Refine design parameters for permanent magnet shape modification of the direct-drive generator

Received Jun 30, 2021 Revised Jan 24, 2022 Accepted Jan 31, 2022 The high cost associated with operation has promoted the progress of wave energy conversion and has higher power output and larger size. However, many countries are bordered by the sea, and the possible area for using wave energy is very small which can generate peak power generation systems with a power output of less than 100 W. The purpose of this article is to introduce the refined parameters of new design of the permanent magnet shape of with tubular longitudinal direct-drive generator. Three designs proposed, which different shapes of permanent magnets with same topology. The parameter optimization process was analysed using finite element analysis to determine the best main parameters of the design, namely the length of the stator length to translation ratio (Ls/Lr), pitch ratio (τmr/τp.), and split ratio (Rm/Re). To evaluate design performance, electrical losses from the proposed design were also evaluated. The optimization results show these designs generator can produce 100 W of peak level output power with higher efficiency at rated current and optimal load.


INTRODUCTION
Wave energy has attracted tremendous attention due to its high energy density all around the world [1], [2], and it is predictability that is better than wind energy [3]. Ocean wave energy has high availability across the world [4]. Malaysia has recorded a lower wave energy availability of 6 kW/m [3]- [6]. However, the low-density wave energy along the coast of Malaysia can be used by peak power generation systems with an output power of less than 5 kW [7]- [9] to facilitate the low power application. The direct-drive linear conversion can be used in wave-activated body (WAB) technology for wave energy conversion purposes [10] [11]. Therefore, the equipment based on this technical principle, especially point absorption equipment [12], may be developed as a portable peak power generation system [13]. The buoy rises and falls according to the movement of the waves to drive the permanent magnet linear generator (PMLG) [14], [15]. No field windings in the moving parts of the machine, resulting in adequate low power induction to generate peak level power [16], [17] and the use of permanent magnet has been considered a good choice in moving part where high performance drives are required to generate high performance of pico-scale output power [18]. Thus, this paper discusses the refined parameters of new design of the permanent magnet shape of with tubular longitudinal direct-drive generator. The refine design parameter involved with length of stator over the length of the rotor ( / ), pitch ratio ( / ), and split ratio ( / ) are discussed.

GENERATOR PROPOSED DESIGNS
The linear generator is proposed using wave energy to construct a pico-scale linear generator with 100W output power by developing multiple forms of permanent magnets. The development of PMLG in this paper is proposed to be in tubular configuration with a short stator for the initial conceptual design. Then, the parameter will be refined by simulate in reverse engineering concept to analyze the efficiency of the performance.

Initial dimension of generator design
As the conventional design of the quasi-Halbach magnetized machine with rectangular, and trapezoid magnets has been reported in [19], three design generator machine, quasi-Halbach magnetized machine with LT-shape, LT-separated and T shape magnets are analysed for the direct drive wave energy converters (WEC) system. Figure 1 shows the schematics and design characteristics in the 2 dimensional (2D) and cross-sectional geometry. Figure 1 (a) shows the T-shape which the axial and radial magnet oppose to the surface of stator. This design will have the higher attraction of magnetic flux. While Figure 1 (b) shows the LT-shape which axial and radial combine in order to analyse the magnetic field that will affect the performance of electromagnetism [20]. Figure 1 (c) which is LT-separated magnet. The axial magnet array does not expose to the air gap which led to the lower magnetic flux. Surface area and volume of the radial array are high which may produce more flux to the armature. The proposed designs machine reported have the same topologies with different magnets shape. The relevant variable and symbols are defined as in Table 1.  The stator is selected to be a slotless stator, which is more preferred in wave energy conversion owing to their electromagnetic characteristic which obtains minimum cogging force and can resist the translating part to move smoothly [19], [21], [22]. The thickness of stator core ℎ is fixed to the 5 mm as it will hold the stator winding in place and helps the winding to transmit the flux. While increase the thickness of the stator winding ℎ is significant as influence on the performance of design machine. The length of stator is usually shorter than length of translator . The common length of the stator and translator affect the power rating of the performance design. Thus, decrease the and increase the is more convenient to improve the power generated. As ℎ is increased, the performance normally improves. Increased volume of rare-earth magnet material, on the other hand, will raise the cost and result in a heavier armature, which is normally a disadvantage for a reciprocating moving-magnet machine [22]. Thus, the thickness of the magnet ℎ considers 50 mm to produce higher flux density and thrust force capability. However, the ℎ are supported ℎ by the ferromagnetic material as external magnetic field so that the flux will be more aligned with the direction of the field. The airgap length, g, is fixed to 1 mm due to minimum assembly tolerance. The influence of the axial length of the radial magnetized magnet and axial length of axial magnetized magnet, also analyzed which have significant influence on the design machine performance and require to be improve the dimension ratios / . The radial and axial magnetization of the magnet plays a predominant role in the design of magnetic bearing for optimum design. The radial width usually has the longer width than the axial width to produce a high attraction force. The designs dimension was improved using the influence parameter ratio calculations to confirm the significant effects on the linear generator efficiency and performance to have the optimum parameters.

