load angle. Thorough analysis of the generators has been carried out using full physics simulations using a finite element method (FEM) of the time dependent ...
Permanent magnet fixation concepts for linear generator Oskar Danielsson, Karin Thorburn, Mikael Eriksson and Mats Leijon Division for Electricity and Lightning Research Department of Engineering Sciences Uppsala University, Box 534, S-751 21 UPPSALA
Abstract - Lately, the field of linear generators for wave energy conversion has attracted large attention, [1], [2]. One encouraging way to convert wave energy into electrical through direct drive is by using a linear, synchronous, longitudinal flux permanent magnet (PM) generator where the rotor piston is driven by, for example, a point absorber. As prices decrease, it has only recently become possible to use high remanence NdFeB magnets in technical applications. This opens up for new possibilities for linear generators, as high magnetic excitation can be achieved with smaller magnets.
converters (WEC), [1][2]. With a linear generator it is possible to couple the motion of a point absorber directly to the generator. Such configuration eliminates the need of complex power take-off schemes. This, in turn, reduces the complexity of the plant and the need for maintenance. Direct driven linear generators for WEC have been investigated by M.A. Muller in a number of articles [3,4]. It is mainly the transverse flux permanent magnet machine (TFM) that has been investigated. The studies have shown that the TFM exhibits very good power to mass ratios but also that it suffers from high inherent synchronous reactance. Another disadvantage of the TFM is the structure of the stator, which demands significant supporting structures to keep the cores in place.
In the present work two concepts of magnet fixation, surface mounted magnets and magnets buried between pole shoes have been studied with NdFeB and ferrite magnets. While the former alternative demands stronger magnets, which are more difficult to handle, the latter yields a somewhat heavier rotor piston. Pole shoes provides better possibilities to shape the magnetic flux curve in the periphery of the air gap, and the magnets are more protected from transients. The surface mounted concept allows for a more efficient use of the magnets, as the leakage is lower than when the pole shoe approach is used. This means that it is possible to reduce the length of the rotor with surface mounted magnets.
In this paper the electromagnetic properties of a longitudinal flux PM machine (LFM) are investigated. The LFM has a simple and robust stator construction with inherently low synchronous reactance. The stator of a LFM also provides a large option of winding configurations: single phase, multiple phase, different slots per pole and phase ratios, etc. Although the properties of LFM have been well investigated and a number of solutions has been proposed for conventional, highspeed rotational generators, the relatively low speeds and the reciprocal motion of a direct coupled linear generator changes the prerequisites fundamentally. Thorough analyses of the magnetic circuit are needed to optimize the use of expensive permanent magnet and other materials, increase the efficiency to a maximum, reduce the ripple in the electromagnetic forces, etc. This paper is based on full physics simulations revealing the time dependent behaviour of the machine. Four different rotor concepts are investigated and the electromagnetic performances of the machines are compared.
The different configurations are compared with respect to total magnet mass, efficiency and load angle. Thorough analysis of the generators has been carried out using full physics simulations using a finite element method (FEM) of the time dependent magnetic field. Magnetic intensity distributions, time dependent currents and voltages are also among the parameters that have been studied. 1
INTRODUCTION
Linear generators have lately been suggested as suitable energy converters in wave energy
1
1.2 Stator
MACHINE CONFIGURATION 1.1 General description
The stator is made of laminated electrical steel, piled into one solid unit, se Figure (2). The conductors are power cables with a circular cross-section and a conducting area of 16 mm2, insulated with a 1.1 mm PVC-layer, which adds up to an outer diameter of 7.2 mm. The coil winding is a three-phase winding with a slot per pole and phase ratio of 5/4. This winding configuration aims at minimizing the fluctuation in the output power caused by cogging. A three-phase LFM with a slot per pole and phase ratio equal to one is proposed as generator in the Archimedes Wave Swing [1].
A possible WEC concept with a linear generator as power take-off is shown in Figure (1). The WEC consists of a buoy coupled directly to the rotor of a linear generator by a rope. The tension of the rope is maintained with a spring pulling the rotor downwards. The rotor will move up and down at approximately the same speed as the waves and the maximum speed will be in the order of 1 m/s. The relatively low speed implies that the reaction force developed between the rotor and stator to be very high. For example, a 10 kW generator needs a reaction force in the order of 10 kN with a rotor speed of 1 m/s. This implies that a directly driven generator must be larger than a conventional high-speed generator. (a)
(
Buoy
Rope
Linear generator
Figure (2): Tilted side view of a section of the stator of LFM linear generator. 1.3 Rotor Two types of magnet fixation methods, surface mounting and burying magnets between pole shoes, are tested with two different types of permanent magnets. The two fixation methods are illustrated in Figure (3). In both configurations adjacent magnets have opposite polarity and a movement of the rotor creates an altering magnetic field in the stator coils.
Stators Rotor
Spring b ) Figure (1): (on top) The principles of a wave energy plant with a linear generator as power take-off. (bottom) Cross-section of the linear generator.
