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670 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997 The Relationship Between Space-Vector Modulation and Regular-Sampled PWM Sidney R. Bowes, Fellow, IEEE, and Yen-Shin Lai, Member, IEEE Abstract— The relationship between regular-sampled pulsewidth modulation (PWM) and space-vector modulation is defined, and it is shown that, under certain circumstances, the two approaches are equivalent. The various possibilities of adding a zero-sequence component to the regular-sampled sinusoidal modulating wave are explored, and these effects are quantified. It is shown that this leads to “equal-null” pulse times, which extend the linear modulation range and simplify the microprocessor implementation. FR Index Terms—PWM control techniques. p.u. NOMENCLATURE , , , Active vector times allocated to the switching states (100), (010), or (001) and (110), (011), or (101), respectively. Null vector times allocated to the switching states (000) and (111), respectively. Sampling period. Polar angle of reference vector referring to . Inverter switching states . Inverter switching states, either (100), (010), or (001). Inverter switching states, either (110), (011), or (101). Voltage vector related to the switching state . Voltage vector related to switching states , and . Reference space vector. , , Active pulse times allocated to the switching states (100), (010), or (001) and (110), (011), or (101), respectively. Null pulse times allocated to the switching states (000) and (111), respectively. Sampling position (angle). Carrier period. Manuscript received May 5, 1995; revised November 15, 1996. This work was supported by the U.K. Science and Engineering Research Council. S. R. Bowes is with the Department of Electrical and Electronic Engineering, Faculty of Engineering, University of Bristol, Bristol BS8 1TR, U.K. Y.-S. Lai was with the Department of Electrical and Electronic Engineering, Faculty of Engineering, University of Bristol, Bristol BS8 1TR, U.K. He is now with the Department of Electrical Engineering, National Taipei Institute of Technology, Taipei, Taiwan, R.O.C. Publisher Item Identifier S 0278-0046(97)06527-1. Angular frequency of modulating wave. Modulation index. Sampled modulating values at . Prepulse and postpulse switching angles, respectively. Prepulse and postpulse switching times, respectively, with respect to sampled position. Pulsewidth of PWM pulse. Frequency ratio (ratio of carrier/modulating frequencies). Per unit (1 p.u. corresponds to maximum fundamental voltage produced by sinusoidal PWM before overmodulation). I. INTRODUCTION R EGULAR-SAMPLED pulsewidth modulation (PWM) [1], [2] and space-vector modulation [3] are two popular techniques for providing PWM control of inverter drives. Although both PWM techniques have been developed from different “points of view,” they have certain similarities and, under special circumstances, can be shown to be identical. Attempts have been made to show this equivalence [3], [4], although these attempts have been made starting from the space-vector point of view and have not fully highlighted many important features. In contrast, this paper is concerned with deriving the many important relationships between regular-sampled PWM and space-vector modulation starting from the “per-phase” point of view in a form which highlights this equivalence. This is done by developing a particular form of regular-sampled PWM based upon adding a particular form of zero-sequence component to the sinusoidal modulating wave. It is shown that this has the effect of making the “inactive” or “null pulse” times equal, which results in an extended linear modulation range. The equations defining the regular-sampled “equal-null” pulse time PWM process are derived and shown to be equivalent to those derived for space-vector modulation, thus proving the equivalence of the two approaches. All the concepts, techniques and derivation of equations associated with regular-sampled PWM will be shown to be based on the “per-phase” three-phase viewpoint, without invoking any concepts of “space-vector” theory. This approach allows the essential features and characteristics of the two approaches to be clearly identified and distinguished, as shown in this paper. It is shown that the effect of using an “equal-null” pulse time in the “per-phase” regular-sampled PWM case is to extend 0278–0046/97$10.00 1997 IEEE BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM 671 the linear voltage range up to , while its use in space-vector modulation does not affect the linear voltage range. II. THEORY