a2.38 thermal modelling - cigrea2.cigre.org/.../3094838/version/1/file/a2.38+thermal+modelling.pdf13...

TRANSFORMER THERMAL MODELLING

Tutorial of CIGRE WG A2.38Convenor: John Lapworth, UK

2 Transformer Thermal Modelling – CIGRE A2.38

Scope & IntroductionThermal modelling in steady state

• Input to thermal models = losses

• Thermal-Hydraulic Network Model (THN)

• Computational Fluid Dynamics

Benchmark of numerical toolsDynamic thermal modellingDirect measurementsShell-type transformer thermal modelling

Content







Content


Transformer thermal design determines insulation ageing and life

Thermal performance is being checked by measuring mean winding temperature rises at the end of factory heat run tests

Traditionally, hotspot temperature were estimated using assumed hotspot factors

Advanced thermal modelling tools are now being developed and implemented to improve the detailed thermal design and the hotspot temperature estimation

Purpose of thermal modelling


‘State of the art’ in transformer thermal modelling

Practical examples of thermal modelling and limitations

Dynamic thermal models for calculation of transient temperatures for transformers subject to conditions of variable load and temperature of cooling medium

Good practices for direct measurements of hotspot temperatures and illustrate use for checking temperature rises and deriving other thermal parameters required for modelling

Consideration of shell-type transformers, for which there are fewer technical publications

Scope of WG A2.38


Basic transformer thermal modelling concepts (from IEC)


Reality is ‘a bit’ more complex…(example of a disk winding with diverting washers)

0

10

20

30

40

50

60

70

20 40 60 80 100 120 140

Disc num

ber

Temperature

Hot Spot

IEC model (oil and winding)

Detailed calculation

Max T corresponds to a min flow rate in radial duct

Oil flow in radial ducts


H = max [Q x S]H: a dimensionless factor to estimate the

increase of the average winding gradient due to• the local increase of losses (Q)

• variation in the liquid cooling flow stream (S)

Hotspot factor definition in a winding

r

r

bow

oh

gHgH

2







Content


FEM used to calculate the radial and axial magnetic field

Losses estimated using analytical formula

Eddy losses in windings

24)(

222 tBP y

axialE

24)(

222 tBP xradialE

Core clamp

Core yoke


Eddy losses calculation depends on the selected cross section







Content


Oil flows in cooling ducts and heat is transferred fromconductors to oil described by two interdependentnetwork models:

1. The hydraulic network model:

Thermal-Hydraulic Network Model (THN)

•Conduction between parts of the solid at

different temperatures

•Convection between the surface of the conductors

and the adjacent oil

•Due to frictional and inertial losses

•2. The thermal network ‘model’:

•…to describe the pressure drop experienced by the oil in the ducts

•…to describe the heat transfer between the conductors and the oil


•Thermal Network Model (Solid)•Possible geometry of a disc winding with zig-zag

cooling ducts•Heat Conduction (Interior nodes)

•Heat Convection (surface nodes)


,,int , ,

eq axialdisc ernal surface south oil surface south oil

KT T h T T

L

eq,, ,north

eq,, ,

eq,radial, , 1

eq,, , 1

axialdisc j i surface

axial

axialdisc j i surface south

axial

disc j i disc j iradial

radialdisc j i disc j i

radial

KT T

L

KT T

L

KT T

L

KT T HeatG

L

,disc j ienerated


Thermal-Hydraulic Network Model (THN)•The implementation of both networks result in a non-linear set of analytical

equations.



•1. The THN models depend on empirical data such as:

•… Physical properties of the materials

•… Correlations - Friction factors, Heat Transfer Convective Coefficients

•2. The THN models also depend on architectural decisions such as:

•Most of the THN models comprise the same physical mechanisms (Pressure Drop, Heat Conduction, Heat Convection). They differ on their interpretation and

implementation.

•3. Most of the THN examples are appliable to the windings but they can also model the radiators and the whole complete cooling cycle.

•… Numerical algorithms employed

•… Spatial Discretization

•… Potential Measurements – Losses, Bottom Oil Temperature, Average Winding Temperatu


1980 and 1984….. Early implementation ‘TEFLOW’ described by Oliver (CIGRE paper 12-09, 1984 and Proc. IEE, 1980)

THN examples

1999…Implementation described by J. Declercq (Transm. and Distrib. Conference IEEE, Vol. 2, 11-16 April 1999)

2010…Implementation described by Radakovic(IEEE Trans. Power Del., Vol. 25, no. 2, pp. 790-802, April 2010)

•[2D-Ax, Rosenhow and Hartnett Correlations, Gaussian Elimination, Jamison and Villemonte Junction Losses,

applicable to OD and OF Designs]

•[2D-Ax, Chu correlations, SIMPLE Algorithm, Péclet number,applicable to OD and ON designs]

•[2D-Ax, Literature Correlations, applicable to OD and ON designs, model complex cooling loops including radiators]


THN examples

2012…Implementation described by Campelo (Transformer Research and Asset Management, Cigré HRO, 2012).

