ANALYTICAL PREDICTION OF PERMANENT MAGNET LINEAR GENERATOR FOR WAVE ENERGY CONVERSION SYSTEM IN MALAYSIA OCEAN. Published online: 20 July 2018

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1 Journal of Fundamental and Applied Sciences ISSN Research Article Special Issue Available online at ANALYTICAL PREDICTION OF PERMANENT MAGNET LINEAR GENERATOR FOR WAVE ENERGY CONVERSION SYSTEM IN MALAYSIA OCEAN N. A. M. Zamri *, T. Ibrahim and N. M. Nor Department of Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak, Malaysia. Published online: 20 July 2018 ABSTRACT This paper presents the analytical approach of radially magnetized permanent magnet linear generator that was designed for wave energy conversion system in Malaysia. Although the wave energy availability in Malaysia has potential for development, however, the power density is lower than other countries with progressive development in this field. Most of the available technologies will be huge for the application in Malaysia. Hence, wave energy conversion system that is suitable for Malaysia ocean is required. A direct drive linear generator with tubular topologies has been designed based on local wave characteristics. Finite Element Analysis (FEA) and analytical calculation were performed on the design. From the analysis, it can be concluded that the proposed design is capable to produce desired output voltage of 240 V. The FEA results of flux density, flux linkage and induced back EMF of the design were validated by the analytical prediction. Keywords: linear generator, wave energy convertor, permanent magnet machine Author Correspondence, naily.akmal_g03220@utp.edu.my doi: Journal of Fundamental and Applied Sciences is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Libraries Resource Directory. We are listed under Research Associations category.

2 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), INTRODUCTION The increase in world electricity consumption [1] has urged the utilization of renewable energy resources as an alternative. Wave energy as one of the available resources has garnered high interest since the pioneer work in year 1779 [2]. In Malaysia, high potential area for wave energy extraction is at South China Sea especially at the offshore of Terengganu and Sabah [3], [4]. The average wave power availability in Malaysia is around 8.5 kw/m with the estimated wave height and period of m and s respectively [4]. Eventhough there is potential for wave energy conversion system development in Malaysia [5], however, the wave power availability is significantly lower compare to countries with progressive development of WEC such as countries in Europe. Thus, renowned Wave Energy Converter (WEC) technologies that were designed for European ocean are a big system to accommodate greater wave power output and hence, will be under utilized if being used in Malaysia ocean [6]. Thus, WEC designs that are suitable for Malaysia wave characteristics is more favorable. Wave can be extracted into useable energy through WEC devices. There are various ways of wave energy harvesting and these energy conversions mechanims are called as Power-Take Off (PTO) [7]. The available PTO mechanisms are as shown in Figure 1. Two conversions take place in all PTOs. Primary conversion is the conversion of wave energy motion into mechanical or potential energy in the WEC bodies. Based on Figure 1, this conversion is indicated by the hydronamic interaction with primary interface. Secondary conversion is the conversion of mechanical energy into electrical energy which involved transmission system and an electrical generator. The transmission system can be categoried as hydraulic, turbine and direct drive system [7], while electrical generator could be either rotary or linear generator. In term of overall technology, there are also numerous WEC technologies that have been introduced, prominently Pelamis, Archimedes Waveswing and OWC LIMPET [8], [7]. Most of the available technologies can be categorized into wide classification of oscillating bodies, Oscillating Water Column (OWC) and overtopping devices. Point absorber oscillating bodies is one of the promising technologies with advantages over other technologies such as smaller size and versatility of the design that allows the technology to be used together with both

