Simple Thermal Modeling of OilImmersed Distribution Transformers
in PEA. Thailand.
Power Quality Control Section
Provincial Electricity Authority
Provincial Electricity Authority, Thailand
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CONTENTS
 OBJECTIVE
 INTRODUCTION
 SOPE OF WORK
 THEORY
 EXPERIMENTAL WORKS
 CONCLUSION
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OBJECTIVE
 To predict load current by measure top surface of
transformer and ambient temperature.
delta T
40.00
35.00
30.00
25.00
20.00
15.00
10.00
5.00
0.00
0.00
20.00
40.00
60.00
80.00
100.00
%Load
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INTRODUCTION
 Transformers are the largest part of investments of
distribution system
It is advisable to know the insulation condition, operating
life, and loading capacitance of a transformer to ensure its
economical operation and secured service.
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INTRODUCTION
 Rule of Thumb for PEA. “ Load current of transformers
should not be greater than 80% of rated current.”
Measure load current of transformer. To ensure its
operation.
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INTRODUCTION
 Now PEA. use IR. Camera to do preventive maintenance
for distribution system.
 We found many electrical connection problems. Easy for
us to identify problems and solve them.
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INTRODUCTION
For distribution transformer, there is no temperature base
for each loading current to consider the operating
temperature.
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SCOPE OF WORK
 Consider 250 kVA (22kV/400-230V) Transformers in 22 kV
distribution system, Chiangmai, Thailand.
 Neglect heat that generate from harmonic current.
 Assume load variation by time of transformers is very
small, raw data may be for steady state.
 Assume all transformers are healthy. No arc, corona,
partial discharge inside transformer.
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THEORY
 Losses in transformers
 Heat transfer
 Equation fitting
 Thermal-Electrical analogy
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LOSSES IN TRANSFORMER
 Core loss
 Copper loss
Ploss
Ploss = Pcore + Pcu
%Load
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1st LAW of THERMODYNAMIC
Ploss
TR.
T surface
Q
T amb
Electrical
losses = HEAT
that transfer to
surrounding
Steady state , no accumulated energy
Ploss
Heat
%Load
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%Load
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EQUATION FITTING
in consideration
range
UA is constant
Q
T oil
Q = UA. ΔT
T surface
T amb
ΔT = Q / UA
Heat
ΔT = a(%L)2+b(%L)+c
ΔT
%Load
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%Load
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THERMAL-ELECTRICAL ANALOGY
1/UA
Q = UA. ΔT
Q
Q = ΔT/(1/UA)
T oil
T surface
T surface
Q
T amb
T amb
1/UA
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I = ΔV/R
V1
I
V2
R
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RESULT
19 examples
 Load Current
 Ambient Temperature
 TR. Surface max. Temperature
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EQUATION FITTING
delta T
40.00
y = 0.0039x2 + 0.0323x + 8.0857
R² = 0.9548
35.00
30.00
25.00
20.00
15.00
10.00
5.00
0.00
0.00
10.00
20.00
30.00
EQUATION:
40.00
50.00
60.00
70.00
80.00
90.00
%Load
dTmax = 0.0039(%Load)2 + 0.0323(%Load) + 8.0857
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EQUATION FITTING
sum of deviations squared (SDS.)
delta T
40.00
n
SDS   (y i  Yi ) 2
35.00
30.00
i1
25.00
FOR 19 EXAMPLES , SDS = 69.59 C2
20.00
15.00
10.00
5.00
0.00
0.00
20.00
40.00
60.00
80.00
100.00
average percent absolute deviation (APD.)
%Load
APD 
n
100

n i1
 Yi  y i 


Y
 i 
2
FOR 19 EXAMPLES , APD = 10.19%
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CONCLUSION
 The top surface temperature of transformer is function of
loading capacitance and ambient temperature.
dTmax = 0.0039(%Load)2 + 0.0323(%Load) + 8.0857
 Temperature rise at 80% of rated load is 35.63 C.
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Question
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