2010…Optimization of the transformers load described by Picher (Cigré Paper A2-305-2010)

•[2D-Ax, Literature Correlations, Detailed Disc Model,Coupled Losses Model, Temperature Correction of theLosses, applicable to ON designs]

•[2D-Ax, Correlations Extracted from CFD, applicable to ON and OD designs]







Content


Idea and concepts behind CFD• Generating a CFD model

• Resouces / investments needed

CFD in transformer thermal modeling• Winding heat transfer analysis

• CFD and winding thermal networks

• CFD and cooling equipment (radiators)

• Other parts of the cooling circuit

Use of CFD in the design processSummary / Conclusions

Computational Fluid Dynamics (CFD)


Accurate modeling• All relevant mass flow and heat

transport processes can be included

• Fine spatial detail on complex geometries

powerful analysis approach (hotspot)

Area growing mature:• Hardware & software support

• Experiences

Resource & investment intensive

Key aspects of CFD


Generate geometryGenerate numerical meshDefine the problemGenerate solutionAnalyze

Key CFD modelling steps


Competence: CFD is an ”art”, requiring competence to be acquired and maintained

Hardware infrastructureCFD SoftwareTime:

• Developing the CFD model for a particular design

• Running the model

• Analysing the results

Resources / investments needed


CFD allows detailed heat transfer analysis Improved understanding on which processes to

include in thermal design

CFD and winding thermal analysis

Internal buoyancy included

Internal buoyancy excluded

Oil velocities

Discs temperature


Improved correlations• Local heat transfer coefficients

• Pressure drop correlations

Comparison / validation / improvement of winding THN models

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80

Channel number

Mas

s flo

w ra

te fr

actio

n (%

) TNMCFD

Pass 1 Pass 2 Pass 3 Pass 4

50

60

70

80

90

100

110

120

0 10 20 30 40 50 60 70

Disc number

Max

. dis

c te

mpe

ratu

re (°

C)

TNMCFD


Velocities Temperature


Radiators CFD modelling / experiments


Validation and improvement of thermal design models • However, thermal design models cannot resolve all

details

CFD as a tool to generate new or improve existing design guidelines• Minimizing effect of hot streaks in oil on hotspot

temperatures

• Improve thermal design reliability

CFD use in the design process


CFD can be applied in several ways• Improve understanding of thermal behavior

• Validate/improve thermal design models (THN models, etc.)

• Support design optimization of complex components

• Improve thermal design guidelines

CFD cannot replace thermal models used in design, because• Requires relatively large computing resources

• Requires long simulation time for obtaining results

Summary – CFD modelling







Content


WG A2.38 experts calculated losses and temperature on a transformer winding having experienced overheating of the top discs

The results were analyzed by WG members

Benchmark activities


Power 40 / 53 / 66 MVACooling ONAN / ONAF1 / ONAF2Voltage HV 225 kV Y

LV 26.4 kV ∆Frequency 60 HzZ 22.7% at 66 MVA

Electrical characteristics


Disc winding with diverting washers

78 discs 4 ‘passes’ of 19 discs

each + 2 discs at the bottom

Thermal characteristics


LV winding temperature rise of 61.6 K

Ambient temperature = 30.2°C

Top oil temperature = 80.4°C

Bottom oil temperature = 46.7°C

Heat-run test results

Temperature

80.4°C

46.7°C

63.4°C91.8°C

28.3°C

Hot Spot

Bottom of the winding

Top of the winding

Top of the tank

IEC model measurementscalculations


Eddy-loss calculated at 75°CMaterial properties (paper, oil, copper)Temperature calculation using

• uniform losses

• non-uniform losses (effect of eddy currents)

Inlet boundary conditions:• Pre-defined total oil flow rate (0.78 kg/s)

• Bottom oil temperature of 46.7°C

Modelling specifications


Eddy-loss calculation

0

200

400

600

800

1000

1200

1400

Loss

es (W

)7875726966636057545148454239

Disc number

Eddy lossDC loss

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Tota

l los

ses

(W)

Q-A

Q-B

Q-C

Q-D Q-E Q-F

Q-G Q-H Q-I

Q-J

Ande

rsen

Aver

age

Team

1383(100%)

1764(128%)

1070(77%)

Average of results (DC and Eddy losses)

Max losses at the top discQ min = 1.79Q max = 2.66

Divergence can be due to: boundary conditions, level of details used in the geometry - number of segments in the winding

modelling, analytical vs. proprietary losses formula


Temperature calculation

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80

Channel number

Mas

s flo

w ra

te fr

actio

n (%

) TNMCFD


50

60

70

80

90

100

110

120

130

0 10 20 30 40 50 60 70

Disc number

Max

. dis

c te

mpe

ratu

re (°

C)

