Experimental Validation of the Capture Chamber Model in Mutriku
MOWC Wave Power Plant
AITOR J. GARRIDO, SALVADOR CAYUELA, AMPARO VILLASANTE, IZASKUN GARRIDO
Automatic Control Group - ACG,
Inst. of Research and Development of Processes - IIDP,
Faculty of Engineering of Bilbao,
University of the Basque Country (UPV/EHU),
Pº Rafael Moreno 3, Bilbao, 48013,
SPAIN
Abstract: - Wave energy holds the potential to fulfill 15% of the EU's energy demand by 2050, thereby
reducing CO2 emissions by 136 million metric tons per megawatt-hour, as outlined in the EU Energy Road
Map. Similarly, the Spanish Renewable Energies Plan underscores the significant marine energy potential in
Spain, particularly emphasizing wave energy. Within this framework, Oscillating Water Column (OWC)
converters currently stand as among the most promising wave energy conversion technologies, offering the
capability to harness ocean energy from various on-shore and floating structures. This paper introduces an
analytical model of the wave capture chamber parameterized for a specific on-shore OWC wave power plant.
The model is specifically adapted and parameterized for the Mutriku Marine Offshore Wave Power Plant
located on the coast of the Spanish Basque Country. Subsequently, validation is conducted using both real wave
entry data measured on-site and experimental output power data generated in the plant.
Key-Words: - Wave Energy, Energy Converter, Modeling, Data Collection, Empirical Verification, Validation,
Marine Energy, Renewable Energy.
Received: April 25, 2023. Revised: February 23, 2024. Accepted: March 29, 2024. Published: May 29, 2024.
1 Introduction
Ocean Energy Europe has reported that wave energy
has the potential to capture over 3000 terawatt-hours
(TWh) annually, a quantity commensurate with the
predominant portion of European energy demand.
Additionally, the United States Department of
Energy has appraised the wave energy resource
potential to range between 1,594 and 2,640 TWh per
year, [1].
Accordingly, estimates for wave energy
production exhibit alignment, indicating an
aggregate potential of approximately 29,500 TWh
annually.
Concurrently, notable initiatives are underway
in the Spanish Basque Country through the Nereida
Marine Ocean Wave Current (MOWC)
experimental/commercial Project. Spearheaded by
the Basque Energy Agency (EVE), this undertaking
seeks to validate the feasibility of Oscillating Water
Column (OWC) technology with Wells turbine
power take-off. Situated within a recently
constructed breakwater in Mutriku on the north
coast of Spain, the project encompasses 16 18.5 kW
turbines, yielding a combined power output of 296
kW (Figure 1). This effort achieved a milestone of
2.4 gigawatt-hours (GWh) in 2021, [2].
Fig. 1: Turbo-generator modules employed within
the Mutriku wave plant
2 System Description
OWC-based converters serve as mechanisms
designed to convert the mechanical energy inherent
in oceanic waves into electrical power. This process
is facilitated through the utilization of a capture
chamber in conjunction with a turbo-generator
module.
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DOI: 10.37394/23203.2024.19.16
Aitor J. Garrido, Salvador Cayuela,
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The capture chamber, a stationary structure,
features a lower section exposed to the sea,
consistently submerged beneath the Still Water
Level (SWL), as depicted in the schematic
representation provided in Figure 2. In this
configuration, the undulating motion of ocean
waves induces an oscillatory airflow within the
chamber, alternately pushing and pulling internal
air, resulting in compression and decompression
cycles. Consequently, a pressure disparity arises
across the turbine, instigating its rotation. The
magnitude of this pressure differential (dp) can be
characterized by the following equation, [3], [4]:
(1)
where:
: Air density (kg/m3).
: Blade’s height (m).
: Blade’s chord’s length (m).
: Blades number.
: Blade’s section area (m2).
: Turbine’s mean diameter (m).
: Turbine’s angular speed (rad/s).
Fig. 2: System’s scheme
Regardless of the direction of airflow, the
rotational motion of the turbine remains unaffected,
primarily attributable to the specific design
characteristics inherent in the conventional turbine
configuration, notably the Wells turbine, [5], [6]
(Figure 3).
Fig. 3: Unused Wells turbine
The symmetric blade configuration
characteristic of self-rectifying turbines facilitates
unidirectional rotation. Nonetheless, this feature
also engenders an undesirable phenomenon known
as the Stalling effect, wherein the turbine ceases
rotation upon reaching a threshold airflow velocity.
Comprising the power take-off system (PTO),
the turbo-generator module incorporates both the
turbine and an induction generator, typically of the
Doubly Fed Induction Generator (DFIG) type [7],
[8], [9]. Its principal function revolves around
converting the oscillatory pressure differentials into
electrical power. Various control strategies may be
implemented to facilitate this process, [10], [11],
[12].
