Fast and Accurate Model for Optimization-based Design of Fractional-Slot Surface PM Machines Benjamin Cheong Power Electronics, Machine and Control Group (PEMC), The University of Nottingham, UK eexbc4@nottingham.ac.uk Michael Galea Power Electronics, Machine and Control Group (PEMC), The University of Nottingham, UK ezzmg@nottingham.ac.uk Paolo Giangrande Power Electronics, Machine and Control Group (PEMC), The University of Nottingham, UK ezzpg@nottingham.ac.uk Pericle Zanchetta Power Electronics, Machine and Control Group (PEMC), The University of Nottingham, UK eezpz@nottingham.ac.uk Xiaochen Zhang Power Electronics, Machine and Control Group (PEMC), The University of Nottingham, UK ezzxz2@nottingham.ac.uk Patrick Wheeler Power Electronics, Machine and Control Group (PEMC), The University of Nottingham, UK eezpww @nottingham.ac.uk Abstract—This paper presents the development and validation of a fast, accurate, and high dimensional Multiphysics analytical model for the optimization-based design of fractional- slot surface permanent magnet (PM) machines. The approach is non-iterative and high dimensional, i.e. considers a high number of input parameters. The resulting model takes an average of 0.03 seconds to run on a standard PC, and its accuracy is verified by both Finite Element (FE) analysis and experimental tests. Due to its accuracy and speed, the model can be easily integrated within a design optimization environment. Keywords— Permanent Magnet Synchronous Machine, Electrical Machine Modelling, Design Optimization I. INTRODUCTION For aerospace applications where power density and efficiency are key requirements, the use of fractional-slot surface PM machine with concentrated windings is highly attractive [1, 2]. The design of such machines is multiobjective in nature, and these objectives are often traded off against each other within an optimization environment. Significant research has been carried out, over the past decade, on methods to perform machine design optimizations more reliably and efficiently [3]. Finite element (FE) analysis is the principal tool in industry for accurate machine modelling and is occasionally incorporated within an optimization environment [4, 5]. However, this modelling approach demands high computational power, limiting the number of evaluations in each optimization run. For better computational efficiency, an analytical approach to machine modelling is often preferred. For example, analytical electromagnetic models have been introduced in [6] and [7] for PM machines, while analytical thermal models have been presented in [8, 9, 10]. This paper proposes a simple yet comprehensive analytical surface PM machine model that considers both its electromagnetic and thermal behaviours. The model evaluates machine electromagnetic performance by calculating the air-gap magnetic field distribution and employing mathematical MMF winding functions. Further, the machine thermal behaviour is predicted using a simplified 2D Lumped Parameter Thermal Network (LPTN). The resulting model is characterized by a low computational time, achieved by its non-iterative approach. FE analysis and experimental tests also reveal that good accuracy is achieved with this analytical model. The speed and accuracy of this model make it particularly suitable for use in an optimization-based design. II. INPUT PARAMETER DEFINITIONS A total of 20 input parameters   are defined for the machine model:   ∋ {,   ,,  ,  ,  ,  ,  ,  } (1) where  is the pole number,   is the slot number,  is a set of machine geometrical parameters,   is the number of turns,   is the strand diameter, and   is the number of strands per conductor,   is the electrical speed,   is the d- axis current, and   is the q-axis current. The geometrical parameters contained in  are:  ∋ {  ,  ,  ,,  ,  ,  ,  ,  ,  ,  , } (2) where  is the machine axial length, and the other parameters can be seen in Fig. 1(a) for a typical surface PM machine. III. PM MACHINE ANALYTICAL MODELLING In this section, details of the fractional-slot surface-PM machine model are presented. The flowchart of the model is Fig. 1: (a) Geometrical input parameters for a typical surface PM machine. (b) Flowchart of machine model.