Design and Simulation study of 40 MW PM Generator for the CRAFT

Design studies of two counter rotating permanent magnet (PM) synchronous generators have been performed. The two 40 MW generators have been designed and compared for the Counter Rotating Axis Floating Turbine (CRAFT) with different air-gap diameters. The generators are modelled with validated full physics finite element method (FEM) which also includes dynamic simulations. The simulations are performed by using an electromagnetic model. The model is described by combined field and circuit equations and is solved in a finite element environment. The stator winding of the generators consists of circular cables and the rotor consists of buried ferrite PM. The generator with smaller air-gap diameter will have lower material costs due to smaller frame but higher due to use of more active materials. A comparison of the counter rotating generators with a traditional direct drive has also been performed by maintaining the same voltage but reducing the rotational speed by half. This shows that a generator with a higher rotational speed will have lower material costs due to smaller dimensions and lower weight. Furthermore, a design variation, to reduce the cogging and harmonic content of the voltage by changing the pole shoe, was analyzed. In conclusions, a 40 MW generator design for the CRAFT has successfully been simulated with a multi-physics-FEM. The advantages of using a counter-rotating generator has been established.


Introduction
The development to a fossil-free future continues to expand and one of the fastest growing renewable energy technologies is wind power [1].During the last couple of years wind power has continued to expand and the technology evolved.Since the energy system is changing the need for wind power technology is more important than ever.Today onshore wind power is dominating the market, but offshore wind power farms keep growing and more countries continue to invest.The possibility to have wind farms longer out at open sea is attractive since there is more undisturbed wind.This had made the development for floating wind power without foundations fixed to the seabed being more interesting and highly relevant [2].
Wind turbines can be divided into two groups depending on the orientation of their axis, the horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT), where the HAWT are the more common and established one.The HAWT consists of a yawing mechanism and need to be placed in the wind direction and their generator is placed on the top of the tower.The types of VAWT on the market today is a Savonius rotor, a Darrieus rotor and a Darrieus rotor with straight blades (H-rotor).VAWT is omni-directional and can accept wind from all directions and the generator can be located at the bottom of the tower [3].Since the size of the generator for a VAWT is not the main concern the design can have more focus on the cost, efficiency and minimize the maintenance.Previous research on different turbine concepts and VAWT have been reviewed [4][5] [6].
In this article a design and simulation study of two 40 MW counter rotating permanent magnets (PM) synchronous generators have been performed for the Counter rotating axial floating turbine (CRAFT) concept.The CRAFT is an integrated design for floating offshore wind.The two turbines have a unique design, originating from the vertical axis wind turbine design.An illustration of the CRAFT can be seen in Figure (1).CRAFT consists of one spar buoy and two 3-bladed turbines on one tower allowing for a counter rotating generator.The generator, located below sea level in a dry submerged housing 'sumarin', will act as ballast.The traditional generator design requirement of low mass is removed when the generator and its weight contribute to the overall stability of the system.Since the CRAFT generator is not sensitive to weight, buried ferrite magnets has been chosen to reduce the cost of the generator.The material has previously been tested in generators for offshore wind turbines and the technology has been shown to reduce the levelised cost of energy for industries.Also, the use of buried ferrite magnets could diminish the demand and avoid the cost insecurity of supply for the more expensive rare-earth metal, Neodymium [7][8] [9].Buried ferrite has also been more popular in areas like electromobility due to the increased interest for electric cars and also the interest for a lower cost and a supply chain that is more stable [10].Buried ferrite PM has previously been built and experimentally verified with FEM simulations [11].
The CRAFT is utilising counter rotating turbines where one turbine is rotating the stator and one turbine is rotating the rotor.Furthermore, the counter rotation of the CRAFT enables a compact direct drive system, as air-gap speed is double when stator and rotor are counterrotating, compared to a direct drive generator for a single turbine system.The generated electric power comes from time series expected in the North Sea.The generator has a full electric control of the rotational speed which ensures the generator to operate at optimal speed.The CRAFT has an active stall control effectuated by controlling the generators torque which will control the speed of the generator given that the generator is designed for high peak torque [12].A comparison between direct drive solutions and generators with different gearboxes can be found in [13] [14].
The two generators for the CRAFT concept have been compared and simulated with two different air gap diameters.A comparison between the counter rotating generators with a traditional direct drive has also been performed by maintaining the same voltage and reducing the rotational speed by half.Furthermore, the cogging of the generator has been analysed as well as the harmonic content of the voltage.

