IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 16, NO. 3, MAY 2001 351 Digital Scalar Pulse-Width Modulation: A Simple Approach to Introduce Non-Sinusoidal Modulating Waveforms Cursino Brandão Jacobina, Senior Member, IEEE, Antonio Marcus Nogueira Lima, Member, IEEE, Edison Roberto Cabral da Silva, Senior Member, IEEE, Raimundo Nazareno Cunha Alves, and Paulo Fernando Seixas Abstract—The digital scalar pulse-width modulation (DSPWM) gathers the characteristics of simplicity of implementation found in the regular sampling with the flexibility of manipulation of the switching patterns in the space vector modulation (SVPWM). This paper establishes a correlation between the SVPWM and DSPWM techniques. It also shows how to make the DSPWM strategy equivalent to the SVPWM technique without loosing its simplicity of implementation. By using such equivalence concept a microprocessor-based scheme, which uses standard timer circuits and a simple software algorithm, is proposed to implement the DSPWM technique. The introduction of the “distribution ratio” in this technique, allows the development of a systematic approach for implementing of either conventional or any modified vector strategies without changing the modulator scheme. This corresponds to generate any attractive nonsinusoidal modulating signals (NSMS) in the carrier-based modulation techniques. Furthermore, the simple digital blocks can be easily implemented as an specialized integrated circuit. Simulated and experimental results demonstrate the validity of the proposed methods. Index Terms—Pulse-width modulation, three-phase inverter. I. INTRODUCTION T HE classical sine-triangle modulation, or natural sam- pling modulation (NSPWM), compares a high frequency triangular carrier with three reference signals, known as mod- ulating signals, to create gating pulses for the switches of the power converter [1]. This technique is basically an analog domain technique and its digital version led to the tech- nique named as regular-sampled PWM (RSPWM) [2]. In the RSPWM technique, the modulating signal is sampled at each period (symmetric regular sampling) or at every peak (asym- metric regular sampling) of the triangular signal to produce a sampled-hold modulating wave. Its digital comparison to a triangular signal, generated by up-down counters, define the switching instants. In other words, the corresponding time in- tervals are computed in real time from the respective sampled value [3]. Differently from the previous methods, the space vector pulse-width modulation (SVPWM) technique [4], [5] does not consider each of the three phases as a separate entity. The three-phase voltages are simultaneously performed within Manuscript received September 1, 1998; revised January 4, 2001. Recom- mended by Associate Editor F. D. Tan. The authors are with the Departamento de Engenharia Elétrica, Universi- dade Federal da Paraíba, Campina Grande, Paraiba 58109-970, Brazil (e-mail: jacobina@dee.ufpb.br). Publisher Item Identifier S 0885-8993(01)04026-1. a two-dimensional reference frame ( plane), the complex ref- erence voltage vector being processed as a whole. Because its flexibility of manipulation, the SVPWM technique is widely employed, nowadays [3]. It is well-known that the addition of proper zero-sequence components to the modulating signals generates nonsinusoidal modulating signals (NSMS). Several different waveform pro- files can be used as modulating signals [3], [6]. These NSMS improve the performance of both NSPWM and RSPWM [7], [8]. On the other hand, the same effect obtained by the use of NSMS in carrier-based techniques, is achieved with both conventional SVPWM and modified SVPWM techniques. It should be noted that the modified SVPWM strategy is known in the literature under names such as “two-phase modulation” [9], “bus-clamping modulation” [10], or “discontinuous modu- lation” [11]. Several authors have discussed the correlation among the NSPWM, RSPWM, and SVPWM techniques, under different focuses. With that purpose, the concept of “ordering of the ref- erence voltages” has been used to establish the analogy among the sectors defined by the active vectors and the segments of 60 , existing in a period of the references. Also, the concept of “distribution ratio” [12], named as “apportioning factor” in [8] and defined as the relation between the time of application of one of the two null vectors and the total null-vector time, has been employed. In fact, properly choosing the distribution factor determines both the distribution of the zero voltage vectors inside the sampling period and its correspondence to the modified SVPWM [8], [12]–[14]. The alternative “digital scalar pulse-width modulation” (DSPWM) technique imposes, to the pole voltage of an inverter leg, an average value that corresponds to each reference phase within the sampling interval [15]. Such strategy is of simpler implementation than the SVPWM technique, reducing the effort of calculation [16]. The technique introduced in [17] has a similar treatment by using the concept of reallocation of the “effective time.” This “effective time” is in fact the sum of the times of application of the active vectors. The pulse-widths are ordered and the sum of times is appropriately moved within the sampling period. Different methods have been employed to implement the re- sultant modulators of these recent studies. In [17], an algorithm is provided and implemented with a DSP TMS320C31. How- ever, because of the correspondence between of the carrier- 0885–8993/01$10.00 © 2001 IEEE