# Self-Sensing Six-Phase PMSM Drive Based on Back-EMF Measurement
## 5 Operation Mode with the Healthy Speed/Position Sensor
Both top and bottom transistors of phases D, E and F in the power inverter are turned off. The control structure is still in the VSD form (Figure 1). However, specific modifications are required. The control of the \(zI\)-\(z2\) subspace is turned off by setting voltages \(V_{zI}\) and \(V_{z2}\) to zero. Currents in the \(zI\)-\(z2\) subspace behave as defined in (16) and (17), considering the second \(\alpha\)-\(\beta\) subspace to be equal to zero. The coefficient \(K\) in (14)-(17) is changed to \(K=1\), so the control remains amplitude-invariant, and the coefficient of proportion changes to 2/3. The torque constant is then, according to (11), reduced to half. Based on (1)-(9), synchronous inductances of the VSD model \(L_{d}\) and \(L_{q}\) are changed to the synchronous inductances of the first three-phase system \(L_{dI}\) and \(L_{qI}\) (3). Modified values of parameters are used for the readjustment of the FOC controllers. Supply voltages and currents flowing through phases D, E and F are now zero. The measured voltage (Figure 12) then theoretically corresponds only to the back EMF produced by the flux of permanent magnets. The elimination of the supply voltage with the third harmonic from  
Figure 5:5 Steady-state three-phase operation: (**a**) electrical rotor position measured by resolver and estimated from back-EMF voltages D, E and F; (**b**) oscilloscopic record of the measured voltage. the measured voltages can be seen in the frequency spectra in Figure 5:6 The remaining third and fifth harmonics are generated with the EMF of the machine, but also through the armature reaction. The position (Figure 14a) has been estimated from transformed \(\alpha\)-\(\beta\) components (Figure 13a) using the PLL method shown in Figure 5:7 The third harmonic and the DC offset have been separated during the transformation, which does not apply to the fifth harmonic, as can be seen in Figure 13a. This fact confirms the results from Figure 5:8 The utilized PLL has a filtrating characteristic. Harmonics of the orders 6k \(\pm\) 1 (k = 1, 3, 5,... ) and 12k \(\pm\) 1 (k = 1, 2, 3,... ), which are not segregated during the transformation process, are damped with the PI controller in the PLL structure. However, to keep the dynamic of the observer useful for control procedures, the damping property cannot be set too high, and the remaining harmonics can appear at the observed speed and position. Therefore, the proposed method is more appropriate for machines with a negligible fifth harmonic of the EMF. The switching frequency can still be observed in the measured voltage (Figure 12). The machine winding of the second system D-E-F has been physically disconnected from the inverter to identify the source of this signal, which is possible in the sensor-based three-phase operation (Figure 14b). The voltage has been measured separately on the machine winding (vF_1a) and the connector of the inverter (vF_1b). The signal with the switching frequency is generated through the machine, and the source is the first set of the active stator winding A-B-C.