0093-9994 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2019.2949545, IEEE Transactions on Industry Applications Optimal Design of a 5 MW Double-Stator Single-Rotor PMSG for Offshore Direct Drive Wind Turbines Warda Gul 1 and Qiang Gao 1,2,* 1. Department of Electrical Engineering Shanghai Jiao Tong University, Shanghai, China 2. Key Laboratory of Control of Power Transmission and Conversion (Ministry of Education, China), Shanghai, China *: gaoqiang@sjtu.edu.cn (corresponding author) Wanchak Lenwari Control System and Instrumentation Engineering King Mongkut’s University of Technology Thonburi Bangkok, Thailand wanchak.len@kmutt.ac.th Abstract -- This paper investigates the optimal design of a double-stator single-rotor permanent magnet synchronous generator (DSSR PMSG) with simulation validation. This scheme of generator is obtained by mechanically combining an interior rotor PMSG and an exterior rotor PMSG. Design of a 5MW radial flux DSSR surface mounted PMSG is developed with the second generation double layered fractional slot concentrated winding (FSCW), which reduces large initial investment, size and weight, in contrast to the usual massive direct drive (DD) generators for wind turbines. Considering analytically calculated performance of the generator, the Genetic Algorithm (GA) is applied to minimize weight and cost of the machine with adequate efficiency. Impact of grade selection of PM is analyzed to optimize cost through GA. Moreover, to show advantages of the proposed strategy, methodically computed magnetic flux density distribution in air gaps, synchronous inductance of windings, electromagnetic torque, copper losses and core losses are compared with the Finite Element Method (FEM) results, and they reveal satisfactory enhanced solutions. Economy of the optimal DSSR PMSG is assured by comparing its total size, weight and cost with optimized surface mounted Inner Rotor PMSG and Outer Rotor PMSG of comparable rated power and rated speed. Furthermore, issue of high cogging torque of this unique topology is resolved by optimizing the relative positioning of both stators’ slots using FEM. Index Terms—DSSR PMSG, FEM, FSCW, GA, Wind Turbine. I. INTRODUCTION The limited amount of fossil fuels and the negativity of global warming have made it necessary to harvest renewable energy. Among all renewable energy resources, wind energy produces cheaper electricity with self-sufficiency abilities. Now trend of direct drive (DD) Permanent Magnet Synchronous Generators (PMSGs) is gaining more popularity for off-shore wind turbines because gearboxes become more complex and more massive for machines with higher power capacity. By eliminating gearbox losses, DD generator produces an overall higher energy with more reliability and longer life. However, very large size of DD generators is one of the challenges, which needs to be addressed [1]. Firstly, in a DD wind turbine, the generator’s rotor spins at a low speed of the turbine shaft. Equation (1) relates the electric power with the air gap tangential stress and size of a generator. 2 * * * * * * 1.11 6.1 wf d m p e K F w D L P    (1) * d e m F A B  (2) where Pe is electric power (W), wm is mechanical speed (rpm), Dδ is air gap diameter (m), L is axial length (m), Fd is air gap tangential stress (Pa), Bm is magnetic loading (T), Ae is electric loading (A/m), Kwf is winding factor and αp is magnet pole arc to pole pitch ratio. One can see that, in order to get the same power with a low rotational speed, a generator requires a high tangential force per unit air gap surface area, Fd, which means a generator with a large air gap diameter is needed to support the high force. Tangential stress cannot be increased blindly to diminish large size of machine. Because PM remnant flux density limits the magnetic loading of machines. Moreover, saturation flux density of stator and rotor material also prohibits large air gap flux density. On the other hand, electric loading has a relation with current density in the slots. In a naturally air- cooled machine, which is the case for the generator design in this work, current density is normally 5-15A/mm 2 to maintain thermal life span of insulation material around copper coils, because a high current density dramatically increases the temperature of coils. Thus for effective cooling, naturally air- cooled generators normally have an air gap tangential stress in the range of 15-60 kPa [2]. Secondly, a wind turbine with a higher torque has a smaller rotational rotor speed, as the tip speed of rotor blades is kept constant [3]. Hence size and mass grow rapidly with power capacity, which is a problem in terms of capital cost, weight, logistics and assembly for offshore turbines. Therefore, the amount of material needs to be reduced significantly to decrease size and weight of a DD PMSG. In order to maximize the energy harnessed, minimize weight and improve power quality, various generator concepts including Electrically Excited Synchronous Generator (EESG) and PMSG, have been employed for DD