# Comparative Study and Overview of Field-Oriented Control Techniques for Six-Phase PMSMs
## 4 System Realization and Comparison
A so-called double zero-sequence injection, which means a third harmonic signal injected into every three-phase system, can be utilized for better DC bus voltage use, as is known from the control of three-phase machines; this is also reusable in \(n\times 3\)-phase machines with separated neutral points for every symmetrical three-phase system [12,28]. In the case of a six-phase machine, that is an option for a dual-star configuration. The modulation techniques shown in Figure 9a for 2 d-q control and Figure 9b for 1 d-q control were realized, using the double zero-sequence injection in both cases, as depicted in Figure 10. The steady-state current responses of these techniques are shown in Figures 7 and 8. Another issue in multiphase systems is current sharing. As shown in Figure 8, if hardware asymmetries are present in the \(n\times 3\)-phase electric drive (\(n=2\), \(3\), \(4\),...), then, for a better current/power sharing, between three-phase sets of windings, 2 d-q control or \(n\) d-q control is more convenient. This is because individual RL circuits, which represent three-phase windings, are controlled separately (dual-star configuration is considered). This behavior is almost negligible around a nominal load, as shown in Figure 7, but it becomes quite crucial with reduced load, as shown in Figure 8. It can be seen from Figure 10 that to keep amplitudes of phase currents at the same level, PWM references, as a result of required voltages, have various amplitudes for the first and the second three-phase systems when applying 2 d-q control. On the other hand, for 1 d-q control, the current sharing problem may be effectively handled when using the VSD method, even when it is designed by default for higher-harmon  
Figure 10: PWM references with double zero-sequence injection: (**a**) 2 d-q; (**b**) 1 d-q. Figure 9: Basic modulation techniques: (**a**) 2d-q 2 \(\times\) 6 sectors; (**b**) 1d-q 2 \(\times\) 6 sectors; (**c**) 1d-q 12-sectors. The speed and position loops were adjusted using a pole-placement method [37], where the zero in the transfer function of the speed loop caused by the speed PI controller, was canceled by a first-order filter. Coefficients \(k_{d}=k_{q}=2/6\) were considered for the 1 d-q control system as explained in Section 3, which led to the same machine parameters transformed in the d-q system for both 2 d-q and 1 d-q control, since the 1 d-q system also became amplitude-invariant. The machine parameters are shown in Table 1. Measured data were captured using the run-time _FreeMaster_ tool (_NXP_), imported into _Matlab_, and compared to a simulation based on a mathematical model [37]. Frequency analysis was executed for every control loop to verify the behavior of the system in dynamic states. The results are demonstrated as a comparison of the two field-oriented control approaches for six-phase electrical machines discussed in this paper. The measurements in Figures 11 and 12 were performed in a fixed rotor state. This approach allowed us to neglect the negative effect of back-EMF voltage since, in the current loop, back-EMF is an error value. The speed loop behavior is presented in Figures 13-15, while the position loop results are shown in Figures 16 and 17. Frequency analysis was conducted by applying the required sinusoidal values with frequencies corresponding to red asterisks (*) depicted in Figures 12, 14 and 17.