A. Per-Phase Sinusoidal Regular-Sampled PWM It is well known that the natural sampling [1]–[2], [5] switching angle equations are transcendental and, therefore, not suitable for microprocessor software implementation. These difficulties led to the development of regular sampling techniques in the early 1970’s [1]. The principles of regularsampled PWM techniques are shown in Fig. 1 for asymmetric regular-sampled PWM. Regular-sampling is a digital process of sampling a modulating wave “ ” at regularly spaced intervals to produce sinusoidally weighted digital samples of the modulating wave, represented by “ ” in Fig. 1. As shown in Fig. 1, two samples “ ” per carrier cycle are generated. The first sample in the carrier cycle is used to sinusoidally modulate the “leading-edge” of the PWM pulse “ ,” and the second sample is used to sinusoidally modulate the “trailing edge” of the PWM pulse. Thus, each edge of the PWM pulse is modulated by a different amount with respect to the regularly spaced pulse centers; hence, the terminology “asymmetric” regular-sampled PWM. The derivation of the switching equations describing asymmetric regular-sampled PWM have been given earlier [1], [2], and the main results are given in the following equations: prepulse angle defining the leading edge— (1) postpulse angle defining the trailing edge— (2) These equations are executed in a software algorithm which simulates the modulation processes shown in Fig. 1, using switching angles and defined in (1) and (2). For sinusoidal modulation, phase uses a modulating wave , and phases and use and , respectively [6], [7]. B. Per-Phase Nonsinusoidal Regular-Sampled PWM The research [8] has shown that using nonsinusoidal modulation can considerably improve the harmonic spectrum. In particular, it has been shown [8] that by adding 25% third harmonic (or zero-sequence component) to the sinusoidal modulating wave, the resulting harmonics could be minimized. This resulted from assuming an arbitrary nonsinusoidal modulating wave as part of the regular-sampled modulating process, then numerically minimizing the “total harmonic current distortion” (THD). In addition, it was shown [8] that the linear relationship between fundamental voltage and modulation index could be extended beyond the usual pure sinusoidal limit p.u. to approximately p.u. before overmodulation and pulse dropping occurred. Fig. 1. Asymmetric regular-sampled PWM. It is important to note that the addition of 25% third harmonic derives specifically from the minimization of the THD, whereas the alternative suggested by others [9], [10] of 1/6 third harmonic addition is based solely on maximizing the fundamental voltage. Indeed, the analysis [10] which produces the 1/6 third harmonic addition is based on adding a third harmonic to a pure sinewave phase voltage and choosing the magnitude of the added third harmonic to maximize the sinusoidal line voltage amplitude. Therefore, as a result of considering only sinusoidal voltages, the harmonics of the PWM voltages are not considered in the analysis, thereby producing an inferior harmonic performance compared with adding 25% third harmonic, as will be confirmed later in Section III and Fig. 6. C. Conditions for “Equal-Null” Pulse Times of Per-Phase PWM The three-phase width-modulated pulse configuration for a typical sample period (half carrier cycle) is shown in Fig. 2. With reference to Fig. 2, the prepulse angles defining the leading edge can be described as follows: (3) and are the three-phase modulating where waves with maximum, middle, and minimum amplitude at the sampling instant, respectively. Similarly, the postpulse angles 672 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997 determining the trailing edge shown in Fig. 2 are defined as: (4) and , shown in Fig. 2, The switching times, represent the sequential switching times of the edges of all the pulses. As illustrated in the figure, the switching times at the beginning and end of the sample period (half carrier cycle) and , respectively, where refers are defined by times to a period when all three inverter phases are connected to the lower voltage rail corresponding to a PWM output represented . Similarly, corresponds to by a switching state all three inverter phases being connected to the high-voltage . These rail, corresponding to a switching state “null” states represent nonswitching or “inactive” inverter and correspond to one of states. In a similar manner, . the six possible inverter switching or “active” states, These switching times can be derived directly from (3) and (4) and inspection of Fig. 2 as: prepulse times— Fig. 2. Pulse pattern and pulse times using per-phase regular-sampling PWM. the zero-sequence components. Thus, the pulse positions are affected by the additional zero-sequence component, and this affects the PWM harmonic content. The additional influence of the zero-sequence component on the position and extension of the linear modulation range will be explained later in the case of the per-phase “equal-null” pulse modulation. Equations (5) and (6) can be used to implement an efficient single-timer implementation to produce harmonic minimized PWM [15]. It is of interest to briefly consider what form the modulating wave would need to be to produce equal null pulse times . One possibility is to add a third harmonic to the three-phase sinusoidal modulating waves to give modulating functions of the form (5) postpulse times— (7) (6) It is important to note that the added zero-sequence component and , as shown does not exist in the active pulse times in (5) and (6) and, therefore, the mean value of the voltage in , is not the half carrier cycle, which depends upon affected by the additional zero-sequence component. However, and , which from (5) and (6), the null pulse times decide the pulse positions in the “per-phase” PWM, includes where “ ” is the amplitude of the third harmonic to be defined later. The conditions for “equal-null” pulse times can be derived from (5) and (6) and stated as follows: (8) Using (7) and (8) provides the equations for the amplitude of the third harmonic “ ” in the form of (9), at the bottom of the page. Equation (9) shows the amplitude of the added harmonics to be a complicated time-varying function, varying between amplitude limits of 1/4 and 1/6, as illustrated in (9) BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM 673 (a) (b) (c) (d) Fig. 3. Added zero-sequence component and composed modulating waves. (a) Amplitude of third harmonic added for equal-null pulse times. (b) Zero-sequence t7 ; M 1 p.u. (c) Harmonic spectrum of sinewave segments shown in Fig. 4(b). component (bold line) added to sinusoidal modulating wave for t0 (d) Modulating waves for t0 = t7 modulation, M = 1 p.u. = Fig. 3(a). While it is not suggested that this function should be used in practice, nevertheless, it does provide confirmation of the complexity of the added harmonics which would be needed to produce equal-null pulse times. This result has confirmed that, in general, there is no simple constant amplitude third harmonic which can be added to the sinusoidal modulating wave to give . The only exception to this occurs for the case of 25% third harmonic addition PWM when . Under this condition, the sampled values and , which depend on samples of the three-phase modulating waves, have the same sample values (with opposite signs) ; this point will be explained in more resulting in detail later in Section III. = In view of this result, it is of interest to enquire what zerosequence component would have to be added to the sinusoidal modulating signal to produce equal-null pulse times. Rewriting (7) to include a zero-sequence component (or common mode signal), “ ” gives (10) 674 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997 From (8) and (10), the required zero-sequence component can be defined as (11) Equation (11) shows that the zero-sequence component “ ” is composed of “segments” of sinewaves, as illustrated in Fig. 3(b). The corresponding modulating signals are illustrated in Fig. 3(d), using p.u. as an example. The harmonic spectrum of the sinewave segments defined in (11) and illustrated in Fig. 3(b) are shown in Fig. 3(c). As shown, this spectrum consists of only triple harmonics, with a third harmonic of 20.67%. Note that it is possible to show that the sinewave segment very closely approximates a triangular wave with an amplitude of 25%. Therefore, as shown in Fig. 3(b), the zero-sequence component “ ” consists of the smallest absolute reference modulating signal at any instant in time, such that . As will be shown later, this result has interesting implications in the explanation of the reasons for adding zero-sequence components. Substituting (11) into (10) gives the modulating wave for phase , with the zero-sequence component added as (a) (b) Fig. 4. PWM waveforms for various PWM strategies. (a) PWM waveform 0:9—(a)(c) PWM pulses and (d) nVs0 n; 1/2 denotes of SPWM, M null vector (pulse) period; 1/6 means active vector (pulse) period. (b) Active pulses in a carrier cycle, FR = 6—(a) SPWM, M = 1:0, (b) t0 = t7 PWM, M = 1:0, (c) t0 = t7 PWM, M = 1:1547, (d) sampled points. = (12) and Noting that similar equations can be