TNMCFD


70

80

90

100

110

120

130

140

150

0 10 20 30 40 50 60 70

Disc number

Max

. dis

c te

mpe

ratu

re (°

C) TNM

CFD


Uniform losses

Non uniform losses

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80

Channel number

Mas

s flo

w ra

te fr

actio

n (%

) TNMCFD



Very high Eddy losses at the top of the winding (calculated Qfactors from 1.79 to 2.66) – this is the main contributor to the high H factor

Hotspot temperature-rise from 97.7 K to 107.2 K

Even if the mean winding rise is below 65 K (61.6 K), the hotspot temperature-rise is much higher than the IEC standard limit of 78 K

This explains the overheating of the top disc and the thermal fault

This example demonstrates clearly the importance of a detailed thermal modelling to calculate the hotspot temperature

Variation in results is an indication of the complexity of such modelling and the importance of experimental validation

Conclusion - Benchmark






Benchmark of numerical toolsDynamic Thermal Modelling (DTM)Direct measurementsShell-type transformer thermal modelling

Content


DTMs provide a simplified solution of a complex three-dimensional physical phenomenon of heat transfer inside transformer in the form of critical transformer temperatures (i.e. top-oil and hotspot temperatures) that can be applied for real-time monitoring, diagnostics and transformer protection applications.

Review of the state-of-the-art• A comprehensive and well‐referenced introduction to state‐of‐the‐art of dynamic

thermal modelling is given

Loading Guide Dynamic Thermal Models (DTMs)• In-service accuracy of dynamic thermal models (DTMs), presented in the

international standard Loading guides are discussed and compared:

• IEC 60354 model (1991)

• IEC 60076-7 model (2005)

• IEEE C57.91 Clause 7 (2011)

• IEEE C57.91 Annex G (2011)

• Models sensitivity to changes in ambient temperature and related phenomena are considered.

Overview


Dynamic Thermal Model Characteristic Temperatures


Hotspot temperature - Summer


Hotspot temperature - Winter


Each of given loading guide models require a set of specific exponents and constants which are empirical values

Corresponding parameters are obtained from extended heat run tests the load profile

Standard exponents and constants of loading guide dynamic models


Loading Guide type algorithms for calculating transient temperatures have been reviewed, in particular the new formulation proposed in the latest edition of IEC 60076 7, which includes a new ‘over shoot’ gradient function and a change to the recommended winding exponent.

It is concluded that further research and development is needed to improve the existing loading guide models, in particular, to increase the modelling accuracy during sub zero ambient condition where the oil viscosity effect is dominant.

Summary - DTM







Content


For large and strategically important transformers, e.g. for transformers the number of sensors should be 8 / main winding.

For mid-size units unitsthe number of sensors should be 6 / main winding.

For small unitsthe number of sensors should be 4 / main winding.

It is normally not of interest to install sensors in regulating windings, tertiary windings or in circulating oil.

Number of sensors

SZ 8.1ˆmax


Location of sensors – axial oil circulationSensors concentrated to the corner with max. losses


Location of sensorsZig-zag oil circulation

Location depends on the direction of the oil flow

In the case of 8 sensors:• The same setup at two locations around the

circumferenceIn the case of 6 sensors:• Double the sensors below disc nr 2 and 3







Content


Shell-type transformer thermal modelling•Shell-type transformers are widely spread in the US, all the nuclear fleet in Belgium,

half of the nuclear fleet in France, more than 85% of the 400 kV network transformers in Spain.

•Cooling ducts opened by pressboard spacers adjacent to the coil.

•Effective heat transfer area between 60-75%.


Shell-type transformer thermal modelling•No THN models known to date. CFD results are showing Hot-Spots under themoulded pieces.

•Not conclusive about possible H factors. Still needs to be better understood.

•Experimental flow field – Measured Optically

•CFD predicted flow field


For more informationBrochure (to be published)


Thanks to CIGRE A2.38 membersJ. Lapworth, Convenor (UK), P. Picher, Secretary (CA)

Task Force leaders: Jérôme Channet (FR), Jurjen Kranenborg (SE), Hasse Nordman (FI), Zoran Radakovic (RS), Oleg Roizman (AU), KeesSpoorenberg (NL), Dejan Susa (NO)

F. Berthereau (FR), H. Campelo (PT), S. Chen (FR), M. Cuesto (ES), V. Davydov (AU), G. Fleck (AT), T. Gradnik (SI), N. Gunter (ZA), W. Guo (AU), J.-K. Kim (KR), J. Lee (KR), A. Portillo (UY), N. Schmidt (DE), E. Simonson (UK), S. Tenbohlen (DE), F. Torriano (CA), F. Trautmann(DE), W. Van der Veken (BE), Z. Wang (UK), J. Wijaya (AU), G. Wilson (UK), W. Wu (UK), S. Yamamura (JP)

a2.38 thermal modelling - cigrea2.cigre.org/.../3094838/version/1/file/a2.38+thermal+modelling.pdf13...

Documents