Time Series-, Time-Frequency- and Spectral Analyses of Sensor Measurements in an Offshore Wave Energy Converter Based on Linear Generator Technology

ABSTRACT

Inside the second experimental wave
energy converter (WEC) launched at the Lysekil research site on the Swedish
west coast in March

Cite this paper

E. Strömstedt, A. Savin, O. Svensson and M. Leijon, "Time Series-, Time-Frequency- and Spectral Analyses of Sensor Measurements in an Offshore Wave Energy Converter Based on Linear Generator Technology,"*Energy and Power Engineering*, Vol. 5 No. 1, 2013, pp. 70-91. doi: 10.4236/epe.2013.51009.

E. Strömstedt, A. Savin, O. Svensson and M. Leijon, "Time Series-, Time-Frequency- and Spectral Analyses of Sensor Measurements in an Offshore Wave Energy Converter Based on Linear Generator Technology,"

References

[1] A. F. de O. Falcao, “First-Generation Wave Power Plants: Current Status and R and D Requirements,” Journal of Offshore Mechanics and Arctic Engineering, Vol. 126, No. 4, 2004, pp. 384-388. doi:10.1115/1.1839882

[2] J. P. Kofoed, P. Frigaard, E. Friis-Madsen and H. C. Sorensen, “Prototype Testing of the Wave Energy Converter Wave Dragon,” Renewable Energy, Vol. 31, No. 2, 2006, pp. 181-189. doi:10.1016/j.renene.2005.09.005

[3] R. Henderson, “Design, Simulation, and Testing of a Novel Hydraulic Power Take-Off System for the Pelamis Wave Energy Converter,” Renewable Energy, Vol. 31, No. 2, 2006, pp. 271-283. doi:10.1016/j.renene.2005.08.021

[4] D. Elwood, S. C. Yim, J. Prudell, C. Stillinger, A. von Jouanne, T. Brekken, A. Brown and R. Paasch, “Design, Construction, and Ocean Testing of a Taut-Moored Dual- Body Wave Energy Converter with a Linear Generator Power Take-Off,” Renewable Energy, Vol. 35, No. 2, 2010, pp. 348-354. doi:10.1016/j.renene.2009.04.028

[5] M. Prado and H. Polinder, “Direct Drive in Wave Energy Conversion—AWS Full Scale Prototype Case Study,” IEEE Power & Energy Society General Meeting, Zijdewind, 24-29 July 2011, pp. 1-7.

[6] S. Lindroth and M. Leijon, “Offshore Wave Power Measurements—A Review,” Renewable and Sustainable Energy Reviews, Vol. 15, No. 9, 2011, pp. 4274-4285. doi:10.1016/j.rser.2011.07.123

[7] M. Leijon, C. Bostrom, O. Danielsson, S. Gustafsson, K. Haikonen, O. Langhamer, E. Stromstedt, M. Stalberg, J. Sundberg, O. Svensson, S. Tyrberg and R. Waters, “Wave Energy from the North Sea: Experiences from the Lysekil Research Site,” Surveys in Geophysics, Vol. 29, No. 3, 2008, pp. 221-240. doi:10.1007/s10712-008-9047-x??

[8] R. Waters, J. Engstrom, J. Isberg and M. Leijon, “Wave Climate off the Swedish West Coast,” Renewable Energy, Vol. 34, No. 6, 2009, pp. 1600-1606. doi:10.1016/j.renene.2008.11.016?

[9] M. Rahm, C. Bostrom, O. Svensson, M. Grabbe, F. Bülow and M. Leijon, “Offshore Underwater Substation for Wave Energy Converter Arrays,” Renewable Power Generation, IET, Vol. 4, No. 6, November 2010, pp. 602- 612. doi:10.1049/iet-rpg.2009.0180?

[10] S. Tyrberg, H. Gravrakmo and M. Leijon, “Tracking a Wave Power Buoy Using a Network Camera-System Analysis and First Results,” 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, 31 May-5 June 2009, pp. 799-807.?

[11] S. Gustafsson, “Measuring of Waves at Islandsberg and Literature Survey of Wave Measurement Technology,” Master Thesis, The Division for Electricity and Lightning Research, Uppsala University, Uppsala, 2004.

[12] O. Langhamer, D. Wilhelmsson and J. Engstrom, “Artificial Reef Effect and Fouling Impacts on Offshore Wave Power Foundations and Buoys—A Pilot Study,” Estuarine Coastal and Shelf Science, Vol. 82, No. 3, 2009, pp. 426-432. doi:10.1016/j.ecss.2009.02.009?

