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Abstract- An improvement over a recently published control strategy is presented. The goal consists in reducing the acoustic noise caused by a PWM-Controlled Induction Machine Drives. It is a technique that uses a sinusoidal modulator wave (with harmonics injection) and a modulated frequency triangular carrier signal, and after comparing them, the modulated wave is obtained. The technique generates an efficient quality voltage for low commutations per cycle and is highly suitable reducing the acoustic noise radiated for any motor. The reason for the technique being so efficient, from the acoustic point of view, is the non existence of the relevant term in the electrical spectrum as in the Random PWM techniques. The main advantage of the proposed method is that only one parameter is necessary to get control over it. Therefore, the space harmonics FMM with high winding factor are avoided modifying this parameter. Results are checked experimentally and compared to other PWM techniques. Index Terms— Acoustic noise, Acoustic noise measurement, Converter, Frequency control, Frequency modulation, Harmonic distortion, Harmonic analysis, Induction motor drives, Magnetic force, Noise spectrum, PWM power controller.

I. INTRODUCTION otor acoustic noise can be classified in three types: The first two types includes the aerodynamic and mechanical

noise produced by the fan and bearings, respectively. This type of noise does not change significantly with different motor load levels. Minimizing this type of noise is dependent on an appropriate design and on appropriate maintenance, [1]-[3].

The last type of noise emitted by motors involves electromagnetic acoustical noise, which varies with the load level. This paper focuses on a modified HIPWM-FMTC (Harmonics Injection PWM Frequency Modulated Triangular Carrier) technique to reduce this last source of noise.

This type of noise is produced by vibration force density waves according to [4]:

20( , ) ( ( , )) (2 )v t b tα = α μ (1)

where b(α,t) is the air-gap flux density harmonic components, α is the angular position; t is the time, and μ0 is the vacuum permeability, 4π·10-7(H/m). This type of noise depends on the following types of harmonics:

a) Space harmonics, which are produced due to the non-linearities that the flux density generates in the air-gap, even when the power supply is sinusoidal. b) Time harmonics, which appear when the motor is fed by a power inverter and therefore, there are other electrical harmonics around the fundamental voltage, which produce pulse pairs, heating in the coils, vibrations and mechanical noise. If the inverter has to operate with a low M value to reduce thermal stress, then a key issue is to choose a suitable modulation strategy in order to avoid excitation at resonance frequencies and space harmonics for sensitive frequencies (with high winding factor) in the lowest vibratory modes.

Since frequency converters were first employed as variable speed motor controllers, many researchers have tried to find how they can reduce electromagnetically-induced acoustic noise. A lot of researchers have been working on reducing the acoustic noise by using PWM voltage fed AC motor drives with random switching control techniques (RPWM) modulating the carrier frequency, ft, in a pseudorandom mode over defined switching bands. This technique causes the regular tonal spectrum to be broken up and spread over a wider spectrum in order to avoid noise at the frequency given in (4). This approach is simple to implement and independent of the motor control strategy, but it requires the contribution of a micro-controlled power converter to generate a suitable probability density function [5]-[7] and further, it lacks adequate control of the THD parameter.

Other solution could be to use a PFM (Pulse Frequency Modulated). This strategy is based on a frequency modulation of the triangular carrier through a periodical signal with fF frequency [8], [9]. The technique HIPWM-FMTC [10]-[12] is

Shaping the HIPWM-FMTC strategy to reduce acoustic noise radiated by Inverter-

Fed Induction Motors

Antonio Ruiz-González(1); Mario J. Meco-Gutiérrez(1); Francisco Vargas-Merino(1), Francisco Pérez-Hidalgo(1), Juan Ramón Heredia Larrubia(2),

(1) Elec. Eng. Dept., University of Málaga; (2) Electronic Tech. Dept., University of Málaga;

Escuela de las Ingenierías. C/ Doctor Ortiz Ramos (Teatinos). 29071-Málaga, Spain e-mail: pacuma@gmail.com

