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Master Thesis

Doc. Title: Revision Page

Effect of harmonics on iron losses 01 2/70

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Summary:

This thesis investigates the effect of non-sinusoidal flux waveforms on iron losses through Epstein frame measurements.

The report includes a survey of empiric loss calculation methods. First, it is investigated how to find the loss coefficients for calculations of losses with sinusoidal wave forms. For this purpose, both new and previously obtained measurement data is used. Different methods to find the coefficients are studied and their short comings are pointed out. It is found that the curve fitting method using a series of measurements, ±4% agreement between empiric and experimental values is possible for wide range of frequencies (e.g. up to 400 Hz). This can be compared to ±30% difference for the constant coefficient method utilizing experimental data for only two test points.

Consequently, an experimental investigation is made on the iron loss in presence of harmonics. One or two harmonics are superimposed on the fundamental flux wave. The effects of both the harmonic amplitudes as well as the phase angles on iron losses are studied experimentally. It is observed that the phase angle between fundamental and harmonic waves is important for low order harmonics (e.g. 5th /7th) but has minor effect on higher order harmonics.

Further, a time domain analytical expression for calculation of iron losses with distorted waveform is recommended and it is found that the recommended expression gives ±10% agreement with the experimental results. However, it is shown that the impact of the phase angle is not covered using the said expression. The results also show that iron loss coefficients found using measurements with sinusoidal wave forms can be used for distorted waveforms as well.

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Effect of harmonics on iron losses 01 4/70 TABLE OF CONTENTS

1 INTRODUCTION....................................................................................................................................6 1.1 PURPOSE..........................................................................................................................................6 1.2 SCOPE..............................................................................................................................................6 1.3 DEFINITIONS .....................................................................................................................................6 1.4 STRUCTURE ......................................................................................................................................7

2 LITERATURE STUDY ON IRON LOSS CALCULATION.....................................................................8 2.1 CALCULATION OF IRON LOSS COMPONENTS ........................................................................................8 2.2 METHOD OF REDUCING IRON LOSSES ...............................................................................................10 2.3 EXPERIMENTAL SETUP FOR MEASUREMENT OF IRON LOSS................................................................11

2.3.1 Epstein frame.........................................................................................................................11 2.3.2 Toroid Tester..........................................................................................................................13 2.3.3 Single Sheet Tester (SST).....................................................................................................14

2.4 METHODS TO PREDICT IRON LOSSES WITH SINUSOIDAL WAVEFORM ...................................................14 2.4.1 Introduction ............................................................................................................................14 2.4.2 Determination of Loss Cofficients ..........................................................................................15 2.4.3 Conclusion .............................................................................................................................20

2.5 EVALUATION OF METHODS FOR LOSS PREDICTION WITH NON SINUSOIDAL WAVEFORMS........................20 3 MEASURMENT OF IRON LOSSES WITH NON SINUSOIDAL WAVE FORMS ...............................24

3.1 AUTHENTICITY OF MEASUREMENTS ..................................................................................................24 3.1.1 Accuracy ................................................................................................................................24 3.1.2 Repeatability ..........................................................................................................................25

3.2 BLOCK DIAGRAM OF EXPERIMENTAL SETUP.......................................................................................26 4 EFFECT OF A SINGLE FLUX HARMONIC ON IRON LOSSES........................................................27

4.1 FUNDAMENTAL FREQUENCY 50 HZ...................................................................................................27 4.1.1 5th Harmonic..........................................................................................................................27 4.1.2 7th Harmonic..........................................................................................................................31 4.1.3 11th Harmonic........................................................................................................................33 4.1.4 13th Harmonic........................................................................................................................35 4.1.5 Conclusion .............................................................................................................................35

4.2 FUNDAMENTAL FREQUENCY 30 HZ...................................................................................................37 4.2.1 5th Harmonic..........................................................................................................................37 4.2.2 7th Harmonic..........................................................................................................................39 4.2.3 11th Harmonic........................................................................................................................41 4.2.4 13th Harmonic........................................................................................................................43 4.2.5 Conclusion .............................................................................................................................44

4.3 FUNDAMENTAL FREQUENCY 70 HZ...................................................................................................44 4.3.1 5th Harmonic..........................................................................................................................44 4.3.2 7th Harmonic..........................................................................................................................46 4.3.3 11th Harmonic........................................................................................................................47 4.3.4 13th Harmonic........................................................................................................................48

4.4 FUNDAMENTAL FREQUENCY 5 HZ.....................................................................................................49 5 EFFECT OF TWO FLUX HARMONICS ON IRON LOSS...................................................................50

5.1 FUNDAMENTAL FREQUENCY (50 HZ) ................................................................................................50 5.1.1 Effect of the 5th and 7th harmonic.........................................................................................50 5.1.2 Effect of the 5th and 13th harmonic.......................................................................................53

5.2 FUNDAMENTAL FREQUENCY 30 HZ...................................................................................................54 5.2.1 Effect of the 5th and 7th harmonic.........................................................................................54 5.2.2 Effect of the 5th and 13th harmonic.......................................................................................56

5.3 FUNDAMENTAL FREQUENCY (70 HZ) ................................................................................................57 5.3.1 Effect of the 5th and 7th harmonic.........................................................................................57

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5.3.2 Effect of the 5th and 13th harmonic.......................................................................................59 5.4 CONCLUSION ..................................................................................................................................60

6 CONCLUSIONS...................................................................................................................................62

7 FUTURE WORK ..................................................................................................................................64

8 REFERENCES.....................................................................................................................................65

9 ENCLOSURES ....................................................................................................................................67 9.1 APPENDIX – 1..................................................................................................................................67 9.2 APPENDIX – 2..................................................................................................................................68 9.3 APPENDIX – 3..................................................................................................................................69 9.4 APPENDIX – 4..................................................................................................................................70

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1 INTRODUCTION

1.1 Purpose

Nowadays, variable speed drives are becoming more and more popular. Variable speed is achieved by use of an inverter. Inverter fed drives experience more iron loss as compared to directly connected ones. The increase in iron loss is a result of the harmonics introduced by the inverter supply and can effect both the lifetime of a machine and efficiency as well. Therefore, it becomes important to have a fair idea about the effect of iron loss. The suggested thesis work deals with quantifying the iron loss due to harmonics. The effect of different harmonic amplitude and effect of phase difference is also studied.

1.2 Scope

This report aims to quantify the increase in iron loss due to introducntion of different time harmonics in the fundamental alternating flux wave. The effect of amplitude and phase angle due to presence of one as well two harmonics are studied. The results described in this report are based upon the experiments made both at Surahammar Bruks AB and KTH. It is to be noted that this report does not describe the iron loss associated with the rotational flux density.

1.3 Definitions

P hys Hystereses Iron loss component

P classical Classical iron losss component

P excess Excess iron loss compenent

P total Total iron loss

n Hystereses loss exponent

Kh Hystereses loss coefficient

Ka Excess loss coefficient

Ke Classical loss coefficient

f Frequency

Bmax Peak flux density

l Length of test specimen strip

ma Active mass of test specimen

d Thickness

� Electrical Conductivity

Ch Hystereses loss correction factor

N1 Total number of primary winding turns

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N2 Total number of secondary winding turns

pw Power measured by wattmeter

W Specific iron loss in W/kg

1.4 Structure

This report has the following structure:

Chapter 2 makes an overview of some previous work that were done in order to understand and predict iron loss with sinusoidal as well as non sinusoial wave forms.

Chapter 3 explains the experimental setup used for measurments for iron loss. Accuracy and repeatability of the setup is also discussed.

Chapter 4 presents the results obtained from measurments in presence of one harmonic at different fundamental frequencies. Observation and conclusions are also made on bases of these measurments.

Chapter 5 investigates the effect of the presence of two harmonics on iron loss.

Chapter 6 presents the conclusion of this thesis work and relates the theory with results made on basis of the Epstein frame measurments during the thesis work.

Chapter 7 includes some recommendations for the future works.

Chapter 8 Specifies a list of references for source material and further reading.

Chapter 9 Encloses some supplementary information.

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Effect of harmonics on iron losses 01 8/70 2 LITERATURE STUDY ON IRON LOSS CALCULATION

In order to calculate iron loss in electrical machines, it is essential to have the information of shape or variation of the flux density. Flux density variation can be alternating or rotational [1]. Alternating flux density can further divide in to sinusoidal or non sinusoidal (due to presence of different harmonics). Depending on the magnitude of the harmonic; non sinusoidal flux density may or may not cause minor loops in the BH loop. On the other hand, rotational distribution of the flux density can also be subdivided in to circular and elliptical (in the case of orthogonal flux density components sinusoidally varying in time with different amplitudes). This can yet be distorted (almost any shape), as happens in the case when alternating distribution in one of the directions is non- sinusoidal. In the case of the alternating flux, there is a quite well known theory, which is generally accepted and essentially based on the works of Bertotti, Fiorillo and Novikov [1]. As for the rotational loss, the situation is not so clear and the problem of measuring and calculating the rotational loss has not yet been completely resolved [1]. In the following part; iron loss calculation due to alternating flux density (sinusoidal and non-sinusoidal) will be discussed.