Theory 2.1. Generator theory
The principle theory of a generator that is explained by Faraday's law of induction is where U is the induced voltage in an electric machine that is depending on N which is the number of turns of the conductor and the time derivative of the magnetic flux.
Generators are suffering from mechanical and electromagnetic losses.The mechanical losses, for lack of a gearbox, is dominated by the bearings and the losses in the couplings.Where the electromagnetic losses consist of the hysteresis losses, eddy current, resistive losses in the copper conductor and excess losses.

Electromagnetic model
The electromagnetic field inside the generator is modelled in two dimensions and is assumed axis-symmetrical.The two-dimensional model is then solved in a finite element method (FEM).It's a combined field and circuit model which is solved with a time-step.Three-dimensional effects have also been considered by including the coil end impedances into the circuit equation of the windings.The PM is modelled by the sources of the surface current.The simulation model has previously been used in studies and verified through experimental results for generators [15] [16].
The electromagnetic model is described by the combined field and circuit equations.The combined field equations come from Maxwell's equation and is where σ is the conductivity, µ 0 is vacuum, µ r is the permeability, A z is the axial magnetic potential and ∂V /∂z is the applied potential.
The circuit equations are described by where I a , I b and I c are the conductor currents.The U ab and U cb are the terminal line voltages.The U a , U b and U c are the terminal phase voltages that is obtained from solving the field equations.The coil end resistance is R s and the coil end inductance is described by L end a , L end b and L end c [17].

Simulation method
The generators are modelled with full physics finite element method (FEM) which also includes dynamic simulations.The geometry of the FEM is divided in small triangle parts and then the equations are solved in the elements.The simulations are performed by using the electromagnetic model described above and is then solved in a finite element environment ACE.The mesh consists of around 3200 elements and it's finer closer to the more critical parts like the cable and is coarser closer to areas like the yoke of the stator.Only a few poles were modelled since both the generators are symmetric.
The simulations can be performed in stationary-and dynamic mode.In the stationary mode the results are given for a fixed position and in the dynamic mode the simulations also include a time dependency which gives a more precise result.

Generator characteristics
The characteristics for both generators come from the results from the stationary simulations by using the method described above, where both generators were constructed with the geometrical dimensions derived by the iterative simulations.Although some of the design parameters for both generators had to be decided before they where modelled.The parameters that were decided was the power-and voltage level and some geometrical constraints.Where other parameters could be varied and the design could be optimized between different and several simulations.The two generators have been named by their air-gap diameter to the 12 m and 15 m generator.The geometric design parameters can be seen in Table (1).Both generators have eight cables per slot.The stator winding consists of circular cables since it gives an electric field that is even distributed in the cables and have a good use of the insulation material PEX [18].The cables have a conductor area of 240 mm 2 and consists of various copper strands.The rated current density results in 2 A/mm 2 .Three phases have been chosen for the winding scheme and the number of slots per pole and phase is 1/1.The airgap has been chosen 0,1 % of the air gap diameter for both generators.The generator has a full electric control of the rotational speed which ensures the generator to operate at optimal speed.The rotor consists of buried Ferrite PM of type Y40 with a density of 4700 [kg/m 3 ], remanence of 0,4437 T and a permeability of 1,06.The material Ferrite has been chosen to reduce the cost of the generator since it's cheaper than the more used material Neodymium PM.Ferrite magnets have a weaker performance than Neodymium but that only implies that more magnets are needed.Since the CRAFT generator is in the sumarin it's not sensitive to weight, because the weight is something that will contribute to the stability.Ferrite magnets also have an excellent resistance to corrosion and oxidation.It's also stable and difficult to demagnetise.Additionally Ferrite magnets are generally regarded to be more environmental friendly than NdFeB-magnets [8].
The suggested electromagnetic design parameters like the power, line-to-line voltage, current, electrical frequency and cogging for both generators can be seen in Table (2).28 25 There are several sources of error which could cause small deviations from the presented simulations for a real generator.However, the agreement between the experimental result and the simulations based on the finite element calculations has previously been validated to be within a percentage [19].

