A Discrete Random PWM Technique for Acoustic Noise Reduction in Electric Traction Drives

Transcription

1 A Discrete Random PWM Technique for Acoustic Noise Reduction in Electric Traction Drives Subhadeep Bhattacharya*, Diego Mascarella, Geza Joos Department of Electrical and Computer Engineering McGill University Montreal, Canada Gerry Moschopoulos Department of Electrical and Computer Engineering Western University London, Canada Abstract This paper investigates various random PWM () techniques for conventional two-level inverter-fed traction drives and proposes a discrete technique for acoustic noise reduction. The proposed technique randomizes within a set of predefined switching frequencies compared with the continuous nature of randomization in conventional techniques. The proposed method was compared with conventional and other techniques with respect to the A-weighted IEC standard acoustic noise profile. The proposed method spreads the narrowband harmonic clusters effectively and, compared to the conventional techniques, reduces broadband noise by 2-6 db over the full modulation index range, thus producing a better acoustic noise profile. Index Terms Random PWM, acoustic noise, traction drives, A-weighting I. INTRODUCTION Traction drives are widely used in many industrial and automotive applications. It is desired that these drives operate as quietly as possible, especially when there are a number of such drives operating in the same vicinity. As a result, acoustic noise standards such as IEC [1] have been developed to set industry-wide noise emission levels which manufacturers must make their products adhere to. Acoustic noise is a cumulative effect of the presence of different frequency components in the noise [2]. The sensitivity of the human ear to those tonal frequencies is normally modeled using different frequency weighting curves A-weighting (db) Fig. 1. A-weighting curve as defined by IEC [1] as the human ear is more sensitive to particular frequencies in the audio frequency range (.1-2 khz). For example, Fig. 1 shows the commonly used A-weighting curve that is specified by the IEC standard. This curve is at its peak in the 1-5 khz frequency range, an indication of the frequencies that are most likely to be heard by the human ear. Acoustic noise in traction drives is caused by three different sources which are: 1) mechanical, 2) aero-dynamical, and 3) electromagnetic. The mechanical noise of a drive comes from the mechanical defects of the system [2-4], rotor balancing issues and bearings. The aerodynamic noise of a drive comes from the air-turbulence created by the cooling fins [2-4] of the motor and other associated apparatus. As mechanical noise and aerodynamic noise are not directly caused by the inverter supplying power to the motor, they cannot be reduced by sophisticated inverter control techniques. Electromagnetic noise, however, is directly related to the inverter output waveform. The inverter, being a nonsinusoidal power supply, injects harmonic currents into the motor windings [5], causing vibrations and associated noises. In this study, the electromagnetic noise due to a two-level inverter has been considered as the acoustic noise of the traction drive. As inverters are controlled by space-vector pulse-width modulation () with a fixed switching frequency, the harmonic spectra of its output waveforms contain narrowband harmonic clusters concentrated around the inverter switching frequency and its multiples [6]. In a traction motor, the harmonic flux waves produced due to these harmonic components interact with the fundamental flux wave and create vibrations proportional to the square of air-gap flux. If these switching frequency harmonics are within the audio frequency range, they create narrowband acoustic noise [5-7]. In the literature, several ways to reduce the acoustic noise created by an inverter have been discussed. Several passive filtering techniques have been investigated [8], however, they introduce passive components in the system and increase its size and cost. Other ways of reducing acoustic noise include implementing traction drives with random pulse-width modulation () switching schemes [9-2]. Such techniques incorporate a non-deterministic (random) component in the switching function that converts the narrowband acoustic noise into broadband noise by spreading the harmonic spectrum so that harmonics are not concentrated /15/$ IEEE 6811