2.1 Calculation of Iron loss components

2.1.1 Iron loss calculation with sinusoidal wave forms Traditionally iron loss had been divided up in to two components, hysteresis loss “Phys” and eddy current or classical loss “Pclassical”. Therefore iron loss was expressed by (2.1). A brief description of each part is given below.

classicalhysTotal PPP += 2.1 i) Hysteresis loss The energy required to move the magnetic domain walls in the core magnetization is called hysteresis loss. The hysteresis loss can be calculated using the empirical Steinmetz formula

BfkP n

hhys max= 2.2

Where “Kh” and “n” are coefficients depending upon the magnetic material used, “f” is the frequency and “Bmax” is the peak flux density. ii) Classical loss Classical losses are caused by circulating currents in the core induced by flux variation. It can be calculated as

6

2max

222 BfdP classical

σπ=

2.3

The equation 2.3 is valid only when flux penetrates in material completely; In other words, the lamination thickness must be smaller than the skin depth.

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f

µπρ<d 2.4

Where “�” is the electrical conductivity, “d” is the thickness and “�” is the resistivity of the lamination. However, equation (2.1) has some limitations as some papers describes that it is only applicable under the assumption that the maximum magnetic flux density of 1.0 T is not exceeded and the Hysteresis loop is under the static situation [17]. When P hys and P classical are added together, the sum is always less than the measured total loss, the difference being referred to as the anomalous or excess loss. The excess loss accounts for 20 % or more of the total loss in electrical steels. In other materials it can comprise 90 % of the loss [3]. The excess loss can be described as below. iii) Excess loss These losses are caused by parasitic micro-currents with high frequency that circulate around of the wall domain in the move of material magnetization. It can be calculated as

fBKp aexcess5,15,1

max= 2.5

Where oa GSVK σ= 2.6

“�” is conductivity of the material, “G” and “Vo” are constants which appear to be material and magnetization condition dependent, and “S” is the cross sectional area of the material. Therefore, now total iron loss can be represented by (2.6), which is a modification of (2.1).

excessclassicalhysTota PPPP ++= 2.7 2.1.2 Iron Loss calculation with non-sinusoidal wave forms i) Hysteresis loss With introduction of harmonics, minor loops are the only thing that influences the hysteresis loss. Minor loops appear due to the occurrence of flux reversal in the flux density wave form which is due to the presence of different harmonics components. The flux density reversal depends on the magnitude as well as the phase angle of the harmonics [18]. There are some other factors that effects the magnitude of minor loops i.e. the order of harmonic components (higher order harmonic component gives more flux reversal in number and magnitude), total peak flux density (fundamental plus harmonic) and location of the minor loops (loops near saturation will cause larger loops and more losses). If the flux density waveform causes minor loops, the actual hysteresis loop area is required for the Hysteresis loss per cycle; the equation (2.2) is no more valid. Lavers [18] suggest a method, as given below

BfkCP n

hhhys max= 2.8

Where “Ch” is the Hysteresis loss correction factor, which is

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�=

+=N

iih db

Bk

C1max

1 2.9

Where “k” varies between 0.6 and 0.7 and dbi, i = 1,2,…, n, represents the flux reversals of the flux density waveforms (the change in the flux density during the excursion around a minor loop). If the minor loops do not occur, the hysteresis loss does not depend on the flux density waveform and is only related to the peak value of flux density. In that case equation (2.2) is still valid. ii) Classical loss The expression for calculation of iron loss for non-sinusoidal flux can be represented as

�∞

==

0

22222

6 nnclassical Bn

fdP

σπ 2.10

where “Bn” are the harmonic flux densities. iii) Excess loss Similarly, the expression for under non-sinusoidal flux can be represented as

dtdtdB

Tp

T

excess �=0

5,11

2.11

2.2 Method of reducing Iron Losses

Following are some methods used to reduce iron losses:

a) Lamination: The core is built up by thin lamination sheets piled on each other and insulated from each other. This has an effect of reducing eddy currents.

b) Alloying: Iron is a good conductor and it is found that the addition of alloying elements increase the electrical resistivity of iron which could help in reducing eddy current intensity. This is normally done by adding silicon contents. A drawback of this method is that the introduction of silicon makes iron brittle and difficult to roll and form.

c) Purification (and annealing): In a soft magnetic material the domains need to be able to alter their disposition rapidly and easily according to overall magnetization of the metal. Things that can hold up the easy movement of domain walls damage this intention. Any non-metallic inclusions in the metal impede domain activity, so great efforts are made to purify electrical steels. Other magnetic in-homogeneties spoil domain activity, such as stressed regions and dislocations of the crystal lattice. Careful heat treatment (annealing) can remove most of these.

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Effect of harmonics on iron losses 01 11/70 d) Grain Size: Since the boundaries between adjacent crystals amount to magnetic in-homogeneities, the less grain boundaries there are the better. As a consequence, efforts are made to end up with grains as large as can be managed as this facilities domain boundary motion.

2.3 Experimental Setup for Measurement of Iron Loss

2.3.1 Epstein frame

The Epstein frame is the most popular equipment used in industry to measure specific iron loss. The detailed operating instructions are described in the international standard IEC 404-2.

The industrial standard frame is usually a 28 cm x 28 cm frame with four coils each having 700 turns both on the primary and the secondary windings [9]. Each side have a primary winding (magnetising winding) on the outer side and a secondary winding (voltage winding) on the inner side as shown in Fig. 2.1.

Fig. 2.1 Epstein frame

The investigated steel samples (strips) should be 28 cm long (±2.05 cm) and 3 cm wide and must be of multiple of 4, with a recommended minimum number of 12 strips. Strips cut across the rolling direction are loaded on the opposite sides of the frame, while those cut along the rolling direction are loaded on the opposite sides. The strips are loaded in the Epstein frame making double-lapped joints as shown in Fig. 2.2.

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Fig. 2.2 Test specimen arrangements in the Epstein frame (double-lapped joint)

The total iron-loss of the test specimen, is given by

( )i

mc R

UP

NN

P

22

2

111,1

−= 2.12

where N1 and N2 are the total number of turns of the primary and secondary winding, “Pm” is the power measured by the wattmeter, “Ri” is the total resistance of the instruments in the secondary circuit and 2U is the average value of the rectified voltage induced in the secondary

winding.

The measured specific total loss, W in W/kg is obtained by dividing “Pc” by the weight of the active mass of the test specimen. Mass of the part of specimen where flux lines are existing is called the active mass.

m

c

a

c

mllP

mP

W4

== 2.13

Where “l” is the length of a test specimen strip, “lm” is the conventional effective magnetic path length and m is the total mass of the test specimen.

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Fig. 2.3 Circuit used to calculate specific loss in the Epstein frame

Some of the shortcomings of this method are that flux density is not uniformly distributed due to leakage flux around the joints [9]. The corners have been found to cause errors. The magnetic length (94 cm) is estimated and is not an accurate value. The 3 cm strips width is not wide enough for cutting stresses not to propagate to the centre of the strips and influence the loss results. Therefore, the material under test must be annealed to relieve stress before testing, especially for grain-oriented steel. The preparation and loading of the strips on to the frame is time consuming [9]. The magnetic flux conditions in the Epstein frame correspond to those found in power transformers where good correspondence between calculation and measurements is obtained. However, such correspondence is not observed for induction motors, where the error from the Epstein test results can be larger than 50% [11].

The standard Epstein test does not include the effect of the flux harmonics that exist in induction motors, since sinusoidal excitation at the fundamental frequency is specified [11]. To perform core loss measurements in electrical steel samples under non-sinusoidal excitation, various test benches are built based on the Epstein frame [11], [12] and [13].

2.3.2 Toroid Tester

The toroid has primary and secondary windings with excitation applied to the primary and the induced voltage measured on the secondary. Toroid geometry is more similar to the geometry of a stator in an electrical machine [14], hence some people prefers toroids over Epstein frames. One of the problems with toroids is the non uniform distribution of flux density.

Fig. 2.4 Geometrical characteristic of the core assembled using two concentric rings

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Effect of harmonics on iron losses 01 14/70 A disadvantage of this tester is that the toroid must be properly wound, which is time consuming compared to the Epstein frame. The toroidal tester takes longer to prepare and set up for testing.

2.3.3 Single Sheet Tester (SST)

In some of the research papers it is mentioned that due to a considerable easier sample preparation and substantial saving of material, the single sheet tester (SST) with yokes is increasingly replacing the Epstein frame [15] and in the future, SST may become the preferred method [9]. In another paper [16], the single sheet method is stated to be the most precise and economic one for magnetization characteristics measurement of the magnetic steel sheets, as compared to Epstein frame and ring specimen method. A small description for the measurement principle of SST is given as below, see Fig. 2.5.

