## PERMANENT MAGNET GENERATORS FOR MARINE CURRENT TIDAL TURBINES

##### Doctoral thesis

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##### Date

2017##### Metadata

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- Institutt for elkraftteknikk [2420]

##### Abstract

The focus of this thesis is the design of a permanent magnet generator for a marine current turbine, more specifically a tidal turbine. Tidal turbines can offer a predictable input of energy to the power grid and help to eliminate the dependency on fossil fuels. The marine current energy industry is currently working to reduce the cost of energy. Optimisation can be used both to optimise the power train topology at the system level and to reduce the cost of each individual component. In this thesis, optimisation is used to minimise the cost of the active materials for a generator and the cost of energy lost in the generator over its lifetime.
A review of various tidal turbine concepts was conducted and resulted in a set of specifications for the generator: a 1,5MWturbine with a nominal speed of 15 rpm and a 3,3 kV voltage rating. The turbine may be geared or directly driven, and the nominal speed of the generator may range from 15 rpm to 1000 rpm.
A radial-flux, inner-rotor, surface-mounted, slotted machine with laminated stator and rotor cores was chosen as the basis for optimisation. A novel feature of the work presented in this thesis is that in the optimisation routine, the numbers of poles and slots can be allowed to freely vary. The optimisation will result in the most optimal winding topology for the given application. The winding topology can be either distributed or concentrated. In the optimisation, constraints are placed on the spatial envelope, the frequency, the power factor, the short-circuit demagnetisation field and machine temperatures.
As part of the optimisation, for each considered machine design, an appropriate winding layout is determined, and a magnetic analysis, an electrical analysis, a loss analysis and a thermal analysis are performed. The outputs of the analysis are the fitness value (cost) and a vector containing the values of all parameters subject to the specified constraints.
This thesis includes a thorough analysis of stator yoke flux patterns in fractionalslot machines. Machine flux densities are often found under the assumption of no load. However, it is shown in this thesis that the armature reaction flux does not have the same amplitude behind all slots. Additionally, the time-varying no-load and armature reaction fluxes are shifted in time, with different phase shifts behind different slots. The on-load flux depends on both the amplitudes of the fluxes and the phase shift between them, and it varies significantly with the stator position. The amplitude variation depends on the winding configuration and is highest in machines with high subharmonic fields. In one of the investigated machines, the on-load flux behind one slot is 10 times higher than that behind another slot. The on-load flux can be significantly higher than the no-load flux in the yoke. The study of the stator yoke flux patterns is one of the major contributions of this thesis. Using this knowledge, it is possible to accurately predict the fluxes in machines at all positions at all times without using finite element analysis (FEA).
An optimisation routine that constrained only the no-load flux densities and not the on-load flux densities would undoubtedly produce optimal machine designs that would be highly saturated at load. It is also possible to use this knowledge when choosing the position of holes and bolts in the laminations. Flux barriers in
the stator have previously been used to reduce the subharmonics in fractional-slot machines. By investigating the positions in which the stator is more saturated, the positions of the flux barriers can be chosen more appropriately.
The analytical estimation of induced eddy-current losses has been identified as the most challenging part of the analysis. Various established methods for the computation of the eddy-current magnet losses were analysed here; however, none of the methods yielded results that matched the FEA results well. In this thesis, it is shown that it is possible to find the area of the magnitude of the eddy-current losses, but when the level of segmentation is either high or low, the analytical results do not match the FEA results very well. Analytical methods for calculating eddy-current losses in magnets should be used with the knowledge that the results are not very reliable. Other methods, which require more computational effort, must be used if a higher degree of confidence is desired.
Two main classes of optimisation methods exist, both with advantages and disadvantages. One gradient-based solver, available through MATLAB, and one direct optimisation method, a genetic algorithm that is also available through MATLAB, were used in this thesis work. The fast gradient-based solver solves a subproblem with a reduced number of possible slot-and-pole combinations. The speed of the solver enables the designer to repeat the optimisation routine with a changing set of requirements. The minimum cost, and the optimal design, can thereby be found as a function of parameters such as the power factor or the energy price. In this thesis, it is shown that in the case of a one-stage gear train, the cost of active materials decreases with an increasing number of poles while the cost of energy loss increases, and an optimal number of poles exists. The optimal generator designs for a direct drive, a one-stage gear train and a two-stage gear train are also shown. It is often claimed that gradient-based solvers are unsuitable for electrical machine design optimisation because such a solver finds only local minima for a nonlinear problem. Here, it is shown that as long as there are no, or very few, integer variables, the tested gradient-based solver is certainly capable of solving the problem when multiple startpoints are used.
The second tested optimisation algorithm, the genetic algorithm, is able to solve the full problem, with freely varying numbers of slots and poles. This capability comes at the cost of additional time spent. Although the genetic algorithm is a global optimisation tool, the genetic algorithm also will find only a local minimum if the number of individuals or generations is too small or if the diversity of the population is either too narrow or too wide.
A hybrid algorithm is ultimately used in this thesis; this algorithm combines the genetic and gradient-based algorithm, such that the genetic algorithm first locates the area of the global minimum and the gradient-based algorithm then locates the exact minimum.
The optimisation reported in this thesis shows that the lowest cost for the turbine generator is achieved using double-layer fractional-slot concentrated winding machines when the speed is less than approximately 1000 rpm. In a generator equipped with a three-stage gear train, either concentrated or distributed windings can be used with a comparable cost.
The optimal generator design has been found for six different generator speeds. The price of the generator decreases with a decreasing gear ratio, as expected. The reduction is most significant for the transition from a direct drive to a one-stage gear train. The curve showing the cost as a function of the generator speed can help guide the system owner in deciding which drive-train topology to choose.