Line Force and Damping at Full and Partial Stator Overlap in a Linear Generator for Wave Power
Abstract
:1. Introduction
1.1. Background
1.2. Paper Objective
2. Method
2.1. WEC Dynamics
2.2. Experimental Set-Up
2.3. Post Processing of Data
3. Results
3.1. Measured Line Force as a Function of Time
3.1.1. Line Force Dependence of PTO Damping
3.2. Measured Line Force as a Function of Translator Position
3.2.1. Oscillations
3.2.2. Losses at No Load
3.3. PTO Force and Damping
4. Discussion
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
WEC | Wave Energy Converter |
FFT | Fast Fourier Transform |
PTO | Power Take-Off |
References
- Drew, B.; Plummer, A.; Sahinkaya, M. A review of wave energy converter technologies. Proc. Inst. Mech. Eng. Part A J. Power Energy 2009, 223, 887–902. [Google Scholar] [CrossRef]
- Falcao, A. Wave Energy Utilization: A review of the technologies. Renew. Sustain. Energy Rev. 2010, 14, 899–918. [Google Scholar] [CrossRef]
- Mueller, M. Electrical generator for direct drive wave energy converters. IEEE Proc. Gener. Transm. Distrib. 2002, 149, 446–456. [Google Scholar] [CrossRef]
- Salter, S.; Taylor, J.; Caldwell, N. Power conversion mechanisms for wave energy. J. Eng. Marit. Environ. 2002, 218, 1–27. [Google Scholar] [CrossRef]
- Polinder, H.; Damen, M.; Gardner, F. Linear generator system for wave energy conversion in the AWS. IEEE Trans. Energy Convers. 2004, 19, 583–589. [Google Scholar] [CrossRef]
- Polinder, H.; Jack, B.M.A.; Dickinsson, P.; Mueller, M. Conventional and TFPM linear generators for direct-drive wave energy conversion. IEEE Trans. Energy Convers. 2005, 20, 260–267. [Google Scholar] [CrossRef]
- Guiberteau, K.; Lee, J.; Liu, Y.; Dou, Y.; Kozman, T. Wave energy converters and design considerations for gulf of Mexico. Distrib. Gener. Altern. Energy J. 2015, 30, 55–76. [Google Scholar] [CrossRef]
- Pastor, J.; Liu, Y. Power absorption modeling and optimization of a point absorbing wave energy converter using numerical method. ASME J. Energy Resour. Technol. 2014, 136, 021207. [Google Scholar] [CrossRef]
- Pastor, J.; Liu, Y. Frequency and time domain modeling and power output for a heaving point absorber wave energy converter. Int. J. Energy Environ. Eng. 2014, 5, 101. [Google Scholar] [CrossRef]
- Leijon, M.; Waters, R.; Rahm, M.; Svensson, O.; Bodström, C.; Strömstedt, E.; Engström, J.; Tyrberg, S.; Savin, A.; Gravråkmo, H.; et al. Catch the wave to electricity. IEEE Power Energy Mag. 2009, 7. [Google Scholar] [CrossRef]
- Eriksson, M.; Waters, R.; Svensson, O.; Isberg, J.; Leijon, M. Wave power absorption: Experiments in open sea and simulation. J. Appl. Phys. 2007, 102, 084910. [Google Scholar] [CrossRef]
- Boström, C.; Svensson, O.; Rahm, M.; Lejerskog, E.; Savin, A.; Strömstedt, E.; Engström, J.; Gravråkmo, H.; Haikonen, K.; Waters, R.; et al. Design Proposal of Electric System for Linear Generator Wave Power Plants. In Proceedings of the IEEE Industrial Electronics IECON2009, Porto, Portugal, 3–5 November 2009.
- Danielsson, O. Wave Energy Conversion—Linear Synchronous Permanent Magnet Generator. Ph.D. Thesis, Uppsala University, Uppsala, Sweden, 20 October 2006. [Google Scholar]
- Sjökvist, L.; Krishna, R.; Castellucci, V.; Hagnestål, A.; Rahm, M.; Leijon, M. On the Optimization of Point Absorber Buoys. J. Mar. Sci. Eng. 2014, 2, 477–492. [Google Scholar] [CrossRef]
- Gravråkmo, H.; Strömstedt, E.; Savin, A.; Leijon, M. Measurments of Extreme Forces on a Wave Energy Converter of Point Absorber Type and Estimation of Added Mass of Cylindrical Buoy. In Proceedings of the ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering, OMAE, San Francisco, CA, USA, 8–13 June 2014.
