Performance of Ocean Wave-Energy Arrays in Australia

Transcription

1 Performance of Ocean Wave-Energy Arrays in Australia Irene Penesis #1, Richard Manasseh *2, Jean-Roch Nader #3, Swapnadip De Chowdhury *4, Alan Fleming #5, Gregor Macfarlane #6, Md Kamrul Hasan *7 # National Centre for Maritime Engineering & Hydrodynamics, Australian Maritime College, University of Tasmania, Locked Bag 1395, Launceston Tasmania 7250, Australia 1 I.Penesis@utas.edu.au, 3 JeanRoch.Nader@utas.edu.au, 5 Alan.Fleming@utas.edu.au, 6 G.J.MacFarlane@utas.edu.au * Faculty of Science, Engineering and Technology Swinburne University of Technology PO Box 218, Hawthorn, VIC 3122 Melbourne, Australia 2 rmanasseh@swin.edu.au, 4 sdechowdhury@swin.edu.au, 7 mdkamrulhasan@swin.edu.au Abstract Wave energy converters (WEC) range significantly in respect of concept, technologies and design maturation, with the majority of devices at an early-commercial stage. To date, most large scale deployments have been conducted with a single WEC, however there is a necessity to expand this to arrays or farms in the future. With this, there are complex hydrodynamic implications which require consideration in the evolution from single device to arrays. This paper considers two main issues in array designs, the positioning and coupling effects, which can be directly related to the diffraction property of the waves and the radiation properties of WECs respectively. The work conducted comprises both theoretical and experimental modelling, the latter a novel approach utilising Australia s most technically advanced wave basin at the Australian Maritime College. The aim is to address a critical knowledge gap: understanding the performance of ocean WEC arrays, and to develop a software tool readily usable by industry, governments and the public to accurately model the performance of arrays of WECs. Keywords Wave Energy Converters, optimisation, numerical and experiment modelling A. Background I. INTRODUCTION Southern Australia has been identified as an area of significant world-class wave energy resources. According to [1], in the southern and western coastal regions of Australia, the mean power in wave fronts varies from 30 to 70 kw/m, with peaks of 100 kw/m. The greatest wave energy resource in Australia is therefore located along its southern coastline from the southwest of Western Australia to the southern coastline of Victoria and on the west coast of Tasmania, where the average inshore wave energy densities range up to 84 kw per metre of crest width [1]. Australian WEC s range significantly in respect of concept, technologies and design maturation, with the majority at an early-commercial stage with further validation required before large scale arrays can be deployed. Large scale devices have been deployed in three locations in Australia; Port Kembla, New South Wales hosted early models of Oceanlinx s devices and Port MacDonnell, South Australia was considered suitable for further testing of the greenwave device prior to a critical failure during transportation. A full scale demonstrator of BioPower Systems BioWave device has recently been installed near Port Fairy, Victoria, while Carnegie Wave Energy has deployed the world s first array of three CETO5 devices at Garden Island, Western Australia. Oceanlinx s first device was tested 50m from shore while the other devices operated nearshore to deep water at depths between 20-50m. B. Need for Studies on WEC Arrays It is understood by the wave-power community and by governments and investors, that once proven by an individual deployment, WECs would not be installed in isolation in the ocean. Like wind turbines, they would be grouped into arrays ( farms ) with a common connection to the electricity grid. This raises two significant issues. The first issue comes from the scattering and radiation effects within farms of WECs. Optimisation of multiple devices has to include positioning as scattering effects can induce constructive or destructive interactions (see [2] and [3]). There is also a need to develop algorithms for the power take-off (PTO) parameters due to the coupling induced by the radiated wave (see [4]). By absorbing wave energy, farms might also impact on the hydrodynamic environment of the site which can lead to changes in current and sediment transport of the coast at proximity (see [5]). C. Review of Experimental and Numerical Approaches A draft paper has recently been submitted with a full detailed review of past work on hydrodynamic interaction between multiple WECs in arrays [6]. Most of the experimental investigations have been carried out using heaving buoys. For example, the work reported in [7] describes a study where twenty-five heaving buoys were put in rectilinear arrays with twelve different configurations. They found that the impact of power absorption on local wave climate is significant. Yet, the estimation of the relative performance of the array through the measurement of the q- factor was not reported (the definition of q-factor, as applied to WEC arrays, is described further in Section III (B)). In fact, presently there are not many works available in open literature where one can find such q-factor measured in experiments. The work reported in [8] is one exception. The devices used were a combination of OWC and overtopping type device. Highest q-

