Transcript Predicting Temperature Rise of Ferrite Cored Transformers

Predicting Temperature Rise of
Ferrite Cored Transformers
George Orenchak
TSC Ferrite International
Temperature Rise is
the difference between a
components initial and final temperatures
expressed in degrees Celsius
Acceptable Temperature Rise of
a Transformer is Dependent on
• the materials used in the construction of
the transformer
• reliability issues associated with other
component parts that are in close proximity
to the transformer
• safety agency regulations
Permissible Temperature Rise
of a Transformer
is a constraint to the component size of a
transformer.
Temperature Rise of a
Transformer is Attributed to
the total power loss of the transformer
dissipated in the form of heat.
This total power loss consists of core loss
and of winding losses.
Core Losses Consist of
• Hysteresis loss which become more
significant & dominate at higher flux densities
• Eddy current loss which become more
significant & dominate at higher frequencies
• Residual loss which is additional loss
unaccounted to hysteresis & eddy currents
Chart #2
Core loss vs Flux Density
@100kHz, 100C
TSC 5099
1,000
900
Core Loss in mW/cc
800
700
600
500
400
300
200
100
0
500
1,000
1,500
2,000
Flux Density in Gauss
2,500
3,000
Flux Density
B = E*108 / (4.44 f N Ae)
Chart #1
Core loss vs Frequency
@1000 Gauss 100C
TSC 5099
1,000
900
Core Loss in mW/cc
800
700
600
500
400
300
200
100
0
50
100
150
200
250
300
Frequency in kHz
350
400
450
500
Calculating Core Loss
Pc = k fx By
Pc = Core Loss in mW/cc
k = Constant for a Specific Material Grade
f = Frequency in kHz
B = Flux Density in k Gauss
x = Frequency Exponent
y = Flux Density Exponent
Creation of Core Loss
Formulas
@ some fixed flux density
x=ln(Pc@1stf / Pc@2ndf ) / ln(1stf / 2ndf )
@ some fixed frequency
y=ln(Pc@1stB/Pc@2ndB ) / ln(1stB/2ndB )
k=Pc@B&f / (By*fx)
Chart #3
Core loss vs Temperature
@100kHz, 1000gauss
TSC 5099
TSC 7070
200
180
TSC 8040
Core Loss in mW/cc
160
TSC 5000
140
120
TSF-50ALL
100
80
60
40
20
0
0
20
40
60
80
Temperature in Celsius
100
120
140
Excitation Wave Forms
Providing the frequency & total flux
density excursions remain the same the
core loss of symmetrical sinusoidal, square
wave & unidirectional square wave voltage
excitations are equivalent.
Core Loss for Non-Square
Pulse Voltage Wave Form
Excitations
Calculate apparent frequency (the inverse of
the time period to complete one cycle of
flux swing)
Use this apparent frequency to obtain core
loss from graphs or formulas then multiply
this result by the duty cycle to estimate core
loss
Winding Coil Losses
Copper loss (I2R)
Skin effect loss
Proximity effect loss
Eddy current loss in the windings
Loss from fringing flux intersecting windings
Edge effect loss
Extraneous conductor losses
Calculate Resistance of Each
Winding
Rp or Rs = MLT * Rcu * N
Rp = Primary Winding Resistence
Rs = Secondary Winding Resistance
Rcu = Copper Resistance (μΩ/cm)
N = Turn Count
(I2R) Copper Losses
Pcu = I2R
Pcu = Copper Loss in Watts
I = Current in Amps
R = Resistance in Ohms
Summarize Transformer Losses
PΣ = PcuΣ + Pc
PΣ = Total Transformer Losses
PcuΣ = Summation of All of the Primary &
Secondary Winding Losses
Pc = Core Loss
Temperature Rise Assumptions
Lump the winding losses & core loss
together and assume the thermal energy is
dissipated uniformly throughout the surface
area of the assembly at all ambient
temperatures
Temperature Rise Estimate
ΔT = (PΣ / At)0.833
ΔT = Temperature Rise in ΟC
PΣ = Total Transformer Losses in mW/cc
(Power dissipated in the form of heat)
At = Surface Area of Transformer in cm2
Creation of the Exponent in the
Temperature Rise Formula
x=ln(PΣ@1stΔT/PΣ@2ndΔT)/ln(1stΔT/2ndΔT)
Temperature Rise Proof
TSF-5099-41-16-12-0000
Ve=11.5cm3, At=27cm2 @100mW/cc
Pc = 100mW/cm3*11.5cm3 = 1.15W
PΣ = 1.15W*2 = 2.3W = 2300mW
ΔT = (2300mW/27cm2)0.833 = 40.5 ΟC
Temperature Rise vs. Transformer Power Loss
Measured on a TSF-7099-41-16-12-0000
80
Temperature Rise in Celsius
70
60
50
40
30
20
10
0
0
500
1,000
1,500
2,000
2,500
3,000
Transformer Total Power Loss in mW
3,500
4,000
4,500
5,000
Conclusion
Temperature rise in transformers result from
core loss & winding losses. Core loss,
winding loss and temperature rise can be
estimated with calculations by making a few
reasonable assumptions.
Conclusion
New ferrite materials that exhibit consistent
core loss over wide ranges of temperature
will simplify ferrite material selection and
prove to be a valuable asset in the
transformer industry