# Comparative Study and Overview of Field-Oriented Control Techniques for Six-Phase PMSMs
## 4 System Realization and Comparison  
The aim of standard electric motor control is to supply a machine with phase voltages in the same order, shift, and shape as the EMF of the supplied machine. Transformations have a large impact on this requirement in field-oriented control. Their correctness can be verified by a comparison of the phase current order, shift, and shape in a motor mode with the phase EMF sensed using an oscilloscope in generator mode, over the same direction of a shaft rotation (Figure 6). For a correct phase identification, the record of the EMF is also required. The same applies to PWM references, except for the shape, which is dependent on the modulation technique used and does not always follow the shape of the EMF. In most real applications controlled by a microprocessor, PWM references are inputs for a timer compare unit, which generates control signals for power transistors. PWM references can be accomplished using many modulation techniques, a few of which are discussed in the next section as a review of the state of the art, with emphasis on the six-phase design implementation. The measured currents of the six-phase PMSM investigated in this experiment are shown in Figures 7 and 8. Figure 5: Axis orientation in a 1 d-q system. Figure 6: Phase electromotive force. Modulation of the 1 d-q control can be accomplished, for example, using a 12-sector diagram [11; 12; 33] (Figure 9c), with separated 2 \(\times\) 6 sector diagrams [12; 28] (Figure 9b) or even a 24-sector diagram [33]. The vector space decomposition (VSD) method is often used in the 1 d-q control approach, which was introduced in probably the most referenced article by worldwide authors in the field of multiphase machines [11] with a stationary reference frame. This technique is focused on the harmonic spectra of stator currents, which might arise in a six-phase machine because of asymmetries, and their elimination can be achieved using various approaches, where the most beneficial for the impact of any kind of asymmetry (inverter, motor) is a VSD transformation to both a synchronous and an anti-synchronous reference frame [15]. VSD control of the six-phase machine is based on a transformation of phase values to an orthogonal \(z1z2\) frame (_xy_ frame according to some authors [15]) through fifth harmonic arguments of goniometric functions. The transformation leads to a separation of currents \(\mathrm{i}_{x1}\), \(\mathrm{i}_{x2}\) from fundamental component. This separated subspace represents unwanted higher-harmonic currents of the fifth order, which are not torque/flux\(-\)producing components in a six-phase machine with the configuration shown in Figure 1b, but which cause additional copper losses. For this reason, \(\mathrm{i}_{x1}\), \(\mathrm{i}_{x2}\) are regulated to zero, as explained in [11; 15]. As a matter of machine design, asymmetries do not have to be present with values demonstrated in [11] for every machine or work condition. The phase current shows that the impact of higher harmonics is minor in conditions near to a nominal load, as shown in Figure 7, while they are quite significant for a lower level of stator currents, as shown in Figure 8. These harmonics might be caused by various system asymmetries, including a dead-time effect. In the case of 2 d-q control, it is standard to use the well-known six-sector modulation for the control of three-phase machines, with separately controlled inputs (Figure 9a). To avoid the impact of controlled system asymmetries, quite large decoupling algorithms  
Figure 8: Phase currents with reduced load: (**a**) 2 d-q; (**b**) 1 d-q. Figure 7: Phase RMS currents (8.5 A): (**a**) 2 d-q; (**b**) 1 d-q. are often used [34]. Some of the decoupling effects might be achieved via appropriate transformations, where the control structure starts to follow the VSD approach, since the required currents for the second orthogonal d-q system have ratings of zero [35]. The VSD approach was used also for separated three-phase control structures in [36].