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Simplified spectrum characterization of soft magnetic materials under PWM excitation
Journal of Magnetism and Magnetic Materials 160 (1996) 27-28
~ i Journalof magnetism J H and magnetic JR
ELSEVIER
materials
Simplified spectrum characterization of soft magnetic materials under PWM excitation Jean-Paul Swan *, Olivier Walti Uniuersit~ des Sciences et Technologies de Lille, L.E.E.P., Bat. P2, F-59650 Villeneuze d'Ascq, France
Abstract This paper explains how to simplify the harmonic description of the behaviour of a soft magnetic material tested by Epstein method under non-sine conditions. PWM waves are used to illustrate the method. Comparison of the harmonic parameters corresponding to a complete characterization and a simplified one validates this method.
Keywords: Soft magnetic materials; Characterization; Harmonics
1. Introduction The harmonic characterization of soft magnetic materials gives a fine representation of their behaviour, especially under non-sine excitation. The great number of characteristic harmonic parameters is not absolutely necessary when a fast characterization is required. Moreover, the dynamic constraints of most PWM waves impose high dynamic characteristics of the characterization bench. That makes the system expensive. Reducing the spectrum of the excitation signals gives a solution to these problems. We illustrate this method with typical characterization results of a PWM wave at a frequency f = 50 Hz. All results have been obtained using an Epstein method.
2. The simplified signal In the example presented, the complete harmonic characterization [1,2] shows that the harmonics highest in magnitude carry the major part of the active and reactive power. We select the harmonics of the simplified excitation signal from the active power spectrum of the original signal. The active power harmonics are classified in a decreasing order of magnitude. The first harmonic to be excluded is such that the sum of the magnitude of the previous ones is close to 90% of the total losses. Experimental study of about hundred PWM waves showed that the nine first higher harmonics of the original signals always carry more than 90% of the total active power.
Figs. l and 2 respectively show a PWM wave and its simplified signal and their corresponding magnetization loops.
3. The harmonic parameters Three series of harmonic parameters have been studied.
b~(t) and hk(t) represent the kth harmonic of the induction B(t) and the field H(t). They are given by:
bk(t ) = Bkx/~ sin(kwt + dbk) ,
(1)
h , ( t ) = H J ' 2 s i n ( k w t + risk).
(2)
The active and reactive power harmonics Pk and Qk are expressed by Eqs. (3) and (4) where S and L represent the cross section and the length of the magnetic circuit under test. A k is defined by Ak = ~k -- qbk-
Pk = 2 kTrSLfB k H~ sin A k,
(3)
Qk = 2krrSLfBk Hk cos Ak .
(4)
OriginalP.W.M,
i
* Corresponding author. Now at Universit~ d'Artois, Laboratoire 'Syst~mes Electrotechniques et Environnement', Technoparc Futura, F-62400 Bethune, France. Fax: + 33-21-61-17-80. 0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0304-8 85 3 ( 9 6 ) 0 0 0 9 4 - 7
[ 1
i
L
Synthesized
signal
Fig. 1. Excitation signals.
i
,
28
J.-P. Swan, O. Wahi / Jourmd q/'MagneHsn~ aJ d Magnetic Malerialx 160 (I996) 27 28 5000 4500 4000 3500 Original P.W.M.
3000 2500
Synthesized signal
2000 1500 1000 500 0 _
Original
P.W.M.
9
Fig. 2. Magnetization loops.
11
17
23
t3
7
43
31
29
Fig. 5. Magnetization permeability. 4000
Pk(W)
."k
1.8 3500 1.6 3000
1.4 1.2
Original P.W.M,
2500
Synthesized signal
Synthesized Signal 2000
1 0.8
1500
/
0.6
1000
0.4
500
0.2
0 1
0 1
9
11
17
23
13
43
7
31
17
23
13
7
43
31
29
information about the behaviour of the material. Concerning the control of the induction, the reduced bandwidth of the synthesized signal eases the feedback control. It only requires a small bandwidth generator.
250 - H k (A/m)
200
Original P.W,M.
5. C o n c l u s i o n
Synthesized signal
100
50
i i
~ m [ 1 I~_, m e _
0 1
11
Fig. 6. Loss permeability.
Fig. 3. Active power.
150
9
29
9
11
17
23
13
7
43
31
29
Fig. 4. Magnetic field.
The harmonic permeability ~ k = / ~ - . J P 2 2
is such that
B/,- =/Xo #~ H--k. 4. E x p e r i m e n t a l results
We present in Figs. 3 - 6 some reduced spectra corresponding to the original and the synthesized signals. These results show that the influence of the minor harmonics on the others is negligible. In other words, the reduced spectra slightly differ from the original ones. That proves that inter-harmonic effects can be neglected when such harmonic selection is used. Consequently, the values of the different harmonic parameters give relatively precise
The simplified characterization method has two advantages. It reduces the number of characteristic parameters without appreciable change of their values. The bandwidth and the control of the characterization bench are also reduced. The results show that the principle of the method is valid for PWM waves. Characterization under other excitation waveforms has to be done to generalize the method. Acknon'ledgemenn We obtained these results from a characterization bench which has been developed in co-operation with UGINE S.A. We thank the company for its assistance. This work was supported by the regional council Nord-Pas de Calais and the regional delegation of Research and Technology. References
[1] O. Walti, J.-P. Swan. Harmonic characterization of soft magnetic materials under non-sine periodic induction, SMM 12, September 1995, Cracow. [2] O. Walti. J.-P. Swan, Harmonic effects of PWM waves parameters on non-oriented Fe-Si magnetic steels, EMMA 95, September 1995, Vienna.