2
Figure (4): Magnetic circuit for a rotor with buried magnets. The magnetic flux is marked by closed curves and arrows indicate the direction of the flux. Leakage flux through the aluminium plate is marked with a dashed line.
Figure (3): Tilted side view of rotor for a LFM linear generator. Buried magnets to the left and surface mounted magnets to the right. The direction of the magnetic flux is indicated with arrows. Figure (4) shows the magnetic circuit of a rotor with buried magnets. The flux is led from the magnets through bars of magnetic steel, called pole shoes. The pole shoe enables control of the magnetic flux distributions in the periphery of the air gap and it also protects the magnets from transient magnetic fields generated by short circuit in the outer circuit. The aluminium plate on the backside of the rotor serves as a barrier for the magnetic flux to pass through the backside of the rotor. A portion of the magnetic flux will unavoidably pass through the back. That flux will not contribute to the magnetic coupling and can be considered as “lost”.
Figure (5): Magnetic circuit for a rotor with surface mounted magnets. The magnetic flux is marked by closed curves and arrows indicate the direction of the flux.
The magnetic circuit of a generator with surface mounted magnets are illustrated in Figure (5). Surface mounted magnets are more exposed to transients and face a larger risk of demagnetization. On the other hand the magnetic circuit has no obvious shortcuts, as is the case for the buried magnets.
The major difference between the two concepts is that the width of surface mounted magnets, wmag, is limited of by the pole width, wpole. Buried magnets have no theoretical limit of the width of the magnet, instead it is the height of the magnet hmag that must be smaller than the pole width. Normally the magnet height should be considerably smaller than the magnet width and a limitation of the height is a minor problem. Two permanent magnets have been examined: ordinary ferrite (Fe) magnets and high-energy Neo-dymium-Iron-Boron (NdFeB) magnets. The basic properties of the magnets are presented in Table (1). NeFeB magnets are considerably more expensive than Fe magnets and the relation of the kilo price is assumed to be 10:1.
3
Table (1): Properties of the magnets
Remanence (T)
1,32
0,3663
volume and cable length is calculated from the geometry and vertical length of the rotor and stator. A fix stator design is used in all simulations to minimize the number of variables affecting the results.
Relative permeability
1,06
1,06
Table (2): Fixed parameters for case linear generators
Density (kg/m3)
7700
4700
Material
2
Neodymium-Iron-Boron Ferrite Magnet (Vacodym 633 PT) (Oe MagnetY30 BH)
METHOD 2.1 Simulations
This work is based on full-physics simulations with a starting point in the electromagnetic field equations. The simulations are based on a 2-dimensional model of a segment of the generator. Design symmetry is used to minimize the size of the simulated segment. In this case, with a slot per pole and phase ratio of 5/6, six poles need to be simulated to achieve symmetry. Maxwell’s equations are solved in two dimensions with nodal finite element method. The grid is automatically generated and the number of nodes depends of the size and geometry of the problem. Material properties such as resistivity, permeability, coercivity, sheet thickness etc. are taken into account in the model. Three-dimensional effects, such as coil end reactance are approximated by empirical factors. Hysteresis losses and eddy current losses are calculated from the maximum magnetic field intensity distribution.
Parameter
Value
Voltage
200 V
Power
10 kW
Number of stator sides
4
Number of cables in each slot
4
Cable cross-section
16 mm2
Slots per pole, phase
5/4
Pole width
55 mm
Airgap width
3 mm
Numerical results along with magnetic intensity distribution plots have been used throughout the work to analyze the results. The maximum magnetic intensity in the stator is kept below 1.8 T in order to avoid saturation and excessive iron losses. 3
RESULTS
To more easily compare the magnet mass the Fe magnet mass is divided by a factor of ten in the graphs. This gives approximately the same values and relates the magnet mass to the relative cost of 10:1 between NdFeB and Fe magnets.
2.2 Evaluation criteria The main factors of interest in this work are the apparent power, the electromagnetic efficiency, the load angle and the amount of material needed. A high electromagnetic efficiency and low material usage is desired. The electromagnetic efficiency includes hysteresis losses, eddy current losses and resistive losses. Furthermore, a low load angle is desired. A machine with inherently low load angle has better performance at both normal and transient conditions and is less affected by changing loads and varying frequencies.
3.1 Magnet dimensions Different heights to width relations of the magnets have been investigated in order to see if there is an optimum. In Figure (6) the magnet volume of single magnet is kept constant and the electromagnetic efficiency and total magnet weight is plotted for different height to width relations of the magnets. As can be seen the electromagnetic efficiency is steadily increasing and the total magnet weight is decreasing with increasing magnet width for the surface mounted magnets. The pole width limits the magnet width and no optimum is reach for the surface mounted magnets. The width of the buried magnets can be chosen
The four rotor concepts are simulated for different magnet dimensions and various pole widths. Output power, voltage and stator width are held constant in the simulation and the vertical length of the rotor is iterated to fulfil these conditions, see Table (2). The material usage such as total magnet volume, stator steel
4
freely and an optimal width to height ratio is somewhere around 5 for both Fe and NdFeB magnets.
