Transformer Efficiency, Regulation and Temperature Rise

1. 1
Chapter # 6
Transformer-Inductor Efficiency,
Regulation, and Temperature Rise
Introduction: -
 Transformer efficiency, regulation, and temperature rise are all interrelated. Not all of the
input power to the transformer is delivered to the load. The difference between input
power and output power is converted into heat. This power loss can be broken down into
two components: core loss , and copper loss .
 The core loss is a fixed loss, and the copper loss is a variable loss that is related to the
current (power) demand of the load. The copper loss increases by the square of the
current and also is termed a quadratic loss.
 Maximum efficiency is achieved when the fixed loss is equal to the copper loss.
 Transformer voltage regulation at unity power factor is the copper loss divided by the
output power.
Voltage regulation of the transformer is
100
sincos 20222022



sV
XIRI 
 (6.1)
At unity power factor, voltage regulation is
100100100
100100
01
0
02
2
022022022




P
P
powerOutput
losscopper
IV
RI
V
RI
V
XIRI
cu
ss
s
ss

(6.2)
Transformer Efficiency: -
 Efficiency of a transformer is a good way to measure the effectiveness of the design. It is
the ratio of output active power to the input active power .

2. 2
 Maximum efficiency of the transformer occurs at that loading condition for which copper
loss (variable loss) is equal to the iron loss (constant loss).
If is the full-load copper loss, then at loading condition copper loss
is . Loading condition corresponding to maximum efficiency can be
determined by equating the copper at that loading condition with the core loss of the
transformer. Let at loading condition the transformer efficiency is maximum.
So,
cufl
fe
fecufl
P
P
x
PPx

2
(6.3)
Maximum efficiency,
fe
cuflfe
PVAx
VAx
PxPVAx
VAx
2cos
cos
cos
cos
2max











(6.4)
Surface Area, At, Required for Heat Dissipation: -
 Temperature rise in a transformer winding cannot be predicted with complete precision.
 The total losses in the transformer is dissipated as heat in the transformer core.
 The effective surface area required to dissipate heat (expressed as watts dissipated per
unit area) is given by:



P
At in cm2
. (6.5)
Where, is the power density or average power dissipated per unit area of the surface.
 Temperature rise is given by:
  826.0
450 rT in0
C. (6.6)
Where the value of is taken as 0.03 watts/cm2
at 25 0
C and 0.07 watts/cm2
at 50 0
C.