The Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.1 Abstract-The objective of this paper is to optimize direct drive permanent magnet synchronous generators for offshore direct drive wind turbines in order to reduce the cost of energy. A 6MW wind turbine design is assumed and parametric electromagnetic and structural generator models are introduced for a surface-mounted magnet generator topology (using magnets with high BHmax) and a flux-concentrating variant (using magnets with lower BHmax). These are optimized using a hybrid Genetic Algorithm and Pattern Search process and the results show that the surface-mounted permanent magnet generator produces the lower cost of energy. The choice of objective function is addressed and it is found that a simplified metric incorporating generator cost and losses proxy produces similar designs to a full cost of energy calculation. Further steps to improve the quality of the model include the effect of generator mass on the design and cost of the turbine tower and foundation, which can add €0.4m to the turbine cost. Further optimizations are carried out to show the impacts of magnetic material costs (doubling this leads to a €1.1/MWh increase in cost of energy) and generator diameter limits (increasing the upper limit from 6m to 8m leads to a 0.9% drop in cost of energy) have on the choice of optimum independent variables.Index Terms-Cost of energy, direct drive wind turbine, optimization, permanent magnet generator, structural model, tower and foundation. I. INTRODUCTIONgrowing proportion of offshore wind turbine designs are now based on directly driven permanent magnet synchronous generators. Direct drive machines can offer higher reliability and reduced maintenance cost because of the omission of the gearbox from the drive train [1]. Some of the downsides of these generators include their large size (due to the high torque rating), requirements for large quantities of rare earth permanent magnets and the significant generator structures required to maintain the small air-gap clearance against the large attraction forces between the rotor and the stator [2]. The generator designer needs to deliver a number of performance characteristics including high efficiency, low power losses at part load, high availability, low machine mass, reduced volume and lower material and manufacturing costs. Normally the designers employ some element of optimization to achieve the best balance of these aspects [3].The main purpose of this paper is to examine the process of optimizing large, low speed generators for offshore direct drive wind turbines, exploring the different objective functions that a A. McDonald and N. A. Bhuiyan are with the Institute of Energy and Environment, Department of Electronic and Electri...

In this paper, the main objective is to optimize permanent magnet synchronous generators for offshore direct drive wind turbine, examining the best choice of magnet grades, BHmax and working temperature. A surface-mounted Nd-Fe-B generator is designed electromagnetically and structurally and optimized for different rated powers of 6, 8 and 10 MW. The results show that the cost of energy decreases as the wind turbine's rated power increases. Further optimizations were carried out using different neodymium magnet grades and it was found that the higher magnet grades produce a lower cost of energy. In addition, steps were taken to estimate the effect of magnet temperature. A detailed thermal model is used to calculate the cooling airflow requirements to bring the magnet operating temperature from 120°C to 80°C. Allowing the use of cheaper temperature grades of magnets, the additional cooling reduces winding losses and improves the effective BHmax of the magnets. IndexTerms-Cooling system, cost of energy, magnet grade, optimization, permanent magnet generator, thermal model, wind turbine. N. A. Bhuiyan is with ASTUTE, College of Engineering, Swansea University, Swansea SA1 8EN and A. McDonald is with the Institute

This version is available at https://strathprints.strath.ac.uk/56794/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the AbstractIn the past few years interest in the use of low speed permanent magnet generators for direct-drive wind turbine generator applications has increased significantly. The significant fluctuations in NdFeB magnet prices has encouraged designers to optimise magnet utilisation and to look at alternative magnet materials for wind turbine electrical generators. In this paper an analytical design model is developed for 6 MW offshore direct-drive wind turbine generators using different magnet materials (one with surface mounted NdFeB and another with flux concentrating ferrite magnet). Finite element method models are used to check key dependent variables calculated by the analytical models. The generator designs are optimised using a hybrid optimisation method incorporating a Genetic Algorithm and Pattern Search approaches. This is applied for four different objective functions, the first two which concentrate on maximising rated torque per unit magnet mass or unit of generator active material cost. They are simple and quick to execute but prioritise cost reduction and ignore lower efficiencies leading to lower turbine energy yields and hence poor cost of energy. A third objective function which seeks to minimise the sum of the generator active material cost and the costs of lost revenue over a finite number of operational years. This gives similar results to a fourth objective function which is an explicit turbine cost of energy calculation. The cost of NdFeB magnets affect the cost of energy of the surface mounted generator which tested with different cost €40/kg, €60/kg and €80/kg. The ferrite magnet generator being better when the NdFeB magnet price rises to €80/kg.

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