2 around certain frequencies. Conventional techniques can be broadly classified into the following categories: Random Carrier Frequency PWM (RCF-) [9-15]: The switching frequency is varied within a band to randomize the switching pulses. By varying the switching frequency, the pulse position and pulse durations are randomly distributed. Fixed Carrier Frequency Random Pulse-Position PWM (FCF-RPP-PWM) [16-2]: In comparison to the RCF-, the switching frequency of the system remains constant while the pulse positions are changed in a random manner. For example, in [17], the zero vector timing is divided in a random manner between two available zero vectors, thus creating a random pulse position distribution. Fig. 1 illustrates the difference between the technique and the techniques presented in [1] and [17]. In, the switching time period (T) is fixed and the total zero vector timing (T z ) is equally distributed between two zero vectors. With FCF-, the switching time period remains constant, however, the zero vector division is changed with a random variable ( ). With RCF-, the switching time period changes in a random manner, whereas, the total zero vector is equally distributed between two zero vectors. Most previously proposed techniques have at least one of the following two drawbacks: The switching frequency is continuously varied within a predetermined range, resulting in a spread spectrum and considerable increase of broadband noise [21] that may produce unpleasant audible noise in the 1-5 khz frequency range. Although these techniques are able to spread the peak harmonic spectrum so that it is not concentrated, it is questionable whether overall audible noise reduction can be achieved. Some techniques, especially FCF-RPP-PWM techniques, cannot operate with high modulation indices [17] as the zero vector timing reduces at high modulation indices. An RCF- method where some pre-defined switching frequencies are selected randomly was proposed in [22] to reduce the harmonic intensity in DC-DC converters. Such a discrete technique, however, has not been used in traction motor drives and in comparison to conventional techniques, its impact on the acoustic noise hasn t been investigated. In this paper, the discrete technique has been proposed for acoustic noise reduction for electric traction drives. The principles and implementation of the new technique are explained relative to those of conventional RCF- techniques. The impact of the discrete and conventional techniques on the frequency spectra of the inverter output waveform is then shown and compared. The effect of the proposed method on the A-weighted acoustic noise profile shown in Fig. 1 is compared with that of other conventional PWM techniques. The comparisons have been done for different modulation indices and switching frequencies. Finally, experimental results showing the effectiveness of the discrete technique are presented. II. DISCRETE RANDOM PWM: ANALYSIS & IMPLEMENTATION Conventional RCF- techniques use uniformly randomized switching frequencies around the nominal switching frequency ( ), within an upper and lower band. The band effectively determines the effectiveness of these techniques as more narrowband noise attenuation can be achieved with a larger band. The upper limit of the switching frequency band depends on the allowable switching loss of the switches; the lower band depends on the dynamics of the system and the amount of lower frequency components in the system. Conventionally, the chosen switching frequencies can be any value within the specified band. A 25% band around is normally selected as it provides a good spread of the harmonic spectrum without drastically impairing output voltage waveform quality. The selected switching frequency band in this study is thus. RCF- techniques can be considered to be continuous due to the continuous nature of the randomization process. The switching frequency of these techniques normally can take any value within the switching frequency band and cannot be controlled due to its stochastic nature. The switching frequency ( ) of continuous techniques can be expressed as where is a uniformly distributed continuous random variable. In the proposed discrete technique, the randomization of the switching frequencies within the T z /4 T z /2 T z /4 T z /4+ /2 T z /2 - T z /4+ /2 T z /4+ /4 T z /2 + /2 T z /4+ /4 a b c T active T active T active T active T active T active T Fixed T z division T FCF- Random T z division T+ RCF- Random T, fixed T z division Fig. 2., FCF- and RCF- vector timings; T active is the active vector timing, T z is the total zero vector timing and is the random variable 6812

3 predefined band is done in the following way. Initially, some predefined switching frequencies within the aforementioned switching frequency band are selected. The selected switching frequencies are then chosen in a random manner. In this way, the switching frequency of the system is randomized in a discrete manner (i.e. randomly chosen between discrete switching frequency values). In this study, the predefined switching frequency values are selected to be uniformly distributed within the switching frequency band. Seven different discrete switching frequencies within the switching frequency band were used for the proposed discrete in this study and the switching frequency ( ) used for any given period can be expressed as where is a uniformly distributed