3 Methodology of project combines theory, simulations and discussions
The methodology used in this project combines theory, simulations and discussions. Firstly, the importance of the project in a greater view was outlined (see Section 1.1–1.2) and previous work was studied. Secondly, the background theory was studied and the analytical expressions were derived (see Section 2). Thirdly, a hypothesis of the project outcome was stated (see Section 3.1) and the simulations were planned (see Section 3.2.1–3.2.3). Thereafter, results were gained from simulations (see Section 4). Finally, the results were analyzed and discussed (see Section 5–7), incorporating the small project in a wider perspective. Throughout the entire project, supervisors at the Division for Electricity at Uppsala University were consulted.
The hypothesis is that the magnetic energy in the stator steel will decrease as parts of the magnets in the translator are changed from a ferrite permanent magnet of type Y40 to a ferrite permanent magnet of type Y30, if the total size of the magnetic material and the overall design of the linear generator are equal. That is, the maximum magnetic energy in the stator steel is generated for a magnetic circuit entirely made of Y40. However , the hypothesis is that changing the shape of the pole shoes, from rectangular to T-shaped, could increase the magnetic energy in the stator, as more of the magnetic flux is passed through the stator. Moreover , the hypothesis is that by shortening the pole shoes, the magnetic energy in the stator steel could increase, as more of the magnetic flux would pass in the desired direction. The hypothesis is that changing a part of the Y40-magnet to Y30, in combination with a different shape of the pole shoes, could lead to a generator with properties similar to a generator with only Y40. Finally, the hypothesis is that the question stated in Section 1.2 can be answered with yes, it is possible to create a linear generator for wave power production, with different types of ferrite permanent magnets and pole shoes, but with a similar amount of magnetic energy in the stator steel as previous designs.
3.2 Simulations of the linear generator
For this study, a two-dimensional segment of a linear generator was simulated by software called Ace, with an interface called Kalk . The simulation software solves Maxwell’s equations (see Equations 1–4 in Section 2.1) on the segment, using the Finite Element Method (FEM) . In order to change the properties of the linear generator , the user can either change parameters in Kalk or program new features in Ace. The results from previous simulations in Kalk for different types of generators have been verified by experiments .
In this project, the main features of the linear generator used for wave energy conversion is set in Kalk and the specific features are programmed in Ace. A segment of a linear generator generated in Ace can be seen in Figure 9. The ferrite permanent magnets are mounted between pole shoes in the translator, and the stator contains windings, as described in Section 2.6.
In Ace, all magnets are simulated as closed current loops, in accordance with the theory in Section 2.2. If the user chooses one of the default types of magnets in Kalk, the software will calculate the equivalent current representing that magnet. However , in this case, different types of magnets are created for the linear generator in Ace. Thus , the equivalent currents for the ferrite permanent magnets of types Y30 and Y40 had to be calculated (with Equation 16 in Section 2.4) and programmed into Ace.
By using the mean values of the remanence and the coercivity from Table 1, and Equation 15 from Section 2.4, it was possible to calculate the relative permeability for Y30 and Y40, which is needed in order to generate the simulations in Ace; all values are shown in Table 2.
Table 2. Used and calculated values for the ferrite permanent magnets Y30 and Y40.
The heights of the ferrite permanent magnets were constant in all simulations. Thus , the values from Table 2 and the height of the ferrite permanent magnets, hpm = 20 mm, were used in Equation 16 (see Section 2.4) to calculate the coil currents representing the ferrite permanent magnets Y30 and Y40. The final resulting coil currents used in the program were 6840 A for Y40 and 3850 A for Y30. Due to programmatic issues, the coil currents had to be divided by two in the simulations.
The result of a simulation run in Kalk is, for example, a plot showing the magnetic field flowing through the linear generator segment, which is shown in Figure 10. Moreover , the results contain a list of the magnetic energy (Ws/m) found in different parts of the stator, which can be summed up to gain understanding of the performance of the linear generator created.
