Variability of wave power production of the M4 machine at two energetic open ocean locations o Albany Western Australia and at EMEC Orkney UK J. Orszaghovaab S. Lemoinec H. Santod P. H. Taylorab A. Kurniawanab N. McGrathab W. Zhaoa M. V. W.

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Variability of wave power production of the M4 machine at two energetic open ocean

locations: oﬀ Albany, Western Australia and at EMEC, Orkney, UK

J. Orszaghovaa,b, S. Lemoinec, H. Santod, P. H. Taylora,b, A. Kurniawana,b, N. McGratha,b, W. Zhaoa, M. V. W.

Cuttlera,b

aOceans Graduate School, University of Western Australia, Crawley, WA 6009, Australia

bMarine Energy Research Australia (MERA), University of Western Australia, Australia

cEcole Centrale de Nantes, 1 rue de la Noe, 44321 Nantes Cedex 3, France

dTechnology Centre for Oﬀshore and Marine, Singapore (TCOMS), Singapore 118411, Singapore

Abstract

Since intermittent and highly variable power supply is undesirable, quantifying power yield ﬂuctuations of wave energy

converters (WECs) aids with assessment of potential deployment sites. This paper presents analysis of 3-hourly, monthly,

seasonal, and inter-annual variability of power output of the M4 WEC. We compare expected performance from deployment

at two wave energy hotspots: oﬀ Albany on the south-western coast of Australia and oﬀ the European Marine Energy

Centre (EMEC) at Orkney, UK. We use multi-decadal wave hindcast data to predict the power that would have been

generated by M4 WEC machines. The M4 machine, as a ﬂoating articulated device which extracts energy from ﬂexing

motion about a hinge, is sized according to a characteristic wavelength of the local wave climate. Using probability

distributions, production duration curves, and coeﬃcients of variation we demonstrate larger variability of the 3-hourly

power yield at Orkney compared to Albany. At longer timescales, seasonal trends are highlighted through average monthly

power values. From a continuity of supply perspective, we investigate occurrences of low production at three diﬀerent

threshold levels and calculate duration and likelihood of such events. Orkney is found to suﬀer from more persistent lows,

causing a more intermittent power output. We also consider the eﬀect of machine size on its power performance. Smaller

machines are found to more eﬀectively smooth out the stochastic nature of the underlying wave resource.

Keywords: M4 wave energy converter, power production, variability, intermittency, hindcast wave data

1. Introduction

The design of any wave energy converter (WEC) relies on knowledge of wave conditions at the intended deployment

location. This is to ensure optimal performance (stemming from WECs’ ﬁnite operational frequency-bandwidth), and

to suitably minimise the risk of failure in severe conditions over the predicted lifespan of the device. Wave resource

assessment is thus carried out to quantify and characterise the wave climate, based on measured or simulated wave data.

The importance of considering the variability of wave climate at a particular site has been recognised for some time, but

often wave resource assessments have focused on quantifying the magnitude of the raw resource via averaged quantities

while neglecting temporal ﬂuctuations. In reality, of course, the incident wave conditions vary over a wide range of time

scales. This has implications on the power yield of WECs, aﬀecting their intermittency and eﬃciency, which have not

been extensively studied. In this paper, we investigate short-term, seasonal and inter-annual (i.e. year-on-year) variations

in power production of the M4 WEC at two wave energy hot spots: oﬀ Albany in Western Australia and oﬀ Orkney, UK.

Email addresses: jana.orszaghova@uwa.edu.au (J. Orszaghova), siane.lemoine@gmail.com (S. Lemoine), harrif_santo@tcoms.sg (H.

Santo), paul.taylor@uwa.edu.au (P. H. Taylor), adi.kurniawan@uwa.edu.au (A. Kurniawan), nicholas.mcgrath@uwa.edu.au (N. McGrath),

wenhua.zhao@uwa.edu.au (W. Zhao), michael.cuttler@uwa.edu.au (M. V. W. Cuttler)

Preprint submitted to Renewable Energy

arXiv:2210.13807v1 [physics.ao-ph] 25 Oct 2022

This work builds directly upon Santo et al. (2020), who studied the mean power output performance of M4, as well as the

device motions in survival mode, at the two locations.