[13] O. Langhamer and D. Wilhelmsson, “Colonisation of Fish and Crabs of Wave Energy Foundations and the Effects of Manufactured Holes—A Field Experiment,” Marine Environmental Research, Vol. 68, No. 4, 2009, pp. 151- 157. doi:10.1016/j.marenvres.2009.06.003

[14] C. Bostrom, R. Waters, E. Lejerskog, O. Svensson, M. Stalberg, E. Stromstedt and M. Leijon, “Study of a Wave Energy Converter Connected to a Nonlinear Load,” IEEE Journal of Oceanic Engineering, Vol. 34, No. 2, 2009, pp. 123-127. doi:10.1109/JOE.2009.2015021?

[15] O. Danielsson, M. Eriksson and M. Leijon, “Study of a Longitudinal Flux Permanent Magnet Linear Generator for Wave Energy Converters,” International Journal of Energy Research, Vol. 30, No. 14, 2006, pp. 1130-1145. doi:10.1002/er.1209

[16] U. Henfridsson, V. Neimane, K. Strand, R. Kapper, H. Bernhoff, O. Danielsson, M. Leijon, J. Sundberg, K. Thorburn, E. Ericsson and K. Bergman, “Wave Energy Potential in the Baltic Sea and the Danish Part of the North Sea, with Reflections on the Skagerrak,” Renewable Energy, Vol. 32, No. 12, 2007, pp. 2069-2084. doi:10.1016/j.renene.2006.10.006

[17] M. Eriksson, J. Isberg and M. Leijon, “Theory and Experiment on an Elastically Moored Cylindrical Buoy,” IEEE Journal of Oceanic Engineering, Vol. 31, No. 4, 2006, pp. 959-963. doi:10.1109/JOE.2006.880387

[18] A. Savin, O. Svensson and M. Leijon, “Azimuth-Inclination Angles and Snatch Load on a Tight Mooring System,” Ocean Engineering, Vol. 40, 2012, pp. 40-49. doi:10.1016/j.oceaneng.2011.12.007

[19] A. Savin, O. Svensson and M. Leijon, “Estimation of Stress in the Inner Framework Structure of a Single Heaving Buoy Wave Energy Converter,” IEEE Journal of Oceanic Engineering, Vol. 37, No. 2, 2012, pp. 309-317. doi:10.1109/JOE.2012.2188614

[20] R. Waters, M. Stalberg, O. Danielsson, O. Svensson, S. Gustafsson, E. Stromstedt, M. Eriksson, J. Sundberg and M. Leijon, “Experimental Results from Sea Trials of an Offshore Wave Energy System,” Applied Physics Letters, Vol. 90, No. 3, 2007, Article ID: 034105. doi:10.1063/1.2432168??

[21] M. Eriksson, R. Waters, O. Svensson, J. Isberg and M. Leijon, “Wave Power Absorption: Experiments in Open Sea and Simulation,” Journal of Applied Physics, Vol. 102, No. 8, 2007, Article ID: 084910. doi:10.1063/1.2801002

[22] S. Tyrberg, R. Waters and M. Leijon, “Wave Power Absorption as a Function of Water Level and Wave Height: Theory and Experiment,” IEEE Journal of Oceanic Engineering, Vol. 35, No. 3, 2010, pp. 558-564. doi:10.1109/JOE.2010.2052692

[23] K. Thorburn and M. Leijon, “Farm Size Comparison with Analytical Model of Linear Generator Wave Energy Converters,” Ocean Engineering, Vol. 34, No. 5, 2007, pp. 908-916. doi:10.1016/j.oceaneng.2006.05.017

[24] C. Bostrom, E. Lejerskog, M. Stalberg, K. Thorburn and M. Leijon, “Experimental Results of Rectification and Filtration from an Offshore Wave Energy System,” Renewable Energy, Vol. 34, No. 5, 2009, pp. 1381-1387. doi:10.1016/j.renene.2008.09.010?

[25] A. A. E. Price, C. J. Dent and A. R. Wallace, “Frequency Domain Techniques for Numerical and Experimental Modelling of Wave Energy Converters,” 8th European Wave and Tidal Energy Conference, Uppsala, 2009, pp. 849-858.

