Calculating core losses in a transformer involves estimating the two main types of core losses: hysteresis losses and eddy current losses. These losses occur due to the magnetic properties of the core material and are dependent on the magnetic flux density and frequency of operation.
Hysteresis Losses:
Hysteresis loss occurs due to the reversal of magnetization in the transformer core as the alternating current (AC) passes through it. The energy expended in this process is dissipated as heat.
The formula for hysteresis loss is given by:
hyst
=
hyst
Ă
Ă
P
hyst
â
=K
hyst
â
ĂfĂB
Îą
Where:
hyst
P
hyst
â
= Hysteresis loss (in watts)
hyst
K
hyst
â
= Hysteresis constant (depends on the core material)
f = Frequency of operation (in Hz)
B = Maximum magnetic flux density in the core (in Tesla)
Îą = Steinmetz exponent (typically ranging from 1.5 to 2.5 for different core materials)
The hysteresis constant,
hyst
K
hyst
â
, and the Steinmetz exponent,
Îą, are material properties and are usually provided by the core material manufacturer.
Eddy Current Losses:
Eddy current loss occurs due to the circulating currents induced in the core material by the changing magnetic field, as the AC current varies with time. These circulating currents create localized heating in the core.
The formula for eddy current loss is given by:
eddy
=
eddy
Ă
2
Ă
2
Ă
2
P
eddy
â
=K
eddy
â
Ăf
2
ĂB
2
Ăt
2
Where:
eddy
P
eddy
â
= Eddy current loss (in watts)
eddy
K
eddy
â
= Eddy current constant (depends on the core material)
f = Frequency of operation (in Hz)
B = Maximum magnetic flux density in the core (in Tesla)
t = Thickness of the core laminations (in meters)
The eddy current constant,
eddy
K
eddy
â
, is a material property and is provided by the core material manufacturer.
In practical transformer design, the total core losses (
core_loss
P
core_loss
â
) are the sum of hysteresis and eddy current losses:
core_loss
=
hyst
+
eddy
P
core_loss
â
=P
hyst
â
+P
eddy
â
To design an efficient transformer, it's crucial to minimize core losses while selecting appropriate core materials and dimensions based on the specific requirements of the transformer application.