1.1. Wave resource and its temporal variability

The incident wave conditions at any location are highly variable: ﬂuctuations occur within an individual wave cycle, as

well as on wave group, sea-state and storm scales, all the way up to seasonal and multi-year changes. The characteristics

of the local wave climate may be derived from wave measurements (in-situ sensors such as wave buoys or remote sensors

such as a wave radar), or from numerical hindcast models which can re-create multi-year records of wave conditions from

the past. The available timeseries wave data is commonly synthesised into scatter diagrams, which provide sea-state

occurrence probability distributions. In these, a sea-state is represented by a (wave height, wave period) variable pair,

with no spectral shape and directional information. Alternatively, the local wave climate can also be described by the

mean wave power density (typically expressed in kW/m). The annual wave power values allow for inter-annual trends to

be studied, while mean monthly values can capture seasonal eﬀects.

There has been a multitude of wave power resource assessment studies covering many oﬀshore and coastal domains, see

for example Coe et al. (2021) who provide tens of suitable references. Works of Cornett (2008), Gunn and Stock-Williams

(2012), Arinaga and Cheung (2012) and Reguero et al. (2015) consider the global oceans. Their analyses identify our two

sites as rather energetic while also noting lower seasonal variation and thus a more stable resource along the southern

Australian coast compared to western Europe.

A number of more detailed, regional assessments have been carried out at both locations. The European Marine

Energy Centre (EMEC) site, oﬀ Orkney, UK (see https://www.emec.org.uk/) has been included in the analyses of Neill

and Hashemi (2013) and Neill et al. (2014), who report over ﬁve times more incident wave power in winter compared to

summer. Santo et al. (2015) and Santo et al. (2016b) consider longer time scales and provide decadal variability of the

mean annual wave power and of the extreme wave conditions respectively for a number of locations in the North-East

Atlantic, including Orkney. Hughes and Heap (2010) and Hemer et al. (2017) quantify the national Australian wave energy

resource. Cuttler et al. (2020) carried out a high spatio-temporal resolution study of the wave conditions oﬀ Albany in

Western Australia. Here the seasonal variations of the wave energy resource are found to be much smaller, with winter

around 2.5 times more energetic than summer.

1.2. WEC performance and its temporal variability

Understandably, consistent wave conditions at a potential WEC deployment site are desirable. As noted by Coe

et al. (2021) and Ringwood and Brandle (2015) for example, lower variability levels in the wave resource could reduce

intermittency of power output and lead to higher capacity factors, as well as decrease the design demands associated with

withstanding high loads. A WEC can be viewed simplistically as a band-pass ﬁlter acting on the incident wave energy

ﬂux; operating eﬃciently over a band of frequencies with a compromised performance elsewhere (see for example the M4

capture width ratio in Figure 3). This suggests that the power production is likely to be smoother than the available

incident wave power, as the resource ﬂuctuations from extremes (i.e. large long waves) would be partially ﬁltered out. In

this work, we conﬁrm this to be the case for both the Albany and Orkney locations.

A number of studies in the literature have assessed consistency of the power supply of wave energy converters. Carballo

et al. (2015) consider intra-annual/seasonal trends of ﬁve diﬀerent wave energy technologies at two locations oﬀ northern

Spain. They ﬁnd between 1.5 to almost 4 times more production during the most energetic winter months, compared to

the quiescent summer months. However, it appears that in their study the characteristics of the devices have not been

matched to the local wave climates. Morim et al. (2019) analyse both intra- and inter-annual (year-on-year) variability of

power production of ten diﬀerent WECs oﬀ New South Wales along the south-eastern Australian coast. They highlight the

importance of optimal sizing of devices. Their results indicate much lower variability in the power production, across both

timescales, for correctly sized WECs compared to oversized non-optimal ones. They also note that the magnitude of the

inter-annual variations in the power production (for suitably downsized WECs) is generally lower than the inter-annual

variability in the wave resource.

Penalba et al. (2018) and Ulazia et al. (2019) consider decadal changes in WEC performance in the North-East Atlantic,

oﬀ the western European coast. They note a progressive increase in the incident wave energy ﬂux and the mean annual

WEC power yield, respectively up to 40% and 30% higher values during 1980-2000 compared to 1900-1920. When the

survival behaviour of the WECs is taken into account (i.e. no production during too severe conditions), the long-term

upwards trend in absorbed power is still notable, though somewhat reduced, while the WEC eﬃciency (ratio of absorbed

to available incident power) actually declines. Both of these are due to increasing occurrence of severe conditions during

the 20th century. Santo et al. (2016a) study the historical power production potential of an M4 WEC at Orkney, dating

back over more than 300 years. The reconstructed time series reveal ±20% ﬂuctuations in annual absorbed power values,

which are much smaller than that of the wave power resource. In contrast to the western Europe locations, a study for

the Chilean coast (see Ulazia et al. (2018)) found the wave resource and the WEC power output to be remarkably stable

over the studied 100 years.