[26] J. B. Saulnier, A. Clément, A. F. de O. Falcao, T. Pontes, M. Prevosto and P. Ricci, “Wave Groupiness and Spectral Bandwidth as Relevant Parameters for the Performance Assessment of Wave Energy Converters,” Ocean Engineering, Vol. 38, No. 1, 2011, pp. 130-147. doi:10.1016/j.oceaneng.2010.10.002?

[27] L. Yang, J. Hals and T. Moan, “Analysis of Dynamic Effects Relevant for the Wear Damage in Hydraulic Machines for Wave Energy Conversion,” Ocean Engineering, Vol. 37, No. 13, 2010, pp. 1089-1102. doi:10.1016/j.oceaneng.2010.04.005

[28] O. Svensson, E. Stromstedt, A. Savin and M. Leijon, “Sensors and Measurements inside the Second and Third Wave Energy Converter at the Lysekil Research Site,” 9th European Wave and Tidal Energy Conference, Southampton, 2011.?

[29] O. Svensson, C. Bostrom, M. Rahm and M. Leijon, “Description of the Control and Measurement System Used in the Low Voltage Marine Substation at the Lysekil Research Site,” 8th European Wave and Tidel Energy Conference (EWTEC), Uppsala, 2009, pp. 44-50.?

[30] E. Stromstedt, O. Svensson and M. Leijon, “A Set-Up of 7 Laser Triangulation Sensors and a Draw-Wire Sensor for Measuring Relative Displacement of a Piston Rod Mechanical Lead-Through Transmission in an Offshore Wave Energy Converter on the Ocean Floor,” ISRN Renewable Energy, 2012, Article ID: 746865. doi:10.5402/2012/746865

[31] R. Waters, O. Danielsson and M. Leijon, “Measuring Air Gap Width of Permanent Magnet Linear Generators Using Search Coil Sensor,” Journal of Applied Physics, Vol. 101, No. 2, 2007, Article ID: 024518. doi:10.1063/1.2403964

[32] S. Tyrberg, O. Svensson, V. Kurupath, J. Engstrom, E. Stromstedt and M. Leijon, “Wave Buoy and Translator Motions—On-Site Measurements and Simulations,” IEEE Journal of Oceanic Engineering, Vol. 36, No. 3, 2011, pp. 377-385. doi:10.1109/JOE.2011.2136970??

[33] C. Bostrom, M. Rahm, O. Svensson, E. Stromstedt, A. Savin, R. Waters and M. Leijon, “Temperature Measurements in a Linear Generator and Marine Substation for Wave Power,” The 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, 6-11 June 2010, p. 8.?

[34] I. A. Ivanova, O. Agren, H. Bernhoff and M. Leijon, “Simulation of Cogging in a 100 kW Permanent Magnet Octagonal Linear Generator for Ocean Wave Conversion,” 2004 International Symposium on Underwater Technology, 20-23 April 2004, pp. 345-348.

[35] I. A. Ivanova, O. Agren, H. Bernhoff and M. Leijon, “Simulation of Wave-Energy Converter with Octagonal Linear Generator,” IEEE Journal of Oceanic Engineering, Vol. 30, No. 3, 2005, pp. 619-629. doi:10.1109/JOE.2005.858373

[36] Z. Q. Zhu, P. J. Hor, D. Howe and J. Rees-Jones, “Calculation of Cogging Force in a Novel Slotted Linear Tubular Brushless Permanent Magnet Motor,” IEEE Transactions on Magnetics, Vol. 33, No. 5, 1997, pp. 4098-4100. doi:10.1109/20.619675

[37] P. J. Hor, Z. Q. Zhu, D. Howe and J. Rees-Jones, “Minimization of Cogging Force in a Linear Permanent Magnet Motor,” IEEE Transactions on Magnetics, Vol. 34, No. 5, 1998, pp. 3544-3547. doi:10.1109/20.717836

[38] M. F. Hsieh and K. H. Hu, “Analysis of a Tubular Linear Motor with Soft Magnetic Composites for Reciprocating Compressors,” Journal of Applied Physics, Vol. 103, No. 7, 2008, Article ID: 07F112.

[39] K. Nilsson, O. Danielsson and M. Leijon, “Electromagnetic Forces in the Air Gap of a Permanent Magnet Linear Generator at No Load,” Journal of Applied Physics, Vol. 99, No. 3, 2006, Article ID: 034505. doi:10.1063/1.2168235

[40] O. Danielsson, “Wave Energy Conversion,” Ph.D. Thesis, Department of Engineering Sciences, Uppsala University, Uppsala, 2006.

