It is well known that control systems, which can modulate the power takeoff force of a wave energy device, have the capability of extending the effective device bandwidth and thereby improve energy capture. For an array of wave energy devices, there is the additional complication that each device is subject to radiated waves from other devices, which are a function of the device motion and, hence, an indirect function of each of the device controllers. This gives the possibility of enhancing the energy harvesting properties of the wave farm as a whole, by giving each controller information about the motion of other devices and employing a global performance function which allows coordinated control for the overall benefit of the farm. This paper examines the possibilities of using such coordinated control and makes conclusions on the types of devices, and types of arrays, that might benefit from such coordinated control. In addition, the overall benefit of a global array control strategy, compared to independent control of each device, is assessed against the added complexity of a coordinated control strategy. Index Terms-Control, power optimization, power takeoff, wave energy arrays. Giorgio Bacelli received the Laurea Magistrale in electronic engineering from Università Politecnica delle Marche, in 2006. He worked on his thesis as a Socrates student at the Electronic Engineering
For renewable wave energy to operate at grid scale, large arrays of Wave Energy Converters (WECs) need to be deployed in the ocean. Due to the hydrodynamic interactions between the individual WECs of an array, the overall power absorption and surrounding wave field will be affected, both close to the WECs (near field effects) and at large distances from their location (far field effects). Therefore, it is essential to model both the near field and far field effects of WEC arrays. It is difficult, however, to model both effects using a single numerical model that offers the desired accuracy at a reasonable computational time. The objective of this paper is to present a generic coupling methodology that will allow to model both effects accurately. The presented coupling methodology is exemplified using the mild slope wave propagation model MILDwave and the Boundary Elements Methods (BEM) solver NEMOH. NEMOH is used to model the near field effects while MILDwave is used to model the WEC array far field effects. The information between the two models is transferred using a one-way coupling. The results of the NEMOH-MILDwave coupled model are compared to the results from using only NEMOH for various test cases in uniform water depth. Additionally, the NEMOH-MILDwave coupled model is validated against available experimental wave data for a 9-WEC array. The coupling methodology proves to be a reliable numerical tool as the results demonstrate a difference between the numerical simulations results smaller than 5% and between the numerical simulations results and the experimental data ranging from 3% to 11%. The simulations are subsequently extended for a varying bathymetry, which will affect the far field effects. As a result, our coupled model proves to be a suitable numerical tool for simulating far field effects of WEC arrays for regular and irregular waves over a varying bathymetry.
One of the key challenges in designing a Wave Energy Converter (WEC) farm is geometrical layout, as WECs hydrodynamically interact with one another. WEC positioning impacts both the power output of a given wave-energy project and any potential effects on the surrounding areas. The WEC farm developer must seek to optimize WEC positioning to maximize power output while minimizing capital cost and any potential deleterious effects on the surrounding area. A number of recent studies have shown that a potential solution is placing WECs in dense arrays of several WECs with space between individual arrays for navigation. This innovative arrangement can also be used to reduce mooring and cabling costs. In this paper, we apply a novel one-way coupling method between the NEMOH BEM model and the MILDwave wave-propagation model to investigate the influence of WEC array separation distance on the power output and the surrounding wave field between two densely packed WEC arrays in a farm. An iterative method of applying the presented one-way coupling to interacting WEC arrays is used to compute the wave field in a complete WEC farm and to calculate its power output. The notion of WEC array ‘independence’ in a farm from a hydrodynamic point of view is discussed. The farm is modeled for regular and irregular waves for a number of wave periods, wave incidence angles, and various WEC array separation distances. We found strong dependency of the power output on the wave period and the wave incidence angle for regular waves at short WEC array–array separation distances. For irregular wave operational conditions, a large majority of WEC array configurations within a WEC farm were found to be hydrodynamically ‘independent’.
In order to produce a large amount of electricity at a competitive cost, farms of Wave Energy Converters (WECs) will need to be deployed in the ocean. Due to hydrodynamic interaction between the devices, the geometric layout of the farm will influence the power production and affect the surrounding area around the WECs. Therefore it is essential to model both the near field effects and far field effects of the WEC farm. It is difficult, however, to model both, employing a single numerical model that offers the desired precision at a reasonable computational cost. The objective of this paper is to present a coupling methodology that will allow for the accurate modelling of both phenomena at a reasonably low computational cost. The one-way coupling proposed is between the Boundary Element Method (BEM) solver NEMOH, and the depth-averaged mild-slope wave propagation model, MILDwave. In the presented cases, NEMOH is used to resolve the near field effects whilst MILDwave is used to determine the far field effects.