discrete random variable. Fig. 3 shows the probability density function of output current waveforms produced by an inverter that operates with conventional space-vector PWM (), with continuous and with the proposed discrete PWM technique. It can be seen that with the conventional technique, the modulator introduces a single switching frequency in the spectrum with probability one, which creates a harmonic spectrum clustered around the switching frequency and its multiples. In conventional continuous techniques, the modulator uses a significant number of switching frequency values within a band defined by (1), which flattens the peak of the harmonic spectrum. These added switching frequencies and their multiples, however, interact with multiples of fundamental frequency to introduce more frequency components in the spectrum, thus increasing the magnitude of the flattened part of spectrum [16]. In the discrete technique, the modulator introduces fewer switching frequency harmonics into the system than the continuous technique, thus having fewer switching frequency components that interact with the fundamental frequency component and its multiples. It therefore provides a localized spread spectrum around the nominal switching frequency instead of a spectrum spread over a wider frequency range. Fig. 4(i) shows how the proposed discrete technique can be implemented. The switching carrier function of the modulator (which is used to generate the active vector and zero vector timings) is randomized in a discrete random manner, as defined by (2). The random number generator randomly chooses one of the predefined switching frequencies and based on the chosen switching frequency, the slope of the switching carrier function is changed. To maintain proper generation of fundamental voltage and to reduce current Probability density F c Probability density Continuous Probability density Discrete F c - F c F c + F c F c - F c F c F c + F c Fig. 3. Probability density function of, Continuous and distortion due to randomization, the following steps are taken: 1) The modulator receives information of a new switching frequency only after the previous triangle switching carrier function has been completely used to generate active and zero vector timings. A switching frequency update before the completion of the previous time-period introduces errors in fundamental voltage generation. 2) The active vector timings in each switching period remain constant to provide the required fundamental voltage. Any randomization in active vector timings would introduce switching cycle errors in fundamental voltage generation and associated distortion. 3) The total zero vector timing is changed directly proportional to the randomized switching time period. The zero-vector timing in each switching cycle is equally distributed between two zero vectors such that the pulses are centered within a time-period; this helps to reduce the current ripple, as discussed in [17]. Duty cycle (d a, d b, d c ) Random Variable Predefined switching frequencies d a d b d c Tz/4 T z /2 f s update Tz/4 update (i) Switching carrier generation f s update Vector timings T active T active T active T active T active T active T T- T+ (ii) III. SIMULATION RESULTS The proposed discrete technique, the conventional and continuous techniques were simulated using MATLAB-Simulink and implemented on a two-level inverter driven permanent magnet synchronous motor (PMSM). As discussed earlier, a switching frequency band of ( was chosen to randomize the switching frequency. The simulations were performed for 2 khz, 4 khz Tz/4+ /4 f s T z /2 + /2 Tz/4+ /4 Fig. 4. (i) Implementation of discrete, (ii) Switching carrier function update and the active, zero vector timings 6813

4 and 8 khz nominal switching frequencies and for different modulation indices ranging from.2 to 1. The impact of the modulation strategies on output waveform harmonic spectra and associated acoustic noise have been analyzed in two different ways. First, the impact on harmonic spectra has been has been analyzed using inverter output waveform distortion and resulting power spectral density. Second, using the A-weighting curve, the impact of the modulation strategies over the complete audio frequency range has been quantified. A. Output waveform analysis Fig. 5 shows the impact of the proposed technique on the frequency spectra and the resulting power spectral density (which correlates to the acoustic noise due to the inverter [2]) of the inverter output current and the result is compared with continuous and conventional technique. The power spectrum was calculated by using the Periodogram method [23] on the inverter output current. As shown in Fig. 5(i), with the technique, the frequency spectra of output current has narrowband harmonic clusters around the switching frequency (8 khz) and its multiple. The two techniques are able to spread the narrowband harmonic cluster in