2 factor was achieved for one specific combination of water depth and separation between devices. A detailed review of analytical and numerical works on WEC arrays have been reported in [9]. A comparison of the performance of few available numerical models in modelling WEC arrays can be found in [10]. Many of these models are based on the well-known potential flow theory solving diffraction and radiation boundary-value problems. Some of the techniques which model WEC arrays based on this theory include finite element method models (see [2] and [4]), and boundary element method models (see [11] and [12]), and the eigenfunction expansion method [13]. The point absorber theory [14] [16] is perhaps the most common theory used for fast calculation of q-factors. However, it is an approximation where the devices are considered small compared to the wavelength and can be erroneous for larger devices. The optimization of power output from WEC arrays in the presence of PTO is another important emerging topic. Related works can be found in [17]. D. Scope of Work This paper presents an overview of a collaborative project between the University of Tasmania s Australian Maritime College (AMC) and Swinburne University of Technology (SUT) s Centre for Ocean Engineering, Science and Technology. The project is funded by the Australian Renewable Energy Agency (ARENA) and supported by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and two Australian wave-power companies, Carnegie Wave Energy and BioPower Systems. The aim of the present project is to deliver a user-friendly tool that will allow government policy-makers and investors to quickly appreciate the potential of ocean wave power at various locations around the Australian coastline. The project comprises both theoretical and laboratory modelling. The project outcome is intended to accelerate the demand and supply aspects of the wave-power infrastructuredevelopment market. It is further hoped that it would empower regional Australian coastal communities to develop local waveresource industries by highlighting the local economic benefits. Moreover, it will also build capacity in the Australian academic sector, permitting academia to further service growing industry needs. The tool will be web-based and enable the general public to estimate the true potential of an array using a generic technology. Generic technology concepts are outlined in Section II below. Furthermore, wave-energy developer companies can apply parameters specific to their own technologies to estimate the true potential of the array using their specific technology. II. WEC CHARACTERISATION The present work is restricted to devices that exploit the principle of resonance. These are the majority of WECs [24]. The underlying assumptions are that the devices operate in a linear fashion, and that the wave physics causing the devices to interact with each other is also linear. The assumption of linearity of device operation is convenient for analysis, but belies to some extent the principle of resonance, for which as large an amplitude as possible to maximise energy extraction. Including the usual assumptions of inviscid and incompressible flow and a sinusoidal time dependence means that the wave physics coupling the devices together can be modelled using potential flow theory. The key feature of potential flow of relevance here is that linearly independent solutions of Laplace s equation can be superposed. The superposition principle is used to divide the overall potential resulting from this motion into one diffraction problem and a number of radiation problems depending on the number of devices and their degrees of freedom. The diffraction part is the potential representing the devices acting as rigid bodies; they simply reflect and refract waves that hit them. The radiation parts are the potential representing each of the devices executing one of its motion they are designed to execute, and which corresponds to power being extracted from the ocean surface. Despite the great variety of WEC designs, we contend that the interactions coupling the devices together can be understood by classifying the devices into only two types: monopolar and dipolar. In reality, any practical device will move in a manner that is more complex than these simple characterisations, but owing to the use of potential flow, we can synthesise any device by linear superposition of different proportions of monopolar and dipolar patterns. A monopolar pattern is characterised by a perfectly axisymmetric wave emitting from the device. This is the characteristic pattern for a heaving device or the effect of the dynamic pressure in an OWC chamber. On the other hand, the dipole pattern has two poles generating waves of same amplitude but opposite phase. This is the characteristic pattern for a surging or pitching device. Once the inter-device interactions are understood, the superposition principle is again invoked to add the incident potential due to the incoming ocean waves that drive the system. Since the solutions to Laplace s equation used to represent the radiated and diffracted waves emanating from the point-like devices are harmonic functions, it is possible to represent the incident potential by sums of these functions. A. Formulation III. HYDRODYNAMIC THEORY Following WEC characterisation, each device was considered as a spherical buoy allowed one degree of freedom, either heave, for the monopolar behaviour, or surge for the dipolar behaviour. For this formulation, we consider an array of n of these WECs, resulting into n degrees of freedom for the whole array system. The WECs are assumed to be fully submerged in order to remove any potential complications from change in buoyancy. The devices operate in constant water depth h and have a constant identical volume V and mass m, as seen schematically in Fig. 1. It is noteworthy that a device with both heaving and surging motion can simply be considered as two different buoys of one degree of freedom in this approach. It is also assumed that the PTO system engenders a linear

