PPT No. 33
Transformer Losses
Transformer is one of the simplest
and also one of the most efficient
of electrical machines.
Experimental models
using superconducting windings
can attain / exceed efficiency/ performance
99.75 percent also.
Transformer Losses
In practice, energy is found to be lost
in the windings, core and surrounding structures
due to various causes as follows
* Copper Losses in Winding resistance
* Eddy Current Losses
* Hysteresis Losses
* Magnetostriction Losses
* Mechanical Losses
* Stray Losses
* Power Loss due to the Cooling system
Each of these losses is described in brief as follows
Transformer Losses
Copper Losses in Winding resistance
Windings are made up of copper wire
which get heated due to Joule heating effect
when current flows through them.
When working at higher frequencies,
skin effect and proximity effect
add to the losses due to winding resistance
Transformer Losses
Eddy Current Losses
If the core is solid and
made up from ferromagnetic materials,
it effectively acts as a single short-circuited turn.
Induced eddy currents
therefore circulate within the core
in a plane normal to the flux,
and cause resistive heating of the core material.
Transformer Losses
Hysteresis Losses
During each A.C. cycle,
current flowing in the forward and reverse directions
magnetizes and demagnetizes the core alternatively.
Energy is lost in each hysteresis cycle
within the magnetic core.
Energy loss is dependant on the properties
(e.g. coersivity) of particular core material and
is proportional to the area of the hysteresis loop (B-H curve).
Transformer Losses
Hysteresis Cycle
Transformer Losses
Magnetostriction Losses
The core undergoes minute
physical expansion and contraction
with the each A.C. cycle
due to the alternating magnetic field.
This effect known as magnetostriction
produces the familiar buzzing sound, and
causes losses due to frictional heating
in susceptible cores.
Transformer Losses
Mechanical Losses
The alternating magnetic field causes
fluctuations in the electromagnetic forces
between the primary and secondary windings.
These produce mechanical vibrations
in nearby metal work and
add to the buzzing noise.
Transformer Losses
Stray Losses
All the magnetic field produced by the primary current
is not linked to the secondary winding
due to the leakage of flux.
It may induce eddy currents
within nearby conductive objects,
such as the transformer's support structure,
and get converted to heat
Which is lost to the surroundings
Transformer Losses
Cooling System
Cooling arrangement like
cooling fans, oil pumps or water-cooled heat exchangers
is necessary for removing heat
generated in large power transformers.
As the power consumption
in the operation of the cooling system is unproductive,
it is considered as power loss of the transformer.
Applications of Transformer
Transformers are encountered
in numerous applications
which serve different purposes:
•For voltage step-up
•(in Electricity generating stations, high voltage power packs)
•For voltage step-down
(in industrial machines, simple household appliances
•e.g. Doorbell, Toys);
Applications of Transformer
•For Impedance matching
(in loud speakers);
•For Coupling
(in different stages of electronic circuits e.g.
•Amplifying systems);
*For varying secondary voltage
(in variac)
Energy in terms of the Magnetic field
Magnetic field surrounding the solenoid
stores magnetic energy
It can be calculated as follows
Consider a uniform solenoid carrying
.
I a current through
it
n number of turns per unit length,
A cross sectional area
ℓ the length.
Energy in terms of the Magnetic field
The self-inductance L of a solenoid is given by expression
L= Aµ0n2l
The field inside the solenoid is uniform having magnitude
B = µ0nI.
Hence substituting in the expression for L and
using the formula for B to eliminate I
The magnetic energy stored by the solenoid is given by
Energy in terms of the Magnetic field
The total Magnetic energy
(1/2)B2/µ0 x A ℓ.
= Energy density multiplied by
the volume of the solenoid
This can be shown to be a general result
=>The magnetic field energy density ηB
(Magnetic field energy/ Volume) is expressed as
Energy in Magnetic Field in terms of Self-inductance
Consider a coil or an inductor
carrying current I and having inductance L.
As the current increases by
an infinitesimal small amount dI in time dt,
an opposing emf (Back emf) is generated in it,
which must be overcome by
the connected source of emf (e.g .a battery).
The battery must do work to
send a maximum current through the coil.
This work is stored in the magnetic field surrounding the coil.
Energy in Magnetic Field in terms of Self-inductance
The electromotance or voltage V
across the coil is given by
V= LdI/dt.
Power = Voltage x Current = V x I
Power = LI dI/dt
Power is the rate at which energy is stored in the inductor
=> The energy stored by the inductor in time dt = LIdI
The total energy UM stored
when the current increases from 0 to I is
Energy in Magnetic field due to Two Coupled Coils
Consider two coupled coils wound on the same former
in the proximity of each other.
the magnetic field of each is linked to the other.
They carry currents I1 and I2 and
have self inductances L1 and L2,
Mutual inductance between them is M.
Then it can be proved that
the total magnetic energy WB
stored in the magnetic field of two coils is given by
Energy in Magnetic field due to Two Coupled Coils
If the currents in the two coils
flow in the same direction then Mutual inductance
increases and their magnetic fields get enhanced.
On the contrary,
if the currents flow in opposite directions then
the mutual inductance term decreases and
the stored magnetic energy decreases.
However, the total stored energy is always positive.