3 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), linear and rotary generator [8], [9]. In recent years, linear generator has been widely used in wave energy conversion application [10], [11],[12]. Linear generator advantages over rotary generator especially its high efficiency with the absence of transmission system [11, 13, 14] is the significant reason for the favorability in WEC. Various linear generators have been studied such as switched reluctance machine, synchronous machine, induction machine, and permanent magnet (PM) machine [15]. Nonetheless, the low speed characteristic of WEC application [10], [11], [13], causes the PM machine to be attractive mainly due to its high efficiency and high force density [11, 13]. Due to the requirement for high force density of the generator for WEC application, a PM generator with slotted iron-cored tubular topologies has been proposed previously in [16]. Further optimization in term of split ratio, pitch ratio, number of coil turn and slot number has produced the finalized proposed design. In this paper, the analytical approach is presented to validate the generator s open circuit distribution results from numerical method, Finite Element Analysis (FEA). The discussed open circuit distribution performances of the design are air gap flux density, flux linkage and induced back EMF. 2. RESEARCH METHODS A direct drive PTO for WEC have been selected to be used in the study. Thus, a linear generator design with slotted iron-cored tubular topologies has been proposed with the dimensions as tabulated in Table 1 and illustration as shown in Figure 2. The design s main dimensions have been chosen based on the wave characteristic of Malaysia ocean which is average wave height of m. The design was analysed numerically using FEA software in 2D transient setting. Translation limit and speed of 400 mm and 0.6 m/s respectively were used in the simulation.

4 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), Fig.1. PTO Mechanisms of WEC Translator Back Iron Winding Stator back iron Permanent Magnet Translational Axis Fig.2. Slotted Iron-cored Tubular PM Linear Generator with Radial Magnetization Table 1. Dimension of the Proposed Design Dimension Value Dimension Value Air gap diameter, g 4 mm Stator tooth width, w t 17 mm Number of slot 10 Height of magnet, h m 7 mm Length of stator, l s 400 mm Outer radius of magnet, r m 56 mm Height of stator back iron, h sbi 15 mm Depression width (slot opening), wd 5 mm Width of slot, w sl 23 mm Outer radius of stator, r e 140 mm Height of slot, h sl 57 mm Total number of coil, N c 3010

5 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), Open-circuit Magnetization Distribution The design was also analysed using analytical approach to validate the open-circuit performances of FEA. These assumptions are considered in establishing the analytical expression for magnetic field distribution: (a) Slotless stator is considered with infinite permeability of the iron. The effects of slotting in the design is accounted by utilizing Carter s coefficient [14] that can be calculated as follows: (1) Where g =g+h m /, g is the air-gap length, is the slotting factor, is the stator slot-pitch and h m is the radial thickness of the magnets. In which, from equation (1), the effective air-gap length, g e can be calculated as: (2) From equation (2), the effective radius of the stator bore is defined as: (3) Where is outer radius of the magnet. (b) The generator has an infinite axial length. The long iron sleeve is infinetly long with a sequence of PM armature. The sequence of PM armatures are disconnected by the axial distance of as illustrated in Figure 3. The analysis of magnetic field is limited to two regions. Region I is the air region that have the permeability of, while region II is the PM region with the permeability of, where is the relative recoil permeability. These two regions are also shown in Figure 3. In term of magnetic vector potential,, the principal field equations in cylindrical coordinates are:

6 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), (4) The magnetization, is defined as: (5) For the design in Figure 2, as the design employed radial magnetization, only, which indicates the components of the magnetization in the r directions, has value as shown in Figure 3. The magnetization of the design can be represented by Fourier series of: (6) (7) Where, as the fundamental period of the series PM armature, is the remanence of the magnet and which is the pole-pitch. Hence, combining (4) (7), (4) can be re-written as: (8) As mentioned in [14], the boundary conditions of the design that need to be fullfiled are:

7 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), (9) Solving for (5) by taking into account the boundary conditions in (6), yields flux density components expressions as follows: (10) Where and are modified Bessel functions of the first kind; and are modified Bessel functions of the second kind, of order 0 and 1, respectively.,,,, and are as given in Appendix A in [14]. B rem /µ o R s R m R o z Fig.3. Analytical Design Model and Open-circuit Magnetic Distribution

