Expert Design and Empirical Test Strategies for Practical ......characterize transformer power dissipation levels. • The transformer developer may work closely with the power system

1

Expert Design and Empirical Test Strategies for Practical Transformer

Development

Victor W. QuinnDirector of Engineering / CTO

RAF Tabtronics LLC

2

• Units• Design Considerations• Coil Loss• Magnetic Material Fundamentals• Optimal Turns• Empirical Shorted Load Test • Core Loss Estimation and Recommended

Empirical Test Method (iGSE,FHD,SED)• Example Application• Summary

Outline

Victor [email protected] Ext 340

3

• Transformer developers strive to design, develop and consistently manufacture transformers based on in depth understanding of application conditions and implementation of best practice design, production and test methods.

• The initial first article transformer must be carefully validated in the respective application circuit to ensure the scope of thecomponent development was sufficient for the end use.

• Based on the challenges of accurate measurement of transformers in complex circuit applications, calorimetric (temperature rise) measurements are often used to characterize transformer power dissipation levels.

• The transformer developer may work closely with the power system developer to correlate loss and thermal measurements under specific conditions.

• Once the transformer design is validated, the transformer developer must implement tight QA controls on component materials and processes to ensure consistent results.

New Product Development PremiseComponent Verification Application Validation

4

Electric Field

VoltMeter

BWebersMeter

WeberMeter

Tesla Gauss

HAmpere Turn

MeterATM

Oe

JAmpereMeter

Ohm MeterHenryMeter

HM

FaradMeter

ff

2 24

2

2

07 6

12

0

1 10

1 10

1 1

4 10 1257 10

885 10

1

1.257

(permeability constant)

(permittivity constant)

where = frequency in Hertz

0

.

.

,

UNITS: Rationalized MKS+

) 20 @ ( 676.0 CelsiusCuinch

inchF12

0 10225.0

) 20 @ ( 6.2 CelsiusCuinchf

1 Oe = 2.02 AT/inch

inchAG

inchH 5.01019.3 8

0

5

Φ

IsIp

Design ConsiderationsCross Sections and Operating Densities

Primary Secondary

CoreCore cross section [Acore] constrained by aperture of coil.

Coil cross section [Awindow]constrained by aperture of core.

ΔB

J

ΔB

J

6

Faraday’s Law

• When a voltage E is applied to a winding of N Turns

E Nddt

( )

(Instantaneous Volt/Turn Equivalence)

E dt

N

pt

t T

p

1

1

2

ET

E dtt

t T

1

1

1

(Average Absolute Voltage)

Voltage

Time

E +

-

Np

E

Ns

7

Voltage

Time

v(t) +

-

i(t) L

v(t)

+

-

i(t)

L

Flux Density Considerations

• Voltage driven coil

• Line filter inductor

Current

Time

(Two induced consecutive, additive voltage pulses)

ENp

E dt

N

pt

t T

p

1

1

2

8

Ampere’s Law

• When a current i is applied to a winding of N Turns

• For ideal core having infinite permeability, Hc=0

(Instantaneous Amp-Turn Equivalence)

Ip

Np Ns

encloseddlCurve C

H i

Is

sspp ININ

Curve C

Hc

Is

Ip

The Amp-Turn imbalance is precisely the excitation required to achieve core flux density. Magnetic material reduces the excitation current for a given flux density.

9

Transformer VA Rating• Faraday’s Law and Ampere’s Law imply that

instantaneous Volt/Turn and Amp-Turn are constant.

• Therefore the winding Volt-Ampere product is independent of turns and is a useful parameter to rate transformers.

• Since core flux excursion is based upon average absolute winding voltageand winding dissipation is based upon RMS current , define:

iRMS

Transformer VA E iRating ii

RMSi

E

10

Fundamental Transformer Equation

• Derive a relationship between Volt-Ampere rating and transformer parameters:

• Therefore, by increasing frequency, current density, flux density, or utilization factors, the area product can be reduced and the transformer can be made smaller.