3 damping coefficient µ i and restoring force coefficient k i on the ith array motion. A monochromatic plane wave of amplitude η 0 and frequency ω propagates toward the array. Linear waterwave theory is assumed with the assumptions of irrotational and inviscid flow. Fig. 1. Schematic diagram representing two WEC devices, moving either in heave or in surge B. General Considerations Let s consider X i being the displacement of the ith device from equilibrium with its related velocity, X i, and accelerations, X i. The equation of motion can be written as, m X i = k i X i μ i X i + F h,i, (1) where F h,i is the hydrodynamic forces. In the frequency domain we can introduce the complex variables, X i = Re{x i e iωt } (2) and F h,i = Re{f h,i e iωt }. (3) The equation of motion becomes γ i x i = f h,i, (4) with γ i = μ i + i ω k i iωm. (5) The mean power output of the device i is P i = 1 T F T 0 h,ix idt, (6) which can be expressed using the complex variables and the equation of motion as P i = 1 2 Re{f h,i(x i) } = 1 2 Re{γ i } x i 2 = 1 2 μ iω 2 x i 2. (7) represents the complex conjugate and T the wave period. This equation can be found in [17] and [18]. And as commented in [17], only the damping term makes a non-zero contribution to the power. The total power absorbed by the array is P tot = i P i. (8) The q-factor is defined as q = P tot n i=1 P 0,i, (9) where P 0,i is the mean power absorption of the device i when in isolation. This q-factor can give a measure of the overall constructive or destructive interactions within the array in terms of performance where the total power output can be greater or lower than the sum of the non-interacting devices. However, the measure is only meaningful if both the power output from the isolated devices and the array have been optimised through their PTO damping. Otherwise, a q-factor higher than unity might become lower if the optimised power from the isolated devices are used whereas a q-factor lower than unity might become higher if the power of the array is optimised. Several experimental studies have been based using this approach aiming to investigate the interaction between WECs in an array [19], however this brings several difficulties. First, additional parameters need to be taken into account for the PTO systems such as losses through bearings and non-linearities in the damping and/or restoring forces. Furthermore, these PTO systems need to be easily and accurately controllable if optimisation of the power output of the array is pursued. Even then, the optimisation can become a largely tedious process. A novel approach has been taken for the experimental analysis part of this project. C. The Phenomenological Theory The phenomenological theory was developed by Falnes [16], and further extended in [20] to include pressure distribution. Following the method, the hydrodynamic forces can be separated as the sum of coefficients from the different wave sources, n f h,i = Γ i η 0 j=0 Z ij x j, (10) where Γ j and Z ji are complex coefficients. Their absolute value is related to the gain in amplitude and their angle is related to the phase difference between the response and the source. Γ j are the excitation coefficients and Z ji are the radiation impedance coefficients. These coefficients are only frequency dependent for a given set-up and by introducing Eq.10 into Eq.4, a system of n equations with n unknowns can be solved for x i. The power output, P i and P tot, and the q-factor can also be processed in function of the hydrodynamic coefficients and any given PTO damping coefficients, μ i, and restoring force coefficients, k i. It follows that by designing an experiment especially targeted to measure Γ j and Z ji, the performance of the array can be derived for any desired μ i and k i. It also allows post-processing optimisation of the total power output and therefore determination of a meaningful q-factor. All the excitation coefficients Γ j can be derived through the diffraction problem by measuring the forces on each of the devices when fixed in waves. The radiation impedance coefficients Z ji can be measured through the radiation problems by measuring the force on each of the devices, in calm water, where the jth device is forced to oscillate.