Fig. 2.5 Measurement principle of SST

The significant difference between the single sheet method and the conventional method is that in SST, an H coil is used for the measurements of magnetic field strength [16]. While a separate B coil is used to measure flux density.

A major drawback of this tester is that it requires calibration with either an Epstein frame or a toroid tester. Moreover, the international standard recommends a double yoke tester which is heavy, costly and large. Further some pneumatic suspension may be required to place the yoke on the magnetic sheet to avoid damaging the sheet [9].

2.4 Methods to predict Iron Losses with sinusoidal waveform

2.4.1 Introduction

The modelling of power losses in Ferro-magnetic material has been continuously under study. As described in section 2.1, Jordan defined the Hysteresis and eddy-current components on

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Effect of harmonics on iron losses 01 15/70 which the analysis of electrical machines is still based [4]. Bertotti proposed a model including third term excess or anomalous loss [5]; mathematical formulation is given as below.

PPPP excessclasshysTotal++=

2.14

fBKBfd

BfKP a

n

hTotal5,15,1

max

2

max

222

max737,8

6++=

σπ 2.15

The most difficult part in finding a correct prediction of iron loss is the determination of loss coefficients. Different researchers have proposed different methods for loss coefficient calculation. A few of those are explained in the following section.

2.4.2 Determination of Loss Cofficients

Constant coefficient Method

One approach of calculating loss coefficients is calculating the classical loss component by the formula stated above (2.21) and assuming n = 2. Using experimental values of total specific iron losses measured from the Epstein frame it is possible to determine the unknown coefficients (Kh & Ka). Hence two unknown coefficients (Kh and Ka) can be found by two known values of specific losses at two different values of flux density or frequency. Figure 2.6 shows the results obtained using the said method. It is observed that using this approach, the difference between calculated and experimental values may become high. For example, coefficient determined at 50 and 60 Hz at 1.5 T fails to give good agreement at 50 or 60 Hz at other values of flux densities (e.g. difference of 14% is observed in case of 1.0 T).

-10

-5

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400 450

Frequency ( HZ ) ( Kh,Ka calculated at 50, 60 Hz at 1,5 T )

Diff

eren

ce (

%)

1.5 T1.4 T1.3 T1.2 T1.1 T1.0 T0.9 T0.8 T0.7 T

Fig. 2.6 Difference B/W measured and calculated values (Ref. Measured values)

Iron loss prediction using curve fitting methods

There are several approaches to find the loss coefficients which are based on curve fitting. One of these methods is described by ( Fig. 2.7). In this method, a graph of the specific loss

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Effect of harmonics on iron losses 01 16/70 (measured from the Epstein frame) versus frequency at a given value of (B or specific loss versus B at a given frequency) is plotted. Similarly, a plot of specific losses calculated by using (2.21) is drawn by assuming some values of kh and ka. Then the relative differences of both values are observed. The values of kh and ka that gives low relative difference are selected.

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500Frequency

Loss

es (w

/kg)

Experimental Values

Analytical Values

Fig. 2.7 Curve fitting Method

There are many other models that claim to give good agreement between calculated and measured loss values e.g. [4], [5], [6], [7]. In the following section, the approach discussed in [4] is studied and implemented for the M400-50A material, together with some suggested changes.

In the first step of the procedure, in order to identify the values of the coefficient, (2.14) is divided by the frequency, resulting in

( )2fcfba

fW ++=

2.16

Where Bka h= 5.1Bkb a= 2Bkc e= 2.17

Using (2.16) and (2.17), values of a, b and c can be calculated using quadratic fitting as shown in Fig. 2.8 .

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y = 0,0004x2 + 0,0013x + 0,0416

0

0,05

0,1

0,15

0,2

0,25

0 5 10 15 20 25

Square root of frequency [Hz]

Spe

cific

Los

s pe

r Fr

eque

ncy

[W/K

g/H

z]

0,1 T0,2 T0,4 T0,5 T0,6 T0,8 T1,0 T1,1 T1,2 T1,3 T1,4 T1,5 TPoly. (1,5 T)

Fig. 2.8 Ratio of core loss and frequency w/f, as function of Sqrt (f) according to (2) for 812737 F Steel

During trials, it is observed that a use of five sample points, represented by measurements at the same induction and different frequencies, is beneficial in improving the overall stability of the numerical procedure [4],[9]. In this case, measurements at one low frequency of 30 Hz, one intermediate frequencies of 50, 100 and 250 Hz and one high frequency of 400 Hz are used. The derivation and use of single ka and ke, as a polynomial function of induction for the entire frequency range introduces very large errors and hence it is recommended to split the data and perform fitting separately on three frequency ranges identified as low (up to 400 Hz), medium (400 to 1000 Hz) and high [9]. The values of the fitting residual for (2.16) were very close to unity i.e. r2, indicating a very good approximation. From (2.16) and (2.17), the eddy-current coefficient ke and the excess loss coefficient ka are calculated. These coefficients are independent of frequency [4]. Third order polynomials were employed for curve fitting of ke and ka as shown in Fig. 2.9 and Fig. 2.10. Then, r2 of 0,94 and 0,92 are obtained for ka and ke.

3

32

210 BkBkBkkk eeeee +++= 2.18

33

2210 BkBkBkkk aaaaa +++= 2.19

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y = -0,0002x3 + 0,0006x2 - 0,0004x + 0,0001

0,00E+00

2,00E-05

4,00E-05

6,00E-05

8,00E-05

1,00E-04

1,20E-04

1,40E-04

1,60E-04

1,80E-04

2,00E-04

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6Induction [T]

Coe

ffic

ient

Ke

[W/K

g/H

z^2/

T^2]

Fig. 2.9 Variation of eddy-current loss component coefficient ke with magnetic induction; ke is independent of

frequency

y = 0,0002x3 - 0,0029x2 + 0,0035x + 0,0007R2 = 0,9431

0,00E+00

2,00E-04

4,00E-04

6,00E-04

8,00E-04

1,00E-03

1,20E-03

1,40E-03

1,60E-03

1,80E-03

2,00E-03

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Induction [T]

Coe

ffic

ient

Ka

Fig. 2.10 Variation of excess (anomalous) loss component coefficient ka with magnetic induction; ka is

independent of frequency

The coefficient “z” represents the ratio of hysteresis loss and frequency, which is calculated from (2.16) by substituting the values of b and c from (2.17) and making use of (2.18) and (2.19). In order to calculate kh and n the following equation was used.

Bnkz h logloglog += 2.20

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Effect of harmonics on iron losses 01 19/70 The plot of logz against induction at a set frequency indicates two intervals of different variation types, which can be approximately set to induction ranges of 0,1 to 0,3 and 0,4 to 1,5 T as shown in Fig. 2.11.

-9

-8

-7

-6

-5

-4

-3

-2

-1

00 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Induction [ T ]

Log

z [W

/Kg/

Hz]

Fig. 2.11 Logarithm of ratio of hysteresis loss and frequency for M400 (822158)

Calculation of core losses using the method described above shows good agreement between experimental and calculated values. Maximum difference is observed at low values of flux density (e.g. difference of -4.16% is observed at 0.2 T) as shown in Fig. 2.12

-5

-4

-3

-2

-1

0

1

2

3

4

30 50 100 250 400

Frequency (Hz)

Diff

eren

ce (%

)

0,1 T0,2 T0,3 T0,4 T0,5 T0,6 T0,7 T0,8 T0,9 T1,0 T1,1 T1,2 T1,3 T1,4 T1,5 T

Fig. 2.12 Difference B/W measured and calculated values (Ref. Measured values)

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Effect of harmonics on iron losses 01 20/70 2.4.3 Conclusion

Depending on the experimental data available and accuracy required, someone can select any of the method described above. For example if very little experiment data is available, one would have no choice except to adopt the constant coefficient method. On the other hand, accuracy of the result has to be compromised a bit. Similarly, curve fitting methods needs a lot of experimental data but results in very good accuracy.

2.5 Evaluation of methods for loss prediction with non sinusoidal waveforms

Iron loss per cycle can mainly be divided in to two parts [18], [23]. One is frequency independent (hysteresis loss or static loss) and the other is varying with frequency (“eddy + excess loss” or dynamic losses). One way of finding hysteresis loss is to excite a test specimen at very low frequency and measure the iron loss. The iron loss at such a low frequency will represent Hysteresis loss as the eddy currents induced in the test specimen will be negligibly small [24]. However when higher frequencies are involved the effect of the frequency dependent part will make the BH loop broader. Keeping above mentioned facts in mind one can say that when higher frequencies are involved there is no or a small increase in the hysteresis loss component. On the other hand, the effect on dynamic loss components will be much higher. Therefore, in the following discussion when comparing experimental measured iron losses with calculated iron losses from analytical expressions, we will assume that the effect of harmonics on Hysteresis loss component is small. The relative difference between measured and calculated iron losses also support the simplification that if we ignore the effect of harmonic on hysteresis loss still an acceptable amount of accuracy can be achieved.