electromagnetic efficiency for different total magnet mass. This is illustrated in Figure (7). It should be noted again that the mass of the Fe magnets are divided by a factor of ten. The buried NdFeB magnet rotor reaches about the same electromagnetic efficiencies but demands approximately the double total magnetic mass compared with the surface mounted NdFeB magnet rotor. The surface mounted Fe magnet rotor has a slowly increasing electromagnetic efficiency that never exceeds 70 %, even for relatively large magnets. In Figure (8) the load angle of the different machines is plotted for different total magnet weight. The surface mounted NdFeB magnet rotor has lower load angle than the buried Fe magnet rotor irrespective of the total magnet weight. Again the surface mounted Fe magnet rotor and the buried NdFeB magnet rotor shows to be poorer than the other two options.
Figure (7): Electromagnetic efficiency for the different rotor concepts plotted against the total magnet weight. The total mass of the Fe magnets is divided by a factor of ten. Figure (6): Total magnet weight and electromagnetic efficiency for different magnet height to with relations. The total mass of the Fe magnets is divided by a factor of ten. 3.2 Comparison of the concepts Two of the alternatives, surface mounted NdFeB magnet rotor and the buried Fe magnet rotor, show stunning similarities in
5
relatively good electromagnetic properties. It should, however, be mentioned that the ferrite magnets needed are about ten times heavier than the NdFeB magnets, which will result in a much heavier rotor. A large and heavy machine will be more expensive than a smaller. Therefore it is obvious that the overall most advantageous is the machine with surface mounted NdFeB magnets, when the magnet cost ratio of 1:10 is used. If the cost of ferrites decrease substantially, the pole shoe mounted ferrite option will be more economical. The surface mounted Fe magnet rotor shows very poor electromagnetic properties. It is clear that Fe magnets are not suitable for surface mounting in machines with small pole widths, which demands high magnetic excitation of the stator. The buried NdFeB magnet rotor shows similar characteristics as the surface mounted NdFeB magnet but demands the double amount of magnet. On explanation can be that a part of the magnetic flux is passing through the back of the rotor when the magnets are buried between pole shoes, se Figure (9).
Figure (8): Load angle for the different rotor concepts plotted against the total magnet weight. The total mass of the Fe magnets is divided by a factor of ten. 3.3 Material usage The material usage is estimated for one machine of each of the four generator types, and is presented in Table (3) with efficiency and load angle. For each type the machine with the highest efficiency in combination with lowest material consumption is chosen. Table (3): Material utilization, efficiency and load angle for simulated generators Surface mounted ferrite
Surface mounted NdFeB
Pole shoe ferrite
Pole shoe NdFeB
2275 kg
N/A
1240 kg
N/A
N/A
120 kg
N/A
242
Core material
3852 kg
893 kg
1020 kg
1334 kg
Cable
3779 m
1272 m
1234 m
1299 m
Efficiency
68.5
85.2
85.1
83.5
Load angle
6.2
4.5
4.8
5.2
Fe magnet NdFeB magnet
4
Figure (9): Magnetic flux lines in a cross section of a linear generator with NdFeB magnet rotor revealing the leakage flux in thick lines. Another circumstance worth mentioning is that the basic properties, i.e. voltage, output power, stator width etc., of the generators have been constant for all simulations. It is possible that an option other than surface mounted NdFeB magnets is most advantageous for another machine configuration. This study, however, lies outside the scope of this paper.
DISCUSSION
The results, presented in the previous section, reveal two concepts, surface mounted NdFeB and buried ferrites, which show similar and
6
5
CONCLUSION
Two simulated generators exhibit similar high efficiencies and low load angles, and are regarded as good options. These two have rotors with surface mounted NdFeB magnets and ferrite magnets buried between pole shoes, respectively. It can be argued, that when the whole generator is examined, the surface mounted NdFeB may be a better option, as it renders a less heavy rotor machine. The cost relation between ferrite and NdFeB magnets is an important evaluation parameter. 6
ACKNOWLEDMENTS
The work in this paper is supported by the Swedish Energy Agency, the Ångpanneföreningen research foundation, the J Gust Richert foundation, Vargön Alloys AB, Göteborg Energi and Draka Kabel. 7
REFERENCES
[1]
H. Polinder, F. Gardner and B. Vriesema, ”Linear PM generator for wave energy conversion in the AWS”, Proceeding of ICEM 2000, pages 309-313, August 2000, Espoo, Finland
[2]
M.A. Mueller, “Electrical generators for direct drive wave energy”, IEE Proceedings, Gener. Transmission and Distribution, Vol. 149 Issue 4:446-456, July 2002
[3]
M.A. Mueller, N.J. Baker and E. Spooner, “Electrical Aspects of Direct Drive Energy Converters”, Proceedings of the 4th European Wave Energy Conference, 2000, Aalborg, Denmark
[4]
M.A. Mueller and N.J. Baker, ”A low speed reciprocating permanent magnet generator for direct drive energy converters”, Conference publication, Power Electronics, Machines and Drives, 16-18 April
7