4 IV. EXPERIMENTAL APPROACH A. General Background and Scaling The overall project is restricted to linear water wave theory. Under this theory, the results are incident wave amplitude independent and wave spectra can be reconstituted from the superposition of a set of monochromatic plane waves. It is therefore only necessary to define the upper and lower bounds for the period or frequency. The southern coast of Australia has been identified as a prime location for the installation of WECs arrays due to its high density of wave power availability as well as the closeness to electrical infrastructure and habitations [21]. The wave climate of this location has therefore been chosen as the reference in choosing the experimental parameters of interest. Three data sets were sourced; these include wave buoy data from Sustainability Victoria and BioPower Systems, and visual data from the Global Wave Statistics database by BMT Fluid Mechanics. From this data it was found that the wave periods of interest varied from 5s to 15s. By applying Froude scaling, in that the water depths and wavelength ratio between real and experimental condition are kept constant, the wave periods in the scale model experimental conditions covered a set of multiple periods between 0.5s and 1.7s. This wave data also allowed the definition of typical power spectra for different sites which can be reconstructed from the experimental results using linear water wave superposition properties. B. Configurations Seven different array configurations were considered for their theoretical and hydrodynamic importance ranging from one device to six devices as seen in Fig. 2. For array configurations #2 and #3 several spacings were explored (500, 750, 1000 and 1500 mm), while two spacings (750 and 1000 mm) were investigated for the remaining four array configurations. C. Experimental Set-up Two primary experiment types were conducted to investigate the radiation and diffraction problems independently. The purpose of the radiation experiments was to quantify the effect of the energy radiated from one model in the array on the others. The experiment consisted of a single active model with up to five other static models in array configuration. The active model was driven for ten sinusoidal cycles with the effect (force) of the radiated waves being measured on the passive models in the array. The diffraction experiment was more traditional in design but importantly, all models were static. The diffraction effect of different array configurations was measured. Experiments were conducted in the AMC s shallow water wave basin with dimensions of 35m x 12m and depth up to 1m (0.6m for these experiments). The basin is fitted with 16 independent piston type wave paddles, and a passive beach at the opposite end. Fig. 2. Representation of the various array configurations investigated experimentally Two primary types of models were used; active and passive, however all models had the following in common: Spherical in shape 250mm in diameter (see Fig. 3); The top of the (static) sphere was positioned 85mm below the still water surface; Instrumented with a 6 degree of freedom (DoF) load cell positioned at its centroid, which was directly coupled to a 50 x 50 mm square vertical post. Fig. 3. Schematic of a static model

5 The post of the active model was rigidly connected to a linear motor mounted in a frame which could be configured to drive the model in a single axis direction of either heave (z) or surge (x). The frame was located in a bespoke pit in the basin floor minimising obstructions which may influence the immediate fluid domain around the model. The post of the static models extended to a base plate. A prefitted template on the basin floor permitted quick and accurate positioning of the static models to the pre-determined arrays. A diagram of a static model is shown in Fig. 3, including the six DoF load cell and vertical post. A photograph of the active model set up in the empty wave basin is shown in Fig. 4. The linear motor and mounting frame is located within the pit (hidden from view by the cover plate over the pit). The base plate for mounting each of the static models in the various array configurations and spacings can be seen surrounding the active model. Other instrumentation consisted of a bespoke stereovideogrammetry system to quantify the surface particle motions (floating ultraviolet fluorescent flake particles of approximate size 5 x 5 x 0.8 mm) and three resistive type wave probes. This novel application of stereo-videogrammetry was adopted to quantify wave patterns and elevations over a wide surface area, to capture radiation and diffraction effects from the presence of multiple WEC models. The conventional pointsource wave probes provided a means of validating these measurements. Videogrammetry data was processed using the Surface Flow module of the software DaVis (version 8.3.1) [22]. Fig. 5. Example of experimental measurement of a monopolar radiated wave field from the heaving active model using stereo-videogrammetry Fig. 4. Photograph of the active model set up in the (empty) wave basin D. Preliminary Results Preliminary analysis of the vast volume of data acquired during the course of the comprehensive series of experiments in the controlled environment has commenced. Examples of the resultant monopole and dipole radiated wave fields are shown in Fig. 5 and Fig. 6, respectively. These experimental measurements were acquired using stereo-videogrammetry techniques. Fig. 6. Example of experimental measurement of a dipolar radiated wave field from the surging active model using stereo-videogrammetry V. ANALYTICAL MODEL A. Model Description Preliminary models have been developed to identify key features and to investigate to what extent they can be used to develop a web-based user interface. A brief description of these models is provided in the following section. These models are based on potential flow theory with its usual assumptions noted