VA A A freq J B K KRating core window Fe Cu

VAP A AVA

freq J B K Kcore windowRating

Fe Cu

11

Current Density (J ),Window Utilization Factor (KCu )and Coil Loss

12

• At low frequencies, for uniform conductor resistivity and uniform mean lengths of turn, minimum winding loss is achieved when selected conductors yield uniform current density throughout the coil.

• For uniform current density J:

or

where

2 JVolCondLossCoilFrequencyLow 2

iiNILossCoilFrequencyLow

AreaWindowCoreKy

Thicknessxy

Cucu

Window Utilization Factor

Coil Loss

13

Coil Insulation Penalty

• Conductor Coatings• Insulation Between

Windings• Insulation Between

Layers• Margins• Core Coatings or

Bobbin / Tube SupportsThese considerations can total more than half of the available core window limiting utilization to less than 35%!

Core Window

Window Utilization Factor (KCu )

14

Example of KCu Estimate (PQ 20/20)

tol

supporttol

tol

margin

2IW2IW

Δx

Δz

318.0KKKK ,

556.00.169

2(0.01)-(0.035)0.0102169.0Δz

2(2IW)-(support)tol2ΔzK

85.0) (K

785.04

) (K

0.858 0.55

2(0.036)-2(0.003)-0.55 Δx

flange) bobbinor 2(margintol2ΔxK

zCuinsulCushapeCuxCu

zCu

insulCu

shapeCu

xCu

CuKSo

wiresolidfilmheavy

squareversusround

15

Window Utilization Penalties

Coil Loss

0

2

4

6

8

10

12

14

0 5 10 15 20

Frequency (kHz)

Loss

(W)

Window Utilization

0%10%20%30%40%50%60%70%80%90%

100%

0 5 10 15 20

Frequency (kHz)

Util

izat

ion

Ideal

Typical Core Window Utilization

0%

25%

50%

75%

100%

Insulation occupies more than 50% of core window.

Eddy current losses can further reduce effective conductor area by more than 50%.

16

Other Design Considerations AffectingWindow Utilization: KCu

MaximumKcu

LeakageInductance

CapacitanceNumber OfWindings

EddyCurrentLosses

InsulationRequirements

Corona / DWVRequirements

17

xRHxzH RMS ˆˆ)( 0

xHxzH RMS ˆˆ)( 0

yzJ ˆ)(

z

x

y

Low Frequency Example Calculation of Loss

z

Effective conductor thickness

zxiydyJzxLoss

zxi

zHR

zH

dzdHJ

xHiR

ixLawsAmpere

RMS

yy

RMSy

RMS

RMS

2

2RMS

RMS 0RMS

RMS 0

RMS 0

)1(

1

1)H-(R '

18

Qualitative ExampleSevere Skin / Proximity Effects

( ) cos( ) H H t x0

H t x0 cos( )

J H J H

H dl i H tilcurve w

0 0

1

2 2

,

cos( )

i

J0

J0

J J0

J

Circulating Current

z

zx

19

Dissipation And Energy As Function Of B (single layer)

0

0.5

1

1.5

2

2.5

0.5 1.5 2.5 3.5 4.50

0.5

1

1.5

2

2.5

DissipationDissipation Average Energy

Average Energy

x y Hs 02

8

Minimum Dissipation @ B=π/2

2SH

2 yx

H H Hs s s1 20 ,

Single layer with one surface field at zero is forgiving of design errors.However, other constructions can yield lower loss.

