1

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

2

Range of rated powers and voltagesRange of rated power: 50 kVA – 40 MVA

Upper value of rated voltage: 36 kV

Fans

Transformer of rated power 40 MVA (the biggest manufactured transformer till now)4.8 m length, 2.8 m width, 4.7 m height

3

Low voltage connectors

Low voltage windingHigh voltage winding

High voltage connectorsCast-resin

Core

Spacers

Transformer construction

Low voltage winding:Folio winding type

High voltage winding:Disc type

4

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)

5

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)

6

From previously measured two temperature rises, value of temperature rise when transformer

is normally loaded is calculated (c‘), witch is guaranteed value:

K1 = 0.8 for natural air flow

K1 = 0.9 for forced air flow

1

11

1'

KK

c

ecc

Example: Transformer of rated power 630 kVA, for rated voltage 15000 V / 420 VHeating 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)

7

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

8

Components of mathematical model:A. Energy balance equationsB. Equations of boundary conditions (on boundary surfaces to air)C. Equations of conduction heat transfer in parts between cooling

channels

ooSiiSrrov SqSqqqVq 111121111

arooSiiSrv qSqSqqVq 222222122

LV windingGenerated heat because losses in winding

Radiation from core

Radiation from LV to HV winding

Convection from inner part of winding

Radiation from HV winding to ambient

A. Example of equation of energy balance for low voltage and high voltage windings

Convection from outer part of winding

HV winding

9

B: Equations of boundary conditions (on boundary surfaces to air)

forSPf

SP

W

Km

W2

2m

K

B1. Convection

1

2

qqR

1" qq 2

1

qqR

2" qq

Outer surface

azzq )()("z

zNuz )()(

21

*

*

Pr

Pr)(

GrHb

Grzb

z

W

2

4* "

bqgGr

3161

1 )(1)( zRCzNu

21

709

124

)(1)1(

)(2

12

RzR

CzNu

Entry region ((z)60) Fully developed region ((z)60)

b – width of channelHW – height of winding

Inner surface

Example for non symmetrically heated channel

z – height coordinate, b – width of axial ccoling duct

10

B2. Radiation

0

1

0

1

2

1

41

40

8

1 112732731067.5 S

SS

q

i

iro

4 482 2 25.67 10 273 273r a o a oq S

F12 – view factor, describing influence of neighbor phase

Between concentric cylinders Between half-cylinders of neighbor phases

21221

112

21

)cos()cos(1 dsdsRS

Fss

Horizontal cross-section

12244

28

2 2732731067.5 FSq oaoar

From half-cylinder radiated to free space (outer phases)

11

Implementation of mathematical method in the software (radiation heat exchange between cylinders of neighbor phases)

),, ,();,, ,();,, ,( dS dS

22113221122221111

2 22 1 11

zzfRzzfzzfdzdRcdzdRc

),, ,(),, ,(

),, ,()0 ,(),, ,()0 ,(),, ,(cos

),, ,()0 ,(),, ,()0 ,(),, ,(cos

2 2 1 112 2 2 1 1

2 2 1 112 12

2 2 1 112 12 2 2 1 12

2 2 1 112 11

2 2 1 112 11 2 2 1 11

zzVzzR

zzVVzzVVzz

zzVVzzVVzz

k

kak

kak

kak

kak

''22 22 1 '

'22 22 1 '

( , ) 90

( , ) 90k a A B

k a A B

if V V

if V V

2/

0

2/

0

2/

2/ 2 2 1 12

2 2 1 12 2 2 1 1112

21

22

),, ,(cos),, ,(cos

22

1F

Hc Hc

Hc

dzddzdR

zzzzHcRc

Coordinates of points B‘, B‘‘ i C are described analytically by using theory of analytical geometry

12

C. Equations of conduction heat transfer in parts between cooling channels

1

2

max

qv

x* d

qS1 qS2

*1 xqq VS

*2 xdqq VS

SppR

1_ Thermal resistance of insulation

between two layers

Pi Losses in one layer

1, 2

PijNrightP

PijleftP

)21)1((

)21)1((

Temperatures of inner and outer surfaces

)1(),,(_21Nj 12

NPiSpR

Temperature 1 depends on Pleft (boundary condition: convection and radiation);2 depends on Pright

13

Average temperature of winding

Example for the case of low voltage winding with no cooling channels in the winding:

NLVjLVNLVjLV

LVIin

jLVNLVjLVNLVjLVNLVPiLVSLVaLVLVpRLVCout

jLVjLVjLVPiLVSLVaLVLVpR

CuaLVCuaLVCuaLV

CuaLV

CuaLV

21

2

1

)(2

13

)122()1(2

),,(_2

13

)12()1(2

),,(_

14

Size and characteristic of complete mathematical model

System in nonlinear and there is big degree of mutual correlation of exposed components ofmathematical 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 core5 for LV winding2 for cylinder between LV and HV winding5 for HV winding

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)

Unknowns in system of 13 equations:

15

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).

16

Input Excel sheet /illustration on parts of sheets with construction data and characteristics of materials

17

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

18

Excel sheet of results /Part of table with calculated characteristic temperature rises

Illustration of connection between Excel and Mathcad

19

Illustration of Mathcad program /o Part of program with air parameterso Part of program for parameterization of calculationo Part of program with initial iterationo Part of program with basic functional dependencies

20

Illustration of Mathcad program / o Part of program that contains equation system

(for illustrated tree equations it is visible only one forth of them)