6 in Section II. A set of different eigenfunction expansions in various zones in the domain are used and the velocity and pressure across the domain boundaries matched. Both of the diffraction and radiation boundary value problems are solved using this technique. The theory of multiple scattering is considered to account for various orders of interactions in between devices. The formulation is adopted from [23]. For fast calculation of radiation boundary value problem, the integral formulation of [24] is integrated with the original multiple scattering formulation. The developed models are then used to compute the q-factor for a given array of two heaving devices and compared with the point absorber theory. B. Preliminary results The first benchmark case attempted was with an array of two heaving cylindrical devices. The schematic of the problem is shown in Fig. 7. This is a case which was used in [25] and [26] for studying the hydrodynamic coefficients in the diffraction and radiation problems respectively. All the dimensions are given in factors of the radii b of the two identical cylinders. The calculated q-factors over various incident wave frequencies for the separation of 10b between the devices are shown in Fig. 8. The prediction from both the theories are found to agree fairly well at all frequencies. Of particular interest, the point-absorber theory continues to agree reasonably with the multiplescattering theory when the device is no longer small compared with the wavelength (when kb approaches unity or less). Fig. 8. Comparison of q-factors predicted by Point Absorber (PA) and Multiple Scattering (MS) approaches for a separation of 10b Fig. 9. Comparison of q-factors predicted by Point Absorber (PA) and Multiple Scattering (MS) approaches for a separation of 5b Fig. 7. Schematic of the problem considered to study the analytic models However, as one decreases the separation between devices, significant differences appear. This is shown in Fig. 9 and Fig. 10 where the comparisons are shown for the separations of 5b and 2.5b respectively. With lower spacing between the devices, the effect of evanescent wave modes becomes dominant and in those cases the prediction from point absorber theory, which neglect such modes, are no longer reliable. On the other hand, even though the multiple scattering theory is applicable to any array configuration, it is more computationally expensive than point absorber theory. Hence, for arrays where the devices are spaced far apart, the point absorber theory is preferred. The multiple scattering theory has to be used when devices are closely spaced, where both the diffraction and radiation boundary value problems are solved separately. Fig. 10. Comparison of q-factors predicted by Point Absorber (PA) and Multiple Scattering (MS) approaches for a separation of 2.5b

7 C. Link with AREMI/ Wave Atlas As an example of the utility of the developed model for aims of the present project, we use the wave climate around the entire coastline of Australia to investigate the availability of wave power in arrays. The source of this wave climate is the Australian Renewable Energy Mapping Infrastructure (AREMI [27]) or the Wave Atlas (see [28]) maintained by CSIRO. Here we specifically consider the spectral wave data for the first Julian day in the year 2014 in the month of July. The data are available on a longitude-latitude coordinate grid at the resolution of 10 minutes of longitude. The distribution of significant wave height is shown in Fig. 11. Preliminary computations on these data sets were done for a pair of devices, leading to the distributions of optimum angle of orientations of the two devices with respect to the peak wave directions and q-factors. The optimum angle of orientation in most of the locations was found to be around o. With this orientation, q-factor as high as 1.5 could be achieved. If the power rating of a single WEC device (e.g., CETO6 of Carnegie Wave Energy) is specified, then this information can readily be utilized for estimating the potential of wave power from an array of two identical devices. Yet, we performed the computations for wave power for a given device based on the wave climate on the gridded data set in addition and then obtained the overall power from an array of two devices. This is provided in Fig. 12 which shows that the wave power more than 0.5 MW per array could be achieved in few locations during the time of the data set (i.e., the first Julian day in the year 2014 in the month of July). Fig. 11. Distribution of significant wave heights for the first Julian day on the month of July in the year The colour bar is of wave heights in metres Fig. 12. Availability of the wave power from the array during the time of the data shown in Fig. 11. The colour map is of power in MW. The colour bar can also be interpreted as MW/km by simply scaling by a factor of Since, the spacing between the devices is 10 times radius (1m) of each device. VI. CONCLUSION An innovative approach to understanding the performance of ocean wave energy converter arrays has been outlined. The approach combines a novel series of physical experiments with a phenomenological theory, whereby the hydrodynamic forces on each WEC are separated as the sum of coefficients from the various different wave sources. Future work will combine the analysed results from the physical experiments briefly outlined in Section IV with a refined numerical model (Section V) from which the goal to develop a web-based tool for estimating the true potential of an array of WECs will be realised. It is anticipated that the outcomes from this project will accelerate the demand and supply aspects of the wave-power development market and empower regional Australian coastal communities to develop local wave-resource industries by highlighting the local economic benefits. ACKNOWLEDGMENT We are grateful to the Australian Renewable Energy Agency (ARENA) who supported this work through their Emerging Renewables Program (grant A00575). We deeply thank Dr Mark Hemer from CSIRO Ocean and Atmosphere for sharing the data source of the Wave Atlas project. We also thank Prof. Alexander Babanin and A/Prof. Alessandro Toffoli from the University of Melbourne, Suhith Illesinghe from Swinburne University of Technology and Dr. Jessica Walker from the University of Tasmania for their contributions to the development of the project. Finally, we would like to express our appreciation for the customer service team from LaVision for their technical support and advices regarding stereovideogrammetry experimental setup and image processing.

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