Bz

20

Loss Equivalent and Energy Equivalent Thicknesses (Single Layer Portion)

magnetic

loss

equivBB

BB

equiv

BB

BB

ThkBeeBee

ThkBeeBee

zwith B

2RMS

022

222

RMS0

2RMS

22

22

2RMS

SS2S1

)(NI x6y ]

)2cos(2)2sin(2[

23)(NI

x6y Energy

/)(NI xy

] )2cos(2)2sin(2[

)(NI xy Power

) HH and 0H(

21

Define Normalized Densitiesfor General Sine Wave Boundary Conditions

),B(R,pHPower 020RMS

yx

• Δx Δy represents the surface area of the conductor layer

• H0RMS=RMS value of sinusoidal magnetic field intensity at one boundary

• R=Ratio of magnetic surface field Intensities

• B=Ratio of conductor thickness to δ (conductor skin depth)

• Ф=Shift of magnetic surface field phases

),B(R,eH Energy Magnetic 020RMS0 yx

Dimensionless densities (p0 , e0)

22

Complex Winding CurrentsDissipation For Frequency Dependent Resistor

For complex waveshape and frequency dependent resistor, Harmonic Orthogonality =>

V IRP I R

P I Rdt

P RT

I dt

P R Irms

IrmsT

I dt

ave TT

aveT

ave

T

2

1 2

2

2

2

1

1

*

P R f Irmsave total n n n ( ) * 2

+ _V

I Power

23

Nonsinusoidal Excitation

• is the RMS current value at the kth harmonic

• is the RMS value of the complex waveshape

• is the ratio of the RMS value of the kth harmonic to the RMS value of the complex waveshape

rmsdc II 0rmsrms II 11

rmskrms IIk

.krmsI

rmsI

k

24

Nonsinusoidal Currents andMulti-Layer Winding Portion

Derive equivalent power density function

Where B1 is the ratio of conductor thickness to skin depth for the first harmonic

Sum results to derive equivalent winding thickness and effective window utilization

,0B iR,piB

RBRp 1iiequiv

02

1

22010 10,,

l

l

n

n1equiv

l1l

Cu

n

n1equiv

l

,0Bn

pnnBn

K

,0Bn

pnn

sn Thicknesing Portioalent WindLoss Equiv

10

2

10

2

,11

1

,11

25

Portion UtilizationSine Wave, No Insulation

Conductor Utilization In PortionNo Insulation

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0.00 1.00 2.00 3.00 4.00 5.00 6.00Portion Thickness (in skin depths)

KCuz

For portions less than 3 skin depths thick, utilization increases with increasing layers.

12

34

56

7Layers

Sum of 10 Harmonics

-2-1.5

-1-0.5

00.5

11.5

2

0 2 4 6 8 10 12 14

Phase (radian)

Am

plitu

de (n

orm

aliz

ed)

26

Conductor Utilization In PortionIL=0.5 δ IW =0.5 δ

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)

KCuz

Portion UtilizationSine Wave, Insulation Penalty

Maximum conductor utilization is achieved with single layer portions, but a large number of portions is required.

12

34

56

7Layers

Sum of 10 Harmonics

-2-1.5

-1-0.5

00.5

11.5

2

0 2 4 6 8 10 12 14

Phase (radian)

Am

plitu

de (n

orm

aliz

ed)

27

Loss Equivalent Portion ThicknessIL=0.0 δ IW =0.0 δ

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)

Equi

vale

nt T

hick

ness

(in

skin

dep

ths)

1

2

34

56

7

Layers

Loss Equivalent ThicknessSine Wave, No Insulation

Sum of 10 Harmonics

-2-1.5

-1-0.5

00.5

11.5

2

0 2 4 6 8 10 12 14

Phase (radian)

Am

plitu

de (n

orm

aliz

ed)

28

2 * Ip

Ip

Amplitude

radian

Ip

2 * Ip

)sin()cos()( tnnbtnnan

tf

Fourier Decomposition Of Theoretical Waveshapes

2/DC 2/DC- DC/2)-(1

2

... 5, 3, 1,

DC)2

sin(DC

80

22

n

nn

Ipb

a

n

n

... 5, 3, 1,0

DC)2

sin(4

nb

nnIpa

n

n

29

)sin()cos()( tnnbtnnan

tf

Fourier Decomposition Of Theoretical Waveshapes

DCDC- DC)-(2

2

... 3, 2, 1,

DC) sin( DC)-(1 DC

20

22

n

nn

Ipb

a

n

n

... 3, 2, 1,0

DC) sin(2

nb

nnIpa

n

n

2 * Ip

Ip * (1- DC)