[41] H. Herlufsen, S. Gade and H. K. Zaveri, “Analyzers and Signal Generators,” In: M. J. Crocker, Ed., Handbook of Noise and Vibration Control, 2007.

[42] T. L. Harman, J. Dabney and N. Richert, “Advanced Engineering Mathematics with Matlab,” 2nd Edition, Brooks/ Cole, Belmont, 2000.

[1] A. F. de O. Falcao, “First-Generation Wave Power Plants: Current Status and R and D Requirements,” Journal of Offshore Mechanics and Arctic Engineering, Vol. 126, No. 4, 2004, pp. 384-388. doi:10.1115/1.1839882

[2] J. P. Kofoed, P. Frigaard, E. Friis-Madsen and H. C. Sorensen, “Prototype Testing of the Wave Energy Converter Wave Dragon,” Renewable Energy, Vol. 31, No. 2, 2006, pp. 181-189. doi:10.1016/j.renene.2005.09.005

[3] R. Henderson, “Design, Simulation, and Testing of a Novel Hydraulic Power Take-Off System for the Pelamis Wave Energy Converter,” Renewable Energy, Vol. 31, No. 2, 2006, pp. 271-283. doi:10.1016/j.renene.2005.08.021

[4] D. Elwood, S. C. Yim, J. Prudell, C. Stillinger, A. von Jouanne, T. Brekken, A. Brown and R. Paasch, “Design, Construction, and Ocean Testing of a Taut-Moored Dual- Body Wave Energy Converter with a Linear Generator Power Take-Off,” Renewable Energy, Vol. 35, No. 2, 2010, pp. 348-354. doi:10.1016/j.renene.2009.04.028

[5] M. Prado and H. Polinder, “Direct Drive in Wave Energy Conversion—AWS Full Scale Prototype Case Study,” IEEE Power & Energy Society General Meeting, Zijdewind, 24-29 July 2011, pp. 1-7.

[6] S. Lindroth and M. Leijon, “Offshore Wave Power Measurements—A Review,” Renewable and Sustainable Energy Reviews, Vol. 15, No. 9, 2011, pp. 4274-4285. doi:10.1016/j.rser.2011.07.123

[7] M. Leijon, C. Bostrom, O. Danielsson, S. Gustafsson, K. Haikonen, O. Langhamer, E. Stromstedt, M. Stalberg, J. Sundberg, O. Svensson, S. Tyrberg and R. Waters, “Wave Energy from the North Sea: Experiences from the Lysekil Research Site,” Surveys in Geophysics, Vol. 29, No. 3, 2008, pp. 221-240. doi:10.1007/s10712-008-9047-x??

[8] R. Waters, J. Engstrom, J. Isberg and M. Leijon, “Wave Climate off the Swedish West Coast,” Renewable Energy, Vol. 34, No. 6, 2009, pp. 1600-1606. doi:10.1016/j.renene.2008.11.016?

[9] M. Rahm, C. Bostrom, O. Svensson, M. Grabbe, F. Bülow and M. Leijon, “Offshore Underwater Substation for Wave Energy Converter Arrays,” Renewable Power Generation, IET, Vol. 4, No. 6, November 2010, pp. 602- 612. doi:10.1049/iet-rpg.2009.0180?

[10] S. Tyrberg, H. Gravrakmo and M. Leijon, “Tracking a Wave Power Buoy Using a Network Camera-System Analysis and First Results,” 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, 31 May-5 June 2009, pp. 799-807.?

[11] S. Gustafsson, “Measuring of Waves at Islandsberg and Literature Survey of Wave Measurement Technology,” Master Thesis, The Division for Electricity and Lightning Research, Uppsala University, Uppsala, 2004.

[12] O. Langhamer, D. Wilhelmsson and J. Engstrom, “Artificial Reef Effect and Fouling Impacts on Offshore Wave Power Foundations and Buoys—A Pilot Study,” Estuarine Coastal and Shelf Science, Vol. 82, No. 3, 2009, pp. 426-432. doi:10.1016/j.ecss.2009.02.009?