The Power Take-Off (PTO) system is the key component of a Wave Energy Converter (WEC) that distinguishes it from a simple floating body because the uptake of the energy by the PTO system modifies the wave field surrounding the WEC. Consequently, the choice of a proper PTO model of a WEC is a key factor in the accuracy of a numerical model that serves to validate the economic impact of a wave energy project. Simultaneously, the given numerical model needs to simulate many WEC units operating in close proximity in a WEC farm, as such conglomerations are seen by the wave energy industry as the path to economic viability. A balance must therefore be struck between an accurate PTO model and the numerical cost of running it for various WEC farm configurations to test the viability of any given WEC farm project. Because hydrodynamic interaction between the WECs in a farm modifies the incoming wave field, both the power output of a WEC farm and the surface elevations in the ‘near field’ area will be affected. For certain types of WECs, namely heaving cylindrical WECs, the PTO system strongly modifies the motion of the WECs. Consequently, the choice of a PTO system affects both the power production and the surface elevations in the ‘near field’ of a WEC farm. In this paper, we investigate the effect of a PTO system for a small wave farm that we term ‘WEC array’ of 5 WECs of two types: a heaving cylindrical WEC and an Oscillating Surge Wave Energy Converter (OSWEC). These WECs are positioned in a staggered array configuration designed to extract the maximum power from the incident waves. The PTO system is modelled in WEC-Sim, a purpose-built WEC dynamics simulator. The PTO system is coupled to the open-source wave structure interaction solver NEMOH to calculate the average wave field η in the ‘near-field’. Using a WEC-specific novel PTO system model, the effect of a hydraulic PTO system on the WEC array power production and the near-field is compared to that of a linear PTO system. Results are given for a series of regular wave conditions for a single WEC and subsequently extended to a 5-WEC array. We demonstrate the quantitative and qualitative differences in the power and the ‘near-field’ effects between a 5-heaving cylindrical WEC array and a 5-OSWEC array. Furthermore, we show that modeling a hydraulic PTO system as a linear PTO system in the case of a heaving cylindrical WEC leads to considerable inaccuracies in the calculation of average absorbed power, but not in the near-field surface elevations. Yet, in the case of an OSWEC, a hydraulic PTO system cannot be reduced to a linear PTO coefficient without introducing substantial inaccuracies into both the array power output and the near-field effects. We discuss the implications of our results compared to previous research on WEC arrays which used simplified linear coefficients as a proxy for PTO systems.
In this study, a series of modules is integrated into a wave-to-wire (W2W) model that links a Boundary Element Method (BEM) solver to a Wave Energy Converter (WEC) motion solver which are in turn coupled to a wave propagation model. The hydrodynamics of the WECs are resolved in the wave structure interaction solver NEMOH, the Power Take-off (PTO) is simulated in the WEC simulation tool WEC-Sim, and the resulting perturbed wave field is coupled to the mild-slope propagation model MILDwave. The W2W model is run for verified for a realistic wave energy project consisting of a WEC farm composed of 10 5-WEC arrays of Oscillating Surging Wave Energy Converters (OSWECs). The investigated WEC farm is modelled for a real wave climate and a sloping bathymetry based on a proposed OSWEC array project off the coast of Bretagne, France. Each WEC array is arranged in a power-maximizing 2-row configuration that also minimizes the inter-array separation distance d x and d y and the arrays are located in a staggered energy maximizing configuration that also decreases the along-shore WEC farm extent. The WEC farm power output and the near and far-field effects are simulated for irregular waves with various significant wave heights wave peak periods and mean wave incidence directions β based on the modelled site wave climatology. The PTO system of each WEC in each farm is modelled as a closed-circuit hydraulic PTO system optimized for each set of incident wave conditions, mimicking the proposed site technology, namely the WaveRoller® OSWEC developed by AW Energy Ltd. The investigation in this study provides a proof of concept of the proposed W2W model in investigating potential commercial WEC projects.
In this paper we compare the optimal configurations for an array of WECs given two control schemes, a real-time global control and a passive sea-state based tuning scheme. In a particular wave climate and array orientation with its axis normal to the prevailing wave direction, closely-spaced symmetrical arrays of 2, 3, 4, 5, and 6 cylinders of different radiative properties are simulated for varying inter-device separation distances. For each device and control type, we focus on the factors that influence the optimal layout, including number of devices, separating distance and angular spreading. The average annual power output is calculated for each optimal configuration.
In the recent years, the potential impact of wave energy converter (WEC) arrays on the surrounding wave field has been studied using both phase-averaging and phase-resolving wave propagation models. Obtaining understanding of this impact is important because it may affect other users in the sea or on the coastline. However, in these models a parametrization of the WEC power absorption is often adopted. This may lead to an overestimation or underestimation of the overall WEC array power absorption, and thus to an unrealistic estimation of the potential WEC array impact. WEC array power absorption is a result of energy extraction from the incoming waves, and thus wave height decrease is generally observed downwave at large distances (the so-called “wake” or “far-field” effects). Moreover, the power absorption depends on the mutual interactions between the WECs of an array (the so-called “near field” effects). To deal with the limitations posed by wave propagation models, coupled models of recent years, which are nesting wave-structure interaction solvers into wave propagation models, have been used. Wave-structure interaction solvers can generally provide detailed hydrodynamic information around the WECs and a more realistic representation of wave power absorption. Coupled models have shown a lower WEC array impact in terms of wake effects compared to wave propagation models. However, all studies to date in which coupled models are employed have been performed using idealized long-crested waves. Ocean waves propagate with a certain directional spreading that affects the redistribution of wave energy in the lee of WEC arrays, and thus gaining insight wake effect for irregular short-crested sea states is crucial. In our research, a new methodology is introduced for the assessment of WEC array wake effects for realistic sea states. A coupled model is developed between the wave-structure interaction solver NEMOH and the wave propagation model MILDwave. A parametric study is performed showing a comparison between WEC array wake effects for regular, long-crested irregular, and short-crested irregular waves. For this investigation, a nine heaving-point absorber array is used for which the wave height reduction is found to be up to 8% lower at 1.0 km downwave the WEC array when changing from long-crested to short-crested irregular waves. Also, an oscillating wave surge WEC array is simulated and the overestimation of the wake effects in this case is up to 5%. These differences in wake effects between different wave types indicates the need to consider short-crested irregular waves to avoid overestimating the WEC array potential impacts. The MILDwave-NEMOH coupled model has proven to be a reliable numerical tool, with an efficient computational effort for simulating the wake effects of two different WEC arrays under the action of a range of different sea states.
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