Amplitude

radian

Ip

- Ip * (DC)

Ip

30

Loss Equivalent Portion ThicknessIL=0.0 δ IW =0.0 δ

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)

Equi

vale

nt T

hick

ness

(in

skin

dep

ths)

1

2

3

4

5

6

7 Layers

Loss Equivalent ThicknessComplex Wave, No Insulation

Sum of 10 Harmonics

-2

-1.5

-1

-0.50

0.5

1

1.5

2

0 2 4 6 8

Phase (radian)

Am

plitu

de (n

orm

aliz

ed)

31

Loss Equivalent Portion ThicknessIL=0.0 δ IW =0.0 δ

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Portion Thickness (in skin depths)

Equi

vale

nt T

hick

ness

(in

skin

dep

ths)

1

2

3

4

5

6

7 Layers

Loss Equivalent ThicknessComplex Wave, No Insulation

Sum of 10 Harmonics

-2

0

2

0 2 4 6 8

Phase

Am

plitu

de

32

Core Loss Introduction

33

Magnetic Material

• One Oersted is the value of applied field strength which causes precisely one Gauss in free space.

• Permeability is the relative gain in magnetic induction provided by magnetic material.

• Magnetic Material consists of matter spontaneously magnetized.– Magnetic Material in demagnetized state is

divided into smaller regions called domains.– Each domain spontaneously magnetized to

saturation level. – Directions of magnetization are distributed so

there is no net magnetization.– Crystal anisotropy and stress anisotropy

create preferential orientation of spontaneous magnetization within each domain.

– Magnetostatic energy is associated with induced monopoles on surface.

– Exchange energy resides in domain wall as a result of nonparallel adjacent atomic spin vectors.

– Domain structure evolves to achieve relative local minimum of total stored energy.

Iex

Φ

34

Magnetization Microscopic Effects

• Soft magnetic material provides increased magnetic induction from induced alignment of dipoles in domain structure.

• Magnetization process converts material to single domain state magnetized in same direction as applied field.

• Magnetization process involves domain wall motion then domain magnetization rotation.

• Low frequency magnetization characteristics for magnetic material display energy storage and dissipation effects.

• Material voids and inclusions =>irreversible magnetization (Br, Hc)

B

H

Hc

Br

35

Optimal Transformer Turns

36

Maximum J

CustomerLimit

MaximumWinding

Loss

ElectricalRequirements

(regulation,efficiency)

MaximumTemperature

Rise

Design Considerations AffectingCurrent Density: J

)( 2JLossCoil Considering insulation and eddy current penalties

37

)( BLossCore

Design Considerations AffectingFlux Density: ΔB

Maximum B

BpeakTransient

OCLLinearity

MaximumCore Loss

BpeakSteady State

ElectricalRequirements

(efficiency)

MaximumTemperature

Rise

Saturation

Where exponent β is determined through empirical core loss testing

38

• For given core and winding regions, J and ΔB function in a competing relationship.– Decreasing ΔB is equivalent to increasing turns of all

windings by the same proportion.– Increasing turns of all windings by a given proportion

generates proportionately higher current density.• For a linear transformer, selection of turns on any one

winding, uniquely determines J and ΔB densities and therefore total loss for a specific application.

J

ΔB

Selection Of Transformer Parameters: J , ΔB , KCu , KFe

39

p

corepcoil N

FNFr losstransformeTotal 2

• For given conductor and core regions, the normalized expression for low frequency winding loss can be extended and combined with an empirically derived core loss result to yield:

• Fcoil and Fcore relate exponential functions of primary turns (Np) to coil and core losses respectively.

• n is the empirically derived exponential variation of core loss with magnetic flux density.