1.3. M4 wave energy converter

A wide variety of diﬀerent wave energy converters designs have been proposed (see Falc˜ao (2010) and Babarit (2017)

for example). In this study, we use the M4 WEC, which falls into the category of wave-activated devices, meaning that

the device, or parts of it, are excited by wave action and the rigid body (or elastic) response drives the power take-oﬀ

machinery. The original M4 design consists of three collinear surface-piercing ﬂoats, each ﬂoat with a circular cross-section

in plan (see Figure 1). The front two ﬂoats are rigidly connected via a beam above the free surface. The rear ﬂoat is rigidly

connected to a second beam, which terminates at a hinge point above the mid ﬂoat. Power is generated due to relative

angular motion between the two bodies. The whole system is soft moored and the progressively increasing ﬂoat diameters

aid weathervaning such that the device self-aligns to the wave propagation direction. The device has been extensively

studied, with over 15 peer-reviewed journal publications to date. The M4 development pathway has focused on innovation

and design optimisation via numerical simulations and experimentally at a reduced scale, thus achieving high Technology

Performance Level (TPL) before advancing its Technology Readiness Level (TRL) via larger-scale ocean deployments.

Such an approach has been suggested by Weber (2012) for example. The early studies (e.g. Stansby et al. (2015a),

Stansby et al. (2015b)) documented the working principles of the WEC, highlighting its broadbanded and relatively high

capture width. A number of numerical models for the device dynamics, based on linear potential ﬂow theory, have been

created (e.g. Eatock Taylor et al. (2016), Sun et al. (2016), Stansby et al. (2016)) and have been used to investigate

eﬀects of geometric variations (such as ﬂoat separation distances and hinge elevation) on the device power absorption.

Further optimisation was carried out by Stansby et al. (2017) who considered multiple mid and stern ﬂoats to increase

the techno-economic performance of M4. Recent advances focused on real-time control (see for example Liao et al. (2020)

and Zhang et al. (2021)), while survivability has been investigated experimentally and numerically by Santo et al. (2017)

and Santo et al. (2020).

hinge with

power take-off

bow float

middle float stern float

Figure 1: Schematic diagram of the three-ﬂoat M4 WEC.

1.4. Aims, novelty and structure of this paper

The wealth of existing studies, including publicly available performance data, makes M4 an ideal technology to adopt

for the investigation of absorbed power variability pursued herein. We build on the work of Santo et al. (2020) who

characterised the performance of M4 at Albany, Western Australia and at EMEC, Orkney, UK. In this study, however, for

Albany we use 38 years long hindcast wave data from Cuttler et al. (2020) instead of the 8 years long wave buoy record

used by Santo et al. (2020). Compared to Santo et al. (2016a) who analysed decadal variability of M4 power output at

Orkney, we consider ﬂuctuations over shorter time scales, spanning 3-hourly, seasonal and inter-annual changes.

There is a need to understand temporal variability of WEC power production across diﬀerent time scales. Although

it arises from the resource, the variability is strongly dependent on the device’s operational range. Absorbed power

ﬂuctuations have direct implications on the cost of wave energy harvesting, which is currently considered too high to be

cost-competitive with other energy sources (Babarit (2017)). It is beyond the scope of this paper to carry out a detailed

cost analysis. However, quantifying the variability of the power production of the M4 WEC provides new insight on the

potential of wave energy, which goes beyond long-term averaged performance indicators. Importantly, we investigate the

role of device sizing when assessing WEC power variability. We also attempt to draw comparisons to wind energy from

published literature.

The paper is structured as follows. We ﬁrst introduce the available wave hindcast datasets and explain the methodology

for calculation of the absorbed power. The calculated M4 power data time series are then processed statistically, with

graphically presented results to compare and contrast the two locations of interest. We examine distributions of 3-

hourly absorbed power, and investigate in detail occurrences of minimal power output characterising their frequency and

persistence. We also assess monthly trends at the two locations, and consider the eﬀect of device sizing on seasonal

variability and intermittency of the power yield.

2. Data and methods

We use hindcast wave data for both locations. For Albany, 38 years of wave data are sourced from Cuttler et al. (2020).

