A comparative study for tidal current velocity prediction using simplified and fast algorithms☆
Introduction
During the last decade, a growing interest has been brought to the development of technologies liable to produce renewable energies and reduce carbon dioxide emissions. Therefore, wind turbines and solar panels are increasingly present in modern grids. Another sustainable power production that has recently emerged is based on the exploitation of renewable marine energy focusing especially on the tidal stream energy resource. The European potential associated with the kinetic energy of tidal currents is estimated at a 12,500 MW installed capacity (Bryden et al., 1998). However, technologies for tidal kinetic energy conversion are still not mature and require technological improvements before being economically viable. One of the major technological limitations is the adjustment in real time of the turbine settings as a function of the incoming (time-averaged) tidal current velocity magnitude for optimising power production. Accurate assessments of the direction and magnitude of the tidal current are required at any time to set and to anticipate the device adjustments (Bahaj, Myers, 2003, Djebarri, Charpentier, Scuiller, Benbouzid, 2015, El Tawil, Charpentier, Benbouzid, 2017). A simple manner to compute tidal current at a given time of the tide cycle is thus required to control the orientation and rotational speed of the turbine’s blades, and therefore adapt nominal power production (El Tawil, Guillou, Charpentier, Benbouzid, 2019, Lewis, McNaughton, Mrquez-Dominguez, Todeschini, Togneri, Masters, Allmark, Stallard, Neill, Goward-Brown, Robins, 2019).
To assess the resource of potential tidal stream energy sites (tidal current magnitude and direction), Acoustic Doppler Current Profiler (ADCP) measurements are usually retained (Carpmand, Thomas, 2016, Epler, Polagye, Thomson, 2010). However, these observations are limited to a number of time periods and locations. Determining technological options and optimal locations of energy converters in the marine environment requires assessing the spatial distribution of the resource over annual time scales. Thus, the use of ADCP data is not sufficient by itself. Therefore, other methods such as numerical simulations or tidal harmonic analysis are used to predict current speed and directions (Chen, Hou, Chu, 2011, Guillou, Chapalain, Neill, 2016, Guillou, Neill, Robins, 2018, Thiébot, du Bois, Guillou, 2015, Thiébot, Guillou, Droniou, 2020). While being an accurate method to estimate tidal currents in the marine environment, numerical modelling requires high computational capacities. In order to reduce the computational time, El Tawil et al. (2019) have proposed an empirical method to approximate tidal current velocities as a function of the (i) tidal range and (ii) reference values and , that account for the velocity vectors (representing the magnitude and direction of the tidal currents during a mean neap or a mean spring tide cycle), respectively. Those reference values can be easily provided by numerical simulations (Section 2) or on-site observations.
This paper extends the analysis of El Tawil et al. (2019) on the relationship between current velocity and tidal range. El Tawil et al. (2019) assumed a linear relation. The present investigation test other formulations: a piece-wise linear and an exponential functions. The aforementioned models have been calibrated and validated against reference values obtained using numerical simulations of the tidal hydrodyanmics (Hervouet, 2007). To assess the performance of the piecewise linear and the exponential models, the computed velocities are compared to these reference values at two sites with strong potential for the exploitation of the tidal stream energy resource along the coast of France: the Fromveur Strait in western Brittany (which has already been studied in [7]) and the Alderney Race in the English Channel where the method is applied for the first time and where the tidal dynamics is different (progressive wave in the Alderney Race and standing wave in the Fromveur Strait) (Fig. 1). The overall objective of this study is to assess the reliability of a simple empirical model or an exponential relationship to represent the tidal flow complexity while sparing computational time.
The paper is organized as follows: Section 2 describes successively (i) the linear approximation method, (ii) the piece-wise linear method, and (iii) the exponential method developed to enhance tidal current velocity predictions. Section 3 shows results, compares and discusses these three methods presented. Conclusions are finally drawn in Section 4.
Section snippets
Study sites
The tidal hydrodynamic data of the Fromveur Strait and the Alderney Race rely on numerical predictions. Those reference data for the empirical model calibration and validation are provided by Telemac, a finite element model dedicated to the modelling of environmental free surface flows (Hervouet, 2007). The hydrodynamic data of the Fromveur Strait derive from the numerical model set up and validated by Guillou and Chapalain (2017). The computational grid was composed of 51,226 nodes duplicated
Results and Discussion
The relative errors between reference values current velocity and the current velocities performed by the different methods are computed. Results of the three different methods are compared in Figure 8 for the Fromveur Strait at the three locations and in Figure 9 for the Alderney Race at the two locations. The black crosses refer to the linear results (Section 2.2), the blue squares are obtained by the advanced linear method (Section 2.3) whereas the red circles refer to the exponential method
Conclusion
In this study, three methods to compute tidal current velocity vector from tidal range data have been presented and compared (one of them already been assessed in a previous study). The methodology has been applied to two tidal stream energy sites (the Alderney Race is a new case study). The reference values are based on a depth-averaged current velocity computed with regional hydrodynamic models simulating the tidal propagation. The first method presented is a linear approximation which
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Numerical simulations in the Brittany region were conducted on HPC facilities DATARMOR of “Pôle de Calcul et de Données pour la Mer” (PCDM) (http://www.ifremer.fr/pcdm).