IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 2, FEBRUARY 2012 943 Geometry Optimization of PMSMs Comparing Full and Fractional Pitch Winding Configurations for Aerospace Actuation Applications Evangelos M. Tsampouris, Minos E. Beniakar, and Antonios G. Kladas National Technical University of Athens, Faculty of Electrical and Computer Engineering, Laboratory of Electrical Machines and Power Electronics, Zografou, Athens 15773 Greece Optimization of electromechanical aerospace actuators requires a multi-objective and comparative analysis in order to account for performance and manufacturing cost terms. This paper introduces a particular optimization methodology presenting stable conver- gence characteristics which has been applied to optimize the geometry of both Fractional Slot Concentrated Winding (FSCW) and Full Pitch Concentrated Winding (FPCW) permanent magnet motor configurations. The proposed algorithm combines technical and phys- ical advantages of the FSCWs and FPCWs into an optimally shaped stator-winding configuration. The resultant motor design has been validated through a prototype and experimental results illustrated its suitability for aerospace actuation applications. Index Terms—Actuators, aerospace engineering, design optimization, finite element methods, permanent magnet motors. I. INTRODUCTION C URRENT trends for more electric aircraft technology favor Fractional Slot Concentrated Winding (FSCW) Per- manent Magnet Synchronous Machine (PMSM) actuators [1]. FSCW actuators are intended to gradually replace hydraulic flight controls, allowing for both safer and “more-green” operations [2]. This is mainly due to the advantages of low cogging torque, short end turns, high slot fill factor, as well as fault tolerance and flux-weakening favoring FSCWs to Full Pitch Concentrated Windings (FPCWs) in the respective applications [3]. However, fractional pitch winding configuration affects the performance of the actuator similarly to the case of a reduced number of turns in the winding, leading to back-EMF voltage amplitude and power-factor reduction when compared to the case of FPCWs [4]. Such a performance related effect can be critical in aerospace ap- plications requiring actuation systems with the ability to comply with maximum efficiency and high power density specifications. As FSCW technical characteristics call for less copper, while FPCW physical characteristics call for maximum EMF per in- ductor, the optimum actuator topology depends on the application specifications and has to be determined analytically [5], [6]. This paper introduces a particular optimization algorithm, fa- cilitating the comparative approach on the stator geometry opti- mization of surface PMSMs involving FPCW and FSCW con- figurations. More specifically, a Rosenbrock based optimization algorithm is introduced in order to minimize an application-spe- cific penalty function through a Sequential Unconstrained Min- imization Technique (SUMT) [7], [8]. The proposed formula of the penalty function includes efficiency-performance related terms, as well as technical terms, related to the manufacturing cost of each stator configuration. Proper sigma terms (penalty terms) ensuring no violation of the optimization constraints have also been introduced. The optimization algorithm offered stable convergence char- acteristics in all FPCW and FSCW design cases considered. The overall performance improvement of the optimized design has been validated through measurements on a prototype. Manuscript received July 06, 2011; revised October 08, 2011; accepted Oc- tober 22, 2011. Date of current version January 25, 2012. Corresponding author: E. M. Tsampouris (e-mail: etsab@central.ntua.gr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2011.2174206 TABLE I MACHINE PROTOTYPE DESIGN CHARACTERISTICS (DIMENSIONS IN MM) II. ACTUATOR MODELING In a first step, an estimation of the actuator structure is achieved by considering classical machine design techniques. Although such an analytical approach does not enable detailed design optimization, due to the approximative electromagnetic field representation, it delivers a sub-optimum set of design variables, within a region of the global optimum. In a further step, such an approach enables the use of fast and robust local optimizers, adopted to handle complex optimization. Table I summarizes the basic properties of the surface mounted PMSM prototype, which are common in all the FPCW and FSCW configurations compared. Finally, parametric 2-D FEMs are introduced. An FPCW topology and two FSCW topologies involving non-overlapping both alternative teeth wound and all teeth wound configurations have been modeled. A. FPCW Topology The FPCW topology produces the largest possible EMF for a given number of inductors in the winding. One pole of the actu- ator has been modeled by using appropriate antiperiodic lateral boundary conditions (3334 nodes). Fig. 1(a) shows the trian- gular mesh employed and the magnetic flux distribution for a sub-optimum actuator design at nominal load. Fig. 1(b) shows the respective magnetic vector potential values, illustrating the magnetic loading of one pole of the FPCW actuator. B. FSCW, Non-Overlapping Topology This configuration can be mainly combined with two types of stator winding, which span the airgap as described in Fig. 2. Figs. 3(a) and (b) show the respective FEMs of the alternative teeth wound (FSCW1) and all teeth wound (FSCW2) configu- 0018-9464/$31.00 © 2012 IEEE