Flux: TransformersFlux: Transformersxxx

Philippe Wendlinginfo@tianyuantech.com

Create, Design, Engineer!, D s g , g

www.magsoft-flux.comwww.cedrat.com

P ibl l iPossible analysisModeling any type of industrial transformers: three-phase, single-phase, auto transformer, reactors..Modeling any type of industrial transformers: three phase, single phase, auto transformer, reactors..

Simulating classical tests:No-loadSh i iShort-circuitInrush current

Analyzingy gIron lossesStray lossesJoule lossesMagnetizing reactanceMagnetizing reactance

Performing thermal and mechanical analysisMultiphysics (3rd party tools)p y ( p y )

ReferencesABB, Alstom, Electricité De France (EDF), Federal Mogul, General Electric, Hydro Quebec, Iskra Stikala, S h id El t i T f T f T il VAT h W ti h

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Schneider Electric, Trafomec, Trasfor, Transrail, VATech, Westinghouse

T fTransformers

Geometry:Geometry:Direct InputImportFull or reduced model

¼th 3-phase transformer

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Fl T f d C ilFlux: Transformers and Coils

Physical domain in FluxPhysical domain in FluxSteady state AC magnetic: common tests (short circuit open circuit rated conditions) common tests (short circuit, open circuit, rated conditions) – Single Frequency/HarmonicTransient Magnetic: Transient Magnetic: common tests (short circuit, open circuit, rated conditions) – Full signalFull signalSteady state thermal : thermal behaviorthermal behavior

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Fl T f d C ilAn example:HV t f

Flux: Transformers and Coils

HV transformer 150 MVA - 132 kV / 14.1 kV

(courtesy of WTC)( y )Flux Model:

The Electric CircuitV1 HV_1 LV_1 R1

V2 HV_2 LV_2 R2

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V3 HV_3 LV_3 R3

Fl T f d C il

Transformer Flux region Description

Flux: Transformers and Coils

Transformer Flux region Description

Core, Shunts:Laminated

Magnetic non conductive volume region µrg

Tank frames:δ<<sheet thickness

Surface impedance (face region) µr, ρ

Shunt for fastening:thin sheet thickness Thin conducting surface region µr, ρ

thickness

Conductive parts with eddy current Solid conductor volume region

µr, ρ

Windings, Bus bars, current sources, no eddy currents

Coil conductor volume region or non meshed coils

Coil component Number of turns

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Modeling of laminated magnetic core in FluxAllows reducing the eddy current losses in FluxAllows reducing the eddy current losses

Problem of dimensional disproportion (sheet length compared to the sheet thickness)

Need to simplify the model

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Si lif i b h i i Simplifying by homogenization techniquetechnique

Equivalent macroscopic modelthe block of insulated laminations is replaced by a homogeneous blocktakes into consideration anisotropy saturation and eddy currentstakes into consideration anisotropy, saturation and eddy currents

Ongoing PhD work taking into account forbidden current loops 

User version Lamination available in Flux 3Dpermits the modeling of the ferromagnetic material by means of the Analytical

(paper)

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anisotropic saturation

Wi di d fi itiWindings definitions

1) Non-meshed coilsFast computationIndependent from the meshIndependent from the mesh

2) Meshed coils : Coil conductor volume regionSimplification of the representation as an homogeneous volume regionhomogeneous volume region

(if thin wires and many turns)

3) Meshed coils : representing every conductor(only for specific studies)

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T f d l Transformer model parametersReal transformer modelReal transformer model

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Fl T fFlux - Transformer

See how it works!See how it works!

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O Ci it Open Circuit Test Case (No Load)

Open Circuit p ( )

Magnetizing current in the primarySaturated coreNeglected leakagesg g

R>>1I=0AV1 HV_1 LV_1 R1

V2 HV_2 LV_2 R2

V3 HV_3 LV_3 R3

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O Ci it

Color shades of B Arrows of B

Open Circuit

Color shades of B

Joule losses on the tank: 10 WEnergy on the domain: 73 Joules Energy on the domain: 73 Joules

Magnetizing reactanceIron losses on the core (Bertotti): 416 Joules

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Iron losses on the core (Bertotti): 416 Joules

