IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009 4119 Space Vector Modulation for Multiphase Inverters Based on a Space Partitioning Algorithm Alberto Lega, Michele Mengoni, Giovanni Serra, Senior Member, IEEE, Angelo Tani, and Luca Zarri, Member, IEEE Abstract—Since the late 1990s, multiphase drives have become a serious alternative to three-phase drives in some particular appli- cations such as electric ship propulsion, locomotive traction, elec- tric vehicles, and high-power industrial applications. Nowadays, the research activity is focused on the development of control strategies that can exploit the degrees of freedom that exist in multiphase machines. As known, a multiphase motor cannot be analyzed using the space vector representation in a single d–q plane, but it is necessary to introduce multiple d–q planes. In this paper, the problem of the space vector modulation (SVM) of multiphase inverters is solved extending the theory of SVM used for traditional three-phase voltage source inverters and intro- ducing the concept of reciprocal vector. The proposed approach, confirmed by experimental tests, allows the full exploitation of the dc input voltage and the simultaneous modulation of voltage space vectors in different d–q planes. Index Terms—Multiphase inverter, space vector modula- tion (SVM). I. I NTRODUCTION N OWADAYS, variable speed ac drives are usually fed by power electronic converters. Although three-phase drives dominate the market, since the converter acts as an interface that decouples the three-phase voltage source from the motor, the number of phases may not be limited to three any more. The advantages of multiphase drives over the traditional three-phase drives, such as improvement of the torque quality, reduction of the stator current per phase, and increase of the fault tolerance [1] have drawn the attention toward this technol- ogy in particular since the late 1990s. Furthermore, multiphase motor drives offer a greater number of degrees of freedom compared with three-phase motor drives, which can be utilized to improve the drive performance [2]–[4]. In multiphase machines with concentrated windings, i.e., with one slot per phase per pole, it is possible to control not only the fundamental harmonic but also the spatial low-order harmonic components of the magnetic field in the air gap of the machine. If the harmonic components with order greater than one are set to zero, the torque pulsations can be strongly Manuscript received December 4, 2008; revised April 1, 2009. First pub- lished April 21, 2009; current version published September 16, 2009. A. Lega is with Magneti Marelli Powertrain S.p.A., 20011 Corbetta, Italy (e-mail: alberto.lega@magnetimarelli.com). M. Mengoni, G. Serra, A. Tani, and L. Zarri are with the Department of Electrical Engineering, University of Bologna, 40126 Bologna, Italy (e-mail: michele.mengoni@mail.ing.unibo.it; giovanni.serra@mail.ing.unibo. it; angelo.tani@mail.ing.unibo.it; luca.zarri@mail.ing.unibo.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2009.2020701 reduced. On the other hand, if all the spatial harmonics are synchronized, the torque production capability of the machine can be increased [5]–[7]. The degrees of freedom available in multiphase motors can be used also for the realization of fault- tolerant drive [8]. Another possibility is related to the so-called multimotor drives. A well-defined number of multiphase machines, having series connected stator windings, with an opportune permuta- tion of the phases, can be independently controlled with a single multiphase inverter [9]–[12]. In order to fully exploit the potential of M -phase motor drives, a suitable and flexible modulation strategy for M -phase voltage source inverters (VSIs) has to be defined. Two different methods are usually adopted, i.e., space vector modulation (SVM) [13]–[18], and carrier-based pulsewidth modulation (PWM) [19]–[24]. For three-phase VSIs, the equiv- alence of the two methods has been proved, and they can be interchangeably implemented. On the contrary, in the case of multiphase VSIs, the carrier- based PWM method seems the most feasible, due to its inherent simplicity. The reason is that PWM focuses the attention on the control of each inverter branch, and this task is relatively simple if compared with the aim of SVM, i.e., the determination of the switching pattern, which involves all the branches of the inverter. Nevertheless, there are several reasons to develop an SVM technique. The main reason is that SVM is well known for three-phase inverters, and it has been integrated in a number of logic devices that can manage the turn-on and turn-off of the inverter switches, such as field-programmable gate arrays (FPGAs) and complex programmable logic devices. For rea- sons related to the technical experience or just for economic convenience, a company could find preferable to update the available SVM algorithms for three-phase inverters rather than to completely renounce to its previous know-how. In addition, the definition of new methods for SVM could avoid potential patent violations. To understand the basics of a M -phase system, the traditional space vector representation in a single d–q plane is not suffi- cient, but it is necessary to use (M − 1)/2 d–q planes. The research activity for the definition of a general SVM in multiple d–q planes has led to some remarkable results. The first proposals [13]–[18] have indeed the merit of demonstrating the feasibility of multiphase drives (in particular five-phase motor drives) but do not exploit all the available de- grees of freedom. For example, the SVM techniques proposed in [13] and [14] require the second voltage space vector to be always zero. The SVM technique defined in [15] and [16] 0278-0046/$26.00 © 2009 IEEE