[13] O. Langhamer and D. Wilhelmsson, “Colonisation of Fish and Crabs of Wave Energy Foundations and the Effects of Manufactured Holes—A Field Experiment,” Marine Environmental Research, Vol. 68, No. 4, 2009, pp. 151- 157. doi:10.1016/j.marenvres.2009.06.003

[14] C. Bostrom, R. Waters, E. Lejerskog, O. Svensson, M. Stalberg, E. Stromstedt and M. Leijon, “Study of a Wave Energy Converter Connected to a Nonlinear Load,” IEEE Journal of Oceanic Engineering, Vol. 34, No. 2, 2009, pp. 123-127. doi:10.1109/JOE.2009.2015021?

[15] O. Danielsson, M. Eriksson and M. Leijon, “Study of a Longitudinal Flux Permanent Magnet Linear Generator for Wave Energy Converters,” International Journal of Energy Research, Vol. 30, No. 14, 2006, pp. 1130-1145. doi:10.1002/er.1209

[16] U. Henfridsson, V. Neimane, K. Strand, R. Kapper, H. Bernhoff, O. Danielsson, M. Leijon, J. Sundberg, K. Thorburn, E. Ericsson and K. Bergman, “Wave Energy Potential in the Baltic Sea and the Danish Part of the North Sea, with Reflections on the Skagerrak,” Renewable Energy, Vol. 32, No. 12, 2007, pp. 2069-2084. doi:10.1016/j.renene.2006.10.006

[17] M. Eriksson, J. Isberg and M. Leijon, “Theory and Experiment on an Elastically Moored Cylindrical Buoy,” IEEE Journal of Oceanic Engineering, Vol. 31, No. 4, 2006, pp. 959-963. doi:10.1109/JOE.2006.880387

[18] A. Savin, O. Svensson and M. Leijon, “Azimuth-Inclination Angles and Snatch Load on a Tight Mooring System,” Ocean Engineering, Vol. 40, 2012, pp. 40-49. doi:10.1016/j.oceaneng.2011.12.007

[19] A. Savin, O. Svensson and M. Leijon, “Estimation of Stress in the Inner Framework Structure of a Single Heaving Buoy Wave Energy Converter,” IEEE Journal of Oceanic Engineering, Vol. 37, No. 2, 2012, pp. 309-317. doi:10.1109/JOE.2012.2188614

[20] R. Waters, M. Stalberg, O. Danielsson, O. Svensson, S. Gustafsson, E. Stromstedt, M. Eriksson, J. Sundberg and M. Leijon, “Experimental Results from Sea Trials of an Offshore Wave Energy System,” Applied Physics Letters, Vol. 90, No. 3, 2007, Article ID: 034105. doi:10.1063/1.2432168??

[21] M. Eriksson, R. Waters, O. Svensson, J. Isberg and M. Leijon, “Wave Power Absorption: Experiments in Open Sea and Simulation,” Journal of Applied Physics, Vol. 102, No. 8, 2007, Article ID: 084910. doi:10.1063/1.2801002

[22] S. Tyrberg, R. Waters and M. Leijon, “Wave Power Absorption as a Function of Water Level and Wave Height: Theory and Experiment,” IEEE Journal of Oceanic Engineering, Vol. 35, No. 3, 2010, pp. 558-564. doi:10.1109/JOE.2010.2052692

[23] K. Thorburn and M. Leijon, “Farm Size Comparison with Analytical Model of Linear Generator Wave Energy Converters,” Ocean Engineering, Vol. 34, No. 5, 2007, pp. 908-916. doi:10.1016/j.oceaneng.2006.05.017

[24] C. Bostrom, E. Lejerskog, M. Stalberg, K. Thorburn and M. Leijon, “Experimental Results of Rectification and Filtration from an Offshore Wave Energy System,” Renewable Energy, Vol. 34, No. 5, 2009, pp. 1381-1387. doi:10.1016/j.renene.2008.09.010?

[25] A. A. E. Price, C. J. Dent and A. R. Wallace, “Frequency Domain Techniques for Numerical and Experimental Modelling of Wave Energy Converters,” 8th European Wave and Tidal Energy Conference, Uppsala, 2009, pp. 849-858.

[26] J. B. Saulnier, A. Clément, A. F. de O. Falcao, T. Pontes, M. Prevosto and P. Ricci, “Wave Groupiness and Spectral Bandwidth as Relevant Parameters for the Performance Assessment of Wave Energy Converters,” Ocean Engineering, Vol. 38, No. 1, 2011, pp. 130-147. doi:10.1016/j.oceaneng.2010.10.002?