O Ci it Open Circuit

Flux Computes Results

Current in each Magnetizing current

primary phaseMagnetizing current

Reactive power/phase/ * * ²

Magnetizing Magnetic energy E on the domain

E=1/2*L*I²Qtot=2*E*ω Q=Qtot/3

X_1=Q/(I_1)²

Magnetizing reactanceXm1, Xm2

Magnetic flux + B t tti ffi i t I Lg

density in core+ Bertotti coefficients Iron Losses

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Sh t i it t t i l ti

Principle

Short-circuit test simulation

PrincipleMagnetizing current neglectedCore non saturated low flux densityCore non saturated – low flux densityLarge flux leakage

R<<1R<<1U=0

V1 HV_1 LV_1 R1

V2 HV_2 LV_2 R2

V3 HV_3 LV_3 R3

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Sh t i it t t i l ti

Color shades of B Arrows of B

Short-circuit test simulation

Color shades of B

Joule losses on the tank: 1395 W Stray lossesEnergy on the domain: 1024 Joules Leakage Reactancegy J gLaplace forcesJoule losses in the windings

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Sh t i it t t i l tiShort-circuit test simulation

Flux computes Results

Voltage in each primary Voltage in each primary phase

Short-circuit voltages

Reactive power/phaseL k tMagnetic energy E on the

domain

p pE=1/2*L*I²Qtot=2*E*ω Q=Qtot/3

X_1=Q/(I_1)²

Leakage reactanceX1, X2

R1, R2, I1, I2Pj=3*R1*I1²+3*R2*I2² Joule losses in the winding

Radial magnetic induction Eddy current losses in the winding

Stray losses density Total Stray losses

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Sh t i it t t i l ti

Stray losses

Short-circuit test simulation

Stray lossesFlux leakage

~Eddy current in conductive partsEddy current in conductive parts~Joule losses - « Stray losses »

In Flux use of surface impedance regionIn Flux use of surface impedance region

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Sh t i it t t i l ti

Eddy current losses in the winding

Short-circuit test simulation

Eddy current losses in the windingLosses per conductor per winding linked to radial magnetic induction BradIn Flux: export on 2D grid of B in the coil use formula

⎤⎡ −− bbaaab 22 )/sin()/sinh()/sin()/sinh(1 δδδδ⎥⎦

⎤⎢⎣

⎡+−

++−

= BaxBrad bbbba

aaaabeddyP

o

222 )/cos()/cosh(

)/sin()/sinh()/cos()/cosh()/sin()/sinh(1)(

δδδδ

δδδδδ

δσ μ

This methods efe to “Calc lation of E t a losses in shell t ansfo me s

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This methods refer to : “Calculation of Extra losses in shell transformers windings”, T.Ngneugueu, IEEE, 1988.

L l f l iLaplace forces analysisDefinition

dF(t)=PVEC(J,B) = F1+F2(t) with F1 = 1/2Re(JxB*) and F2(t) = cos(2wt).F21+sin(2wt).F22

Display color shades or arrows of Laplace force density on coilsDisplay color shades or arrows of Laplace force density on coilsDF Laplace/DV = Component F1 (Fundamental)

DF Laplace/DV 2w = Pulsating component F2(t) (double frequency)

Compute total forceIntegral of the above quantities in all coils

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Th l l i f h tiThermal analysis of heatingExport Joule losses from short-circuit simulation

For example the Joule losses on the tankDefine a Steady State Thermal application

U f hi d i i i h h d h l Use of thin conducting region with exchange and thermal sourceCreate a spatial parameter for import

Imported losses will be used as heat sourceImported losses will be used as heat source

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E l Edd C tExample Eddy Currents

Computation of eddy currents in tank – Surface Impedance formulationComputation of eddy currents in tank Surface Impedance formulation

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P T fPower Transformer

A th h t f ith i t i id f th t k A three-phase transformer with an air core reactor inside of the tank was considered as the application of this analysis

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Obj tiObjectives

Calculate eddy current losses in the clamping plate tank and Calculate eddy current losses in the clamping plate, tank and electromagnetic shielding of a power transformer using FLUX3D

Analyze the effects of electromagnetic shielding and magnetic Analyze the effects of electromagnetic shielding and magnetic shunts on the eddy current loss reduction in the transformer tank

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S f I d M th dSurface Impedance Method

The 3D Time-Harmonic Magnetodynamic Formulation was used in this analysisThe 3D Time-Harmonic Magnetodynamic Formulation was used in this analysisThis formulation takes into account the currents induced in the conducting regions (eddy currents) and also considers the skin effects and the proximity effects in the conducting regions.

