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Modelling Wave Power by Equivalent Circuit Theory
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Electricity. (Wave Energy)ORCID iD: 0000-0002-6660-2827
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

The motion of ocean waves can be captured and converted into usable electricity. This indicates that wave power has the potential to supply electricity to grids like wind or solar power. A point absorbing wave energy converter (WEC) system has been developed for power production at Uppsala University. This system contains a semi-submerged buoy on the water surface driving a linear synchronous generator placed on the seabed. The concept is to connect many small units together, to form a wave farm for large-scale electricity generation.

A lot of effort has gone into researching how to enhance the power absorption from each WEC unit. These improvements are normally done separately for the buoy, the generator or the electrical system, due to the fact that modelling the dynamic behavior of the entire WEC system is complicated and time consuming. Therefore, a quick, yet simple, assessment tool is needed.

This thesis focuses on studying the use of the equivalent circuit as a WEC system modelling tool. Based on the force analysis, the physical elements in an actual WEC system can be converted into electrical components. The interactions between the regular waves, the buoy, and the Power Take-off mechanism can be simulated together in one circuit network. WEC performance indicators like the velocity, the force, and the power can be simulated directly from the circuit model. Furthermore, the annual absorbed electric energy can be estimated if the wave data statistics are known.

The linear and non-linear equivalent circuit models developed in this thesis have been validated with full scale offshore experimental results. Comparisons indicate that the simplest linear circuit can predict the absorbed power reasonably well, while it is not so accurate in estimating the peak force in the connection line. The non-linear circuit model generates better estimations in both cases. To encourage researchers from different backgrounds to adapt and apply the circuit model, an instruction on how to establish a non-linear equivalent circuit model is supplied, as well as on how to apply the model to accelerate the decision making process when planning a WEC system.

##### Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. , 75 p.
##### Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1309
##### Keyword [en]
Wave energy, hydrodynamics, electric circuit, electrical analogy, energy absorption, force, system modelling, Simulink, engineering science, renewable energy
##### National Category
Engineering and Technology
##### Research subject
Engineering Science with specialization in Science of Electricity
##### Identifiers
ISBN: 978-91-554-9390-5 (print)OAI: oai:DiVA.org:uu-265270DiVA: diva2:864285
##### Public defence
2015-12-11, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
##### Funder
Swedish Energy AgencyStandUpSwedish Research Council, KOF11 2011-6312Swedish Research Council, 621-2009-3417 Available from: 2015-11-19 Created: 2015-10-26 Last updated: 2016-01-13
##### List of papers
1. Modelling a point absorbing wave energy converter by the equivalent electric circuit theory: A feasibility study
Open this publication in new window or tab >>Modelling a point absorbing wave energy converter by the equivalent electric circuit theory: A feasibility study
2015 (English)In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 117, 164901Article in journal (Refereed) Published
##### Abstract [en]

There is a need to have a reliable tool to quickly assess wave energy converters (WECs). This paper explores whether it is possible to apply the equivalent electric circuit theory as an evaluation tool for point absorbing WEC system modelling. The circuits were developed starting from the force analysis, in which the hydrodynamic, mechanical, and electrical parameters were expressed by electrical components. A methodology on how to determine the parameters for electrical components has been explained. It is found that by using a multimeter, forces in the connection line and the absorbed electric power can be simulated and read directly from the electric circuit model. Finally, the circuit model has been validated against the full scale offshore experiment. The results indicated that the captured power could be predicted rather accurately and the line force could be estimated accurately near the designed working condition of the WEC.

wave energy
##### National Category
Ocean and River Engineering
##### Identifiers
urn:nbn:se:uu:diva-252486 (URN)10.1063/1.4918903 (DOI)000353831100058 ()
##### Funder
Swedish Research Council, KOF11 2011-6312Swedish Energy AgencySwedish Research Council, 6212009-3417
##### Note