• Without a constraint of core saturation, minimum transformer loss is achieved with primary turns:

implying =>

Selection Of Transformer Parameters

22

coil

corep F

FN

Insulation and eddy current impacts

2

LossWinding

LossCore

Empirical tests characterize core material in application conditions

40

2

sec

2

2

sec

sec

2

pp

windowCucoil

pp

pwindowCu

pp

pi

i

ii

VVAI

AKyF

NV

VAIAK

yLossCoil

NV

VAINI

NILossCoilFrequencyLow

Determination Of Fcoil

Reflects insulation and eddy current loss penalties

41

Determination Of Fcore

core

pcoreFecore

pcore

pcoreFe

coreFe

corep

p

fA

VKKVolumeFand

NfA

VKKVolumeCore Lossthen

BKVolumeLossCoreIf

AfN

VKB

0

0

0

1

,

Reflects empirical characterization of core loss for specific operating conditions and environment

42

Empirical Test: Verify

43

Φ

IsIp

leakageΦ leakageΦ

Transformer Realities

Winding loss

Leakage magnetic flux

Core Loss and Magnetic Energy applied to excite core

44

Coupled Coils

vp(t)

ip(t)

+

-Lp

is(t)

Ls

M , k

RL

+

-vs(t)

Zi

k is coupling coefficientM is mutual inductance

dtdiM

dtdi

L sppp v

dtdiL

dtdi

M ss

ps v

45

Finding k and M Empirically

spLLkM

shortedsecondary with sc inductanceprimary L re whe1 p

sc

LLk

vp(t)

ip(t)

+

-Lp

is(t)

Ls

46

vp(t)

ip(t)

+

-Lp

is(t)

Ls

M , k

RL

+

-vs(t)

Zi

Leakage Inductance

• Leakage inductance represented if Qp <<1

s

L

LR

pQ where Q1

)1()(p

2s

j

kLjRLL

jZ L

s

pi

47

Lumped Series Equivalent Test Method

Primary Lp Ls

Rp Rs

Secondary

ss

pp

p

ss

RLL

kR

)Lk(

RLIf

2

2

Resistance EquivalentPrimary

1Inductance Leakage EquivalentPrimary

,

48

Empirical Shorted Load Test

ip(t)

+

-Lp

is(t)

Zi

n

nfIn )(

n n

n n

nfIergyAverage EnMeasuredEnergyAverage

nfILossWindingMeasuredLossWindingAC

)]([

)]([

LossDC Winding LossAC WindingCoil Loss

49

Core Loss Test Method Challenges

• Core magnetization is nonlinear process with nonlinear loss effects so Fourier Decomposition may be problematic

• Application waveshapes are difficult to generate– Rectangular voltage– Triangular current– Commercial impedance test equipment is

based on sinusoidal testing at low amplitude• Accurate loss measurement for complex

waveshapes is challenging

50

Sine Voltage Loss Measurement Challenge

Measured Loss Error from Uncompensated Phase Shift vs Inductor Q

Sine Wave

0

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120

Q

Pow

er M

easu

rem

ent E

rror

Mul

tiplie

r (x

% p

hase

err

or)

Q of 100 causes power measurem

ent

error ~158x phase error

51

Empirical Open Load Testir(t)

+

-Lp

ip(t)

ZiParallel resonant capacitor

facilitates accurate loss

measurem

ent

52

Rectangular Voltage Loss Measurement Challenge

Rectangular Voltage Loss MeasurementPotential Time Delay

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (Period)

Nor

mal

ized

Am

plitu

de

VoltageCurrent

Loss Impact

Time Delay

53

Rectangular Voltage Loss Measurement Challenge

Loss Measurement Error vs Uncompensated Time Delay0.5 Duty Cycle (Q ~ 31.83)

-100

-80

-60

-40

-20

0

20

40

60

80

100

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Time Delay (% of Period)

Loss

Mea

sure

men

t Err

or (%

)

Rectangular Voltage Loss MeasurementPotential Time Delay

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (Period)

Nor

mal

ized

Am

plitu

de

VoltageCurrent

Time Delay0.05% period time delay causes

20% loss measurement error

54

Normalized Rectangular Wave Loss vs Duty Cyclecalculated from fixed core loss resistance

(α=β=2)