In literature, quite a few methods to predict iron loss with non-sinusoidal flux wave forms can be found. These methods are based on the prior information about the iron loss with sinusoidal waveforms. Most of the researchers have proposed different methods for loss prediction with and without minor loops [1], [9], [19], [20]. The method explained in [1] is already discussed in section 2.1. Whereas [18] has proposed a method comprising of different imperial multiplying factors for hysteresis and eddy loss components without reveling any details about these. Marubbini [22] has proposed a method that accounts both for sinusoidal and non-sinusoidal wave forms. It can be expressed as

�� +��

��

�+= dtdtdB

TKdt

dtdB

TKPP

aehTotal

5.12

11 2.21

Equation (2.21) is similar to the sum of equations (2.2, 2.3, and 2.4). The big difference is that equation 2.21 is in time domain, in order to account for the presence of harmonics in the flux wave forms. As a consequence, Ke must be divided by 2�2 and ka by (1.41�) 1.5 in case of a pure sinusoidal waveform. For the sake of simplicity and because less knowledge of material science is needed, equation 2.21 is preferred to calculate the iron losses, and later on compared with experimental results. Phys, Ka and Ke can be calculated using any method explained in the early part of this chapter. However, the detail of another method used by [23] that is widely used and gives relative good results is explained below.

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Effect of harmonics on iron losses 01 21/70 In this method, information about the total iron loss at different frequencies and at a particular flux density is required. In order to explain the method, an example to calculate the individual loss components at 1.5 T is given. Total iron losses (WT) for 1.5 T at three different frequencies (30, 50, 100 Hz) are measured using the Epstein frame method. At each frequency the total iron loss (WT) is subtracted from the eddy current loss (We) and scaled by dividing by frequency; (WT- - We) / f, whereas eddy current loss is calculated using equation 2.6. Now a graph is drawn between scaled losses and the square root of frequency, as shown in Fig. 2.13 .

Fig. 2.13 Loss separation

The interception with the y-axis gives hysteresis loss and the excess loss can be calculated by subtracting eddy current and hysteresis from total loss. Ka is now calculated from excess loss while Ke is from eddy current loss component. Once hysteresis loss, Ka and Ke is known equation 2.27 can be used to calculate the iron loss with distorted waveforms. The Fig. 2.14 and Fig. 2.15 show the difference between calculated and measured iron losses.

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 0.052

0.054

0.056

0.06

0.062

0.064

Square Root of Frequency

y = 0.0023*x + 0.041

Data 1 Linear

(W total - W eddy) / f

Master Thesis



Fig. 2.14 Comparison of measured and calculated values (Ref. Measured Values)


It is observed that in case of 20% 5th and 7th harmonic the calculated losses are less then the measured losses. This is due to that we assumed that hysteresis losses will not increase with introduction of harmonics. This difference can be acceptable and it can conclude that equation 2.27 can be used to predict iron loss in machine with fair amount of accuracy in the circumstances where many researchers agree that any methods which results in ±10% accuracy is good enough [22].

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -8

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0

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6

Peak Flux density (T)

10% 5th 10% 7th 10% 11th 10% 13th

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -15

-10

-5

0

5

10


20% 5th 20% 7th 20% 11th 20% 13th

Difference (%)

Difference (%)

Master Thesis


Effect of harmonics on iron losses 01 23/70 Similarly if we compare the calculated and measured losses in case of two flux harmonics we also came to the same result that still equation 2.27 can be used to predict the iron loss with fair amount of accuracy (See Fig. 2.16 and Fig. 2.17).



0 0.2 0.4 0.6 0.8 1 1.2 1.4 -2

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10% 5th + 10% 7th

0 0.2 0.4 0.6 0.8 1 1.2 1.4 -10

-5

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15


10% 5th + 10% 13th

Difference (%)

Difference (%)

Master Thesis


Effect of harmonics on iron losses 01 24/70 3 MEASURMENT OF IRON LOSSES WITH NON SINUSOIDAL WAVE FORMS

The following section describes accuracy and repeatability of apparatus used for measuring iron loss. The measurements were performed at KTH, Stockholm. The measurements from the said setup are compared with the measurements obtained from apparatus at Cogent, Surahammar. The apparatus at cogent is believed to be accurate and according to international standards.

In the end of this section, a brief description about the experimental setup used for measurements is given.

3.1 Authenticity of Measurements

3.1.1 Accuracy

Iron losses at different frequencies were compared with the losses measured from apparatus at Cogent. Fig. 3.1 shows the difference between the two measurements (Ref. measurements at cogent).

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0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

B (T)

Diff

eren

ce (%

)

50 Hz30 Hz

Fig. 3.1 Comparison b/w cogent and KTH measurements (Ref. Cogent)

Following important observation are made from Fig. 3.1.

• Nearly same results are obtained for 30 and 50 Hz.

• Maximum difference is observed at low and high value of induction.

• Difference is positive (losses measured with KTH apparatus are higher) at low value of peak flux density (<0.3 T).

• Difference is negative (losses measured with KTH apparatus are lower) at high value of peak flux density (>1.2 T).

Master Thesis



• Good agreement of measurements is obtained at flux densities between 0.3 T to 1.2 T.

Therefore we can conclude that the apparatus used during the thesis work is very accurate from 0.3T to 1.4T. A small difference at very high flux density will make no difference in comparative study.

3.1.2 Repeatability

Repeatability is another parameter that indicates the credibility of measurements. Repeatability of apparatus was also checked at different frequencies and the results found are shown in Fig. 3.2 and Fig. 3.3.

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B (T)

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%)

Experiment No. OneExperiment No. Two

Fig. 3.2 Repeatability at 30 Hz

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B (T)

Dif

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nce

(%)


Fig. 3.3 Repeatability at 50 Hz

Master Thesis


Effect of harmonics on iron losses 01 26/70 Following important conclusions are made from Fig. 3.2 and Fig. 3.3.

• Repeatability at 30 Hz for lower values of induction (< 0.4T) has the maximum difference of 7%, while for higher value of peak flux density it is less then 2%. This even improves with increasing values of peak flux density.

• At 50 Hz for lower values of induction (< 0.4T) has the maximum difference of 2.3%, while for higher value of induction it is less then 1%.

• Repeatability graph at 70 Hz (See annexure-4) shows good agreements between experiments with maximum difference of 2.2 % at 3 T.

• Repeatability graph at 5 Hz (See annexure-4) also shows good agreements between experiments with maximum difference of 1.2 %.

3.2 Block diagram of Experimental setup

Fig. 3.4 Block diagram of apparatus

A block diagram of the experimental setup is shown in

Fig. 3.4. A computer is used as a signal generator, controller as well as data recorder. The programming is made in Simulink. The compiled program is then downloaded to a dSpace system. Real time control of different parameters such as the amplitude of the fundamental, harmonics as well as the phase angle is possible via a graphical interface. Digital to analogue converters supplies the amplifier with input signals. The signal is amplified by an amplifier and fed to the Epstein frame.

A flux-meter and an ampere-meter are used to record flux and current through the Epstein frame. The flux values are used in a feed-back loop so that it is possible to specify the flux wave-form (i.e. the B-field) instead of the current wave-form (i.e. the H-field). Iron loss is calculated by integrating the area of BH loop.

Simulink

dSPASE

DAC Amplifie

Computer

ADC

A

Flux Meter

Epstein frame

Master Thesis


Effect of harmonics on iron losses 01 27/70 4 EFFECT OF A SINGLE FLUX HARMONIC ON IRON LOSSES

To understand the effect of harmonic on iron loss, a quantitative study of the 5th, 7th, 11th and 13th harmonic with different fundamental frequencies is made. Fundamental frequencies of 5, 30, 50 and 70Hz are selected, as a wide range of the machines operates in these frequencies.

Different graphs are shown to indicate the percentage increase of iron loss in presence of each harmonic. Effect of the harmonic amplitude and phase angle is discussed. Reasons for increase in loss iron with respect to pure sinusoidal wave (non harmonics) as well as the effect of change in phase angle are also explained.

4.1 Fundamental Frequency 50 Hz

4.1.1 5th Harmonic

4.1.1.1 Effect of harmonic amplitude

In order to analyze effect of the 5th harmonic on iron losses, different percentage of the 5th harmonic were introduced on the fundamental frequency (50 Hz). Fig. 4.1 and Fig. 4.2 show the trends observed.

Fig. 4.1 Specific loss due to introduction of the 5th harmonic

0 0.5 1 1.5 0

0.5

1

1.5

2

3

3.5

4

Fundamental peak flux density B (T)

Sin With 20% 5th harmonic With 15% 5th Harmonic With 10% 5th harmonic

Specific Loss (w/kg)

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40

50

60

70

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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ce (%

)20 % Harmonic15 % Harmonic10 % Harmonic

Fig. 4.2 Effect on Iron loss due to introduction of the 5th harmonic (Ref. Sin)

Following observations are made from Fig. 4.1 and Fig. 4.2

• Increase of loss is observed with increase of magnitude of 5th harmonic.

