss

The series field copper loss is given by

W_cu = I_se² R_se

Where I_se = Series field current

R_se = Resistance of series field winding.

Mechanical Losses

Winding loss due to rotation of armature
Friction loss occurs due to friction between brushes and commutator surface.

Stray Losses

The iron loss and mechanical losses are collectively known as stray losses.
The shunt field copper loss is practically constant in the DC shunt and compound generators.

Therefore constant losses

W_c = Stray Losses + Shunt field copper loss
Total Losses = Armature copper loss + Constant losses

= I_a²R_a + W_C

Usually, the copper losses are known as variable losses and iron losses are known as fixed or constant losses.

Pages

19/09/2017