derived for . These modulated signals can be stored in a lookup table (LUT) to generate equal-null pulse PWM using the same approach used previously for conventional regular-sampled sinusoidal PWM. Alternatively, the reference modulating signal can be computed in “real time” by adding half the demand voltage of that phase with the smallest absolute value, as illustrated in Fig. 3(b). III. EFFECT OF ADDING ZERO-SEQUENCE COMPONENT The effect of adding the zero-sequence component of (12) is to flatten the peaks of the modulating wave shown in Fig. 3(d). As a result of this, the modulation index and, thus, fundamental voltage, can be increased beyond to before overmodulating and pulse dropping occurs. This extends the linear voltage control range and thereby increases the maximum output voltage. Note, of course, that a similar effect is produced when adding 1/6 third harmonic [9], [10] or 25% third harmonic [8]. It is of interest to consider in more detail the reasons for this extension of the linear voltage range in terms of what is happening to the PWM pulsewidths and positions. Fig. 4(a) shows the sinusoidal modulated three-phase PWM two-level voltages – (line-to-inverter center-tap voltages), together with the absolute value of the zero-sequence voltage (starto-inverter center-tap voltage, assuming an isolated star point at the load). As illustrated in Fig. 4(a), line “ ,” the zero sequence voltage assumes the larger of its two magnitudes (1/2) at the beginning and end of each sample period (1/2 carrier period), as delineated by the dotted lines. Also shown in the figure are the “null” pulse times, corresponding to the inactive switching states designated by (state 000) and (state 111) and, as shown, these are not necessarily equal. As the modulation index increases, one of the “null” pulse times or will become zero and limit the linear voltage range. This is illustrated in Fig. 4(b), where “ ” is for sinusoidal modulated PWM (SPWM) where for . If, however, the active pulse is centered in the 1/2 sample period using , as shown in Fig. 4(b), line “ ,” then the modulation index can be increased beyond up to a maximum modulation before , as shown in Fig. 4(b), line “ .” The above has provided a clear explanation of how adding a third harmonic BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM 675 (a) Fig. 6. THD for four PWM strategies, FR = 9. (b) 0 Fig. 5. Errors in (t7 t0 ) for various PWM strategies. (a) Maximum error of (t7 t0 )=T for various additional zero-sequence component. (b) Error of (t7 t0 ) for various additional zero-sequence component M = 1 p.u. 0 0 (or zero-sequence component) to the sinusoidal modulating wave affects the positioning of the PWM pulses and thereby extends the linear voltage range to give an increased maximum voltage. In light of the above explanation, it is clear that the effect of adding the sinewave segment (zero-sequence component), derived earlier in (11) and shown in Fig. 3(a), is to shift the to the center of half the carrier period to active pulse . In contrast, in SPWM, when either or make , the linear modulation range ends and overmodulation occurs for further increases of modulation index. However, the PWM will not finish until linear modulation range for . The conclusion can be confirmed by comparing Fig. 4(b), lines “ ”–“ .” involved The maximum pulse-time error in using the various third harmonic additions as a function of frequency ratio (FR) is shown in Fig. 5(a). As shown in this figure, whichever harmonic addition is used, the maximum error is less than 4%. Increasing the added triple harmonics shown in Fig. 3(b) can dramatically reduce the error. It is of interest to consider what error exists between and for each of the various third harmonic component addition strategies. Fig. 5(b) shows the errors in a 1/3 fundamental period. As illustrated in the figure for 1/4 third harmonic addition, at , the error is zero. sampling points This explains why the two PWM strategies, and 1/4 third harmonic addition, result in the same PWM waveform for , as stated earlier. It is, however, important to note that while all the cases considered in Fig. 5(a) extend the linear modulation range, these are not all necessarily optimum with regard to minimizing harmonic distortion. This can be seen in Fig. 6, which shows the THD for the four main PWM strategies and, as illustrated, the equal-null pulse time strategies are better than adding a 1/6 third harmonic, but not as good as the 25% third harmonic addition. This is to be expected, since the 25% third harmonic addition PWM strategy was specially designed to minimize