• Gradual increase in iron loss up to 1.2T.

• At higher values of peak flux density there is less effect of introduction of the 5th harmonic as the core is already saturated and that results in a sharp decrease ( see figure 4.2 ) at higher values of peak flux densities (>1,2 T).

• A maximum Increase of 58% in case of 20% of the 5th harmonic, 37% in case of 15% of the 5th harmonic and 20% in case of 10% of the 5th harmonic is observed.

4.1.1.2 Effect on the BH loop

Fig. 4.3 shows minor loops existence due to the presence of the 5th harmonic at 1.1 T.

It can be seen that minor loops are generated with introduction of 20% 5th harmonics as shown in figure 4.3; however area of minor loop is not so large and no minor loop generation is observed in case of 10% and 15% of the 5th harmonic.

Master Thesis



Fig. 4.3 Effect of 5th harmonic on BH curve

4.1.1.3 Effect of phase angle

The effect of phase angle on iron loss was studied at different phase angles (30, 60, 90 and 120 degrees). Fig. 4.4 shows the effect of different phase angles for 20% of the 5th harmonic.

It can be seen that the effect on iron loss increases with increasing phase difference and a small phase difference has little effect on iron losses, such as in the case of 30 degrees and 60 degrees the effect is very small. On the other hand, high phase angle difference plays an important role. In fact a decrease in losses is observed for flux densities less than 1.1 T. This is due to the fact that an introduction of the 5th harmonic with increasing phase shift causes a reduction of total flux density. A typical example of a phase shift of 90 degrees with 20% of the 5th harmonic is shown in Fig. 4.5. It is further observed that the differences above 1.1 T first decreases and eventually ends up with increase in the iron loss that can be contributed to the following factors:

• The core gets more saturated in case of the phase angle of zero degrees due to a relatively high peak flux density.

• The occurrence of minor loops near to saturation results in an increase of the minor loop area itself, as seen in Fig. 4.6.

Similar kinds of trend of iron losses are observed with 15% and 10% of the 5th harmonic.

-200 -100 0 100 200 300 400 500 -1.5

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1.5

H(A/m)

B (T) Minor Loops

Master Thesis



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0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

B (T)

Diff

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ce (%

)30 degree 60 degree 90 degree120 degree

Fig. 4.4 Effect of Phase angle with 20 % of the 5th harmonic ( Ref. Zero Phase Shift)

Fig. 4.5 Effect of Phase Angle difference on the peak flux density

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -1.5

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0

0.5

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1.5

Time (Sec)

B (T)

90 Degree phase shift Zero Degree phase Shift

Master Thesis



Fig. 4.6 Effect on minor loop in saturation

4.1.2 7th Harmonic

4.1.2.1 Effect of harmonic Amplitude

There is a sharp decrease at higher values of induction (>1.2 T) and the increase in losses is higher as compared to the 5th harmonic. For example, 20% of the 5th harmonic causes maximum 58% difference (Fig. 4.2) as compared to 20% of the 7th which causes maximum 85%.

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90

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Diff

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20%15%10%

Fig. 4.7 Effect on Iron loss due to introduction of the 7th harmonic (Ref. 50 Hz)

-1500 -1000 -500 0 500 1000 1500

-1.5

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0

0.5

1

1.5

H (A/m)

B (T)

Master Thesis


Effect of harmonics on iron losses 01 32/70 The same trend is observed in the case of the 7th harmonic as in the case of the 5th harmonic:

4.1.2.2 Effect on the BH Curve

It is seen from the Fig. 4.8 that the number of minor loops appearing in the BH curve has increased compared to the introduction of the 5th harmonic which results in an increase of iron loss and the area covered by minor loops has become larger as compared to the 5th harmonic. Further, maximum six numbers of minor loops are observed.

Fig. 4.8 Effect of 20% of the 7th harmonic on the BH curve

-400 -300 -200 -100 0 100 200 300 400 -1.5

-1

-0.5

0

0.5

1

1.5

B (T)

H (A/m)

Minor Loops

Master Thesis


Effect of harmonics on iron losses 01 33/70 4.1.3 11th Harmonic


It is seen from Fig. 4.9 that the same amplitude of the 11th harmonic causes more iron loss as compared to the loss caused by lower order harmonics and 20% of the 11th harmonic causes maximum 168% increase in losses while 15% of the 11th harmonic causes maximum about 95% increase.

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160

180

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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20%15%10%

Fig. 4.9 Effect on Iron loss due to introduction of 11th Harmonic (Ref. 50 Hz)

4.1.3.2 Effect on the BH curve

It is seen from the Fig. 4.10 that the Increase in number as well as areas of minor loops are observed, therefore an increase in iron loss is expected and maximum ten number minor loops are observed.

Master Thesis



Fig. 4.10 Effect of 20% of the 11th harmonic on the BH curve


In general the effect of phase angle on 11th harmonic is very small in fact it can be called neglect able (see Fig. 4.11). The reasons are that a change in phase angle for higher order harmonics has not much effect on the minor loop area. Further, the total peak flux density also does not experience any large change.

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5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

B (T)

Diff

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45 degree90 degree135 degree

Fig. 4.11 Effect of phase angle on 10% of the 11th harmonic (Ref. zero phase shift)

-200 -150 -100 -50 0 50 100 150 200 -1.5

-1

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0

0.5

1

B (T)

H (A/m)

Master Thesis




It is observed in Fig. 4.14 that the increase in iron loss due to an introduction of 20% of the 13th harmonics is 222% and the effect of 13th order harmonic is higher as compare to lower order harmonics in terms of in iron losses.

0

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250

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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20%15%10%

Fig. 4.12 Effect on Iron loss due to introduction of the 13th harmonic (Ref. 50 Hz)

4.1.4.2 Effect on the BH Loop

Twelve numbers of minor loops are observed in all cases (10%, 15% and 20% 13th harmonic).

4.1.5 Conclusion

The over all effect of harmonic on 50 Hz can be summarized as below:

• At a fixed harmonic order, an in iron losses is observed with increasing harmonic amplitude; this is due to an increase in area of the BH curve itself as well as an introduction of minor loops if any.

• For a given amplitude of the harmonic, increase in the order of the harmonic results in an increase of iron losses.

• Gradual increase in iron loss is observed with increasing peak flux density. The reason to this can be found if we review the theory of iron loss components

Master Thesis



variations with induction in case of sinusoidal wave forms. Fig. 4.13 shows the variation of individual iron loss components with flux density. It shows that the hysteresis loss component decreases with increasing flux density while eddy current and excess loss components increase with increasing in flux density. Therefore, it can be concluded that with the introduction of harmonics eddy current and excess losses increase, while the effect of hysteresis loss is small.

• At higher values of peak flux density, the increase in losses tends to decrease as the iron gets more and more saturated.

• In case of low order harmonic phase angle effect iron loss to some extent but this effect seems vanishing with increasing harmonic order.

• The number of minor loops appearing in BH curve depends on the following:

i. Relative amplitude of harmonic with fundamental signal e.g. In case of 20% 5th harmonic total 4 minor loop are observed while no minor loop is observed in case of 10% for the same harmonic order, as shown in Figure 1 and 2 (see annexure-2 ).

ii. Harmonic order also plays an important role in generation of minor loops e.g. 4 no. of minor loops are generated in case of 20% 5th harmonic while number of minor loops increases to 6 in case of 20% 7th harmonic as shown in Figure 1 and 2 (see annexure-3). This is due to the fact that minor loop appear if the dB/dt for the harmonic is negative and bigger than for the fundamental.

iii. With increasing harmonic order minor loops are more likely to appear even at relatively low amplitude of harmonic (e.g. 15% 5th harmonic do not generate minor loop while 15% 7th harmonic results in to generation of minor loops)

Fig. 4.13 Iron loss compenents versus flux density

0.5 1 1.5

10

20

30

40

50

60

70


Hysteresis

Eddy current Excess

Percentage of total Iron loss

Master Thesis




4.2.1 5th Harmonic


The general trend of increase in losses is the same as it was in the case of 50 Hz (fundamental). As it is seen in Fig. 4.14 that the gradual increase in loss up to 1.2 T in case of higher harmonic amplitude while the Increase remains nearly same for lower harmonic amplitude. Further, as core is forced to saturation above 1.2 T that causes reduction in percentage increase. The increase of 52 % is observed in case of 20% of the 5th harmonic that was 56% in case of 50Hz fundamental with 5th harmonic.