0

1

2

3

4

5

6

7

8

9

10

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Duty Cycle

Nor

mal

ized

Los

s Fixed VoltageFixed ET

Linear System AssumptionIllustrates Loss Variation(Function of Duty Cycle)

Duty CycleIncrease

Reverse Voltage

Increase

Fixed ET

Nonlinear loss variation

despite linear system

v(t)

+

-

i(t)

LR

55

Modified Core Loss Estimation

56

Notions for Modified Core Loss Calculation Method

• Characterize a given piecewise flux excursion using a sinusoidal equivalent derivative which provides same peak flux and average slope over the interval

• The resultant induced loss by this sinusoidal equivalent derivative will be weighted by the effective duty cycle of the induced loss

• Leverage benefits of sinusoidal empirical test methods

• Facilitate consistent and application relevant transformer core loss test results– Correct peak flux density– Consistent piecewise flux

derivative

[1]

Sinusoidal Equivalent DerivativeSED

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (Period)

Nor

mal

ized

Am

plitu

de

Sinusoidal Equivalent DerivativeSEDLinear Flux Trajectory

57

Further Loss Weighting

If instantaneous loss is presumed to vary with the power of the flux derivative [1]:

then a further weighting factor can be determined to scale the measured sinusoidal loss

Note that for an exponent greater than 1, sine wave voltage generated loss is greater than square wave voltage generated loss as demonstrated historically

dtdBtP densityflux peak fixed)(

Ratio of Sine Wave Loss to Square Wave Loss vs Alpha α

calorimetric

calorimetric

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1 1.2 1.4 1.6 1.8 2 2.2 2.4

Alpha α

Nor

mal

ized

Rat

io

58

Compare Three Core Loss Estimation Methods

• iGSE– Improved Generalized Steinmetz Equation [1]

• FHD – Fourier Harmonic Decomposition

• SED– Sinusoidal Equivalent Derivative

Initial comparisons will be based on Steinmetz power law representation as established for specific domains of sinusoidal excitation.

59

Comparison of Core Loss Calculation MethodsTriangular Flux ShapeFixed Equivalent Core Loss Resistanceα=β=2

Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=β=2)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=β=2)

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Methods consistently calculate loss for linear system

Duty CycleDuty Cycle

Duty Cycle = 1.0 Duty Cycle = 1.0

60

Comparison of Core Loss Calculation Methods Triangular Flux ShapeEddy Current Shielded Laminationα=1.5 , β=2

Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=1.5 β=2)

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=1.5 β=2)

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Derivative Based Methods Underestimate

Flux Crowding Impacts

Duty CycleDuty Cycle

Duty Cycle = 1.0Duty Cycle = 1.0

61

Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=1.71 β=1.95)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=1.71 β=1.95)

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Comparison of Core Loss Calculation MethodsTriangular Flux Shape 0.001 Permalloy 80 α=1.71 , β=1.96

Duty CycleDuty Cycle

Duty Cycle = 1.0Duty Cycle = 1.0

Potential Flux Crowding Im

pact

62

Calculated Core Loss: Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=1.5 β=2.6)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Calculated Core Loss: Quasi Triangle Wave(normalized to peak flux equivalent sine wave at fundamental frequency)

(α=1.5 β=2.6)

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Duty Cycle

Nor

mal

ized

Los

s

iGSE

FHD

SED

Comparison of Core Loss Calculation MethodsTriangular Flux Shape 3C85 Ferriteα=1.5 , β=2.6

Duty Cycle

Duty Cycle = 1.0

FHD underestimates ferrite triangular loss

Duty Cycle

Duty Cycle = 1.0

63

Calculated Normalized Harmonic Loss: FHD

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10

Harmonic Order

Nor

mal

izee

d to

Tot

alHarmonic Decomposition Problemα=1.5 , β=2.6

Sum of 10 Harmonics

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10 12 14

Phase (radian)

Ampl

itude

(nor

mal

ized

)

Sum of 1 Harmonic

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10 12 14

Phase (radian)

