Properties of cast resin transformers
Advantages of cast resin transformers compared to oil transformers
• Do not produce polluting gases when they are on fire and don’t support fire
• They are protected from wetness
• Environmental friendly
• There are no limitations for placement (can be mounted in buildings)
• Less needed height and area for placement
• Better possibilities of repair (on site)
• Maintenance is on minimum
• Smaller add losses, especially if static converter is load
• Position of high voltage and low voltage connectors is very flexible
Advantages of oil transformers compared to cast resin transformers
• Outdoor installation without special demands
• Protection against direct touch voltage is easy to implement
• They can operate in extremely polluted environment
• They have smaller no load losses
1
Range of rated powers and voltages
Range of rated power: 50 kVA – 40 MVA
Upper value of rated voltage: 36 kV
Fans
4.8 m length, 2.8 m width, 4.7 m height
Transformer of rated power 40 MVA (the biggest manufactured transformer till now)
2
Transformer construction
Low voltage winding:
Folio winding type
Low voltage
connectors
Core
Spacers
High voltage winding:
Disc type
Low voltage
winding
High voltage
winding
High voltage
connectors
Cast-resin
3
Construction versions (according to our experience):
• Core – without cooling channels or with one cooling channel in the middle of core
• Standard construction is following radial disposition:
core – folio (LV) winding – disc (HV) winding.
There are also other constructions (radial dispositions of the windings):
folio-folio-disc, disc-disc, folio-folio-folio.
Further in presentation, standard configuration will be considered.
Software for thermal design has been made only for standard configuration,
but it can be extended to all other configurations.
• Insulation cylinder between core and low voltage winding (folio): 0, 1 or 2 cylinders
• Low voltage winding (folio) build from 1, 2, 3, 4 or 5 parts (up to 4 cooling channels);
if there is more than one part, „dog bones“ spacers are used for forming cooling ducts
• Insulation cylinder between low voltage winding (folio) and high voltage winding (disc):
without, only in middle phase or in all tree phases
• High voltage winding (disc) made of 1, 2 or 3 parts (up to 2 cooling channels)
4
Checking of guarantee values of temperatures with heat run test
Standards (IEC 60076–11, 2004) predicts tree possibilities for loading and heating of
transformer:
 Simulated load method
 Back to back method
 Direct loading method
Minimum equipment is needed for Simulated load method.
There is two parts of test, and each of them last until steady state is reached:
 Heating with no load losses, with rated losses in core
(e will be designation for winding temperature rise measured in steady state)
 Heating in short circuit test, with rated current
(c will be designation for winding temperature rise measured in steady state)
5
From previously measured two temperature rises, value of temperature rise when transformer
is normally loaded is calculated (c‘), witch is guaranteed value:
   
 c '   c 1  e 
   c 

Example:
1
K1




K1
K1 = 0.8 for natural air flow
K1 = 0.9 for forced air flow
Transformer of rated power 630 kVA, for rated voltage 15000 V / 420 V
Heating in open circuit test (duration 16 hours):
– Core temperature rise 49.7 K
– LV winding temperature rise 24.1 K
– HV winding temperature rise 5.0 K
Heating in short circuit test (duration 18 hours):
– Core temperature rise 30.8 K
– LV winding temperature rise 72.5 K
– HV winding temperature rise 75.7 K
Calculated temperature rises when transformer is normally rated loaded
– Temperature rise of LV winding 87K
– Temperature rise of HV winding 78K
Rises are less then permissible 100K
(class F, supposed ambient temperature 40°C)
6
Physic of heat transfer from active parts of transformer
Example:
 Standard configuration
 Core without cooling channels
 Folio winding in one part
 Disc winding in one part
 Without insulation cylinders
General principles:
 AN cooling of surfaces
 Radiation heat exchange
between opposed surfaces
 In active parts between cooling
channels there is conduction
heat transfer with distributed heat
generation
7
Components of mathematical model:
A. Energy balance equations
B. Equations of boundary conditions (on boundary surfaces to air)
C. Equations of conduction heat transfer in parts between cooling
channels
A. Example of equation of energy balance for low voltage and high voltage windings
Radiation from core
qv1 V1  qro1  qr12  qS1i S1i  qS1o S1o
Generated heat
because losses in
winding
Convection from inner
Radiation from
LV to HV winding part of winding
LV winding
Convection from outer
part of winding
qv 2 V2  qr12  qS 2i S 2i  qS 2o S 2o  qr 2a
HV winding
Radiation from HV winding to ambient
8
B: Equations of boundary conditions (on boundary surfaces to air)
Example for non symmetrically heated channel
B1. Convection
z – height coordinate, b – width of axial ccoling duct
P
S
  f   or   f  
P  S 
W 
q"   ( z )  ( z ) a 
( z ) 
K 
 W 
 2 
m K 
m 
 ( z) 
b *
  Gr Pr
z
 b

 H W
 * 
 Gr Pr 


1
Gr * 
2
 Nu( z )
z
g  q"b 4
 2
2
Entry region ((z)60)
Nu ( z )  C1 1 R   ( z )
16
Fully developed region ((z)60)
1
3
Nu( z ) 
C2
 1  24  12 9  1

