N POWER electronics, various pulse-width modulation. (PWM) techniques are widely employed to control the output of static power converters. The reason for ...
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 11, NO. 4, JULY 1996
“Dead-Band’’ PWM Switching Patterns Vassilios G. Agelidis, Member, IEEE, Phoivos D. Ziogas, Fellow, IEEE, and Geza Joos, Senior Member, IEEE
Abstract-Reference/modulating waveform continuity is not a necessary condition for the implementation of switching patterns for three-phase pulse-width modulated (PWM) converters if the load or the source are Y-connected. This is based on the fact that the converter phase-voltages do not need to be sinusoidal and switching pattern discontinuities-“dead-bands”-do not degrade the quality of outpuffinput voltage/current waveforms by introducing low-order harmonics if certain parameters are optimized. This paper discusses general characteristics of various discontinuous switching patterns for PWM converters and shows that they can yield better performance than their continuous counterparts in some operating regions. Performance is defined as harmonic distortion normalized with respect to effective switching frequency and serves as a measure of comparison with continuous PWM techniques. The applications considered include general purpose and application specific solid-state power supplies using voltage source inverters and PWM rectifiers. Theoretical considerations are verified on an experimental unit.
I. INTRODUCTION
N POWER electronics, various pulse-width modulation (PWM) techniques are widely employed to control the output of static power converters. The reason for using PWM techniques is that they provide voltage andlor current waveshaping customised to the specific needs of the application under consideration. A three-phase voltage source inverter (VSI) (Fig. 1) is typically used to convert a dc voltage into three-phase switching waveforms that are filtered to produce a symmetrical threephase sinusoidal system. A similar power circuit structure can be used as a rectifier if the load becomes the ac mains. Generally, two classes of PWM techniques for static power converters can be identified. The programmed or optimal PWM techniques that produce switching patterns based on optimization of specific performance criteria are the first [I]. In this case, the converter switching patterns are calculated a priori for given operating conditions and then stored in memory (look-up tables) for use in real time. Reduction in converter effective switching frequency is achieved and higher gain due to overmodulation is possible when compared with the conventional sine PWM scheme [I]. However, the considerable computational effort of solving nonlinear equations to derive the switching angles, the large memory required to store the information for various modulation indexes, and Manuscript received September 24, 1992; revised March 12, 1996. V. G. Agelidis was with the Department of Electrical and Computer Engineering, Concordia University, Montreal, Quebec, Canada. He i s now with the School of Electrical and Computer Engineering, Curtin University of Technology, Perth, WA, 6001, Australia. P. D. Ziogas, deceased, was with the Department of Electrical and Computer Engineering, Concordia University, Montreal. Quebec, Canada. G. Joos is with the Department of Electrical and Computer Engineering, Concordia University, Montreal, Quebec H3G lM8, Canada. Publisher Item Identifier S 0885-8993(96)05163-0.
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Voltage-source inverter power circuit
the relatively sophisticated control to allow smooth transient pat tern changes are considered serious practical difficulties. ‘The other class is based on certain low-frequency reference or modulating waveform, which is compared with a highfrequency carrier waveform. These techniques are known as carrier PWM techniques [2]. To illustrate the main idea associated with the carrier PWM techniques, Fig. 2 shows the more common one, the sinusoidal pulse-width modulation (SPWM) technique. It is based on the principle of comparing a triangular carrier signal with a sinusoidal reference waveform (natural sampling) [3]. Although the implementation of this technique is relatively simple, there are two drawbacks when compared with the six -step inverter as follows: 1 ) attenuation of the fundamental component of the output waveform or in other words the maximum line-to-line amplitude voltage is 0.866 pu ( E = 1 pu); 2,) high switching frequency, when compared with the six-step inverter, which means increased stresses on converter semiconductor elements. To overcome these problems, improved PWM techniques have been proposed in the technical literature over the last 25 years. There are numerous technical papers dealing with PWM control in inverterkectifier systems. Furthermore, when the microprocessors became available, significant work is reported in [4]-[8] where problems associated with the online computation of the switching signals had to be dealt with. However, some proposed techniques improve only the gain of the modulator, and some others improve the gain and provide reduction in the effective switching frequency. Converter effective switching frequency is defined as the number of current interruptions normalized over the output period. A simple scheme to improve the gain of the pulse-width modulator is the third harmonic injection PWM pattern (HIPWM-first and third) [9]-[ 1 I]. This technique has been
0885-8993/96$05.00 0 1996 IEEE
AGELIDIS et al.: “DEAD-BAND’ PWM SWITCHING PATTERNS
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derived from the conventional sinusoidal PWM technique through the addition of the 17% third-harmonic component to the sine reference waveform. Fig. 3 illustrates this scheme. It should be noted that the 15% increase in gain over the conventional SPWM technique is achieved at the expense of introducing third harmonics on the line-to-neutral waveforms [Fig. 3(c)]. However, for a balanced load with a floating neutral point, third harmonic currents cannot flow and therefore third harmonic voltages are not present on the line-to-line waveforms [Fig. 3(e)]. Based on the same idea, an alternative pattern is the multiple HIPWM (first, third, and ninth) [2]. This technique is a variation of the previously presented HIPWM (first and third). In particular, additional harmonic component multiple of three (i.e., ninth) is also injected in the reference waveform [ 2 ] . Although these switching patterns provide increased gain compared with the conventional SPWM technique, they also imply that the reference or modulating waveforms have to be continuous, despite their shape. As a result, they do not provide any reduction in effective switching frequency compared with the original SPWM technique.
