The use of multiphase motor drives, i.e., with a phase number higher than three, is an increasingly important trend nowadays. The common procedure to analyze or to design the control algorithm for multiphase motors is to use a decoupling transformation method that transforms the model from the original phase-variable reference frame, where the electrical variables are cross-coupled, into a model decoupled in orthogonal subspaces. One such transformation is the vector space decomposition (VSD), in which each variable is represented by a complex number called spatial vector. When the multiphase induction motor model is decoupled by means of the VSD, different types of subspaces are obtained. The main type of subspace is the one where there is coupling between the rotor and the stator, i.e., where the electromechanical energy conversion happens. There are other types of subspaces in which there is no coupling between the stator and the rotor; these planes do not produce electromechanical energy conversion and their impedance can be very high (in case of homopolar components with isolated neutral points) or low.

In multiphase machines, as happens in three-phase ones, some non-ideal characteristics give rise to harmonics that can lead to undesirable effects such as torque ripple and electrical losses. They can be produced by the converter deadtime, the pulse-width modulation (PWM), flux saturation, the non-perfectly sinusoidal distribution of the windings, non-uniform airgap and some other non-linearities. The characterization of such harmonics in the decoupled motor model and the estimation of the spatial vector of each harmonic is interesting from the point of view of understanding the motor and control. One of the main reasons for identifying the subspace where each current component maps and its spatial vector rotation (SVR) speed is that it is necessary for setting up the controllers. Knowing the subspace where some specific current components map and their SVR speed is essential for sensorless speed measurement algorithms and machine current signature analysis (MCSA). Moreover, the subspace where each current component maps and its SVR speed predict if such a component is going to contribute to the overall motor torque, produce torque ripple or generate losses. Therefore, from the standpoint of the motor performance analysis, the characterization by using the VSD of the current harmonics is also important.

Most of the previous works about multiphase drive harmonics are focused only on machines with a specific number of phases, such as five-, six- and seven-phase motors and they deal only with odd order harmonics, which are the most common low order ones. Furthermore, some studies about series-connected multimotor drives have suggestedthat the plane where some current harmonics map depends not only on the harmonic frequency, but also on the phase arrangement in the stator windings connection. As far as the author knows, there are no previous studies about how the phase connection order changes affect the harmonic mapping or studies about how harmonics map in series-connected multimotor drives.

Regarding the topic of spatial harmonics modeling, it has been extensively researched in the three-phase machines field, from the thorough analyses focused on one specific spatial harmonic origin to the more general studies that include the more common causes of spatial harmonics, such as the healthy MCSA. Some spatial harmonic proposals in multiphase motors are directly adapted from three-phase cases and do not take into account the different motor subspaces. Other multiphase spatial harmonic studies, although taking into account the motor subspace decomposition, analyze only particular spatial harmonic causes or are focused just on motors with a specific phase number. The particular case of MCSA for machine status monitoring is also a broadly researched topic in the three-phase field and most of the methods proposed for multiphase motors are based on the adaptation of the three-phase ones, such as the classic MCSA approximation that categorizes the current harmonics according to their frequencies only. However, the study of the motor current harmonics by means of the subspace and the SVR-speed provides more degrees of freedom for classifying such current components than the methods based only on the current harmonic amplitudes and frequencies. Furthermore, the additional subspaces that a multiphase motor has in comparison with the three-phase counterpart provides more levels of classification. Therefore, a MCSA method designed to take advantage of the additional classification variables and the extra subspaces obtains more information about the harmonics origins and avoids some cases of symptoms overlapping in the phase current spectrum. There are some previous works that use the analysis of the currents in the decomposed model of the motor for specific fault detection, such as open-phase or broken bar MCSA, but its application for the identification of faults such as static, dynamic and mixed eccentricity is still to be done.

This thesis presents the study and characterization, by means of the VSD, of the stator current and voltage components due to time and spatial harmonics in a n-phase motor with a symmetrical arrangement of phases. First, an analysis of the stator voltage and current harmonics in a multiphase induction motor, by means of the VSD, that includes the effects of each time harmonic and the phase sequence is developed. As a result it is proposed a very simple time harmonic mapping method valid to predict the subspace where each time harmonic maps and its SVR speed (frequency and direction) in symmetrical multiphase induction motor drives of any phase number and in series-connected multimotor drives. Then, equations to study the subspace mapping and SVR speed of the current harmonics produced for some non-ideal characteristics of a squirrel cage motor such as non-perfect sinusoidal winding distributions, rotor bars, airgap variations due to the stator and rotor slots and magnetic saturation are obtained. These equations are used to study the current signature of healthy multiphase induction motors by means of the VSD. Finally, the model is extended for covering also the static and dynamic eccentricities and, based on it, a VSD MCSA method to detect pure-static, pure-dynamic and mixed eccentricity in multiphase induction motors is proposed.

Contributions of this dissertation have been published in one JCR-indexed journal paper and presented at two international conferences.

Electronics
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