# Self-Sensing Six-Phase PMSM Drive Based on Back-EMF Measurement
## 1 Introduction  
This paper focuses on the sensorless control of six-phase PMSMs. Multiphase machines have been demonstrated as propulsion equipment in the marine industry [1], as generators in windmills power plants [2] and also as propulsion equipment for electric aircrafts [3] and electric vehicles [4]. The reason for the utilization of multiphase machines is the reduction in per-phase current and torque ripple [5]. Their benefit lies also in the improvement in the system redundancy and post-fault characteristics [6]. The six-phase machine with 30\({}^{\circ}\) displacement between two three-phase windings is one of the most discussed types of multiphase machines. The dual three-phase solution allows utilization of the standard three-phase power inverters, and the 30\({}^{\circ}\) displacement is beneficial for harmonics reduction in the magnetomotive force [7] and produced torque [8].  
Sensorless control represents the replacement of the speed/position sensors. The replacement can be permanent, usually for reasons regarding price and space reduction. Sensorless control can also be used as a backup during speed/position sensor failure [9]. In this case, sensorless control is in temporary, emergency operation. The sensorless control of permanent-magnet synchronous machines for low-speed regions utilizes high-frequency signal injection with salience tracking algorithms, which has been applied in [10] to a six-phase PMSM. For middle- and high-speed regions, back-EMF observers are the standard solution [11]. Observers belong to model-based sensorless control techniques, which makes them sensitive to changes in parameters. Stator winding resistance is highly dependent on temperature changes. Synchronous inductances change significantly with the saturation of the magnetic core. The EMF constant changes with temperature and can also be influenced by the flux-productive component in the field-oriented control. The inertia is difficult to define or measure for real complex systems and changes with changes in the system mechanically coupled with the machine. The standard Luenberger-type back-EMF observer in the \(\gamma\xi\) reference frame has been applied to a six-phase PMSM in [12]. This paper focuses on middle- and high-speed sensorless control for a six-phase PMSM, utilizing a new procedure that can be applied to multiphase electric drives as a promising alternative toback-EMF observers. The proposed method is similar to the search coil method, where an additional winding is placed in the stator [13]. The search coil usually has only a few turns with a small cross section and represents the inbuilt resolver. With the method proposed in this paper, additional sensors such as search coils and resolvers are not required, and one three-phase set of the six-phase stator winding is utilized instead. The proposed method is applicable to multiphase permanent-magnet synchronous machines. A six-phase PMSM with field-oriented control (FOC) and the vector space decomposition (VSD) method [14] have been utilized in this work. The speed and the position of the rotor are obtained via the resolver in healthy conditions (Section 5), and via the novel sensorless procedure in the case of resolver failure (Section 6). In an emergency operation, the drive continues with reduced power since only one three-phase winding is utilized for torque generation, while the disconnected winding is used as the back-EMF sensor. The drive can also operate at the nominal power if the system is designed for the overload conditions, which usually applies to discontinuous operation.