a similar manner. Similarly, the power spectral density, shown in Fig. 5(iii), shows a similar spread spectrum effect. Compared with the 6 4 Magnitude (A) 2 Magnitude (A) technique, the techniques are able to reduce the narrowband noise by around 1 db; hence, they are able to reduce the single tone noise of the system. On the other hand, the techniques introduce a significant amount of harmonics, lower than the switching frequency at the output current spectra. This introduces broadband noise in the audio frequency range (1-5 khz frequency range). As seen from Fig. 5(i) and Fig. 5(iii), the discrete technique does not spread the narrowband frequency cluster well beyond the switching frequency and introduces fewer harmonics in the audio frequency range than the continuous technique, thus reducing the broadband noise. In Fig. 5 (iii) and Fig. 5(iv), the impact of the conventional and proposed PWM techniques on the frequency spectra and the resulting power spectral density of the inverter output current are shown with 4 khz switching frequency. Unlike 8 khz switching frequency, which is outside the 1-5 khz range of the audio frequency zone, using a of 4 khz switching frequency creates narrowband harmonic clusters in the audio frequency range. As can be seen, the proposed discrete technique and the continuous technique flatten the frequency spectrum. Referring to Fig. 5(iv), they reduce the noise peak by 9-1 db. Its effect in the 1-5 khz needs to be quantified using some other technique as the difference between the continuous and discrete technique is not (i) (iii) Power Spectral Density (dbm) Power Spectral Density (dbm) (ii) (iv) Fig. 5. Comparison of frequency spectra of inverter output current and power spectrum density (dbm) at (i-ii) 8 khz switching frequency (iii-iv) 4 khz switching frequency. The RMS value of fundamental current is approximately 166 A in all cases. 6814

5 visually clear. The effect of these PWM techniques on cumulative acoustic noise needs to be quantified so that the techniques can be properly compared. This is done in the next section where the A-weighting scale shown in Fig. 1 is used. B. A-weighted Acoustic Noise Analysis The A-weighted acoustic noise analysis is normally done to assess the cumulative effect of the noise amplitudes at each frequency on the overall noise value. Fig. 6 shows the procedure of the cumulative A-weighted noise calculation procedure [24]. At first, the power spectral density is found using the periodogram method, applied on the output current waveform. The power spectral density values (in db) is then added with the weighting factors of the A-weighting curve. This operation converts the unit of the power spectral density to dba. Subsequently, the cumulative acoustic noise is calculated using the following where n is the number of frequency components considered and is the value of the frequency component in dba. To assess the effect of the PWM techniques, two different frequency range has been considered: (i) Range I: 1-5 khz, (ii) Range II: 1-2 Hz. Fig. 7 shows the A-weighted [1] acoustic noise profile of the system when the, continuous and discrete techniques are used with 8 khz switching Output Current Waveform Power Spectral Density using Periodogram Method A-weighted scaling factor (in db) addition (Fig. 1) A-weighted Acoustic noise in dba (Figs. 7) Cumulative Acoustic noise in dba (Eq. 3) Fig. 6. The flowchart to use A-weighting curve frequency. It can be seen that the acoustic noise profile has peaky tones with the technique and the Noise Noise Noise (i) (ii) (iii) Fig. 7. A-weighted acoustic noise for (i) (ii) Continuous (iii) techniques increase the acoustic noise at the 1-5 khz frequency range. It can also be seen that, with the help of the discrete technique, the acoustic noise in that range is reduced considerably compared to the continuous technique. In Table I, the effect of these PWM techniques on acoustic noise is shown. Table I shows the cumulative effect on acoustic noise over ranges of 1-2 Hz and 1-5 khz, for an inverter operating with modulation index.8, and 2, 4, 8 khz switching frequency. These two frequency ranges were selected as the first range covers the full spectrum of A- weighting curve and the second range covers the part of the spectrum where the human ear is most sensitive. It can be seen from Table I that with 8 khz switching frequency, the technique has the least noise in the 1-5 khz range as the switching frequency is outside that range, but the most noise over the 1-2 Hz range. For 2 khz and 4 khz switching frequencies, the technique causes the maximum noise over both frequency ranges. Compared to the technique, both techniques reduce noise over the 1-2 Hz frequency range, but 6815