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0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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)

20 % 5th harmonic15 % 5th harmonic10 % 5th harmonic

Fig. 4.14 Effect of the 5th harmonic on iron loss (Ref. 30 Hz,Fundamental)


Same no of minor loops are observed as it was in case of 50 Hz that indicates the number of minor loops appearing depends on the relative amplitude of harmonic with the fundamental signal not on the frequency of the fundamental signal itself.

Master Thesis



Fig. 4.15 Effect of the 5th harmonic on the BH curve with 30Hz fundamental


As shown in Fig. 4.16, the effect of phase angle on iron loss is low at low value of phase angle difference but at higher values of the peak flux density different trend is observed due to the reasons already explained in section 4.1.1.3. Similar trend is observed in case of 15 and 10% of the 5th harmonic.

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45 degree 90 degree

Fig. 4.16 Effect of phase angle on 20 % of the 5th harmonic (Ref. Zero Phase Shift)

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0

0.5

1

H (A/m)

B (T)

Master Thesis




As suggested by the Fig. 4.17, same trend is observed as it was in the case of 50Hz with 7th harmonic. However percentage increase is little less as compare to 50Hz with 7th harmonic. For example maximum increase in case of 30 Hz with 20 % of the 7th harmonic is 72% while in case of 50 Hz it is 86%.

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0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


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20% 7th harmonic15 % 7th harmonic10 % 7th harmonic

Fig. 4.17 Effect of the 7th harmonic on iron loss (Ref. 30 Hz, Fundamental)


The effect of introduction of the 7th harmonic on the BH loop is same as it was in case of 50 Hz fundamental frequency (with 7th harmonic).


In general increase in the iron loss is caused with introduction of phase angle shift however the increase is small (about 5%). The increase is due to the fact that the total peak flux density is increase with introduction of the 7th harmonic (See figure Fig. 4.19) which is quite opposite to the 5th harmonic case. Further, introduction of the phase angle does not affect the location of minor loop, hence the trend of increase in loss in saturation is not observed as it was evident in case of 5th harmonic (At higher value of peak flux density).

Master Thesis



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0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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)20% 7th Harmonic15% 7th Harmonic10% 7th Harmonic

Fig. 4.18 Effect of 90 degree phase Shift (REF Zero degree)

Fig. 4.19 Effect of the phase angle difference on peak flux density

0.005 0.01 0.015 0.02 0.025 0.03

-1

-0.5

0.5

1

Time (Sec)

B (T)


Master Thesis



Fig. 4.20 Effect of the phase angle difference on minor loops

s

4.2.3 11th Harmonic


The increase in loss with introduction of 10% of the 11th harmonic is nearly same as it was in case of 50 Hz fundamental. Maximum increase in case of 30 Hz (10% of the 11th harmonic) is 38 % while it is 41% in case of 50 Hz fundamental (10 % of the 11th harmonic).

-800 -600 -400 -200 0 200 400 600 800 -1.5

-1

-0.5

0.5

1

1.5

H(A/m)

B (T)

90 Degree phase shift In Phase

Master Thesis



0

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35

40

45

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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ce (

%)

10 % 11th harmonic5% 11th harmonic

Fig. 4.21 Increase in Iron loss due to introduction of the 11th Harmonic (Ref. Sin)


Same effect of 11th harmonic on the BH loop is observed as it was in case of 50 Hz.


The effect of phase angle on iron loss is very little as shown in Fig. 4.22. Maximum of 1.9% increase is observed.

Master Thesis



-5

0

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20

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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90 Phase Shift

Fig. 4.22 Effect of phase shift on the iron loss (Ref. Zero Phase Shift)

4.2.4 13th Harmonic


Maximum Increase in the iron loss with introduction of 10 % of the 13th harmonic is 37 % while in case of 50 Hz it was above 50%. Therefore we can say that at higher harmonic order effect of the harmonic in 30 Hz fundamental frequency is much less than 50 Hz fundamental.

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Diff

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10 % 13th harmonic5% 13th harmonic

Fig. 4.23 Increase in iron loss due to the introduction of the 13th harmonic (Ref. Sin)

Master Thesis


Effect of harmonics on iron losses 01 44/70 4.2.5 Conclusion

We can conclude that the increase in loss due to introduction of different harmonic with 30Hz fundamental is slightly less than 50Hz fundamental. However this gap seems to be increasing at the higher order harmonic.


4.3.1 5th Harmonic


The increase in iron loss due to introduction of the 5th harmonic with fundamental 70Hz is nearly same as it was in the case of 50Hz or 30Hz fundamental e.g. the increase of about 55% in iron loss is observed in all the three cases.

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0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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20 % Harmonic15 % Harmonic10 % Harmonic

Fig. 4.24 Effect on iron loss due to introduction of the 5th Harmonic (Ref. Sinusoidal)

4.3.1.2 Effect on the BH loop

Four numbers of minor loops are observed at 20% of the 5th harmonic. Further, the flux reversals are observed in case of 15% and 10% of the 5th harmonic that it is not enough to cause minor loops however effects the shape of the BH loop.


Small decrease in loss in observed up to 1.2 T peak flux density for different percentage of the 5th harmonic and change of phase angle will create minor loop in case of 15% of the 5th

Master Thesis


Effect of harmonics on iron losses 01 45/70 harmonic near the saturation which were not there in case of harmonic being in phase with fundamental (See figure 4.25). However the minor loop is so small that it has little effect on iron loss. Further, with the phase shift of 90 degree, In case of 20% of the 5th harmonic area of existing minor loop will increase as minor loop will shift towards saturation. Saturation will cause increase in loss at higher flux density.

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20%15%10%

Fig. 4.25 Effect of the phase angle on iron loss (Ref. Phase Shift Zero)

Fig. 4.26 Creation of minor loops with the phase angle shift

-1000 -800 -600 -400 -200 0 200 400 600 800 1000 -1.5

-1

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0

0.5

1

1.5

H (A/m)

B (T)

90 degree phase shift In phase

Master Thesis



4.3.2.1 Effect of 7th harmonic amplitude

Maximum 90% increase of the iron loss is observed in the case of 20% of the 7th harmonic. Similarly 50% increase is observed in case of 15% of the 7th harmonic and 20% in case of 10% of the 7th harmonic is observed (see Fig. 4.27).

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Fig. 4.27 Effect on the iron loss due to introduction of the 7th Harmonic (Ref. Sinusoidal)


Maximum 5.2% of increase in iron loss is observed due to phase shift of 90 degrees (see Fig. 4.28).

Master Thesis



-5

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Diff

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20%15%10%

Fig. 4.28 Effect of the phase angle on iron loss (Ref. Phase shift Zero)

4.3.3 11th Harmonic


Maximum increase in loss of 177% is observed with introduction of 20% of the11th harmonic while increase in case of 15% and 10% of the 11th harmonic is about 100% and 40% respectively.

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Fig. 4.29 Effect on iron loss due to introduction of 11th Harmonic (Ref. Sinusoidal)

Master Thesis




Maximum increase of about 4.5% is observed with the phase shift of 90 degrees.

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Fig. 4.30 Effect of the phase angle on iron loss (Ref. Phase Shift Zero)

4.3.4 13th Harmonic


Maximum increase of 56% in the iron loss is observed in case of 10% of the 13th harmonic while the maximum increase was 16% in case of 5% of the 13th harmonic.

Master Thesis



0

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70

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

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10 % Harmonic5 % Harmonic

Fig. 4.31 Effect on iron loss due to introduction of the 13th harmonic (Ref. Sinusoidal)


The effect of different harmonic with the fundamental frequency 5 Hz is also studied and following results can be concluded

• The increase in the iron loss due to different harmonic with the fundamental 5 Hz is nearly same as it was for other fundamental frequencies (i.e. 50 Hz, 70 Hz and 30 Hz).

• Effect of the phase angle on iron loss is more on low order harmonic while phase angle has less effect in case of higher order harmonics.

Master Thesis


Effect of harmonics on iron losses 01 50/70 5 EFFECT OF TWO FLUX HARMONICS ON IRON LOSS

In electrical machines several harmonics are present simultaneously. These harmonics may or may not be in phase with the fundamental frequency. As in section 4 it was observed that the phase angle is important for the iron losses generated by lower order harmonics while the effect is very minor for losses generated by higher order harmonics. In the following section, the effect of two flux harmonics on iron loss is studied. The combination of (5th + 7th) and (5th + 13th) harmonic is selected because these are often dominant in electrical machines. The effect of the phase angle is studied when:

• Two low order harmonic (5th and 7th ) are present

• One low order (5th) and one high order (13th) harmonic is present.

One should know that in the following section when the effect of phase angle is reported in case of the 5th and 7th harmonics, the 5th harmonic is in phase with the fundamental frequency while the 7th harmonic is having a 90 degrees phase shift.

Similarly in case of the 5th and 13th harmonics, the 5th harmonic is in phase with the fundamental frequency while the 13th harmonic is having a 90 degrees phase shift.

However, the cases with the 5th harmonic having a phase shift of 90 degrees and the other harmonic in phase with the fundamental frequency is also studied but this leads toward similar kind of trends and conclusions.