8 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), Flux Linkage and Induced Back EMF The flux linkage of the designs can then be acquired by integrating the radial flux density component at r= and thus, the total flux linkage can be represented by: (11) and can be defined as: (12) In which, is the number of turns per phase, and of an iron-cored machines can be expressed as: (13) (14) From flux linkage, the induced back-emf of a single-phase stator winding can be obtained by differentiating the flux linkage over time: (15) 3. RESULTS Figure 4 shows open-circuit flux distribution of the design during the armature position at zero displacement. From the figure, the flux flow of the design is justified with only small flux leakage at the stator back-iron. Figure 5 compares the analytical prediction and FEA of air gap flux density of the design. As can be seen, the rms percentage difference over a fundamental period is relatively small which is approximately 6 %. However, the fringing effect at end of the stator teeth due to finite length stator core [14] is not accountable in analytical approach due to the second assumption

9 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), mentioned previously. The fringing effect can be clearly seen in FEA graph at each end of the waveform. Fig.4. Open-circuit Flux Distribution at Zero Displacement Fig.5. Air-gap Flux Density The analytical prediction and FEA comparison of flux linkage and induced back EMF of the design are as shown in Figure 6 and Figure 7 respectively. The displacement and speed of translator are 0.08 m (two pole-pitch) and 0.6 m/s respectively. Good agreement can be observed for flux linkage waveforms with only ~2 % of difference between the rms values. For induced back EMF, the rms value of FEA fulfilled the desired voltage output of the design which is 240 V. In term of its comparison with analytical prediction, the difference is more pronounced in which analytical prediction is lower than FEA. This is due to the effect of the fringing flux associated with the finite length stator core [14]. Nonetheless, both waveforms

10 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), agreed well with each other with percentage difference of ~8 %. Fig.6. Flux Linkage Fig.7. Induced Back EMF 4. CONCLUSION A slotted iron-cored tubular PM linear generator with radial magnetization for wave energy conversion system in Malaysia has been proposed. Prediction of open-circuit magnetic field distribution, flux linkage and back EMF analytically have been established. The established analytical formulae have been used for validation with FEA results of the design. Based on the FEA result of induced back EMF, the targetted output voltage of 240 V for the generator

11 N. A. M. Zamri et al. J Fundam Appl Sci. 2018, 10(7S), was achieved. 5. ACKNOWLEDGEMENTS The authors would like to thanks Universiti Teknologi PETRONAS (UTP) and FRGS grant under Ministry of Higher Education (MOHE), Malaysia for the financial support. 6. REFERENCES [1] Current Capacity Status. Tenaga Nasional Berhad, [2] E. E. Shpilrain. Renewable energy sources charged with energy from the sun and originated from earth-moon interactions - Volume II. EOLSS Publishers Company Limited, [3] N. A. M. Nasir and K. N. A. Maulud. Wave power potential in Malaysian territorial waters. IOP Conference Series: Earth and Environmental Science, 2016, vol. 37. [4] E. P. Chiang, Z. A. Zainal, P. A. AswathaNarayana, and K. N. Seetharamu. Potential of renew-able wave and offshore wind energy sources in Malaysia. Marine Technology 2003 Seminar, [5] A. Muzathik, W. S. Wan Nik, M. Z. Ibrahim, and K. Samo. Wave energy potential of Peninsular Malaysia. ARPN Journal of Engineering and Applied Sciences, 2010, vol. 5, pp [6] J. Jaswar, C. L. Siowa, A. Maimun, and C. G. Soaresc. Estimation of Electrical-wave power in Merang Shore, Terengganu, Malaysia. Jurnal Teknologi, 2014, vol. 66, pp [7] B. Drew, A. R. Plummer, and M. N. Sahinkaya. A review of wave energy converter technology. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2009, vol. 223, pp [8] R. Kempener and F. Neumann. Wave energy: technology brief [Online]. Available: [9] A. F. d. O. Falcão. Wave energy utilization: a review of the technologies. Renewable and Sustainable Energy Reviews, 2010, vol. 14, pp

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