6 TABLE I A-WEIGHTED ACOUSTIC NOISE OVER 1-2, HZ AND 1-5 KHZ 1-2 Hz 1-5 khz Switching Frequency Disc. Disc. 2 khz khz khz increase noise over the 1-5 khz range when the switching frequency is 8 khz. For both frequency ranges and for the three different switching frequencies, more acoustic noise reduction is achieved with the discrete technique than with the continuous technique. For example, with 8 khz switching frequency, the discrete technique reduces the increased noise created by the continuous technique at 1-5 khz range by 1.4 dba. This decrease, however, is not appreciable over the 1-2 Hz range. Fig. 8 shows a comparison between these three Magnitude (A) Noise Disc Fig. 8. Comparison over change in modulation index techniques over a complete modulation index range with 8 khz switching frequency over a 1-5 khz frequency range. It can be seen that the techniques creates more acoustic noise compared to conventional technique over that frequency range. The discrete technique, however, creates appreciably less broadband acoustic noise compared to the continuous techniques. IV. EXPERIMENTAL RESULTS The proposed discrete, conventional and continuous techniques were implemented on a hardware setup. The setup consisted of a two-level inverter feeding a permanent magnet synchronous motor (PMSM). The inverter pulses were generated by an OPAL-RT rapid prototyping tool. The nominal switching frequency was chosen to be 4 khz as it is within the most sensitive range of audio frequency (1-5 khz). A band of 3-5 khz was selected to randomize the switching frequency. The results are shown in Fig. 9. As expected, the conventional sequence exhibits narrowband switching frequency components at integral multiples of the switching frequency. It can be seen that the techniques are able to spread the peaky spectrum of technique. This reduces the multiple narrowband tones in the acoustic Fig. 9. Experimental Results showing (i) techniques spreading harmonic spectrum (ii) less spread in 1-5 khz range compared to Continuous noise, namely the narrowband noise. Also, compared with the continuous technique, the discrete technique introduces fewer frequency components around the switching frequency and its multiples. The resulting impact on the A-weighted cumulative noise is calculated using (3) and tabulated in Table II. It can be seen that compared with the conventional technique, the techniques reduces cumulative acoustic noise As the discrete technique introduces less frequency components, it also reduces the cumulative noise compared with the continuous technique. As the switching frequency is within the most sensitive range of audio frequency, the cumulative noise value is similar for all three types of PWM technique over both Range I and Range II. To assess the impact of the various PWM techniques operating with 8 khz switching frequency (with 25% switching frequency randomization) on acoustic noise, similar results were experimentally obtained. As the switching frequency is outside the most sensitive range of audio frequency, the margin of cumulative noise reduction using the Switching Frequency (khz) TABLE II A-WEIGHTED ACOUSTIC NOISE Frequency range (Hz) Continuous Discrete 1-2, ,-5, , ,-5,

7 techniques is less when calculated over Range II. The cumulative acoustic noise calculated for Region I, however, shows an increase in acoustic noise due to the techniques due to an increase of the broadband noise although they reduce narrowband noise. It can be seen that the discrete technique lowers acoustic noise by 1.66 db more than the continuous technique in the audio frequency range. V. CONCLUSION In this paper, a new discrete technique was proposed for a two level inverter fed traction drive. Its impact on the acoustic noise profile was demonstrated with the help of simulation and experimental results of the harmonic spectra of the inverter output current waveforms. It was shown that the discrete technique reduces broadband noise by 2-6 db over a complete modulation index range in comparison to conventional techniques and reduces the peaky noise by 9-1 db in comparison to conventional techniques. The proposed discrete technique thus reduces the single tone acoustic noise produced by the inverter supply while containing the broadband noise produced due to pulse position randomization. ACKNOWLEDGMENT The authors would like to thank the Natural Science and Engineering Research Council of Canada (NSERC) and the industrial partners: TM4 Electrodynamic Systems, Linamar and Infolytica Corporation for their contribution under Automotive Partnership Canada (APC) project. REFERENCES [1] Electroacoustics Sound Level Meters, IEC Std , 213. [2] J.F.Gieras, C.Wang, and J.C.Lao, Noise of Polyphase Electric Motors. Boca Raton, Florida: Taylor & Francis, CRC press, 26. [3] Máthé, L.: Product sound: Acoustically pleasant motor drives, Ph.D. dissertation, Aalborg University, Denmark, 21 [4] IEEE Test Procedure for Airborne Sound Measurements on Rotating Electric Machinery, IEEE Std , 198. [5] W.C. Lo, C.C. Chan, Z.Q. Zhu, L. Xu, D. Howe and K.T. 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