M

A. Ruiz-González, M. J. Meco-Gutiérrez, F. Pérez-Hidalgo, and F. Vargas-Merino are with the Department of Electrical Engineering, Unversity of Málaga, 29071 Málaga, Spain (e-mail: pacuma@gmail.com)J. R. Heredia-Larrubia is with the Department of Electronics Technology, University of Málaga, 29071 Málaga, Spain

XIX International Conference on Electrical Machines - ICEM 2010, Rome

978-1-4244-4175-4/10/$25.00 ©2010 IEEE

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used to decrease acoustic noise and to achieve a reduction in THD and the mathematical development is in [12]. Remaining the same fF, an improvement with the periodical signal that it modules the frequency of the carrier signal is proposed. The main advantage of the new periodical signal (triangular instead of sinusoidal) is that it is possible to modify the electrical spectrum using one parameter α while the number of pulses per period, M, remains unchanged and raise the instantaneous frequency of the carrier wave, reducing the amplitude of the side bands of the switching frequency, fsw.

A. Acoustic Noise with a Sinusoidal Power Supply

When the motor is connected directly from an equilibrated power supply, noise and vibration will appear from an aerodynamic, electromagnetic and mechanical origin. The noise frequency due to the fan blades is k times the number of fan blades and the circumferential speed of the fan. Likewise, the mechanical noise is related to the circumferential speed of the rotor.

Finally, the electromagnetic noise from radial magnetic forces produced by higher space harmonic is easily identified [4].

B. Inverter-Fed Motors

Power inverters regulate the three-phase voltage fed to induction motors both in terms of amplitude and frequency, using a specific control strategy in each case.

The output voltage can be controlled in several different ways. The most common method consists of controlling the pulse width applied to the electronic switches and its pulse width modulation (PWM). The wave frequency spectrum obtained at the output contains many harmonics, which increase the amount of loss, vibration and noise, thereby reducing the performance of the system.

The traditional pulse width modulation technique involves a high frequency triangular carrier signal with a constant value, ft, and a sinusoidal modulator signal whose fundamental frequency is fm. By comparing both, the modulated signal that turns on/off the power switches is obtained. Although this technique is easy to implement, its main disadvantage is that it generates a fundamental term with small amplitude and a significant amount of undesired harmonics.

The acoustic noise radiated by induction machines increases when they are fed by non-sinusoidal power supplies, such as PWM converters. The electromagnetically generated acoustic noise (with a non-sinusoidal power supply) follows (1) and is analyzed in [4], [13-18]. New radial forces will appear using an inverter: the products of stator harmonics of the same time harmonic number n, produce radial magnetic forces with frequencies, 12 (2 1)rf f km= ± . On the other hand, the frequencies of the radial magnetic forces due to products of rotor harmonics of the same number n, will be n times the frequency of (2), with the same mode r.

Although the most important origin of the radial magnetic force using an inverter will be the interaction of the switching frequency fsw and higher time harmonics [19]. In this case,

noise frequencies must be located around a multiple of the switching frequency, fsw, with r = 0.

The interaction between the fundamental air-gap field and the first-order field harmonics produced by the currents generated by the control strategy produce the most significant electromagnetic noise with noise frequencies, fr:

··

( ) -swk

r k

c ff a f

f f f

±=

= ± (2)

where f is the fundamental component of the frequency of the modulated signal and fk is the electrical harmonic. If a is an odd integer, c will be an even integer and vice versa, i.e., fk = fsw ± 2f, fsw ± 4f,..., and, fk = 2fsw ± f, fk = 2fsw ± 3f,…

II. HIPWM-FMTC2 STRATEGY. This technique, named HIPWM-FMTC2, obtains the

commutation pulses by comparing a sinusoidal with harmonics injection modulator wave, and a triangular carrier frequency modulated wave, both of which have the same amplitude, as seen in Fig. 1. The triangular carrier frequency is modulated by a triangular signal (HIPWM-FMTC2) instead of a sinusoidal signal, used in the past (HIPWM-FMTC) with frequency fF double of f, to maintain low the THD parameter [8].