  
(1 R) 
70  2
 ( z )  1 R 


b – width of channel
HW – height of winding
Inner surface
R
q2
q1
q"  q1
Outer surface
R
q1
q2
q"  q2
9
B2. Radiation
Between concentric cylinders
qro1 
5.6710
8
  273  
4
0
1  2 S 0

1
 1 S1i
1i
 273
4
1
Between half-cylinders of neighbor phases
S

4
 
F12 – view factor, describing influence of neighbor phase
F12 
space (outer phases)

4
0
From half-cylinder radiated to free


qr 2a  5.67108 2o  273  a  273 S2o F12
1 cos( 1 ) cos( 2 )
ds1 ds2
2
S1 s

R
1s 2
 
qr 2a  5.67108 2o  273  a  273 S2o
4
4
Horizontal
cross-section
10
Implementation of mathematical method in the software
(radiation heat exchange between cylinders of neighbor phases)
dS1  Rc d1 dz1 dS2  Rc d 2 dz2
 1  f1 (1 , z1 ,  2 , z2 );  2  f 2 (1 , z1 ,  2 , z2 ); R  f 3 (1 , z1 ,  2 , z2 )
1
F12 
Rc Hc
2 2
 / 2 Hc / 2  21 Hc / 2
  
0
0
22
cos  1 (1 , z1 ,  2 , z 2 ) cos  2 (1 , z1 ,  2 , z 2 )
d1 dz1 d 2 dz 2
2

R
 Hc / 2
cos  1 (1 , z1 ,  2 , z 2 ) 
Vk1a (1 , 0) Vk12 (1 , z1 ,  2 , z 2 )
Vk1a (1 , 0) Vk12 (1 , z1 ,  2 , z 2 )
cos  2 (1 , z1 ,  2 , z 2 )  
Vk 2 a (1 , 0) Vk12 (1 , z1 ,  2 , z 2 )
Vk 2 a (1 , 0) Vk12 (1 , z1 ,  2 , z 2 )
R(1 , z1 ,  2 , z 2 )  Vk12 (1 , z1 ,  2 , z 2 )
22  22'' if
(Vk1a ,VAB ' )  90
22  22' if
(Vk1a ,VAB ' )  90
Coordinates of points B‘, B‘‘ i C are
described analytically by using
theory of analytical geometry
11
C. Equations of conduction heat transfer in parts between cooling channels
1 
R _ p 
 Sp
Pi
1, 2
Thermal resistance of insulation
between two layers
max
1
Losses in one layer
2
Temperatures of inner and
outer surfaces
qS
qv
q S 1  qV x *

qS 2  qV d  x *

qS
2
1
x*
d
Temperature 1 depends on Pleft
(boundary condition: convection and radiation);
2 depends on Pright
1
P left  (( j 1 )  ) Pi
2
1
P right  (( N  j 1 )  ) Pi
2
j
2  1
N 1

2
R _ p( ,  , S ) Pi ( N  1)
12
Average temperature of winding
Example for the case of low voltage winding with no cooling channels in the winding:
R _ p (LV , LV , SLVa) PiLV  ( jLV  1) (2 jLV  1) jLV 1 



2
3
2


R _ p (LV , LV , SLVa) PiLV  ( NLV  jLV 1) (2 NLV  2 jLV 1) NLV  jLV 1 
CuaLV 2  LVCout 



2
3
2


jLV CuaLV 1  ( NLV  jLV ) CuaLV 2
CuaLV  LVIin 
NLV
CuaLV 1 
13
Size and characteristic of complete mathematical model
System in nonlinear and there is big degree of mutual correlation of exposed components of
mathematical model. Because of that the complete model contains large number of nonlinear
equations.
For example, if there is cylinder between LV and HV winding, there would be 13 equations:
1 for outer surface of core
5 for LV winding
2 for cylinder between LV and HV winding
5 for HV winding
Unknowns in system
of 13 equations:
11 temperatures:
- outer surface of core,
- outer and inner surface of:
- cylinder carrying LV winding
- insulation over LV winding
- cylinder between LV and HV winding
- inner layer of cast resin of HV winding
- outer layer of cast resin of HV winding
2 radial positions of hot-spots (in LV and HV winding)
14
Realized software for thermal design
 Software is done by using and connecting Excel + Mathcad programming tools.
 Mathcad is used for solving complex system of nonlinear equations
 Excel is used as input and output user interface
 One Excel sheet is used as input sheet for construction data about transformer
 Other sheet contains results of calculation of characteristic temperatures
 It is possible to enter data from heat run test, and make database with compared
measured and calculated values of temperatures
 Results of this database can be used as basis for increase of accuracy of calculation
methods, i.e. for fine tuning of coefficients (for example those in formulas on slide 10).
15
Input Excel sheet /
illustration on parts of
sheets with
construction data and
characteristics of
materials
16
Input Excel sheet /
Illustration on part of
table with data about
HV winding and losses
in HV winding
Input Excel sheet /
Data from heat run test
17
Excel sheet of results /
Part of table with
calculated characteristic
temperature rises
Illustration of connection between Excel and Mathcad
18
Illustration of Mathcad program /
o
Part of program with air parameters
o
Part of program for parameterization of calculation
o
Part of program with initial iteration
o
Part of program with basic functional dependencies
19
Illustration of Mathcad program /
o
Part of program that contains equation system
(for illustrated tree equations it is visible only one forth of them)
20