For EMEC in the Orkneys, Scotland, 54 years of wave data come from Santo et al. (2016a). This section describes the

available datasets and outlines the incident wave power and the absorbed power calculations.

The Albany wave data is from a high spatio-temporal hindcast over 1980−2017, with three nested grids with resolutions

of 0.5, 0.165 and 0.05 km. The site of interest is located at S 35◦11052.800 , E 117◦43019.200 , approximately 15 km oﬀshore,

in 60 m water depth, and is fully exposed to waves from the south and south west approaching across the Southern Ocean

(see Figure 2). The chosen location coincides with a Datawell Directional Waverider Mark III wave buoy, operated by

the Western Australia Department of Transport, which had been used for validation of the hindcast. The wave data is

hourly, in the form of two-dimensional free-surface variance density spectra. However, for consistency with the Orkney

40°S

30°S

20°S

Latitude

120°E 135°E 150°E

Longitude

ALBANY

500 mi

1000 km

50°N

55°N

Latitude

15°W 10°W 5°W 0° 5°E

Longitude

ORKNEY

200 mi

200 km

36°S

35°30'S

35°S

34°30'S

Latitude

117°E 118°E 119°E

Longitude

20 mi

50 km

58°30'N

59°N

59°30'N

Latitude

5°W 4°W 3°W

Longitude

20 mi

50 km

Figure 2: Left: Map of Australia with the Albany site on the south-west coast of Western Australia highlighted (zoomed-in view bottom-left).

Right: Map of the UK with the EMEC site, west of Orkney highlighted (zoomed-in view bottom-right). Maps have been generated with an

in-built function geoplot in Matlab.

data, in our calculations we utilise one-dimensional JONSWAP spectral shapes and consider 3-hourly intervals (by simple

averaging of the available hourly Albany data). We note that the long-crested assumption is justiﬁed as the directional

spread is rather narrow; over 50% of sea-states annually exhibit (standard deviation of) directional spreading below 10◦

(see Hlophe et al. (2022)). More details on the calculation of the spectra is provided in the next paragraph and in the

Appendix. The Albany hindcast dataset is continuous (with no data gaps) and almost 5 times longer than the 8-year long

wave buoy record used by Santo et al. (2020), both of which are advantageous for the analysis herein.

The Orkney wave data is from the Norwegian 10 km Reanalysis Archive (NORA10) hindcast from 1958 −2011 (see

Reistad et al. (2011)). The location of the NORA10 grid point is N 58◦5801200 , W 3◦360000 , which is approximately 15 km

west of the EMEC test site for marine renewable energy machines on the west coast of Orkney (see Figure 2). The water

depth is assumed to be 60 m. The NORA10 wave data available is in 3-hour intervals, with bulk parameters of signiﬁcant

wave height Hs, peak spectral wave period Tp, mean wave period Tm, wind speed, wind and wave directions. We use

JONSWAP spectra calculated using the hindcast bulk parameters Hsand Tp, with the value of the peak enhancement

parameter γchosen so as to match the hindcast Tm. Since spectral bandwidth plays an important role in WEC power

output calculations (see Saulnier et al. (2011)), our procedure helps achieve reasonably representative energy distribution

(across frequencies) in the absence of the full spectral content. More information on this ﬁtting method is provided in the

Appendix A, together with indication of the appropriateness of this approximation.

To quantify the wave resource, we calculate the incident wave power per unit length of wave-front for each sea-state

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VariabilityofwavepowerproductionoftheM4machineattwoenergeticopenoceanlocations:oAlbany,WesternAustraliaandatEMEC,Orkney,UKJ.Orszaghovaa,b,S.Lemoinec,H.Santod,P.H.Taylora,b,A.Kurniawana,b,N.McGratha,b,W.Zhaoa,M.V.W.Cuttlera,baOceansGraduateSchool,UniversityofWesternAustralia,Crawley,WA6009,Australia...

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Variability of wave power production of the M4 machine at two energetic open ocean locations o Albany Western Australia and at EMEC Orkney UK J. Orszaghovaab S. Lemoinec H. Santod P. H. Taylorab A. Kurniawanab N. McGrathab W. Zhaoa M. V. W..pdf

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Variability of wave power production of the M4 machine at two energetic open ocean locations o Albany Western Australia and at EMEC Orkney UK J. Orszaghovaab S. Lemoinec H. Santod P. H. Taylorab A. Kurniawanab N. McGrathab W. Zhaoa M. V. W.

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