However, there exist PWM techniques that provide not only increased gain similar to the previous ones, but also a reduction in the effective switching frequency since switching elements are kept inactive for a specified interval. For instance, when the neutral point of the load is floating in a voltage source inverter, converter phase legs can be “relaxed’ to achieve lower effective switching frequency by avoiding intersections for some interval. This can be done by modifying either the modulating/reference waveform or by employing a special carrier waveform. Therefore, two such sets of PWM techniques can be identified. One technique that belongs to the first set (when the carrier waveform is modiified to avoid intersections) is known in the literature as modified sinusoidal PWM (MSPWM) technique 1121. The other set of improved PWM techniques introduces a modified reference/modulating waveform, which results in a “dead-band’ total of 360” for a three-phase converter. Examples of such “dead-band’ PWM switching patterns are shown in Fig. 4 [13] and Fig. 5 [14], [15]. Specifically, the respective reFerence waveforms as shown in Figs. 4(a)
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. I I , NO. 4, JULY 1996
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and 5(a) introduce a “dead-band.’’ This means that for the same carrier frequency, the effective switching frequency is significantly reduced since the switches are kept inactive for some time. Therefore, switching losses and resulting stresses of the PWM converter for the same carrier frequency are potentially reduced when comparing with continuous PWM techniques [ 171, [ 191, [20].This set of PWM techniques will be referred in this text as “dead-band” PWM switching patterns. The objective of this paper is to present and critically discuss various “dead-band’’ PWM switching patterns proposed in the technical literature for three-phase converters and to identify their generalized common characteristics. These techniques are suitable for example in high-performance ac drives when “silent” due to high-frequency operation can be achieved with a reduction in the effective switching frequency. It is also shown that “dead-band” switching patterns for PWM converters can yield better performance than their conventional continuous counterparts for the same resulting effective switching frequency. This paper is organized in the following way. Section I1 presents the mathematical explanation as to why nonsinusoidal
reference signals can be used for three-phase PWM converters. Section I11 outlines the general rules and optimization criteria of the modulating or reference functions when including “dead-band.’’ Section IV presents harmonic analysis of the different reference waveforms. In Section V, another “deadband” PWM scheme based on the rules identified in Section I11 is developed. An evaluation of the schemes under consideration with respect to harmonic distortion is provided in Section VI. Finally, Section VI1 presents some selected experimental results. 11. THREE-PHASECONVERTER
Considering the inverter circuit shown in Fig. 1, it can be seen that if the load is Y-connected, the load line-to-line voltages ( V A B . V B C . U C A ) do not clearly define the respective inverter phase voltages ( U A N ,V B A T ,V C N ) . which are defined, on an instantaneous basis, as ?)AN =
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AGELIDIS et al.: “DEAD-BAND PWM SWITCHING PATTERNS
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= 0 . 8 . f O = 30 Hz, f c = 1200 HZ (24 Fig. 4. First example of a “dead-band” PWM switching pattern [13]. (a) Reference and carrier waveforms, pu). (b) Line-to-neutral switching pattern. (c) Spectrum of the line-to-neutral switching pattern. (d) Line-to-line output voltage waveform. (e) Spectrum of the line-to-line output voltage waveform.
The voltage W,N between the neutral point of the load and the neutral point (midpoint) of the dc source, which is not defined by (I), can have any time variation. Furthermore, the inverter phase voltages (phase switching functions) can only have two distinct potentials, &E/2. This is true if the Y -connected load becomes the source and the power circuit operates as a PWM rectifier. Similar relationships exist for the respective reference signals as
Again, only e A n , e B n , and eCn of the reference signals for the inverter phase voltages are directly defined according to the desired reference signal for the load voltages.