In order to maintain M constant it is necessary to adjust the maximum instantaneous frequency, fmax to the slope of the triangular signal. Because of a triangular signal modulates the frequency carrier signal, it is possible to match its highest value (maximum frequency of the carrier signal) with the highest slope of the modulator signal. And cancel it in the periods where it has a reduced slope, and therefore, transmits less information [13]. The carrier wave is formed by two parts: an oscillatory part (a triangular waveform with variable frequency with linear mode) and another part which is constant.

The modulation order M (number of pulses per cycle) is fixed by the α/fmax relationship. It is important to keep in mind that, any α value is feasible for any M. The function that results from Fourier series that controls the carrier signal (periodic function of the middle graphic in Fig. 1) is:

max max

21

· 2 1[ (1 cos( · )]2 ·n

i nn

∞

=

α ω ωω + − απ π α

= ∑ (3) Where α in radians, is the angle where the instantaneous

modulation order function reaches the null value (α = π/2 corresponds to a triangular shape for this function. Any other lower value represents a trapezoidal shape), and ωmax is the maximum pulsation value (for t = 0, 0.01, 0.02.... s).

This new approach allows us to: • reduce the level of all the electrical harmonics at the

output of the inverter in comparison to other traditional strategies,

• provide a high fundamental term, which for a given value of the R.M.S. voltage , allows to reduce the DC

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link level, using the harmonics injection technique for the modulator signal.

• get a smooth variation over the electrical spectrum, avoiding mismatches between the space harmonics and the time harmonics of the inverter output.

Fig.1. Signals in the HIPWM-FMTC2 technique. Upper graphics: sinusoidal modulator signal with harmonics injection, and triangular carrier signal modulated in frequency; middle graphic: instantaneous modulation order with α=50º (2.7 mseg with f=50 Hz); lower graphic: modulated signal.

Since the vibration force density waves depend on the product of the induction harmonics and due to the logarithmic nature of sound, the resulting radiated sound and the sound pressure level can be reduced if this mismatches are avoided. A theoretical study has been simulated in order to select an interval of frequencies were there are no space harmonics. The time harmonics, for each tested strategy, have been generated in this interval of frequencies to avoid mixing both space and time harmonics.

Firstly, the acoustic noise generated by the motor when powered by a balanced three-phase network is measured and depicted in order to identify the frequencies at which space harmonics are generated. Then the same measurements are taken when the motor is powered with an inverter and using several control strategies: a traditional Sinusoidal Pulse Width Modulation (SPWM), a trapezoidal modulator and a modulator with harmonic injection (HIPWM) in order to identify and separate the time harmonics produced under each strategy. Finally, these values are compared to the results obtained using the technique HIPWM-FMTC and the modified technique, named HIPWM-FMTC2, with sinusoidal and triangular functions to modulate the carrier signal, respectively. All the techniques use the same M values, which

represent the number of pulses per period of the modulated wave applied to the inverter's electronic switches, but modifying the parameter α. By modifying this parameter, the forbidden frequencies to be avoided in operation can be identified and the optimal value for α can be selected.

Fig. 2. Comparison between the electrical spectra (line to line, p.u. referred to DC-LINK voltage: a) α=17º; b) α=20º; c) α=30º;d) α=40º;e) α=60º. Fig. 2 shows the electrical spectra for several values of α. So, it is possible to avoid resonances machine frequency and FMM harmonics with high winding factor. The fundamental voltage, V1, is controlled by the DC-link voltage.