Comparisons between counter rotating and direct drive
The generator with smaller air gap diameter (12 m) has also been compared to a direct drive solution that has no counter rotation.This has been carried out to see the difference between a counter rotation and a direct drive solution.In order to study the difference between counter rotation and a direct drive solution the latter is studied by reducing the rotational speed to half.When the rotational speed between the rotor and stator is reduced by half it will affect the generator power output since it's in an angular motion, where the power is equal to the torque multiplied with the rotational speed.

Analyse of the cogging and the harmonic content of the voltage
The cogging of the 12 m generator was studied as well as the harmonic content of the voltage.This was analysed by using dynamic simulations to see the possibility to reduce the cogging and get a more smooth magnetic flow by changing the pole shoe.The new pole shoe can be seen in Figure (2) below.The new pole shoe has a design that keeps the magnets more in place and will give a more sinusoidal EMF [20].

Result and discussion
The two generators total weight, efficiency and losses can be seen in the Table (3).The generator with smaller airgap diameter renders to be cheaper than the generator with a larger airgap diameter due to a smaller frame and less material.A smaller generator will however have more active materials than a larger generator.As indicated, the traditional design requirement of low mass is removed when the generator contributes to the overall stability of the system.
The electromagnetic field for both the 12 m and 15 m generators can be seen in Figure (3).The figure shows the magnetic flux with field lines for one pole and the scale shows the magnetic field in Tesla (T).The red and yellow areas indicate a stronger magnetic field, and the green and blue areas indicate a weaker magnetic field.The comparison between the counter rotating generator with a direct drive solution by reducing the rotational speed by half can be seen in Table (4).Table (4) shows that by reducing the rotational speed by half the generator becomes much heavier and the weight increases from 842 ton to 1700 ton.It also shows that the length of the generator increases from 6690 mm to 13 554 mm.A counter rotation makes the generator much smaller and lighter.Furthermore, the counter rotation of the CRAFT enables a compact direct drive system, as air-gap speed is double when stator and rotor are counter-rotating, compared to direct drive generator for a single turbine system.
The analyse of the cogging and the harmonic content of the voltage shows that by changing the pole shoe the cogging was reduced from 28 % to 7 %.The reduction of the pole shoe increased the generators length to 6860 mm.The magnetic flux with field lines for one pole for the new pole shoe can be seen in Figure (4).The scale in Figure (4) indicates that the electromagnetic field is stronger with this pole shoe.
The harmonic content of the voltage was also reduced.Table (5) shows the harmonic content of the voltage with the new pole shoe.
Table 5. Harmonic content of the phase voltage presented as of the first harmonic.

Conclusions
A design and simulation study of two 40 MW counter rotating generators for the CRAFT concept have been performed and both has been successfully simulated.The generator with a smaller air gap diameter will have lower material costs due to a smaller frame but it will be higher due to use of more active materials.A comparison of the generator with smaller air gap diameter to a direct drive solution by reducing the rotational speed by half would render the generator to be much larger and heavier.By analysing the pole shoe for the generator with smaller airgap diameter made the cogging and the harmonic content of the voltage decrease.
In conclusions, 40 MW generator designs for the CRAFT concept has been successfully simulated with multi-physics-FEM.The advantages of a counter rotating generator have been established.

Figure 1 .
Figure 1.The different parts of the CRAFT

Figure 2 .
Figure 2.An illustration of the new pole shoe

Figure 3 .
Figure 3.The magnetic flux with field lines for one pole.The left is the 12 m generator and the right is the 15 m generator.The scale indicates the magnetic field in Tesla (T).

Figure 4 .
Figure 4.The magnetic flux with field lines for one pole for the 12 m generator.The scale indicates the magnetic field in Tesla (T).

Table 1 .
Geometric design parameters

Table 2 .
Electromagnetic design parameters

Table 3 .
Generator results

Table 4 .
Comparison between a counter rotating and direct drive