Ampl

itude

(nor

mal

ized

)

Presumed Significant Waveshapingwith Minimal Incremental Loss

64

Observations of Loss Methods• iGSE and SED deliver consistent loss estimates from

Steinmetz parameters since both methods presume instantaneous loss to be proportional to the power of the flux derivative

• SED facilitates meaningful empirical test implementation beyond mathematical application of Steinmetz equation:– Evaluates core capacity for application driven flux

density– Generates application rated average winding voltages– Generates rated instantaneous loss over flux excursion

interval– Facilitates resonant test methods for accurate and

consistent results in production environment

65

Evaluate Loss using Harmonic Coil Loss Analysis and SED Core Loss Estimating Method

66

Sum of 10 Harmonics

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10 12 14

Phase (radian)

Am

plitu

de (n

orm

aliz

ed)

Example Of Coil Harmonic Loss Testing

Total

Radian

168 W Forward Transformer 300 kHz3 Watt Maximum Winding Dissipation

Losses By Harmonic: 16 V in

0.0

0.5

1.0

1.5

2.0

2.5

3.0

DC 2 4 6 8 10Harmonic Order

Loss

(Wat

t)

Calculated

Actual (5 harmonics)

Losses By LayerTabtronics: 568-6078, 16 V in,

53% Duty Cycle

0.00.10.20.3

0.40.50.6

1 2 3 4 5 6 7

Layer Number

Loss

(Wat

t)

ACDC

67

Loss Summary168 W Forward Converter

DC

Coil

AC

Coil

AC

Core

Total

00.5

11.5

22.5

33.5

Loss Summary

Po

we

r L

oss (

W)

8 V, 21 A, 300 kHz

68

Other Observed Core Loss Factors

• Fundamental variables (peak field density, frequency, temperature)

• Biased operating application waveshape [2]• Flux density relaxation during circuit commutation

intervals• Flux crowding from eddy current shielding• Designed air gap => fringing effects• Nonuniform core cross sections => nonuniform

magnetic field densities => nonuniform loss density• Unintended micro-crack(s)• Mechanical Stress (magnetic anisotropy)• Irregular or mismatched core segment interfaces• Material manufacturing lot variances (unintended

substitutions !)

69

Core Loss Experiences

Transformer Loss (PSFB, 214W, 100 kHz)

Core Loss

Core Loss

Core Loss

Core Loss

Coil Loss

Coil Loss

Coil Loss

Coil Loss

0

1

2

3

4

5

6

7

20˚C 100˚C 100˚C Coated Type A 100˚C Coated Type D

Condition

Pow

er (W

atts

)

EFD20/10/7

Table 1: expected performance comparison on ungapped core set

Material NLP Terminals (4-5) 350Vrms @ 200kHz

20˚C

NLP Terminals (4-5) 350Vrms @ 200kHz

100˚C 3C94 1.92W 1.022W 3C96 2.05W 0.74W

(3C96 - 3C94) 0.13W -0.282W

Micro-cracks – Misalignment

>3x core loss increase

70

Summary

71

Recommendations

• Rigorously measure performance of magnetic components used in demanding applications prior to commencing production.– Use application relevant high frequency and high

amplitude test methods to ensure consistent application results throughout production.

• If the magnetics have significant impact on the end system’s market differentiation then a collaborative Design Partnership between power system developer and transformer developer will maximize the custom magnetics’ utility for the end system.– Capable and trustworthy design partners with

effective project management is necessary.

72

References

[1] J. Li,T. Abdallah, and C. R. Sullivan, “Improved calculation of core loss with nonsinusoidalwaveforms,” in Industry Applications Conference, 36th IEEE IAS Annual Meeting, vol. 4, pp. 2203-2210, 2001.

[2] J. Muhlethaler, J. Biela, J. W. Kolar, and A. Ecklebe, “Core losses under DC bias condition based on Steinmetz parameters,” in Proc. of the IEEE/IEEJ International Power Electronics Conference (ECCE Asia), pp. 2430–2437, 2010.

73

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