The emitted acoustic noise level, Leq decreases for a lower value of fsw, (which involves the same number of commutations per unit time and thus represents a similar amount of thermal stress for the switches as with the traditional SPWM strategy). The output line-to-line RMS voltage for the inverter has been fixed at 300 V for all measurements in order to filter out the noise from magnetic saturation flux density. The switching frequency fsw has been fixed at 750 Hz for all the strategies, with low values for a high-power inverter. The Fig. 3 shows the noise spectrum emitted by the motor when it is fed by a three-phase sinusoidal power supply of 300 V RMS, f = 50 Hz. It is possible to identify:

• The aerodynamic noise, whose frequency is expected at

around 300 Hz (12 fan blades regularly spaced turning at approximately 25 revolutions per second gives 12·25 = 300 Hz).

• Acoustic noise due to products of rotor space harmonics of the same harmonic number, with frequencies (2), with k = 0, 1, 2, 3,… The lowest harmonic is 28f = 1400 Hz, and r = 2p = 4.

• The electro-magnetic noise due to the products of stator space harmonics of the same harmonic number, whose frequency of the radial magnetic forces is equal to 2f = 100 Hz and r = 4.

0

20

40

60

0

0.5

1

1.5

a=60º

alpha=40º

alpha=30º

alpha=20º

Electrical spectrum

alpha=17º

Electrical Harmonic Order

Am

plitu

de R

MS

(pu)

4

• Interaction of stator and rotor space harmonics, fr = f·[k(13(1-s) ± 2)] ≈ 11f and 15f, for k = 1; 24f and 28f, for k = 2; 37f and 41f, for k = 3; 50f and 54f, for k = 4; 63f and 67f for k = 5, etc. The terms: 24f, 28f, 37f, 63f are shown in the Fig. 3, where f is the operating frequency of the induction motor.

The frequencies and the vibration mode orders for the motor

have been calculated [10]. There is an important component at 550 Hz (11·f) with r = 2 [10] due to the motor exhibiting a mechanical resonance at this frequency. A frequency range up to 5 kHz was chosen to be analyzed because the frequencies of radial forces are most significant in terms of acoustic noise inside this range. [ID=4] G1 - Record - 66.5 dB Hz; (Pa, RMS) 550.00 2.64e-02

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Fig. 3. Radiated noise spectrum with a sinusoidal power supply.

Fig. 4 shows the result for SPWM strategy with M = 15. Besides the noise due to space harmonics (11 and 37), it can be observed how electrical harmonic 13 generates sound harmonic 12, and likewise electrical harmonic 17 produces sound harmonic 18 (4) (in both cases a is odd and c is even). Also, when a is even and c is odd, 2·fsw equals 30·f, and sound harmonic 28 is a consequence of electrical harmonic 29, and likewise sound harmonic 32 is due to electrical harmonic 31. The sequence repeats itself with 3·fs equal to 45·f, with an fk value of 43 and 47, and the resulting sound harmonics. Also, it is necessary to keep in mind that, the winding factor kw17=kw37=0.9019.

By using this new modulation strategy and modifying the α parameter it is possible to spread the harmonic in the spectral windows to avoid the mechanical resonance produced by electromagnetic noise, and FMM´s harmonics with high winding factor, thereby reduce the overall noise produced by the motor.

Radiated acoustic noise versus current line spectra with SPWM M=15 strategy

0,00E+00

5,00E-03

1,00E-02

1,50E-02

2,00E-02

2,50E-02

3,00E-02

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

f/50 (Hz)

Pres

sure

(Pa)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Cur

rent

Lin

e (A

)

Pressure (Pa) Current Line (A)

PRESSURE

CURRENT LINE

Fig. 4. Radiated noise and electric spectra with SPWM, M = 15.

TABLE I

COMPARISON BETWEEN SOUND PRESSURE LEVELS, LEQ, LEQ(A) AND THD

Fig. 6 shows the sound results from Fig. 4 and 5 to highlight the comparison. The non-electromagnetic sound harmonics (i.e. those whose origin are due to mechanical and aerodynamic causes) coincide in both cases.