The mechanical dynamics governing the turbo-
generator block can be described by the following
equation:
(2)
3 Theoretical Model Framework
Various system modeling approaches may be
employed to derive an appropriate model, [13], [14],
[15]. In this endeavor, the initial step entails
determining the pressure drop value based on the
characteristics of the input waves. As indicated by
equation (1), the properties of the input waves
directly influence the airflow speed. Consequently,
it is essential to establish a relationship between the
waves and airflow speed, [16], [17], [18].
To achieve this, wave dynamics must be taken
into account, which are governed by different
theories contingent upon the specific attributes of
the wave under consideration. According to Airy
linear theory, a wind wave can be represented as an
ideal sinusoidal wave, [19]. The mathematical
expression delineating the surface profile of such
waves is formulated as follows:
(3)
Furthermore, the calculation of the volume of
water in the chamber can be performed by
considering the volume of air present within the
Oscillating Water Column (OWC):
(4)
where denote the volumes of the capture
chamber and water, respectively.
The water volume can also be determined by
integrating the variation of the water level across the
Oscillating Water Column (OWC) area, yielding the
expression:
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(5)
being l the length of the chamber.
Hence, the instantaneous airflow can be represented
as:
(6)
Now, by considering the geometry of the
chamber, it becomes feasible to derive the airflow
velocity required in equation (1):
(7)
being D the duct’s diameter.
However, as it may be observed from equation
(1), the rotational speed is also a required parameter.
This rotational speed is contingent upon the torque
exerted by the turbo-generator module, which can
be derived from Equation (2).
(8)
The Torque Coefficient (Ct) is, in turn,
interconnected with the Flow Coefficient (ф)
through the characteristic curves of the turbine, as
show in Figure 4, [20].
Fig. 4: Torque Coefficient vs. Flow Coefficient
Where the parameter ф represents a dimensionless
quantity associated with the tangent of the angle of
attack at the blade tip that can be straightforwardly
calculated as:
(9)
Hence, the rotational speed of the turbo-
generator is derived from the established DFIG
equations.
By taken into account all the aforementioned
relationships outlined from Equation (1), an
expression for the pressure drop across the turbine,
in terms of the wave entry, can be formulated as
follows:
(10)
Here, the function f(·) denotes the characteristic
curve specific to the turbine at hand.
4 Model Evaluation
In this section, the OWC plant model is computed
and subsequently validated through the use of
experimental data. To achieve this, the model output
is calculated using actual wave surface data series
gathered at the Mutriku plant breakwater using an
acoustic Doppler current profiler RDI 600, with the
aim of computing the theoretically predicted
pressure drop. The obtained results are subsequently
juxtaposed with in situ measured experimental dP
data furnished by the Mutriku OWC plant (Basque
Energy Board/EVE - BIMEP) for the corresponding
time frame. All procedures were conducted in
adherence to the requisite safety protocols and
occupational health guidelines within the production
facilities:
Fig. 5. dP comparison
As illustrated in Figure 5, the results present a
substantial level of agreement between the values
predicted by the model and the experimental data
acquired.
5 Conclusion
This paper outlines a thorough methodology for
modeling and simulating on-shore Oscillating Water
Column (OWC) systems. Building upon prior
relevant knowledge, the proposed approach marks a
notable progression in engineering proficiency, with
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Aitor J. Garrido, Salvador Cayuela,
Amparo Villasante, Izaskun Garrido
E-ISSN: 2224-2856
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Volume 19, 2024
a particular emphasis on addressing control aspects.
The investigation focuses on the Mutriku MOWC
power plant and proceeds to validate its findings
utilizing experimental data.
The model incorporates the wave, chamber, and
turbo-generator modules, laying the groundwork for
validation via experimental data. The outcomes
reveal a significant congruence between model
projections and experimental observations, thereby
enabling deeper exploration into digital twin
implementation and advanced control strategies.
Acknowledgement:
The authors would like to thank the collaboration of
the Basque Energy Board/EVE - BIMEP through
Agreement UPV/EHUEVE23/6/2011. They would
also like to thank the colleagues of WAKE
European project and the BIMEP for their
collaboration and help.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
The authors would like to thank the Basque
Government for partially funding their research
work through Grant IT1555-22 and they thank
MICIU/AEI/ 10.13039/501100011033 and ERDF/E
for partially funding their research work through
Grants PID2021-123543OB-C21 and PID2021-
123543OB-C22.
Conflict of Interest
The authors have no conflicts of interest to declare.
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