the THD by optimally positioning the pulses to give the “best” harmonic spectrum. In contrast, the other two strategies were only designed to extend the linear voltage range without regard to harmonic minimization, thereby giving an inferior harmonic performance, as shown in Fig. 6. The above results and discussion of the “zero-sequence addition” concept and techniques, leading to the “equal-null” pulse time concept, has been developed using only the “perphase” concepts of the three-phase PWM techniques without recourse to any “space-vector” concepts or techniques. It is, however, of considerable interest to compare this “per-phase” PWM development with the parallel space-vector techniques in the context of regular-sampling PWM techniques. IV. COMPARISON WITH SPACE-VECTOR TECHNIQUES Space-vector modulation (SVM) techniques have become very popular over the past few years, particularly for vector drive control applications. It is, therefore, of interest to compare SVM with regular-sampled PWM and identify the relationship between the two approaches to PWM inverter control. It will be shown that the regular-sampled “equal-null” pulse time PWM presented in the previous section is exactly equivalent to SVM, although the two approaches have been developed from entirely different “viewpoints.” 676 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997 (a) (b) (c) (d) = = Fig. 7. Simulation and experimental results for t0 t7 PWM, M 0:8 p.u. FR = 15. (a) PWM voltage and current waveforms. (b) PWM voltage spectrum, simulation. (c) Current spectrum. (d) PWM voltage spectrum, experiment. The basic concepts, theory, and development of SVM is well known [3] and, therefore, only those SVM results necessary to appreciate the comparison with regular-sampled PWM will be considered. SVM is based on time-averaging techniques over a sampling period and can be expressed in Sector 1 (0 –60 ) by the following equations [3]: PWM, the active pulse times for the leading edge can be derived as (14) Similar equations exist for the trailing edge of the pulse by the same procedure. Since , (14) can be rewritten as (13) (15) To make a direct comparison between the two approaches on the basis of active pulse times and (for SVM) and (for regular-sampled PWM) is necessary to and consider a sampling instant corresponding to . From (2), (5), and (12) for regular-sampled Comparing (13) for SVM with (15) for regular-sampled PWM shows that the active pulse times and providing the SVM sample time equals half the carriercycle period and . The same relationship holds for other sectors. Also, since equals in both SVM and regular-sampled PWM, then all the pulse times are equal, confirming that both approaches are exactly equivalent with regard to these switching where dc link voltage, and BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM (a) (c) 677 (b) (d) Fig. 8. Simulation and experimental results for 25% third harmonic added PWM. (a) PWM voltage and current waveforms. (b) PWM voltage spectrum, simulation. (c) Current spectrum. (d) PWM voltage spectrum, experiment. times. It is also possible to show that the switching pattern is the same in both approaches. For example, in Sector and for 1, the switching pattern for , therefore, the switching pattern for the . For first sample period is asymmetric regular-sampled PWM, as shown in Fig. 3(d) which is plotted according to (10) and (11), the maximum in this sector is phase , and modulating wave is phase . Therefore, from Fig. 2, the switching for the leading pattern will be for the trailing edge. edge and Note that, as shown, only one inverter leg switches between each transition, resulting in minimum switching frequency in the three-phase modulation case. Thus, the switching patterns for both SVM and asymmetric regular-sampled PWM are exactly equivalent, and this equivalence can be confirmed for all sectors. The above results have proved that both the switching times and switching patterns are exactly equivalent in both approaches and, therefore, will produce the same three-phase PWM voltage waveforms and harmonic spectra. It is important to note that, while the equal-null pulse times in the SVM approach considered have improved the THD, as compared to sinusoidal PWM, it is not optimum and, as shown in an earlier section, harmonic minimization with minimum THD results from adding 25% third harmonic, as shown in Fig. 6. It has been common practice in SVM [3] to allocate the and switching states equally and to null pulse times to locate them at the beginning and end of each sample period. However, this was not done to extend the linear voltage