Fig. 5 shows the results with the HIPWM-FMTC2 strategy for α = 17º. It can be noted that (4) is followed by electrical harmonics 19. Sound harmonic 11 (550 Hz) is space harmonic and it has been reduced to approximately the same value as that in which the motor radiates when it is fed by a sinusoidal voltage supply as it can be observed in the fig. 3. The winding factor kw37 is 0.9019 for the motor analyzed. This is the reason because the FMM harmonic 37 produces a very high noise level.

Modulation Strategy Leq (dB)

Leq (A) (Pa)

Current THD (%)

Sinusoidal supply 66.5 2.22e-2 0 HIPWM-FMTC2 (α=17º) 69.9 4.75e-2 24.10 HIPWM-FMTC2 (α=18º) 70.2 4.91e-2 23.87 HIPWM-FMTC2 (α=20º) 70.1 4.86e-2 22.14

HIPWM-FMTC 70.9 5.27e-2 15.17 SPWM (M=15) 72.0 7.12e-2 32.75 HIPWM (M=15) 71.3 6.43e-2 33.18

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Radiated acoustic noise versus current line spectra with HIPWM-FMTC2 alpha=20 strategy

0,00E+00

5,00E-03

1,00E-02

1,50E-02

2,00E-02

2,50E-02

3,00E-02

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61

f/50 (Hz)

Pres

sure

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Cur

rent

Lin

e (A

)

Pressure (Pa) Current line (A)

Fig. 5. Radiated noise and electric spectra HIPWM-FMTC2, α=20º.

For most modulations tested changing the α parameters in the HIPWM-FMTC2 strategy, the sound pressure levels (both Leq and A-weighted Leq) show improvements over the noise levels under the SPWM technique, though the best result is presented here, which was obtained by testing different potential k values to avoid mixing both space and time harmonics. Table I presents the results of the SPL of several modulations tested with M = 15. Note that the amplitude modulation order, Ma has been fixed to 1 for all the strategies implemented in this paper because the best results are obtained with this value.

The motor used in tests was a three-phase AEG motor with a squirrel-cage rotor, a nominal power of 0.76 kW and 380 V. line-to-line voltage, 50 Hz, with 36 slots in the stator, 26 bars on the rotor and 4 poles.

The experimental setup consists of a PC-DSP for generating control signals and a Skiip 132GDL 120-412 CTV inverter by Semikron, whose output voltages were measured with a TeamWares Equa network analyzer. This equipment provides the spectrum of the 50 first harmonics of the line-to-line voltage, as well as the current. The radiated acoustic noise was measured in a semi-anechoic room and the results of the acoustic measurements were analyzed with a 01dB METRAVIT Symphonie model sonometer for both linear and A-weighted results (Pa RMS).

Therefore, the sound pressure level is lower than that obtained in other traditional techniques, which would require a change in the value of M if a match with certain natural frequencies must be avoided.

SPWM versus HIPWM-FMTC2

0,00E+00

5,00E-03

1,00E-02

1,50E-02

2,00E-02

2,50E-02

3,00E-02

1 11 21 31 41 51 61

f/50

SPL(

Pa)

SPWM HIPWM-FMTC2 20º

SPWM

HIPWM-FMTC2

v

Fig. 6. Comparison of radiated noise spectra with SPWM M=15 and HIPWM-FMTC2, α=20º.

III. CONCLUSION A key issue in a noise control strategy involves avoiding

the excitation of the stator resonance frequencies and the matches between the higher space harmonics (i.e. the space harmonics with higher winding factors) and the time harmonics of the stator current. By using HIPWM-FMTC2 strategy (a modified strategy HIPWM-FMTC) and electing appropriate values for α, it is possible to keep THD with similar values to HIPWM-FMTC strategy, while the control to displace the time harmonics to avoid the resonance frequencies and “forbidden” FMM’s is improved.