Manuscript title: An equivalent circuit for hydrodynamic modelling in wave power system

Corrections in Journal of Applied Physics Vol 118, Issue 8, article number 189903. DOI: 10.1063/1.4935617

Available from: 2015-05-07 Created: 2015-05-07 Last updated: 2017-12-04Bibliographically approved
2. A Methodology of Modelling a Wave Power System via an Equivalent RLC Circuit
Open this publication in new window or tab >>A Methodology of Modelling a Wave Power System via an Equivalent RLC Circuit
2016 (English)In: IEEE Transactions on Sustainable Energy, ISSN 1949-3029, E-ISSN 1949-3037, Vol. 7, no 4, 1362-1370 p.Article in journal (Refereed) Published
##### Abstract [en]

The equivalent circuit method can be an effective modelling technique for system studies of point absorbing wave energy converters (WECs). For the continuously evolving design and study of WEC systems, an instruction on how to draw the corresponding equivalent RLC circuit model is needed. It is not only vital to make sure the model is correct, but to allow the model to be easily adapted for different cases and implemented by different researchers. This paper presents a force analysis oriented methodology based on a typical WEC unit composed of a heaving buoy and a linear generator. Three cases are studied in order to demonstrate the procedures: the generator with a retracting spring, the connection line with a rubber damper, and buoy motion in both heave and surge directions. The presented methodology serves as a guide to produce non-linear circuit models that give a reliable description of the dynamics of real wave energy systems.

##### Keyword
RLC circuit, Simulink, point absorber, system modeling, wave energy
##### National Category
Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers
urn:nbn:se:uu:diva-265215 (URN)10.1109/TSTE.2016.2538803 (DOI)000384640900002 ()
##### Funder
Swedish Energy AgencySwedish Research Council, KOF11 2011-6312, 621-2009-3417StandUp Available from: 2015-10-25 Created: 2015-10-25 Last updated: 2017-12-01Bibliographically approved
3. Planning a wave energy conversion system by equivalent circuit modelling method
Open this publication in new window or tab >>Planning a wave energy conversion system by equivalent circuit modelling method
##### National Category
Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers
urn:nbn:se:uu:diva-265214 (URN)
##### Funder
Swedish Research Council, KOF11 2011-6312StandUpSwedish Research Council, 621-2009-3417Swedish Energy Agency Available from: 2015-10-25 Created: 2015-10-25 Last updated: 2017-01-18
4. Experimental results on power absorption from a wave energy converter at the Lysekil wave energy research site
Open this publication in new window or tab >>Experimental results on power absorption from a wave energy converter at the Lysekil wave energy research site
2015 (English)In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 77, 9-14 p.Article in journal (Refereed) Published
##### Abstract [en]

Power generation from wave power has a large potential to contribute to our electric energy production, and today, many wave power projects are close to be commercialized. However, one key issue to solve for many projects is to decrease the cost per installed kW. One way to do this is to investigate which parameters that have a significant impact on the wave energy converters (WEC) performance. In this paper, experimental results on power absorption from a directly driven point absorbing WEC are presented. The experiments have been carried out at the Lysekil research site in Sweden. To investigate the performance of the WEC, the absorbed power and the speed of the translator are compared. The result confirms that the buoy size and the translator weight have a large impact on the power absorption from the generator. By optimizing the buoy size and translator weight, the WEC is believed to produce power more evenly over the upward and downward cycle. Moreover, to predict the maximum power limit during normal operation, a simulation model has been derived. The results correlates well with experimental data during normal operation.