Refine design parameter
The determination of optimal parameters from the proposed PMLG designs was carried out by varying the leading design parameters to quantify the influences on the performances of the design. The ratio of / provided the essential part in determining the optimal amount of magnetic flux that interacts with the coils inside the armature. / influenced the magnetic flux that passed through the coil and was correlated with the voltage induced by the coil. The leading parameter of / ratio reflected the combined effects of radially and axially magnetized magnets to achieve a maximum fundamental radial flux density in the air gap [23]- [26]. The dimension sizes of all the permanent magnet designs were different due to the different shapes of the permanent magnets used during the designing process. The variation of pitch ratio was created by varying the length of , but the length of the was kept constant. The initial / depended on the best variation ratio performance from the / . Meanwhile, refining of / ratio dimension represents the optimal balance between electrical and magnetic loading to achieve maximum motor efficiency. The motor efficiency was optimized in this study in terms of both dimensional ratios. This leading parameter produced the highest force density. This design refinement was conducted using the finite element analysis (FEA) to acquire the optimal leading parameters that produce maximum efficiency. The efficiency can be calculated is being as.
The , , and symbols refer to the output power, copper loss, and iron loss. can be calculated as: where the I symbol is referring to the current, and the symbol is referring to the resistance. is taking place magnetically in the iron parts of the permanent magnet due to time-varying flux density.
can be further divided into eddy currents, hysteresis, and excess losses. The total can be determined is being as; where the ℎ , , and symbols refer to the hysteresis, excess, and eddy current losses, respectively. The magnitude of these losses strongly depended on the size of the conductive iron.

OPEN-CIRCUIT SIMULATION OF INITIAL DESIGN
The open-circuit simulation of the initial design was performed using finite element analysis. The back electromotive force (EMF) was produced when the permanent magnet-based rotor moved at the rated velocity within the static armature limits. The back-EMF is determined by taking the derivative of flux linkage  which is found by stepping the stator through the translator at a constant velocity and measuring the flux linkage at each step. Thus, the results back-EMF waveforms with a sine wave, as shown in Figure 2. The back-EMF waveform of the proposed designs displays distorted sine waveforms. However, the back-EMF values for all the proposed designs exceeded the rated designs 100 V for the generation of open circuit and pico-scale generator output power. The designs were further tested for refining design parameters analysis. The optimal leading parameters involved the length of stator over the length of translator ratio ( / ), pitch ratio ( / ), and split ratio ( / ).