The only difference with the HIPWM-FMTC technique focuses in the instantaneous modulation order function (a sinusoidal function with the HIPWM-FMTC technique). HIPWM-FMTC2 technique, uses a trapezoidal function and consists in a linear variation of the relationship between the frequency of the carrier wave and the modulator signal phase, i.e., with α parameter. The harmonic spectrum presents a progressive evolution when α varies over a range, therefore it is possible to optimize the inverter behavior in order to achieve the THD and reduce the acoustic noise. With low values of α, the acoustic results are better than with high values because electric harmonics spectrum does not have significantly high terms, and therefore, sprayed harmonic terms are obtained. .

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REFERENCES [1] C. Grabner, “Design impacts to the acoustic noise emission of a

converter driven squirrel cage induction motor”, International Symposium on Power Electronics, Electrical Drives, Automation and Motion, Italy, pp. 711-716, SPEEDAM 2008, July 2008.

[2] S. Guthridge, R.E. Harper, H. Marr, B. Abali, “Acoustic noise cancellation by phase alignment of cooling fans”, 23 rd IEEE SEMI-THERM 2007 Symposium, pp. 131-135, 18-22 March 2007.

[3] W. Helmut, Z. Peter, X. Jian, “On acoustic noise reduction procedure for inverter-fed induction machines”, 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008), pp. 1722-1728, 2008.

[4] J.F. Gieras, C. Wang And J. Cho Lai, Noise of polyphase electric motors, 1º ed., Taylor & Francis: Boca Raton, FL33487-2742 U.S.A., pp. 1-76, 2006.

[5] K. Ki-Seon, J. Joung-Gook, L. Joung-Cheol, “A new hybrid Random PWM scheme” IEEE Transactions on Power Electronics, vol. 24, no. 1, pp. 192 – 200, January 2009.

[6] A.M. Trzynadlowski, F. Blaabjerg, J.K. Pedersen, L. Kirlin, S. Legowski, “Random Pulse Width Modulation Techniques for Converter-Fed Drive Systems- A Review”, IEEE Transactions onIndustry Applications, vol. 30, No. 5, pp.1166-1175, Sep/Oct. 1994.

[7] A.M. Trzynadlowski, K. Borisov and. L. Qin, “A novel random PWM technique with low computational overhead and constant sampling frequency for high-volume, low-cost applications”, IEEE Transactions on Power Electronics, vol. 20, No. 1, pp. 116-122, January 2005.

[8] H. Stemmler, T. Eilinger, “Spectral analysis of the sinusoidal PWM with variable switching frequency for noise reduction in Inverter-Fed induction motors”, Power Electronics Specialist Conference PESC 94, pp. 269-277; 1994.

[9] H. Bülent Ertan and N. Balkan, “Comparison of PWM and PFM induction drives regarding audible noise and vibration for household applications”, IEEE Transactions on Industry Applications, Vol. 40, No: 6, pp. 1621-1628, Nov/Dec. 2004.

[10] A. Ruiz-Gonzalez, M. Meco-Gutierrez; F. Perez-Hidalgo; F. Vargas-Merino; J.R. Heredia-Larrubia, “Reducing acoustic noise radiated by PWM inverter-fed motors controlled by a new PWM strategy”, IEEE Transactions on Industrial Electronics, vol. 57, nº 1, pp.228-236, January 2010.

[11] M.J. Meco-Gutierrez, F. Perez-Hidalgo, F. Vargas-Merino, J.R. Heredia-Larrubia, ”A new PWM technique frequency regulated carrier for induction Motors supply”, IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1750-1754, October 2006.

[12] M. Meco-Gutierrez; F. Perez-Hidalgo; F. Vargas-Merino; J.R. Heredia-Larrubia, “Pulse width modulation technique with harmonic injection and frequency modulated carrier: formulation and application to an induction motor”, Electric Power Applications, IET, vol. 1, Issue 5, pp. 714 – 726, Sept. 2007.

[13] F. Vargas-Merino, M.J. Meco-Gutierrez, J.R. Heredia-Larrubia, A. Ruiz-Gonzalez, “Low Switching PWM Strategy Using a Carrier Wave Regulated by the Slope of a Trapezoidal Modulator Wave” IEEE Transactions on Industrial Electronics, Vol. 56, Issue 6, pp. 270 – 274, June 2009.