[27] L. Yang, J. Hals and T. Moan, “Analysis of Dynamic Effects Relevant for the Wear Damage in Hydraulic Machines for Wave Energy Conversion,” Ocean Engineering, Vol. 37, No. 13, 2010, pp. 1089-1102. doi:10.1016/j.oceaneng.2010.04.005

[28] O. Svensson, E. Stromstedt, A. Savin and M. Leijon, “Sensors and Measurements inside the Second and Third Wave Energy Converter at the Lysekil Research Site,” 9th European Wave and Tidal Energy Conference, Southampton, 2011.?

[29] O. Svensson, C. Bostrom, M. Rahm and M. Leijon, “Description of the Control and Measurement System Used in the Low Voltage Marine Substation at the Lysekil Research Site,” 8th European Wave and Tidel Energy Conference (EWTEC), Uppsala, 2009, pp. 44-50.?

[30] E. Stromstedt, O. Svensson and M. Leijon, “A Set-Up of 7 Laser Triangulation Sensors and a Draw-Wire Sensor for Measuring Relative Displacement of a Piston Rod Mechanical Lead-Through Transmission in an Offshore Wave Energy Converter on the Ocean Floor,” ISRN Renewable Energy, 2012, Article ID: 746865. doi:10.5402/2012/746865

[31] R. Waters, O. Danielsson and M. Leijon, “Measuring Air Gap Width of Permanent Magnet Linear Generators Using Search Coil Sensor,” Journal of Applied Physics, Vol. 101, No. 2, 2007, Article ID: 024518. doi:10.1063/1.2403964

[32] S. Tyrberg, O. Svensson, V. Kurupath, J. Engstrom, E. Stromstedt and M. Leijon, “Wave Buoy and Translator Motions—On-Site Measurements and Simulations,” IEEE Journal of Oceanic Engineering, Vol. 36, No. 3, 2011, pp. 377-385. doi:10.1109/JOE.2011.2136970??

[33] C. Bostrom, M. Rahm, O. Svensson, E. Stromstedt, A. Savin, R. Waters and M. Leijon, “Temperature Measurements in a Linear Generator and Marine Substation for Wave Power,” The 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, 6-11 June 2010, p. 8.?

[34] I. A. Ivanova, O. Agren, H. Bernhoff and M. Leijon, “Simulation of Cogging in a 100 kW Permanent Magnet Octagonal Linear Generator for Ocean Wave Conversion,” 2004 International Symposium on Underwater Technology, 20-23 April 2004, pp. 345-348.

[35] I. A. Ivanova, O. Agren, H. Bernhoff and M. Leijon, “Simulation of Wave-Energy Converter with Octagonal Linear Generator,” IEEE Journal of Oceanic Engineering, Vol. 30, No. 3, 2005, pp. 619-629. doi:10.1109/JOE.2005.858373

[36] Z. Q. Zhu, P. J. Hor, D. Howe and J. Rees-Jones, “Calculation of Cogging Force in a Novel Slotted Linear Tubular Brushless Permanent Magnet Motor,” IEEE Transactions on Magnetics, Vol. 33, No. 5, 1997, pp. 4098-4100. doi:10.1109/20.619675

[37] P. J. Hor, Z. Q. Zhu, D. Howe and J. Rees-Jones, “Minimization of Cogging Force in a Linear Permanent Magnet Motor,” IEEE Transactions on Magnetics, Vol. 34, No. 5, 1998, pp. 3544-3547. doi:10.1109/20.717836

[38] M. F. Hsieh and K. H. Hu, “Analysis of a Tubular Linear Motor with Soft Magnetic Composites for Reciprocating Compressors,” Journal of Applied Physics, Vol. 103, No. 7, 2008, Article ID: 07F112.

[39] K. Nilsson, O. Danielsson and M. Leijon, “Electromagnetic Forces in the Air Gap of a Permanent Magnet Linear Generator at No Load,” Journal of Applied Physics, Vol. 99, No. 3, 2006, Article ID: 034505. doi:10.1063/1.2168235

[40] O. Danielsson, “Wave Energy Conversion,” Ph.D. Thesis, Department of Engineering Sciences, Uppsala University, Uppsala, 2006.

[41] H. Herlufsen, S. Gade and H. K. Zaveri, “Analyzers and Signal Generators,” In: M. J. Crocker, Ed., Handbook of Noise and Vibration Control, 2007.

[42] T. L. Harman, J. Dabney and N. Richert, “Advanced Engineering Mathematics with Matlab,” 2nd Edition, Brooks/ Cole, Belmont, 2000.