Influence of length of stator over length of rotor, /
Length of stator over length of rotor, / , ratios provide a study bond between the dimension of the stator and translator geometry and the motion of the translator. The power losses and efficiency of the proposed designs were acquired by injecting varying currents at the input (i.e., operates as a motor) to achieve a constant 100 W power output by neglecting the power losses Figure 3 (a) shows the achieved 100W output power by varying the currents between 0.6 A to 1.4 A as in Figure 3 (b). The input current for the designs was increaseed when the ratio of the stator length over the rotor length increased to 100 W.
The average air-gap flux density, average back-EMF, losses, and efficiency of Ls/Lr variations are tabulated in Table 2. The stator length influenced and affected the electromagnetic field's strengths. The proposed LT shape and T-shape designed were showing higher air gap flux density at the ratio of 1.2 and 1.4, respectively, while the proposed LT-separated shape showed higher air gap flux density at the of ratio 0.6. The findings observed that when the magnet end pointed to the end of the stator exhibited magnetic force and was probably caused by the shape that affects the magnetic energy distribute in the space occupied. However, the influence dimension / variation effects on the copper loss. The increased copper loss was increasing the ratio changes, which increases the length of the stator. The proposed LT shape, T-shape, and LT-separated designs were reported to have a lesser copper loss at the ratio of 0.4, caused by the considerable reduction of the stator length and consequently resulted from the decrease in copper losses. Meanwhile, the proposed slotless stator configuration for the detent force reduction in the designs found that the effects to the smaller winding inductance. Thus, minimal magnetic flux leakage was produced. The LT shape, T shape, and LTseparated shape designs presented the best efficiency values at the / ratio of 0.4, with the recorded efficiency values of 67.77%, 75.06%, and 76.39%, respectively. The designs that showed the optimal / ratio variation was used to optimize the / leading parameter.  3.2. Influence of pitch ratio, / The pitch ratio variation analysis was conducted by varying the length of, while the length of was kept constant.
/ was carried out to study the influences of rare earth permanent magnetism potential for each pole pair. This variation provides an optimally balanced ratio of magnet pole configuration and enhances the shape of resultant electromagnetic characteristics waveforms. The data collected of the average air-gap flux density, back-EMF, losses, and the efficiency of the influences of / variation are tabulated in Table 3. All the designs showed the of / ratio variation with different average air-gap flux density values in which flux density magnitude for each cycle was not constant. Thus, significant to the different volumes of magnets per pole and resulted in the amount of magnetic flux attraction that was not constant. The proposed T-shape design demonstrated higher air-gap flux density at the ratio of 0.25. Meanwhile, the LT shape and LT-separated designs revealed a higher average air-gap flux density at the ratio of 0.50 because both LT shape has redundant axial and radial magnetization at the edge flux at the same ratio. The back-EMF values of this variation reached the induced voltage generated to have pico-scale output power. The average value of back-EMF was acceptable and still higher than the leading Ls/Lr parameter for the pico-scale power generation. The variation of of τ_mr/τ_pfrom the initial design value for LT-shape and LT separated gave rise to the amount of copper loss, found at a ratio of 1.0, which possibly due to the increment of magnet volume in all the proposed designs thus, it improved the magnetic flux density and the back-EMF. In contrast to the copper loss of the T-shape design, the larger magnet volume caused a higher copper loss. In the overview, the designs were showing highefficiency values of above 70% for the pitch ratio. As the proposed designs were created with minimum copper losses, the resulting high-efficiency values of 89.9% and 88.7%, respectively, were reported at the ratio of 1.0. The proposed T-shape design was having a higher efficiency value of 77.2% at a ratio of 0.25. Therefore, the best efficiency for the designs in the varied τ_mr/τ_pratio was further optimized for the split ratio.

Influence of split ratio,
/ Based on the previous analyses reported regarding the / variation, the best efficiency with the minimum power loss was selected for further improve design parameter. The split ratio is defined as the optimal balance between the magnetic and electrical loading. The external diameter of the stator core is maintained while varying the magnet's outer radius. The average air-gap flux density waveform of / variation is as tabulated in Table 4. There were different average airgap flux density values observed between all the designs variations of / ratio due to the higher volume of radius magnet per pole and higher magnetic flux attractions. Therefore, it was observed that the air-gap flux density value increases due to / ratio  [25]. The findings demonstrated that the back-EMF reached the induced voltage produced to have the output power at the pico-scale. Thus, more input currents are being injected into the designs. The decreasing copper loss affected the higher efficiency performances of the designs and leads to the decreasing of the magnetic flux. So, this can contribute to the smaller PMLG designs into a portable form. From all the designs, the proposed LT shape and LT-separated shape designs were showing the higher efficiency of 93.36% and 94.09%, respectively, while T-shape, 87.28%. The efficiency performance of the designs was extracted from the leading parameter which is the last variation of the split ratio. As summarized in this refined design parameter process, all the designs can generate ±100 W output power despite the pico-scale power output. The highest efficiency obtained by the LT-separated and LT shape design was shown to be above 90%. This is because of the magnet shape and the double magnetization caused by the axial and radial arrays.

CONCLUSION
Three pico-scale proposed PMLG designs for WEC in Malaysia has been analyzed in term of leading parameters variation against the same rated output of 100 W. All proposed designs are capable to produce 100 W as desired. Moreover, all design also yields satisfactory efficiency above the 90%. Even though all design has the same magnetization of Halbach array and same volume but in different shape of the permanent magnet, however, affect to the magnetization in increasing the resistance of the winding. Therefore, the final designs have been selected for further validation using analytical computation which are LT separated designs that have higher efficiency at the least ratio of Rm/Re variations.