_applied_  
_sciences_  
_Article_  
**Online Adaptive Set of Virtual Voltage Vectors for Stator**  
**Current Regulation of a Six-Phase Induction Machine Using**  
**Finite State Model Predictive Controllers**  
**[PERSON] 1,*,+\({}^{\text{(c)}}\), [PERSON] 1,1+\({}^{\text{(c)}}\), [PERSON] 2,2+\({}^{\text{(c)}}\) and [PERSON] 3,1+\({}^{\text{(c)}}\)**  
Footnote 1: The term “\(\sum\)” is called “\(\sum\)”. Footnote 2: The term “\(\sum\)” is called “\(\sum\)”. Footnote 3: The term “\(\sum\  
VVV is that harmonic content can be reduced by combining Voltage Vectors (VV) within a single sampling period. The basic VVV scheme combines two Voltage Source Inverter (VSI) configurations sharing the sampling period \(T_{s}\). The combination is such that the average \(x-y\) voltage is zero. For example, a Medium-Large VV is applied during \(T_{1}\) seconds and a Large VV is applied for \(T_{2}\) seconds. In 5-phase and 6-phase systems \(T_{1}=0.73\times T_{s}\) and \(T_{2}=0.27\times T_{s}\) as explained in [12]. Many variants of this concept have been presented in the multi-phase drives' literature. Among these, the following are useful to put the contribution into context. In [13], a nine-phase induction machine (IM) is considered. Several strategies are proposed using two and four VVs. In [14], VVV are combined with modulated predictive current control considering space vector modulation. A bi-subspace predictive current control based on VVV is presented in [15], where two groups of VVV are considered to regulate the fundamental and harmonic components, respectively. In this way, the \(x-y\) components due to non-linearities are regulated. Furthermore, different VVV sets are considered for the bi-subspace scheme. In [16], VVV of two different magnitudes are used with a lookup table to exclude some combinations. CF tuning is avoided by transforming the torque and flux amplitude into an equivalent reference flux vector. The work in [17] utilizes VVV that are synthesized using a transformation method to consider both flux and torque. In [18], the increase in the predicted current caused by all VVs is divided into a combination of a group of basic VVs. In this way, the global optimization is converted into the optimization of just the basic voltage vector. In [19], a group of four candidate VVs is generated based on a lookup table. The selection allows for just one commutation. The method is applied to an asymmetrical six-phase IM. Finally, additional auxiliary vectors of two different magnitudes are used in [20] to reduce the torque ripple. Regarding CF tuning, the usual practice is the use of Weighting Factors (WF) to give more relevance to some terms over others. Early publications use simulations and/or experiments to guide trial-and-error procedures for WF tuning, but more recently a Pareto analysis combined with a non-linear optimization method has been proposed in [21], and similar approaches have been presented in [8; 22], to tackle the complexity of WF and CF tuning in conventional (not VVV-based) FSMPSCC for six-phase IM drives. In the previously cited literature, several figures of merit are considered. In this work, the objective is to minimize current tracking errors by keeping the switching frequency below limits. The criterion is relevant, as it leads to reduced losses without compromising dynamic performance. For a thorough assessment, the performance map analysis is carried out for a six-phase motor drive using FSMPSCC and considering all operating points, where the typical Medium-Large + Large VVV set is contemplated in conjunction with the Small + Medium-Large VVV set. The main contribution of our work is the proposal of a novel VVV structure that combines two VVV sets, where the optimal tuning for each VVV set is obtained for every operating point following the previous work in [22]. In order to manage the continuous operating space, it is discretized by taking 12 subdivisions of the load and 12 subdivisions of speed.