- Waters, R.; Rahm, M.; Eriksson, M.; Svensson, O.; Strömstedt, E.; Boström, C.; Sundberg, J.; Leijon, M. Ocean wave energy absorption in response to wave period and amplitude offshore experiments on a wave energy converter. IET Renew. Power Gener. 2011, 5, 465–469. [Google Scholar] [CrossRef]
- Leijon, M.; Bodström, C.; Danielsson, O.; Gustafsson, S.; Haikonen, K.; Langhamer, O.; Strömstedt, E.; Stalberg, M.; Sundberg, J.; Svensson, O.; et al. Wave energy from the North Sea: Experiences from the Lysekil research site. Surv. Geophys. 2008, 29, 221–240. [Google Scholar] [CrossRef]
- Savin, A.; Svensson, O.; Strömstedt, E.; Boström, C.; Leijon, M. Determining the Service Life of a Steel Wire Under a Working Load in the Wave Energy Converter. In Proceedings of the ASME 28th International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2009, Honolulu, HI, USA, 31 May–5 June 2009.
- Svensson, O.; Leijon, M. Peak force measurements on a cylindrical buoy with limited elastic mooring. IEEE J. Ocean. Eng. 2014, 39, 398–403. [Google Scholar] [CrossRef]
- Göteman, M.; Engström, J.; Eriksson, M.; Leijon, M.; Hann, M.; Ransley, E.; Greaves, D. Wave loads on a point-absorbing wave energy device in extreme waves. J. Ocean Wind Energy 2015, 2, 176–181. [Google Scholar] [CrossRef]
- Lejerskog, E.; Boström, C.; Hai, L.; Waters, R.; Leijon, M. Experimental results on power absorption from a wave energy converter at the Lysekil wave energy research site. Renew. Energy 2015, 77, 9–14. [Google Scholar] [CrossRef]
- Stalberg, M.; Waters, R.; Danielsson, O.; Leijon, M. Influence of generator damping on peak power for a direct drive wave energy converter. J. Offshore Mech. Arct. Eng. 2008, 130, 031003. [Google Scholar] [CrossRef]
- Rahm, M.; Svensson, O.; Bodström, C.; Waters, R.; Leijon, M. Experimental results from the operation of aggregated wave energy converters. IET Renew. Power Gener. 2012, 6, 149–160. [Google Scholar] [CrossRef]
- Mueller, M.; Polinder, H. Electrical Drives for Direct Drive Renewable Energy Systems; Woodhead Publishing: Cambridge, UK, 2013. [Google Scholar]
- Czichos, H. Tribology, A Systems Approach to the Sicience and Technology of Friction, Lubrication and Wear; Elsevier: Amsterdam, The Netherlands; Oxford, UK; New York, NY, USA, 1975. [Google Scholar]
- Shek, J.K.H.; Macpherson, D.E.; Mueller, M.A.; Xiang, J. Reaction force control of a linear electrical generator for direct drive wave energy converter. Renew. Power Gener. 2007, 1, 17–24. [Google Scholar] [CrossRef]
- Castellucci, V.; Abrahamsson, J.; Svensson, O.; Waters, R. Algorithm for the calculation of the translator position in permanent magnet linear generators. J. Renew. Sustain. Energy 2014, 6, 063102. [Google Scholar] [CrossRef]
- Danielsson, O.; Leijon, M. Flux distribution in linear permanent-magnet synchronous machines including longitudinal end effects. IEEE Trans. Magn. 2007, 43, 3197–3201. [Google Scholar] [CrossRef]
Parameter | Symbol | Value |
---|---|---|
Nominal power | 20 kW | |
Main RMS voltage | 450 V | |
Free stroke-length | 2 m | |
Translator length | 2.8 m | |
Translator mass | 6350 kg | |
Stator length | 2 m | |
Upper endstop-spring constant | κ | 250 kN/m |
Equipment | Accuracy |
---|---|
Force transducer | Linearity error: kg |
