# Performance Analysis of Direct Torque Controllers in Five-Phase Electrical Drives
## 1 Introduction
Benchmark solutions adopted by important companies are: the Hyundai ultra-high-speed elevator, based on a 1.1 MW nine-phase electric drive; the 5 MW 12-phase electric drives in the Gamesa wind turbines for onshore and offshore plants; and the 20 MW 15-phase electric drive for ship propulsion introduced by the GE Power Conversion company in the Royal Navy. To create a body of knowledge, recent research works review advances in the field of multiphase drives including their industrial applications, machine design and modeling, types of converters, modulation techniques, and control strategies; and explore innovative uses of their degrees of freedom (i.e., multimotor drives, battery chargers, post-fault control, or dynamic breaking) [8; 9; 10; 11]. Then, these state-of-the-art analyses in the multiphase drives' topic set the advances in the area in the last decades. In general, they show that symmetrical five-phase and asymmetrical six-phase machines with isolated neutrals are the most popular multiphase machine types in the research community, while an evolution in the control techniques has been necessary in order to optimally exploit their inherent advantages. In this regard, asymmetric six-phase machines with isolated neutrals can be considered as two conventional three-phase machines coupled in a common case, while the five-phase drive can be considered the ideal case example to illustrate any study in the multiphase drive field. Although field-oriented control (FOC) methods, based on decoupled control of the flux and electromagnetic torque and assisted by modulation stages, can be considered as the most popular control technique for conventional and multiphase drives [8; 9], direct control techniques have recently been presented as interesting competitors [12; 13; 14]. The essence of direct controllers is to eliminate any form of modulation, forcing the states of the power switches to rapidly track a reference value. Then, the meaning of 'direct control' techniques is related to control strategies without the intervention of a pulse width modulation or any other form of modulation, providing control commands that are applied directly to the power converter. As a main consequence, direct controllers, being direct torque controllers (DTC) are the most extended industrial alternative, can favor fast torque responses and control robustness with respect to the variation of the electrical parametersof the machine. In this regard, DTC appears to be a viable (from a commercial perspective) control alternative in conventional three-phase drives due to an easy formulation and high flexibility to incorporate different control objectives. However, the use of DTC in multiphase drives is restricted in normal operation due to the impossibility of regulating more than two degrees of freedom (electrical torque and stator flux). The objective of our work is to review the main concepts and interest of DTC controllers and to perform a performance analysis in multiphase drives, particularizing to the five-phase case. Different operating conditions, including normal operation and limited electrical/magnetic or faulty situations, are analyzed, where the DTC technique is effectively extended to face the operation of the five-phase induction machine. Experimental tests are provided to show that the speed, torque, and flux references are successfully tracked in all cases. The Case Study: Five-Phase Distributed Windings Induction Motor Drive Using a Conventional Two-Level VSI  
The system under study will be analytically examined in this section. It is based on a five-phase Induction Machine (IM) with a squirrel-cage rotor and symmetrically distributed stator windings (spatial equal displacement between windings) fed by a DC power supply through a five-phase two-level voltage source inverter (VSI).