##### National Category
Engineering and Technology
##### Research subject
Engineering Science with specialization in Science of Electricity
##### Identifiers
urn:nbn:se:uu:diva-238267 (URN)10.1016/j.renene.2014.11.050 (DOI)000349504800002 ()
Available from: 2014-12-11 Created: 2014-12-11 Last updated: 2017-12-05Bibliographically approved
5. Force in the connection line for a wave energy converter:simulation and experimental setup
Open this publication in new window or tab >>Force in the connection line for a wave energy converter:simulation and experimental setup
(English)In: Journal of Offshore Mechanics and Arctic Engineering, ISSN 0892-7219Article in journal (Other academic) Submitted
##### National Category
Engineering and Technology
##### Identifiers
urn:nbn:se:uu:diva-265269 (URN)
Available from: 2015-10-26 Created: 2015-10-26 Last updated: 2016-01-13
6. Measurement System for Evaluating Wanted and Unwanted Forces on a Point Absorbing Wave Energy Converter during Offshore Operation
Open this publication in new window or tab >>Measurement System for Evaluating Wanted and Unwanted Forces on a Point Absorbing Wave Energy Converter during Offshore Operation
2015 (English)In: Proceedings of the 25th International Ocean and Polar Engineering Conference,, 2015Conference paper, Published paper (Refereed)
##### Abstract [en]

A force measurement system has been developed and installed in awave energy converter at Uppsala University. The force in theconnection line as well as the vertical and horizontal strain in thegenerator hull is measured. With these measurements the forces actingon the generator during offshore operation can be monitored andanalyzed. This paper presented the principle, implementation and testresults of the measurement system. A brief discussion of error sourcesand possible improvements is also given.

##### Keyword
Wave energy converter; strain gauges; offshore measurement system; offshore monitoring; force, strain
##### National Category
Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers
urn:nbn:se:uu:diva-265217 (URN)
##### Conference
ISOPE 2015, Kona Island, Hawaii
Available from: 2015-10-25 Created: 2015-10-25 Last updated: 2017-09-21
7. Wave Energy Research at Uppsala University and The Lysekil Research Site, Sweden: A Status Update
Open this publication in new window or tab >>Wave Energy Research at Uppsala University and The Lysekil Research Site, Sweden: A Status Update
2015 (English)Conference paper, Published paper (Refereed)
##### Abstract [en]

This paper provides a summarized status update ofthe Lysekil wave power project. The Lysekil project is coordinatedby the Div. of Electricity, Uppsala University since 2002, with theobjective to develop full-scale wave power converters (WEC). Theconcept is based on a linear synchronous generator (anchored tothe seabed) driven by a heaving point absorber. This WEC has nogearbox or other mechanical or hydraulic conversion systems,resulting in a simpler and robust power plant. Since 2006, 12 suchWECs have been build and tested at the research site located atthe west coast of Sweden. The last update includes a new andextended project permit, deployment of a new marine substation,tests of several concepts of heaving buoys, grid connection,improved measuring station, improved modelling of wave powerfarms, implementation of remote operated vehicles forunderwater cable connection, and comprehensive environmentalmonitoring studies.

##### Keyword
Wave energy, point absorber, experiments, arrays, generators, ROVs
##### National Category
Electrical Engineering, Electronic Engineering, Information Engineering Ocean and River Engineering
##### Identifiers
urn:nbn:se:uu:diva-265218 (URN)
##### Conference
Proceedings of the 11th European Wave and Tidal Energy Conference. Nantes, France, September 2015
Available from: 2015-10-26 Created: 2015-10-26 Last updated: 2017-09-21Bibliographically approved
8. Lysekil Research Site, Sweden: A status update
Open this publication in new window or tab >>Lysekil Research Site, Sweden: A status update
2011 (English)In: 9th European Wave and Tidal Energy Conference, Southampton, UK, 2011, 2011Conference paper, Published paper (Refereed)
##### National Category
Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject
Engineering Science with specialization in Science of Electricity
##### Identifiers
urn:nbn:se:uu:diva-160039 (URN)
##### Conference
9th European Wave and Tidal Energy Conference, Southampton, UK, 5-9 September 2011
Available from: 2011-10-13 Created: 2011-10-13 Last updated: 2017-01-25

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Cite
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