-Sensy 5050 Load pin | Repeatability error: kg |
Zero shift after loading: kg | |
Differential voltage probes | |
-TESTEC TT-SI 9001 | |
Current probes | |
-Fluke i310s | at range mA |
Data acquisition | 6.23 at range V |
-NI9205 | 690 V at range V |
Experiment Case | Resistive Load | Endstop Hit? | |
---|---|---|---|
run 1 | low speed | no load | yes |
run 2 | - | 6.6 Ω | yes |
run 3 | - | 4.4 Ω | yes |
run 4 | - | 2.2 Ω | yes |
run 5 | - | short circuit | yes |
run 6 | high speed | no load | yes |
run 7 | - | 6.6 Ω | yes |
run 8 | - | 4.4 Ω | no |
run 9 | - | 2.2 Ω | no |
run 10 | - | short circuit | no |
Load Case | Speed up (m/s) | Line Force up (kN) | Speed down (m/s) | Line Force down (kN) |
---|---|---|---|---|
Average line force and speed at the full active area-low speed | ||||
no load | 0.11 (s = 0.03) | 68.0 (s = 1.7) | 0.12 (s = 0.03) | 59.5 (s = 1.8) |
6.6 Ω | 0.11 (s = 0.01) | 75.5 (s = 0.9) | 0.11 (s = 0.01) | 53.5 (s = 1.6) |
4.4 Ω | 0.10 (s = 0.01) | 75.7 (s = 0.9) | 0.12 (s = 0.01) | 48.2 (s = 1.9) |
2.2 Ω | 0.09 (s = 0.01) | 84.0 (s = 1.0) | 0.12 (s = 0.01) | 37.0 (s = 2.9) |
short circuit | 0.10 (s = 0.01) | 109.2 (s = 2.2) | 0.11 (s = 0.01) | 9.4 (s = 5.6) |
Average line force and speed at the full active area-high speed | ||||
no load | 0.43 (s = 0.05) | 67.0 (s = 2.1) | 0.39 (s = 0.04) | 58.8 (s = 1.7) |
6.6 Ω | 0.34 (s = 0.01) | 89.6 (s = 0.9) | 0.42 (s = 0.03) | 34.3 (s = 3.3) |
4.4 Ω | 0.28 (s = 0.01) | 91.6 (s = 1.2) | 0.36 (s = 0.06) | 28.1 (s = 6.2) |
2.2 Ω | 0.25 (s = 0.01) | 111.3 (s = 1.8) | 0.33 (s = 0.03) | n/a a |
short circuit | 0.136 (s = 0.01) | 121.3 (s = 0.7) | 0.04 (s = 0.06) | n/a a |
Load Case | Speed before Endstop Hit (m/s) | Peak Force (kN) | ||
Line force peaks at low speed | ||||
no load | 0.112 | 88.36 | ||
6.6 Ω | 0.119 | 94.49 | ||
4.4 Ω | 0.103 | 97.93 | ||
2.2 Ω | 0.104 | 102.2 | ||
short circuit | 0.127 | 109.3 | ||
Line force peaks at high speed | ||||
no load | 0.423 | 99.08 | ||
6.6 Ω | 0.403 | 98.06 |
Load Case | PTO Damping Factor, Upward Stroke | PTO Damping Factor, Downward Stroke |
---|---|---|
short circuit | 440 kNs/m | 440 kNs/m |
2.2 Ω | 185 kNs/m | 185 kNs/m |
4.4 Ω | 95 kNs/m | 85 kNs/m |
6.6 Ω | 80 kNs/m | 40 kNs/m |
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Ulvgård, L.; Sjökvist, L.; Göteman, M.; Leijon, M. Line Force and Damping at Full and Partial Stator Overlap in a Linear Generator for Wave Power. J. Mar. Sci. Eng. 2016, 4, 81. https://doi.org/10.3390/jmse4040081
Ulvgård L, Sjökvist L, Göteman M, Leijon M. Line Force and Damping at Full and Partial Stator Overlap in a Linear Generator for Wave Power. Journal of Marine Science and Engineering. 2016; 4(4):81. https://doi.org/10.3390/jmse4040081
Chicago/Turabian StyleUlvgård, Liselotte, Linnea Sjökvist, Malin Göteman, and Mats Leijon. 2016. "Line Force and Damping at Full and Partial Stator Overlap in a Linear Generator for Wave Power" Journal of Marine Science and Engineering 4, no. 4: 81. https://doi.org/10.3390/jmse4040081
APA StyleUlvgård, L., Sjökvist, L., Göteman, M., & Leijon, M. (2016). Line Force and Damping at Full and Partial Stator Overlap in a Linear Generator for Wave Power. Journal of Marine Science and Engineering, 4(4), 81. https://doi.org/10.3390/jmse4040081