5.1 Fundamental Frequency (50 Hz)

5.1.1 Effect of the 5th and 7th harmonic

5.1.1.1 Effect of the harmonic amplitude

Let us take the expample of a wave form that contains two harmonics, having amplitude of 10% of the 5th and 7th harminics (both in phase with the fundamental frequency). It is observed that the maximum iron loss induced by such wave form is about 23%. Further, gradual Increase in iron loss with increasing flux density untill saturation comes in to effect, as it is the case with single harmonic.

Master Thesis



0

5

10

15

20

25

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)10% 5th and 10% 7th harmonic

Fig. 5.1 Effect on iron loss due to introduction of the 5th and 7th harmonic (Ref. Sin)


Six minor loops are created in case 10% of the 5th and 10% of the 7th harmonics are introduced. This suggests that the number of created minor loops are totally dependent on the wave form of the flux density as shown in Fig. 5.3. However in this particular case the minor loops appearing at peak is so small that it is not visible in Fig. 5.2.

Fig. 5.2 Effect of 10% of the 5th and 10% of the 7th harmonic on BH curve

-150 -100 -50 0 50 100 -1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

H (A/m)

B (T)

Master Thesis



Fig. 5.3 Flux density as function of time


It is seen in Fig. 5.4 that the increase in iron loss up to 1 T is observed in case of introduction of the phase angle difference of 90 degrees. It is because of the increase in peak flux density. It is also observed, the introduction of the phase angle causes increase in peak flux density it is obvious that saturation will be reached early and the difference will tends to decrease after the saturation reaches. Further, the percentage increase in the iron loss due to the phase shift is nearly equal to the percentage increase in the peak flux density.

0

2

4

6

8

10

12

14

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

90 degree phase shift

Fig. 5.4 Effect of the phase angle (Ref. Phase angle zero)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -1.5

-1

-0.5

0

0.5

1

1.5

Time (Sec)

B (T) Flux reversal causing minor

Loops

Master Thesis



Fig. 5.5 Flux density as function of time



Maximum increase of 75% in iron loss is observed and the saturation effect at high peak flux density is also evident here, as it is in almost every case.

0

10

20

30

40

50

60

70

80

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

10% 5th and 10% 13th harmonic

Fig. 5.6 Effect on the iron loss due to introduction of the 5th and 13th harmonic (Ref. Sinusoidal)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -1.5

-1

-0.5

0

0.5

1

1.5

Time (Sec)

B (T)


Master Thesis


Effect of harmonics on iron losses 01 54/70 5.1.2.2 Effect on the BH Loop

Six numbers of the minor loops are seen following the flux reversals in flux density wave form.


The effect of phase angle on iron loss is very little. In fact, it can be neglected. This confirms the conclusion that at higher order harmonics phase angle effect on iron loss is very small.

-10

-8

-6

-4

-2

0

2

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

10% 5th and 10% 13th harmonic

Fig. 5.7 Effect of phase angle on the 5th and 13th harmonic (Ref. Phase angle zero)




It is observed in the figure below that the increase in iron loss is slightly less as compare to the increase with the fundamental frequency of 50 Hz and the maximum increase of about 20% is seen in case of the fundamental frequency of 30 Hz while it is 23% in case of 50 Hz.

Master Thesis



0

5

10

15

20

25

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)10 % both harmonic

Fig. 5.8 Increase in iron loss due to introduction of the 5th and 7th harmonic (Ref. Sinusoidal)


The effect on BH loop is same as it is in case of the 50 Hz. i.e. same numbers of the minor loops are observed in both the cases.


On average 14% increase is observed with the introduction 90 degrees phase shift until saturation effects losses at 1.2 T.

Master Thesis



0

2

4

6

8

10

12

14

16

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

90 degree phase shift

Fig. 5.9 Effect of phase angle on the 5th and 7th harmonic (Ref. Zero degree phase shift)



Maximum 65% increase in the iron loss is observed that is slightly lower then in case of the 50 Hz fundamental frequency.

0

10

20

30

40

50

60

70

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

10 % 13th harmonic

Fig. 5.10 Increase in the iron loss due to introduction of the 5th and 13th harmonic (Ref. Sinusoidal)

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Effect of harmonics on iron losses 01 57/70 5.2.2.2 Effect on the BH Loop

Similar kind of effect on the BH loop is observed as it is in case of 50Hz.


In general decrease in iron loss is observed with introduction of phase shift of 90 degrees. Following figure suggests that maximum decrease of 4% is observed.

-10

-8

-6

-4

-2

0

2

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

90 degree Phase shift

Fig. 5.11 Effect of the phase angle on iron loss (Ref. Zero degree phase shift)




Maximum increase due to introduction of 10% of the 5th and 7th harmonics with 70Hz fundamental is about 27% that is slightly larger than same harmonics with 50Hz fundamental.

Master Thesis



0

5

10

15

20

25

30

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

10% 5th, 10% 7th (In Phase)

Fig. 5.12 Effect on iron loss due to introduction of the 5th and 7th harmonic (Ref. Sinusoidal)


Effect on the BH loop is same as it was in case of the 50 Hz fundamental frequency.


The maximum increase in iron loss due to phase shift of 90 degree is about 10% that is about the same as it is in case of 50Hz with same harmonics.

Master Thesis



0

2

4

6

8

10

12

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)90 degree Phase Shift

Fig. 5.13 Effect of the phase angle on iron loss (Ref. Phase angle Zero)



Maximum increase with introduction of 10% of the 5th and 7th harmonics is about 77%. It is further observed that the gradual increase in loss in observed with increasing the peak flux density, the trend that is observed in almost every case.

0

10

20

30

40

50

60

70

80

90

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

10% 5th, 10% 13th (In Phase)

Fig. 5.14 Effect on iron loss due to introduction of the 5th and 13th harmonic (Ref. Sinusoidal)

Master Thesis


Effect of harmonics on iron losses 01 60/70 5.3.2.2 Effect of phase angle

Generally small decrease in observed due to phase shift of 90 degrees phase shift. This small decrease is due to decrease in the peak flux density as already stated.

-10

-8

-6

-4

-2

0

2

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6


Diff

eren

ce (%

)

90 degrees phase shift

Fig. 5.15 Effect of the phase angle on iron loss (Ref. phase shift zero degree)

5.4 Conclusion

The overall effect of two flux harmonics is the same for all three fundamental frequencies (i.e. 30Hz, 50Hz and 70Hz). However it is noted that the increase in iron loss is slightly increasing with increase in fundamental frequency (e.g. increase in loss in case of 50 Hz fundamental frequency is slightly more than 30Hz while it is slightly less than 70Hz) as shown in figure 5.15. This is due to the fact that with increasing fundamental frequency, eddy current and excess losses becomes more and more effective or in other words; the percentage of eddy current and excess losses in total iron loss increases with increasing fundamental frequency.

In case of low order harmonic a change of phase angle may result in either a decrease or an increase in iron loss. There may be two reasons for such a behavior.

• The main reason is “change in phase angle results into a change in total peak flux density (fundamental + harmonic)”.

• The area of the minor loops can also be affected with a phase shift. However, most of the time it has a less important role to play regarding the iron loss.

In case of higher order harmonics both of the factors mentioned above do not exist, hence a change in phase angle does not change the iron loss.

Master Thesis



0

5

10

15

20

25

30

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Fundamental peak flux density B(T)

Diff

eren

ce (%

)

30 Hz50 Hz70 Hz

Fig. 5.16 Increase in iron loss due to 10% of the 5th and 7th harmonic at different fundamental frequencies (Ref.

fundamental frequency)

Master Thesis


Effect of harmonics on iron losses 01 62/70 6 CONCLUSIONS

Some methods for prediction of iron loss coefficients are discussed in chapter 2, these methods can basically be divided into two main categories. One is called the constant coefficient method and the other is referred to as the curve fitting method. It is found that the constant coefficient method is not feasible to use for a wide frequency range although it requires fewer amounts of experimental data. On the other hand, different curve fitting methods are found in literature. These methods usually give fairly accurate information about the total iron loss but if correct information about individual loss components is required one has to be careful in selecting among these different curve fitting methods. In such a case, methods in section 2.4.2.2 are not recommended at all. The first method in section 2.4.2.2 involves a lot of guessing while the second method described in the same section shows slightly too high hysteresis loss. Therefore, it is recommended that the method described in section 2.5 should be followed. Table 6.1 shows loss coefficients for M400 at 50 Hz using the method given in section 2.5 with the assumption of n = 2.