Some devices such as clamping plate bus bars of transformers and shielding Some devices such as clamping plate, bus bars of transformers and shielding are mainly made up of sheet or line type parts of thin air-gaps.

Modeling these parts using traditional finite volume elements available in 3D f d bl 3D software is tiresome, and even impossible. Moreover, the skin effect in ferromagnetic materials increases the

difficulties of meshing eddy current problems in under sinusoidal g y pconditions.

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S f I d M th dSurface Impedance Method

An alternative to this difficulty of meshing the thin regions is the use special “shell elements” for the modeling of magnetic or thin conducting regions, and “surface impedance” elements for the modeling of conducting regions having a strong skin depth

Special “surface elements”, using the concept of surface impedance, which describe the surface of the conducting region allow the exponential decay to describe the surface of the conducting region, allow the exponential decay to be taken into account. They also allow the magnetic field to only be calculated on the surface and outside

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P T f D i tiPower Transformer Description

The tank and the clamping plates are made of mild steel (modeled by Surface The tank and the clamping plates are made of mild steel (modeled by Surface Impedance Method - SIM)

The core and the magnetic shunts are made of silicon-steel laminations The tank wall (side A) was modeled considering three cases:

No ShieldingAluminum Electromagnetic Shielding (modeled by SIM)Aluminum Electromagnetic Shielding (modeled by SIM)Magnetic Shunts

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FLUX-3D Geometry – Electromagnetic Shielding

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FLUX 3D G t M ti Sh tFLUX-3D Geometry – Magnetic Shunts

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FLUX 3D C l d Ci itFLUX-3D Coupled Circuit

Electrical circuit feeding the Electrical circuit coupled to the active part of the transformer winding of the air core reactor

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FLUX 3D M hFLUX-3D Mesh

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RESULTSRESULTS

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M ti Fi ld Di t ib ti i th Oil Magnetic Field Distribution in the Oil –No Shielding

There is only t ti ltangential component of the magnetic field in the tank walls (modeled by Surface Impedance)

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M ti Fi ld Di t ib ti i th Oil Magnetic Field Distribution in the Oil –Aluminum Electromagnetic Shielding

There is only tangential component of thecomponent of the magnetic field in the tank walls and Electromagnetic Shielding (modeled by Surface Impedance)

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M ti Fi ld Di t ib ti i th Oil Magnetic Field Distribution in the Oil –Magnetic Shunts

The magnetic flux tends to pass through thepass through the shunts

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Edd C t L i th T f Eddy Current Losses in the Transformer Tank – No Shielding

The eddy current losses in ythe tank are larger in this first case

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Edd C t L i th T f Eddy Current Losses in the Transformer Tank – Aluminum Electromagnetic

Shi ldiShielding

The eddy current losses in ythe tank are reduced in this second case

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Edd C t L i th T f Eddy Current Losses in the Transformer Tank – Magnetic Shunts

The tank wall protected by p ythe magnetic shuntshas a loss concentration bigger than the tank wallbigger than the tank wall protected by the aluminum electromagnetic shielding

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Th l I f th T k W ll ith Thermal Image of the Tank Wall with Magnetic Shunts

One can see the presence of hot spots in position behind themagnetic shunts (red region). This shows that the magnetic shunts concentrate

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ag et c s u ts ( e eg o ). s s ows t at t e ag et c s u ts co ce t ate the eddy current losses at the top of shunts

T f i diTransformer winding

HV windingHV winding

• The winding on leg A and B are

Leg Leg

• The winding on leg A and B are parallel connected.

• LV winding has 2 layers for each leg and 2 layers are seriesLeg

ALeg B

leg and 2 layers are series connected with each other.

LV winding

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Edd C t L i C ilEddy Current Losses in Coils1 • Section1 to section 54 are series.

HV

TAP

HV

TAP

• Section55 to section 108 are series.• Then, upper and lower part are parallel

connected.

HV HV54

• Each section is consist with 9-turn continuously transposed conductors (CTC).

HV HVleg A

55

HV

TAP

HV

TAPA

Single sectionHV HV

108 CTC

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FLUX MODEL A i t iFLUX MODEL – Axisymmetric

Just take 3 sections of HV winding and 1 section of LV winding.

corecore

8571.9 A for this area

1004.9 /2 A for this area

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E t l i itExternal circuit

HV

LV

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C t d it hCurrent density - hv

DC

60Hz

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C t d it lCurrent density - lv

DC 60 Hz

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J l L F HVJoule Losses vs. Frequency on HV

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