[14] Vargas-Merino, F.; Meco-Gutierrez, M.J.; Heredia-Larrubia, J.R.; Perez-Hidalgo,F.M.; Ruiz-Gonzalez, A. :”Slope modulation strategy for generated PWM”; Electronic Letters, IET 2008. Volume 44; Issue 24.

[15] F. Vargas-Merino, M.J. Meco-Gutierrez, J.R. Heredia-Larrubia, F.M. Perez-Hidalgo, A. Ruiz-Gonzalez, “Slope modulation strategy for generated PWM” Industrial Electronics 2008, ISIE 2008, IEEE International Symposium, pp. 403-405.

[16] J. Le Besnarais; V. Lanfranchi; M. Hecquet; and P. Brochet, “Characterization and reduction of audible magnetic noise due to PWM supply in induction machines”, IEEE Transactions on Industrial Electronics, 2009. Accepted for publication.

[17] J. Sagarduy, A.J. Moses and F.J. Anayi “Eddy Current Losses in Electrical Steels Subjected to Matrix and Classical PWM Excitation Waveforms”, IEEE Transactions on Magnetics, vol. 42, Issue 10, pp. 2818 – 2820, Oct. 2006.

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[19] W.C. Lo, C.C. Chan, Z.Q. Zhu, Lie Xu; D. Howe and K.T. Chau; “Acoustic Noise Radiated by PWM-Controlled Induction Machine Drives”, IEEE Transactions on Industrial Electronics vol. 47, Issue 4, pp. 880 – 889, Aug. 2000.

A. Ruiz-González was born in Málaga, Spain. He received the B. Eng., M.S. and Ph.D. in Industrial Engineering from University of Málaga, Spain, in 1986, 2006, and 2009 respectively. He worked in Alcatel for five years as a testing engineer in several areas of the electronics industry (telephony and line switching). Currently, he is an Associate Professor of the Department of Electrical Engineering at the University of Málaga. His research interests include

three-phase converters control and analysis of quality signal for motor drives.

M. J. Meco-Gutiérrez was born in Málaga, Spain. He received the B.S. in Mechanical Engineering from the University of Málaga, Spain, in 1983; M.S. degree in Electronics and Automatic Engineering from the UNED of Madrid, Spain, in 1983 and Ph. D. degree in Engineering from the University of Málaga, Spain, in 2003. He worked as project and consulting engineer. Currently, he is Professor of the Department of Electrical Engineering at the

University of Málaga. His research interests include development of signal quality and PWM control for converters.

F. Pérez-Hidalgo was born in Málaga, Spain. He received the M.S. degree in industrial engineering form the Polytechnic University of Madrid, Spain, in 1989 and the Ph. D. degree in industrial engineering from the University of Málaga, in 1993. Since 1995, he has been a Proffesor with the Department of Electrical Engineering, University of Málaga. He research interests include power electronics, motor drives control, and analysis of quality signal for motor drives.

F. Vargas-Merino was born in Málaga, Spain, on January, 1962. He received the M.S. degree in Industrial Engineering from the University of

Seville, Spain, in 1988 and Ph. D. degree in Industrial Engineering from the University of Málaga, Spain, in 2002. He worked in several areas of the construction industry and the design of industrial plants. Currently, he is an Associate Professor of the Departament of Electrical Engineering at the University of Málaga. His research interests include three-phase converters control and analysis of quality signal for motor drives. J.R. Heredia-Larrubia was born in Málaga, Spain, on February, 1964. He received the M.S. degree in Telecommunication from Polytechnic University of Madrid, Spain, in 1991 and Ph. D. degree in Industrial Engineering from the University of Málaga, Spain, in 2000. He worked in Alcatel for two years as a design engineer. Currently, he is an Associate Professor of the Department of Technology Electronic at the University of Málaga.

His research interests include hardware implantation of motor drives control and analysis of quality signal for motor drives.

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