range, as was the case in regular-sampled PWM described earlier, and in SVM does not limit the since the distribution of maximum voltage range. This can be shown to be the case by considering the process of calculating the various pulse times in SVM. For example, determines the in SVM, the reference (or demand) vector . Thus, active vector times and and provides an additional degree of the distribution of freedom which can be arbitrarily chosen and, therefore, does not contribute to the restriction of the maximum voltage range. Therefore, the range of linear modulation and voltage in SVM , is only decided by the active pulse times . which are determined from a given reference vector and only determine the positioning of Consequently, the pulses and switching patterns which, in turn, influence the THD and commutation frequency. In contrast, in SPWM, the 678 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997 range of linear modulation is determined by the modulating signals and is, therefore, influenced by both the active pulse times and, also, the null pulse times, as discussed earlier. V. EXPERIMENTAL RESULTS Which approach and form of PWM implementation is adopted in a particular application will depend largely upon the form of the control strategy used. For example, if the reference voltage is given in terms of two-axis quantities, for example, in a vector control system, then using space-vector modulation has some advantages, since the 2/3 transformation is not necessary. However, if the reference voltage is given in terms of three phase voltages, for example, in a feedforward control system, then the “per-phase” implementation will have some advantage, since the intensive computation required for locating the position (sector) of the reference vector and 3/2 transformation are not necessary. In this case, the fourtimer [11]–[14] implementation will be superior to one-timer implementation [15], [16]. The authors hope to report in more detail on the implementation of each approach in a future paper. The experimental drive system used a TMS 320 C26 digital signal processor (DSP), and the PWM control software was programmed using the four-timer approach [11]–[13], [15], [16] in assembly language. Figs. 7 and 8 show the simulation and experimental results for a PWM waveform voltage harmonic spectrum. Noting that these voltage harmonic spectra correspond to the line-to-center-tap voltage and, therefore, the triple harmonics shown in Figs. 7 and 8 will not appear in the phase-voltage and the line-voltage spectrum, due to the three-phase connection with isolated star point. Figs. 7 and 8 show the PWM and current waveform and current harmonic spectrum, which clearly confirm that the triple harmonics have been eliminated in the current spectrum. The simulation results are included to show clearly the harmonics present in the voltage spectrum and as a basis of comparison and confirmation with the experimental results. As clearly shown in these figures, the experimental results agree very well with simulation results and confirm the results of the analysis presented earlier in this paper. In particular, Figs. 7 and 8 show that the voltage harmonic spectrum for 25% third harmonic addition is slightly better than PWM (or, equivalently, SVM), confirming the THD results shown in Fig. 6. VI. CONCLUSION This paper has shown the relationship between asymmetric regular-sampled PWM and space-vector modulation techniques. This comparison was based upon showing the various developments leading to the regular-sampled “equal-null” pulse time PWM techniques. It was shown how these developments only involved three-phase concepts and considerations based on well-established regular-sampling techniques. It was also illustrated how the PWM strategy evolved naturally from these three-phase regular-sampled considerations without invoking any of the concepts, theory, or techniques normally associated with “space vectors.” It has been shown that the “equal-null” pulse time regularsampled PWM is derived by adding a zero-sequence component, in the form of sinewave segments, to the modulating wave of SPWM. Detailed considerations on the reasons for adding this zero-sequence component to extend the linear modulating range wave were also presented. It has also been confirmed that the use of the “equal-null” pulse times does not give minimized THD and that adding 25% third harmonic does provide minimized THD. It has been shown that the equations used to calculate the pulse times are the same in both SVM and regular-sampled PWM and, therefore, the SVM presented in this paper can