IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 52, NO. 6, NOVEMBER/DECEMBER 2016 5355 Discussion of “A Variable Switching Frequency PWM Technique for Induction Motor Drive to Spread Acoustic Noise Spectrum With Reduced Current Ripple” Yakov L. Familiant and Alex Ruderman Variable frequency modulations for motor drives that include de- terministic, probabilistic (random or randomized), and chaotic pulse width modulation (PWM) are aimed at acoustic noise frequency spec- trum spreading [1]–[4]. The discussed paper [1] suggests a determin- istic variable frequency PWM method for induction motor drives that is about a deterministic variation of a switching period (subcycle) of a conventional PWM. The results of [1] clearly demonstrate achieved effective acoustic noise spreading. However, there are a couple of claims about motor current ripple that, in our humble opinion, deserve more discussion. The first claim is that “the major disadvantage of random PWM (RPWM) methods is that the current total harmonic distortion (THD) cannot be predicted” with reference to [3]. Current THD calculation may be done in time domain by evaluation of current ripple mean square to further find the current ripple rms value. This is because, by Parseval theorem (Rayleigh energy equality), average squared ripple is an integral measure of undesirable harmonic content that appears in THD definition. Current ripple mean square is found by successive averaging of the squared current ripple on a PWM period and on an ac fundamental period. For a fixed PWM frequency (switching period), these deter- ministic calculations can be found in [5] and [6] (harmonic loss factor). For a fixed frequency PWM, the successive averaging on a PWM period and an ac fundamental period is justified for switching frequen- cies that are much higher (at least, 20–25 times) than a fundamental one (asymptotic assumption [7]). As stated in the paper, the rms current ripple over a switching period scales with the switching period duration. So, if it is about an RPWM, assuming a moderate switching pe- riod incremental variation (quasi-steady-state current ripple assumption similar to asymptotic one), once PWM method probabilistic properties (switching period probability distribution and time correlation func- tion) are known, it becomes possible to find current ripple probabilis- tic mean square. Roughly speaking, for the current THD calculation switching period, rms value is required. The second claim is about current ripple reduction, and similar claims can be found in [2]–[4]. The question is about a common basis for current ripple fair com- parison. It is clear that, for variable frequency PWM, maximum and minimum instantaneous ripples take place for maximum and minimum switching periods, respectively. Too large switching period has a dis- advantage of increased instantaneous current ripple, while too small one has a disadvantage of increased instantaneous switching loss. Manuscript accepted October 10, 2016. The authors are with Power Electronics Research Lab, Nazarbayev University, Astana 010000, Kazakhstan (e-mail: yakov.familiant@nu.edu.kz; alexander. ruderman@nu.edu.kz). Digital Object Identifier 10.1109/TIA.2016.2618298 Current THD is proportional to current ripple rms value, that is, under asymptotic or quasi-steady-state assumption, proportional to the switching period rms value. This way, current THD is solely a matter of switching period rms value and fixed frequency PWM with a switching period equal to rms switching period of a variable frequency PWM that should have the same current THD. Normalized current ripple envelope characteristics for a fixed fre- quency PWM can be found in [8]. As for peak current ripple, it is proportional to a switching period and, due to scaling, maximum and minimum peak current ripples are achieved for maximum and mini- mum switching periods, respectively. For a variable frequency PWM, it may make sense to consider peak current ripple rms value and, again, it will be proportional to switching period rms. There is no doubt that a proper variable frequency PWM can atten- uate/eliminate the switching-related energy in certain frequency spec- trum parts achieving acoustic noise and EMI reduction. However, cur- rent THD is a matter of switching period rms and, therefore, the claims about current ripple (current THD) reduction must be more accurate and specific. REFERENCES [1] A. C. Binojkumar and G. Narayanan, “A variable switching frequency PWM technique for induction motor drive to spread acoustic noise spec- trum with reduced current ripple,” IEEE Trans. Ind. Appl., vol. 52, no. 5, pp. 3927–3938, Sep./Oct. 2016. [2] K. L. Shi and L. Hui, “Optimized PWM strategy based on genetic al- gorithms,” IEEE Trans. Ind. Electron., vol. 52, no. 5, pp. 1458–1461, Oct. 2005. [3] A. Ruiz-Gonzalez, M. J. Meco-Gutierrez, F. Perez-Hidalgo, F. Vargas- Merino, and J. R. Heredia-Larrubia, “Reducing acoustic noise radiated by inverter-fed induction motors controlled by a new PWM strategy,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 228–236, Jan. 2010. [4] B. Jacob and M. R. Baiju, “A new space vector modulation scheme for multilevel inverters which directly vector quantize the reference space vector,” IEEE Trans. Ind. Electron., vol. 62, no. 1, pp. 88–95, Jan. 2015. [5] D. G. Holmes and T. A. Lipo, Pulse Width Modulation for Power Convert- ers: Principles and Practice. Hoboken, NJ, USA: Wiley, 2003. [6] H. W. van der Broeck, H.-C. Skudelny, and G. V. Stanke, “Analysis and realization of a pulse width modulator based on state space vectors,” IEEE Trans. Ind. Appl., vol. IA-24, no. 1, part 1, pp. 142–150, Jan. 1988. [7] A. Ruderman, B. Reznikov, and S. Busquets-Monge, “Asymptotic time do- main evaluation of a multilevel multiphase PWM converter voltage quality,” IEEE Trans. Ind. Electron., vol. 60, no. 5, pp. 1999–2009, May 2013. [8] A. Ruderman, “Understanding PWM current ripple in star-connected AC motor drive,” IEEE Power Electron. Soc. Newslett., vol. 21, no. 4, pp. 14–17, Apr.–Jun. 2009. 0093-9994 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.