**7. References**


[10] Ghanes, M. & Zheng, G. [2009]. On sensorless induction motor drives: Sliding-mode observer and output feedback controller, *Industrial Electronics, IEEE Transactions on* 56(9): 3404–3413.

**The Asymmetrical Dual Three-Phase Induction**

**Chapter 16**

Recent research has focused on exploring the advantages of multiphase<sup>1</sup> machines over conventional three-phase systems, including lower torque pulsations, less DC-link current harmonics, higher overall system reliability, and better power distribution per phase [1]. Among these multiphase drives, the asymmetrical dual three-phase machines with two sets of three-phase stator windings spatially shifted by 30 electrical degrees and isolated neutral points is one of the most widely discussed topologies and found industrial application in more-electric aircraft, electrical and hybrid vehicles, ship propulsion, and wind power systems [2]. This asymmetrical dual three-phase machines is a continuous system which can be described by a set of differential equations. A methodology that simplifies the modeling is based on the vector space decomposition (VSD) theory introduced in [3] to transform the original six-dimensional space of the machine into three two-dimensional orthogonal subspaces in stationary reference frame (*α* − *β*), (*x* − *y*) and (*z*<sup>1</sup> − *z*2). From the VSD approach, can be emphasized that the electromechanical energy conversion variables are mapped in the (*α* − *β*) subspace, meanwhile the current components in the (*x* − *y*) subspace represent supply harmonics of the order 6*n* ± 1 (*n* = 1, 3, 5, ...) and only produce losses, so consequently should be controlled to be as small as possible. The voltage vectors in the (*z*<sup>1</sup> − *z*2) are zero due to the separated neutral configuration of the machine, therefore this

Model-based predictive control (MBPC) and multiphase drives have been explored together in [5, 6], showing that predictive control can provide enhanced performance for multiphase drives. In [7, 8], different variations of the predictive current control techniques are proposed to minimize the error between predicted and reference state variables, at the expense of increased switching frequency of the insulated-gate bipolar transistor (IGBTs). On the other hand are proposed control strategies based on sub-optimal solutions restricted the available voltage vectors for multiphase drive applications aiming at reducing the computing cost and

<sup>1</sup> The multiphase term, regards more than three phase windings placed in the same stator of the electric machine.

©2012 Gregor Recalde, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

©2012 Gregor Recalde, licensee InTech. This is a paper distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Machine and the MBPC in the Speed Control**

Raúl Igmar Gregor Recalde

http://dx.doi.org/10.5772/50559

**1. Introduction**

Additional information is available at the end of the chapter

subspace has no influence on the control [4].

cited.