It is, therefore, advantageous that the time variation of the zero-sequence component enN of the reference signals [see
( 2 ) ] is chosen so that 1) the gain of the modulator is increased as much as possible; 2) the number of switchings of each semiconductor element is reduced as much as possible while the switching period remains constant. In other words only the effective switching frequency over the output period is reduced. With pulse-width modulation control, reducing the effective switching frequency is only possible if there are no crossing points between the reference and the carrier waveform. Symmetry requires that all the three ac reference voltages must have the same form and be out of phase by &T,/3. This implies that the zero sequence e n N component added in each phase reference signal must have three times the frequency of the load voltages. However, injecting third harmonics and all multiples is not a problem since on a line-to-line basis they are cancelled. This is a common characteristic for all “dead-band”
band”-modulatingheference waveforms shown in Figs. 4(a) and 5(a) have been obtained arbitrarily. However, they share
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(e) Fig. 5. Second example of a “dead-band” PWM switching pattern [14], [15]. (a) Reference and carrier waveforms, M = 0 . 8 . f O = 50 Hz, f c = 1050 HZ (21 pu). (b) Line-to-neutral switching pattern. (c) Spectrum of the line-to-neutral switching pattern. (d) Line-to-line output voltage waveform. (e) Spectrum of the line-to-line output voltage waveform.
one common “hidden” feature. It consists of the fact that any function phase-shifted by -120” and +120° can produce a perfect sinusoidal waveform if and only if it is comprised of pieces of “balanced” three-phase sinusoidal system. This is clearly illustrated in Fig. 6. In particular, Fig. 6(a) shows a waveform eA(w,t) and Fig. 6(b) and (c) depict the same waveform phase-shifted by - 120” and f120”. respectively eB(w,t), e c ( w o t ) ) . On the line-to-line basis, that is, if any two waveforms are subtracted a perfect sine waveform is obtained as shown in Fig. 6(d). This is true because at any interval, when the waveform eA(w,t) is not constant, it follows a part of “balanced” three-phase sine waveforms. Constants being added to or subtracted from the modulating function do not create any problem on a line-to-line basis. Such waveforms appear across one semiconductor element (either diode or thyristor) in a three-phase converter between the anode and the positive of the dc bus. Furthermore, such waveforms have only odd harmonics. This observation suggests that there are infinite waveforms that satisfy the conditions discussed above, therefore being suitable for use with threephase PWM converters provided that they do not include
any odd nontriple harmonic that cannot be cancelled on the line-to-line basis. The maximum “dead-band” that can be introduced on each modulatingkeference waveform is investigated next. Let W A B ( W , ~ ) ; u ~ ~ ( w , t and ) , v c ~ ( w , t )be the three line-to-line converter voltage waveforms. Since, it is a three-phase system the above waveforms are
With respect to the reference signals eAN(wot) - eBN(wot) =eAB(wot) e ~ ~ ( w ,t )ecN(w,t) = eBc(w,t) ecN
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Now, if at any interval one of e A N ( w o t ) , e B N ( w o t ) ,and e c N ( w , t ) has a constant value that is zero in the case of a unipolar carrier [Fig. 5(a)], or positivehegative and equal to the carrier peak value to avoid intersections [Fig. 4(a)], then in order for the line-to-line waveforms [see (4)] not to be zero, both the other two reference signals have to be pieces
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of a sine waveform. Two modulating waveforms cannot have constant value simultaneously, since in this case some line-toline waveforms will have zero or dc value as an amplitude. This is not acceptable because control of the amplitude of these waveforms is achieved through the modulating waveforms themselves and it will also introduce low-order harmonics. Therefore, from symmetry and for a three-phase system, its modulating or reference waveform can have at most 120" interval that has constant value and obviously the other two waveforms control directly the three line-to-line waveforms. These 120" can be distributed half in the positive and half in the negative part of the waveform if a bipolar modulatingkeference waveform is employed [Fig. 4(a)]. The 60" positive section can be broken down into two subsections, each being equal to 30". It can also be a continuous part of 120" in the period of the modulatingh-eference waveform if a unipolar waveform is employed [Fig. 5(a)]. Following these rules, there are infinite waveforms that can be used with three-phase PWM converters. However, not all of them are optimum for use in PWM applications if their harmonic content is not free from odd nonmultiple of the third harmonic. This is discussed further in the next section.
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