When the magnetic circuits are subjected to time varying flux densities,mainly there are two causes of power loss in the form of heat in the iron core.The first losses is hysteresis loss and the second is the eddy current loss.Both of the losses are significant in determining the heating,rating,and efficiency of rotating electrical machines,transformers.
Hysteresis losses
In an ferromagnetic material ,not of all the energy of the magnetic field is returned to the circuit ,when the mmf is removed,hysteresis loss is seen.The energy expended in taking a specimen through a magnetic cycle is also known as hysteresis loss.Hysteresis loss per cubic metre per cycle of magnetization of a magnetic material depends upon
- the maximum value of flux density and
- the magnetic quality of the material.
Determination of Hysteresis loss
consider a ring of specimen circumference l meters,cross sectional area a meter square and having N turns of an insulated wire.Let the current flowing through the coil be of I amperes.
Magnetizing force,
B=flux density at this instant.
Φ=total flux through the ring=Ba webers.
The flux produces in the iron ring alters as the current flowing through the solenoid alters.Hence the emf(e’)is induced and given by,
According to the Lenz’s law,this induced emf will oppose the flow of current.so therefore to maintain the current I in the coil the source of supply must have an equal and opposite emf.
hence applied emf,
Energy consumed in short time dt,during which flux density has changed,
Thus the total work done or energy consumed during one complete cycle of magnetization,
Now,
aL=volume of the ring.
HdB = area of elementary strip of B-H curve.
=the total area enclosed by hysteresis loop.
Energy consumed per cycle=volume of ring*area of the hysteresis loop
This energy expended in taking specimen through a magnetic cycle is wasted as heat and termed as hysteresis loss.
For determination of hysteresis loss
area of loop is measured in units of H and B
For example,
if one metre represents x AT/m on H-axis and y Wb/m^2 on B-axis,then,
Hysteresis loss,Wh=Area of hysteresis loop in m^2*x*y joules/m^3/cycle.
one of the popular method for the calculation of the hysteresis loss is Steinmetz method.this methods states that hysteresis loss per cubic metre per cycle of magnetization of a magnetic material depends upon
- the maximum value of flux density and
- the magnetic quality of the material.
where ,
η=constant for a given specimen,range of flux density and also known as Steinmetz hysteresis coefficient.
f=frequency of reversals of magnetization and
V=volume of magnetic material in m^3
Minimization of Hysteresis loss
Hysteresis loss can be minimized by choosing a core material with low hysteresis coefficient such as low carbon steel,silicon alloys,alloy steel.
Eddy current losses
voltage induced in the core material (conducting material) by the alternating flux causes circulating currents known as eddy currents.Eddy currents are associated with I^2R loss called eddy current loss.The eddy current loss depends upon:
- the maximum value of flux density.
- number of complete magnetization cycles per second.
- thickness of the lamination.
- volume of the core material.
Eddy current loss is given by ,
where ,
Ke = eddy current coefficient and depends upon the type of magnetic material used.
f=number of complete magnetization cycles per second.
Bmax=maximum flux density in teslas(Wb/m^2)
t=thickness of lamination in metres.
v=volume of core material in m^3.
Minimization of eddy current losses
To increase the core resistance and to minimize eddy currents magnetic cores subjected to alternating fluxes are assembled from thin sheets with an insulating layer between successive lamination. Hence the eddy currents loss can be minimized by using thin lamination.
Application of Eddy current
- eddy current heating.
- eddy current breaking.
- develop damping torque in measuring instruments.
Refrences:
Theory and performance of Electrical machines by JB GUPTA