Three different types of simulation experiments were performed in this project. The first simulation experiment, called Simulation 1, was to determine the magnetic energy in the stator steel as one of the magnets in the linear generator was divided into two magnets with different magnetic properties (see Section 3.2.1). The second simulation experiment, called Simulation 2, was to change the shape of one of the pole shoes in the linear generator and calculate the magnetic energy in the stator steel (see Section 3.2.2). The third simulation experiment, called Simulation 3, was to combine two of the cases in Simulation 1 (that is, divided magnets) with one of the pole shoe designs (T-shaped) from Simulation 2 (see Section 3.2.3). Moreover , an investigation of the magnetic energy in the stator for a divided magnet and a shorter T-shaped pole shoe was performed. The different configurations of ferrites and pole shoes were chosen with the help of supervisors and other experts in the field.
3.2.1 Simulation 1, mixed ferrite permanent magnets
The ferrite permanent magnets were Y30 and Y40, where the former has lower magnetic properties than the latter (see Table 2). Only one of the magnets in the simulated linear generator was changed; all other magnets were of type Y40.
Table 3. The different cases for the simulation of divided magnet.
Simulation 1 was restricted to eight different cases, which are described in Table 3. In the first case, Case 1, the magnet was only made of Y40; in the last case, Case 5, the magnet was only made of Y30. In the other cases, the magnet was divided into two parts, one made of Y40 and one made of Y30. Case 2 was 75% Y40 and 25% Y30. Case 3 was 50% Y40 and 50% Y30. Case 4 was 25% Y40 and 75% Y30. In Case 2, 3 and 4, Y30 is placed closest to the stator steel, whereas in Case 2b, 3b and 4b, Y40 is placed closest to the stator steel. The geometry for Case 2 and Case 4b, can be seen in Figure 11.
The geometry for Case 3 and 3b is shown in Figure 12. The geometry for Case 4 and 2b can be seen in Figure 13. The geometry of the cases 1 and 5 are depicted in Figure 9 in Section 3.2.
The entire magnetic material had the same total size in all cases. The length of the magnetic material was 120 mm and the width was 20 mm. The pole shoes had the length of 120 mm and the width of 15 mm. The magnetic energy in the stator steel was calculated in the simulation program and the results from the different cases were compared.
3.2.2 Simulation 2, different designed pole shoes
Simulation 2 was restricted to two different shapes of pole shoes, as described in Table 4. The first design, called R, was a rectangular shaped pole shoe with a width of 15 mm and a length of 120 mm. R was the design used in Simulation 1 and is therefore shown in Figure 11-13. The second design, called T, was a T-shaped pole shoe with a width of 15 mm and a length of 120 mm. T is illustrated in Figure 14. All other magnets were of type Y40.
Table 4. Different designs of a pole shoe in the linear generator.
3.2.3 Simulation 3, mixed magnets and different pole shoe
For the final simulation experiment, Simulation 3, some divided magnets were combined with different shapes and sizes of the pole shoes. The different combinations were tested in five different investigations, as can be seen in Table 5.
Table 5. Divided ferrites and different shapes of permanent magnets
For the first investigation, called Investigation 1, Case 3b was combined with the pole shoe T; that is, the ferrite permanent magnet consisted of 50% Y30 and 50% Y40, where Y40 was closest to the stator steel, and the pole shoe had a T-shape, with a width of 15 mm and a length of 120 mm, as can be seen in Figure 15.
For the second investigation, called Investigation 2, Case 2b was combined with the pole shoe T; that is, the ferrite permanent magnet consisted of 25% Y30 and 75% Y40, where Y40 was closest to the stator, and the pole shoe was T-shaped, as can be seen in Figure 16.
For the Investigations 3–5, Case 2b was used in combination with a T-shaped pole shoe, with the width of 15 mm, but with a different length, which is illustrated in Figure 17. For Investigation 3, the pole shoe was shortened to 85% of its initial value; the new length was 102 mm. For Investigation 4, the pole shoe was shortened to 80% of its initial value; the new length was 96 mm. For Investigation 5, the pole shoe was shortened to 75% of its initial value; the new length was 90 mm.
The magnetic energy in the stator steel for the five different cases was calculated and compared.
[Figures 9–17 omitted]