~ i Journalof magnetism J H and magnetic JR
ELSEVIER
materials
Simplified spectrum characterization of soft magnetic materials under PWM excitation Jean-Paul Swan *, Olivier Walti Uniuersit~ des Sciences et Technologies de Lille, L.E.E.P., Bat. P2, F-59650 Villeneuze d'Ascq, France
Abstract This paper explains how to simplify the harmonic description of the behaviour of a soft magnetic material tested by Epstein method under non-sine conditions. PWM waves are used to illustrate the method. Comparison of the harmonic parameters corresponding to a complete characterization and a simplified one validates this method.
Keywords: Soft magnetic materials; Characterization; Harmonics
1. Introduction The harmonic characterization of soft magnetic materials gives a fine representation of their behaviour, especially under non-sine excitation. The great number of characteristic harmonic parameters is not absolutely necessary when a fast characterization is required. Moreover, the dynamic constraints of most PWM waves impose high dynamic characteristics of the characterization bench. That makes the system expensive. Reducing the spectrum of the excitation signals gives a solution to these problems. We illustrate this method with typical characterization results of a PWM wave at a frequency f = 50 Hz. All results have been obtained using an Epstein method.
2. The simplified signal In the example presented, the complete harmonic characterization [1,2] shows that the harmonics highest in magnitude carry the major part of the active and reactive power. We select the harmonics of the simplified excitation signal from the active power spectrum of the original signal. The active power harmonics are classified in a decreasing order of magnitude. The first harmonic to be excluded is such that the sum of the magnitude of the previous ones is close to 90% of the total losses. Experimental study of about hundred PWM waves showed that the nine first higher harmonics of the original signals always carry more than 90% of the total active power.
Figs. l and 2 respectively show a PWM wave and its simplified signal and their corresponding magnetization loops.
3. The harmonic parameters Three series of harmonic parameters have been studied.
b~(t) and hk(t) represent the kth harmonic of the induction B(t) and the field H(t). They are given by:
bk(t ) = Bkx/~ sin(kwt + dbk) ,
(1)
h , ( t ) = H J ' 2 s i n ( k w t + risk).
(2)
The active and reactive power harmonics Pk and Qk are expressed by Eqs. (3) and (4) where S and L represent the cross section and the length of the magnetic circuit under test. A k is defined by Ak = ~k -- qbk-
Pk = 2 kTrSLfB k H~ sin A k,
(3)
Qk = 2krrSLfBk Hk cos Ak .
(4)
OriginalP.W.M,
i
* Corresponding author. Now at Universit~ d'Artois, Laboratoire 'Syst~mes Electrotechniques et Environnement', Technoparc Futura, F-62400 Bethune, France. Fax: + 33-21-61-17-80. 0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0304-8 85 3 ( 9 6 ) 0 0 0 9 4 - 7
[ 1
i
L
Synthesized
signal
Fig. 1. Excitation signals.
i
,
28
J.-P. Swan, O. Wahi / Jourmd q/'MagneHsn~ aJ d Magnetic Malerialx 160 (I996) 27 28 5000 4500 4000 3500 Original P.W.M.
3000 2500
Synthesized signal
2000 1500 1000 500 0 _
Original
P.W.M.
9
Fig. 2. Magnetization loops.
11
17
23
t3
7
43
31
29
Fig. 5. Magnetization permeability. 4000
Pk(W)
."k
1.8 3500 1.6 3000
1.4 1.2
Original P.W.M,
2500
Synthesized signal
Synthesized Signal 2000
1 0.8
1500
/
0.6
1000
0.4
500
0.2
0 1
0 1
9
11
17
23
13
43
7
31
17
23
13
7
43
31
29
information about the behaviour of the material. Concerning the control of the induction, the reduced bandwidth of the synthesized signal eases the feedback control. It only requires a small bandwidth generator.
250 - H k (A/m)
200
Original P.W,M.
5. C o n c l u s i o n
Synthesized signal
100
50
i i
~ m [ 1 I~_, m e _
0 1
11
Fig. 6. Loss permeability.
Fig. 3. Active power.
150
9
29
9
11
17
23
13
7
43
31
29
Fig. 4. Magnetic field.
The harmonic permeability ~ k = / ~ - . J P 2 2
is such that
B/,- =/Xo #~ H--k. 4. E x p e r i m e n t a l results
We present in Figs. 3 - 6 some reduced spectra corresponding to the original and the synthesized signals. These results show that the influence of the minor harmonics on the others is negligible. In other words, the reduced spectra slightly differ from the original ones. That proves that inter-harmonic effects can be neglected when such harmonic selection is used. Consequently, the values of the different harmonic parameters give relatively precise
The simplified characterization method has two advantages. It reduces the number of characteristic parameters without appreciable change of their values. The bandwidth and the control of the characterization bench are also reduced. The results show that the principle of the method is valid for PWM waves. Characterization under other excitation waveforms has to be done to generalize the method. Acknon'ledgemenn We obtained these results from a characterization bench which has been developed in co-operation with UGINE S.A. We thank the company for its assistance. This work was supported by the regional council Nord-Pas de Calais and the regional delegation of Research and Technology. References
[1] O. Walti, J.-P. Swan. Harmonic characterization of soft magnetic materials under non-sine periodic induction, SMM 12, September 1995, Cracow. [2] O. Walti. J.-P. Swan, Harmonic effects of PWM waves parameters on non-oriented Fe-Si magnetic steels, EMMA 95, September 1995, Vienna.