Table 6.1 Loss coefficient for M400 (813727F) at 50 Hz

Ke = 0.1437 * 10-3 [W/kg/Hz2/T2]

Kh [W/kg/Hz/T2] Ka [W/kg/Hz1.5/T1.5]

0,1 T - -

0,2 T - -

0,3 T 0.0306 0.000344

0,4 T 0.0285 0.000324

0,5 T 0.0245 0.000515

0,6 T 0.0218 0.000638

0,7 T 0.0199 0.000725

0,8 T 0.0186 0.000790

0,9 T 0.0173 0.000869

1,0 T 0.0165 0.000930

1,1 T 0.0158 0.001016

1,2 T 0.0156 0.001058

1,3 T 0.0159 0.001102

1,4 T 0.0167 0.001167

1,5 T 0.0180 0.001226

Master Thesis


Effect of harmonics on iron losses 01 63/70 In general similar kind of trends is observed in the presence of one or two harmonics. It is found that an increase in peak flux density, generation of minor loops and involvements of high frequencies are the main reason of increase in losses with distorted waveforms. Table 6.2 describes the maximum increase of iron loss with an introduction of 20% of different order harmonics at 50 Hz fundamental frequency.

Table 6.2 Maximum increase in iron loss due to an introduction of 20% of different orders of harmonics at 50 Hz

fundamental frequency.

Harmonic order 5th 7th 11th 13th

Maximum increase

58% 85% 168% 222%

It is important to note that the eddy current and excess losses increase with the introduction of harmonics while hysteresis loss is less affected. The effect of harmonics on increase in iron loss is observed with increasing harmonic amplitude as well as harmonic order. Further, it is found that the higher the fundamental frequency the higher will be the increase in iron loss, as seen in Table 6.3.

Table 6.3 Percentage increase in iron loss with the introduction of 10% of the 5th and 7th harmonics at different

fundamental frequencies

0.8 T 0.9 T 1.0 T 1.1 T 1.2 T

30 Hz 18 20 17 20 17

50 Hz 22 21 22 22 23

70 Hz 25 25 27 28 28

Section 2.5 discusses different methods to predict iron loss with distorted flux waveforms. Following the time domain expression (6.1) to predict iron loss in such conditions is recommended.

�� +��

��

�+= dtdtdB

TKdt

dtdB

TKPP

aehTotal

5.12

11 6.1

It is found that no additional information is needed. However, the correct prediction of loss coefficients is very important. Use of the time domain equation accounts for change in phase angle in the resultant waveform. However, the change in iron loss due to a phase angle shift is even bigger in reality. Therefore, loss coefficients need to be changed accordingly. It was found that the percentage change (increase/decrease) in iron loss due to a phase angle shift is nearly equal to the percentage change in peak flux density (e.g. in case of which 20% of the 5th harmonic 90 degrees phase shift results in average decrease of 3% in iron loss that is nearly equal to the percentage decrease in peak flux density).

Master Thesis



7 FUTURE WORK

For continuation of this work the following aspects should be considered:

• The impact of rotational iron losses.

• Defining an imperial coefficient to account for phase angle effects, or some other method could be followed.

• Other iron materials, having different grades and thickness should be studied.

• Implementation of the recommended expression in suitable software and calculation of iron loss in the complete motor.

Master Thesis


Effect of harmonics on iron losses 01 65/70 8 REFERENCES

[1] Julus Saitz “Calculation of Iron losses in Electrical Machines”,PhD dissertation at Helsinki University of Technology. March 1997.

[2] Chandur Sadarangani “Electrical Machines”Department of Electric Power Engineering, Royal Institute of Technology, Stockholm, August 2000

[3] Anthony J. Moses “Loss Prediction in Electrical steel Laminations and Motor Core”, Cardiff university, Cardiff school of Engineering, Cardiff/ U.K.

[4] Dan M. lonel “On the variation with flux and frequency of the core loss coefficients in Electrical Machines”, IEEE transactions on Industry Applications vol. 42 no. 3, pp658-667, May/june 2006

[5] G. Bertotti, “General properties of power losses in soft ferromagnetic materials”, IEEE transaction on magnetics, vol.24, no. 1, pp621-630, jan 1988.

[6] E. Della Torre, “Magnetic Hysterisis”, Piscataway, NJ: IEE, 200. 1998.

[7] H. Domeki “Investigation of benchmark model for estimating iron loss in rotating machine” IEEE transaction on magnetics, Vol 40, no 2 pp794-797, Mar 2004”

[8] Mircea Popescu “A best fit model of power losses in cold rolled moter lamination steel operating in a wide range of frequency and magnetization”, IEEE trans on magnetics. Vol.43, no. 4, pp 1753-1756 April 2007.

[9] Lotten Tsakani “Core losses in Motor laminations exposed to high frequency or nonsinusoidal excitation”, IEEE transaction on Industrial applications. Vol40, no. 5, pp -1325-1332 sep-oct 2004.

[10] M. S. Lancarotte “Predection of magnetic losses under sinusoidal or nonsinusoidal induction by analysis of magnetization rate”, IEEE transaction on Energy conversion. Vol 16, pp. 174-179.

[11] Andre G. Torres “A generalized Epstein test method for the computation of core losses in induction motors” IEEE transaction on industrial electronics, pp 1150-1155, 2002.

[12] Lotten T. Mthombeni “Lamination core loss measurements in machines operating with PWM or non-sinusoidal excitation”,IEEE Electric machines and drives conference. Pp-742-748, 2003.

[13] Aldo Boglietti “About the possibility of defining a standard method for iron loss measurment in soft magnetic material with inverter supply”, IEEE transaction on industry applications vol. 33, no. 5, sept. 1997.

[14] A. Boglietti “The annealing influence onto the magnetic and energetic properited in soft magnetic material agter punching process”, IEEE Electric machines and drives conference , pp 503- 508, 2003.

[15] T. Nakata “Numerical analysis and experimental study of the error of magnetic field strength measurements with single sheet testers”, IEEE transaction on magnetics, Volume 22, pp 400 – 402, Sep 1986.

Master Thesis



[16] Liu Shuo “Study of single sheet tester for A.C magnetization characteristics measurment”, IEEE transaction on Electrical machines and systems, Volume 1, pp 361 – 364, 18-20 Aug. 2001.

[17] Yicheng Chen “An improved formula for lamination core loss calculations in machines operating with high frequency and high flux density excitation”, IEEE transaction on industry applications, pp 759-766, 2002.

[18] J. D Lavers “A simple method of estimating the minor loop Hystereses loss in thin laminatios”, IEEE transactions on magnetics, vol. MAG-14, No. 5, September 1978.

[19] Edoardo Barbisio “Predicting loss in magnetic steels under arbitrary indiction waveform and with minor Hystereses loops”, IEEE transactions on magnetic, vol40, no 4, July 2004.

[20] A. Boglietti “Iron loss prediction with PWM supply:an overview of proposed methods from and engineering applocation point of view”, IEEE transactions on magnetics , 2007.

[21] M. Amar “A general formula for prediction of iron losses under nonsinusoidal voltage waveform”, IEEE transactions on magnetic, vol 31, no 5, September 1995.

[22] Marubbini J. “Low voltage high current PM traction motor design using recent core loss results”, IEEE transaction on industry applications,pp 1560-1566, 2007

[23] A. Broddefalk “Dependence of the power losses of a non-oriented 3% Si-steel on frequency and guage”, Journal of Magnetism and Materials 304 (2006) e586-e588.

[24] P. C. Sen “Principles of electric machines and power electronics”, Second edition, Queens university, Kingston, Ontario, Canada.

Master Thesis



9 ENCLOSURES

9.1 Appendix – 1

-200 -150 -100 -50 0 50 100 150

-1

-0.5

0

0.5

1

B (T)

H(A/m)

50 Hz 30 Hz

Fig. 1 BH loop with the 5th harmonics at different frequencies

Master Thesis


Effect of harmonics on iron losses 01 68/70 9.2 Appendix – 2

-150 -100 -50 0 50 100 150

-1

-0.5

0.5

1

H (A/m)

B (T)

-150 -100 -50 0 50 100 150 200

-1

-0.5

0

0.5

1

H (A/m)

B (T)

Fig. 1 (4 No. minor loops are generated with introduction of 20% of the 5th harmonic)

Fig. 2 (no minor loop generated with introduction of 10% of the 5th harmonic)

Master Thesis



9.3 Appendix – 3

-200 -100 0 100 200 300

-1

-0.5

0

0.5

1

H (A/m)

B (T)

-250 -200 -150 -100 -50 0 50 100 150 200 250 -1.5

-1

-0.5

0

0.5

1

1.5

B (T)

H (A/m)

Fig. 1 (4 No. minor loops generated with introduction of 20% of the 5th harmonic)

Fig. 2 6 No. minor loops generated with introduction of 20% of the 7th harmonic

Master Thesis


Effect of harmonics on iron losses 01 70/70 9.4 Appendix – 4

Repeatability at 70 Hz

-2,5

-2

-1,5

-1

-0,5

0

0,5

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1,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

B (T)

Diff

eren

ce (%

)


Repeatability at 5 Hz

-1,5

-1

-0,5

0

0,5

1

1,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

B (T)

Diff

eren

ce (%

)


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