# Design Optimization of the Magnet-Free Synchronous Homopolar Motor of a Subway Train
###### Abstract  
Synchronous homopolar motors have no permanent magnets and their excitation winding is fixed at their stator. However, they can be a good alternative to induction and permanent magnet motors in traction applications requiring a wide constant power speed range. They provide an excitation flux control and a highly reliable brushless rotor design. This article presents the procedure and results of optimizing a 370 kW synchronous homopolar motor for driving subway train. The optimization procedure was developed to take into account the subway train moving trajectory. The analysis considers only a limited number of steady-state operating points of the motor to reduce computation time. The optimization results show a significant improvement of the target parameters of the traction drive. The optimization makes it possible to significantly reduce the losses in the operating cycle, as well as the torque ripple of the motor and the current rating of the traction inverter. synchronous homopolar motor; electrically excited synchronous motor; Nelder-Mead method; optimal design of electric machines; subway train; constant power speed range; traction drive +
Footnote †: journal: Applied  
leading car manufactures such as BMW (models BMW iX3) and Renault (models Renault Zoe, Fluence, Megane E-TECH) have developed DC-excited synchronous motors (DCESM) with the excitation winding on the rotor (BMW [10; 11], Renault [12]). The constant power speed range is provided by means of the flux regulation of DCSM [13; 14]. However, the electrical machines of BMW iX3 and Renault Zoe have the slip rings and a brushed contact to feed the excitation winding on the rotor, which limits the motor speed and reduces its reliability [14]. An alternative could be high-reliable and brushless synchronous homopolar machines (SHM) having both excitation and power winding on stator, and a salient-pole rotor. The main advantages of SHMs compared to DCSMs are highly reliable brushless rotor design and concentrated excitation winding, the number of coils of which is small and does not depend on the number of motor poles, while in a DCSM the number of coils (and, therefore, the length of the wire and losses) increase with the number of poles. Such SHMs are widely used as the high-reliable generators in passenger railway cars, on-board generators for ships and aircraft [15; 16], automotive generators [17], and in welding units [18]. In papers [7; 19; 20; 21; 22; 23], the SHM is used as a traction motor of a mining truck. In [19], the simplified computation method of the traction SHM was described, and the experimental verification of the proposed method was performed. In [20], the control strategy of such traction motor was considered. In [21], this machine was optimized by means of the developed optimization procedure, which is now used at the design stage of the new motors. In [22], the optimization was made in order to minimize the installed power of the traction inverter of the mining truck. In [7], the parameters of the SHM are compared with the interior permanent magnet synchronous motor of the same power driving the same mining truck. In [23], the parameters of the SHM are compared with the parameters of the DCSM in the same application. However, the review shows absence of use of SHM in other traction applications. This paper considers an optimization process for the synchronous homopolar motor for a traction electric drive of a subway train. The optimization was performed with respect to the typical speed and torque profile during transition between station considering acceleration and deceleration phases. The following optimization targets were selected: decrease in average losses along the way from station to station, decrease in installed power capacity of the traction inverter, and reduction of the torque ripple. The one-criterion Nelder-Mead method is applied in this study to optimize the SHM design.