be viewed as a particular form of asymmetric regular-sampled PWM. However, the reasons for using “equal-null” pulse times has been shown to be different in each approach and has, therefore, highlighted the significant differences between SPWM and SVM. ACKNOWLEDGMENT The authors gratefully acknowledge the University of Bristol for providing excellent computing and experimental facilities. REFERENCES [1] S. R. Bowes, “New sinusoidal pulsewidth-modulated inverter,” Proc. Inst. Elect. Eng., vol. 122, no. 11, pp. 1279–1285, 1975. [2] S. R. Bowes and R. R. Clements, “Computer aided design of PWM inverter systems,” Proc. Inst. Elect. Eng., vol. 129, pt. B, no. 1, pp. 1–17, 1982. [3] H. W. van der Broeck, H. C. Skudelny, and G. V. Stanke, “Analysis and realization of a pulsewidth based on voltage space vectors,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1986, pp. 244–251. [4] D. G. Holmes, “The general relationship between regular-sampled pulsewidth-modulation and space vector modulation for hard switched converters,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1992, pp. 1002–1010. [5] A. Schonung and H. Stemmler, “Static frequency changers with subharmonic control in conjunction with reversible variable speed ac drives,” Brown Boveri Rev., vol. 51, pp. 555–577, 1964. [6] S. R. Bowes and M. J. Mount, “Microprocessor control of PWM inverters,” Proc. Inst. Elect. Eng., vol. 128, pt. B, no. 6, pp. 293–305, 1981. [7] S. R. Bowes and T. Davies, “Microprocessor-based development system for PWM variable-speed drives,” Proc. Inst. Elect. Eng., vol. 132, pt. B, no. 1, pp. 18–45, 1985. [8] S. R. Bowes and A. Midoun, “Suboptimal switching strategies for microprocessor-controlled PWM inverter drives,” Proc. Inst. Elect. Eng., vol. 132, no. 3, pp. 133–148, 1985. [9] G. S. Buja and G. B. Indri, “Improvement of pulse width modulation techniques,” Arch. Electrotech. (Germany), vol. 57, pp. 281–289, 1975. [10] J. A. Houndsworth and D. A. Grant, “The use of harmonic distortion to increase voltage of a three phase PWM inverter,” IEEE Trans. Ind. Applicat., vol. IA-20, pp. 1224–1228, Sept./Oct. 1984. [11] S. R. Bowes and P. R. Clark, “Transputer based harmonic-elimination PWM control of inverter drives,” IEEE Trans. Ind. Applicat., vol. 28, pp. 72–80, Jan./Feb. 1992. [12] S. R. Bowes and P. R. Clark, “Simple microprocessor implementation of new regular-sampled harmonic-elimination PWM techniques,” IEEE Trans. Ind. Applicat., vol. 28, pp. 89–95, Jan./Feb. 1992. [13] S. R. Bowes and A. Midoun, “A new PWM switching strategy for microprocessor-controlled inverter drives,” Proc. Inst. Elect. Eng., vol. 133, pt. B, no. 4, pp. 237–254, 1986. [14] S. R. Bowes and A. Midoun, “Microprocessor implementation of new optimal PWM switching strategies,” Proc. Inst. Elect. Eng., vol. 135, pt. B, no. 5, pp. 269–280, 1988. [15] S. R. Bowes, “Novel real-time harmonic minimized PWM control for drives & static power converters,” IEEE Trans. Power Electron., vol. 9, pp. 256–262, May 1994. BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM [16] S. R. Bowes, “Advanced regular-sampled PWM control techniques for drives and static power converters,” IEEE Trans. Ind. Electron., vol. 42, pp. 367–373, Aug. 1995. Sidney R. Bowes (M’89–SM’89–F’96) received the B.Sc., Ph.D., and D.Sc. degrees from the University of Leeds, Leeds, U.K. He was with the Chief Mechanical and Electrical Engineer’s Department, British Rail, for six years before joining the Reluctance Motor Drive Research Group, University of Leeds, as a Research Fellow. He subsequently became a Lecturer, Reader, and Professor at the University of Bristol, Bristol, U.K. He has been engaged in the research and development of PWM-controlled drives and power electronic systems for over 25 years. He has also been a consultant to numerous international companies. Dr. Bowes is a Fellow of the Institution of Mechanical Engineers, the Institution of Electrical Engineers (IEE), U.K., and the Royal Society of Arts. He has been awarded three IEE Premiums, the F. W. Carter Prize, and the European Globe Award. He has also served on several IEE committees. 679 Yen-Shin Lai (M’96) received the M.S. degree from the National Taiwan Institute of Technology, Taipei, Taiwan, R.O.C., and the Ph.D. degree from the University of Bristol, Bristol, U.K., both in electronic engineering. In 1987, he joined the National Taipei Institute of Technology, Taipei, Taiwan, R.O.C., as a Lecturer. He became an Associate Professor in 1996. His research interests include design of microprocessorbased systems, development of PWM techniques, and drives and converter control.