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Evaluation of the Wave Energy Resource

Info: 17382 words (70 pages) Dissertation
Published: 2nd Feb 2022

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Tagged: Energy


When the topic of renewable energy is approached, more often than not the images that come to mind are swathes of land covered in wind turbines or solar panels. For the United Kingdom, an island which has over 17,000 km of coastline (Rae, 2016), why is the instinctive mental image not offshore sources of energy, and in particular, wave generated power?

Renewable energy generation is gradually increasing at a healthy rate within the UK. 2015 was the first time that renewable sources of power had overtaken coal, making it now the second highest source of energy in the UK behind gas, with roughly 25% of electricity being generated from renewables (Nicholls, 2016). Offshore generation is gradually contributing to that increase. However, in the offshore sector, wind power dominates the market, producing around 18TWh, while offshore hydroelectrical generation (which includes tidal and wave power) is generating less than 2TWh in comparison. So why has offshore wind and alternative renewable sources of energy taken off in a manner that wave power has yet to do so?

When looking at wave power sites and devices that have been commissioned around the United Kingdom, one is given an initial impression that the resource is not living up to its potential. It has been estimated that the overall practical and attainable resource of wave power in the UK is in excess of 146TWh/year (UK Wave Energy Resource, 2012). To put that into context, this can potentially power over 5 million houses a year (Agency, 2012). Using the European Marine Energy Centre’s (EMEC) Map (Wave & tidal projects : EMEC: European Marine Energy Centre, 2016), which shows commissioned wave power sites, cancelled projects, and those awaiting development and construction around the UK, it can be gleaned that in fact only 7 sites around the entirety of British shores are operational, with the majority of these sites owned by EMEC themselves. New technology within the wave power sector is consistently being developed, so what is limiting the production of these wave power sites?

This dissertation delves deeply into the current wave climate, exploring the existing technologies, and providing an analysis of the reasons why wave power generation is experiencing hindrances. This project begins by looking at the renewables sector as a whole, before reviewing the topic from the surrounding related literature.

After which, the dissertation provides an investigation of how a device generates electricity, stating the benefits of the current devices, evaluating the current limitations of said devices, whilst making necessary comparisons to other renewable energy sources. To attempt to fully understand this subsector of renewable energy, one must explore the environment that wave power devices are deployed within. Hence an analysis of the deployment environment has been made, in conjunction with a following evaluation of how the same device would behave if relocated to a more extreme and varied wave environment, with the goal of discovering how a wave power device would respond.

Continuing from that, an evaluation of the financial viability has been conducted; investigating the costs, generation income, and lead time that a device would experience in the current wave energy climate within the UK. If wave energy is to continue its expected growth within the sector, then knowledge of whether deployment of wave power generators is financially beneficial must be discovered.

Currently, the wave resource seems vastly underused, despite being abundant throughout coastal locations. As devices are situated at great distances offshore, they provide a minimal visual impact which personnel have often complained about with other renewable sources, and other benefits of wave energy will be discussed in this dissertation. This dissertation will analyse if there is a future for wave energy, or whether the situation appears to be this dire for justifiable reasons.


Click to expand Contents

1.0 – Introduction

1.1 – Waves

1.2 – Capturing Wave Energy

1.3 – The Problem with Wave Energy

1.4 – The Scope of Work

2.0 – Literature Review

2.1 – Initial Reading

2.2 – Detailed Reading

3.0 – The Current Situation

4.0 – Theoretical Background

4.1 – Wavelength

4.2 – Wave Energy and Power

5.0 – Analyses of the Wave Power Resource

5.1 – Power Analyses of Wave Hub

5.1.1 – Power Calculations of PA1 Wave Device

5.1.2 – Wave Environment at Wave Hub

5.1.3 – Device Behaviour at Other Locations

5.1.4 – Capacity Factor

5.2 – Economic Viability of PA1 Device

6.0 – Conclusion

7.0 – References


Appendix 1A – EMEC Hourly Wave Event Recordings Over 10 Years

Appendix 1B – EMEC Hourly Wave Event Recordings Over 10 Years

List of Figures

Figure 1 – A diagram showing the wave power per metre of wave crest around the shores of the United Kingdom (Gray, 2014)

Figure 2 – A graph showing Madagascar and other wave power location power output per metre of wave crest (Rusu & Onea, 2015)

Figure 3 – A chart showing the breakdown of electricity generation in the United Kingdom in the year 2015 (Nicholls, 2016)

Figure 4 – A graph to show the comparison of theoretical wave power and device PA1 output power

Figure 5 – Visual representation of wave period occurrences at Wave Hub

Figure 6 – Visual representation of wave height occurrences at Wave Hub

Figure 7 – A comparison of capital expenditure, lifetime operating expenditures, and lifetime revenue generated by the PA1 device

Figure 8 – A graphical representation of how the number of devices affects lead time

Figure 9 – A visual representation of how the number of devices affects the percentage that initial financial outlay makes up of total lifetime cost

List of Tables

Table 1 – A selection of wave environments to show how the output power of PA1 varies

Table 2 – Wave energy and power for a common wave event over a half hourly period assuming wave height and period to be constant throughout

Table 3 – A frequency table showing the number of times events of a certain wave height and wave period occurred

Table 4 – Wave energy and power for infrequent wave events over a half hourly period assuming wave height and period to be constant throughout

Table 5 – A comparison of wave events of varying frequency at EMEC and Wave Hub sites

Table 6 – A comparison of device output power during the most common wave event at each test site

Table 7 – Table showing the brackets at which costs alter for the PA1 device

Table 8 – Lifetime costs and profits over lifetime for varied numbers of devices

Table 9 – Profit generated from a 4kW domestic solar panel scheme in association with the feed-in tariff (Solar Panels Cost, 2017)

List of Symbols

d Depth of water/depth to seabed m
E Total mechanical energy for one wavelength J
Einterval Total energy for a specified time interval J
Ek Kinetic energy J
Ep Potential energy J
Average energy per unit of surface area Jm-2
g Acceleration due to gravity ms-2
H Wave height m
k Wavenumber m-1
n Constant which simplifies elements of wave power equations  
P Power W
Pdevice Power output of a wave power device W
Pinterval Total power for a specified time interval W
T Wave period s
Tp Peak wave period s
Tz Means wave period s
t Time s
u Horizontal particle velocity ms-1
w Vertical particle velocity ms-1
λ Wavelength m
π Pi  
ρ Density kg/m3

List of Abbreviations

ANREV - Annual Revenue Generated

CAPEX - Capital Expenditure

EIA - Energy Information Administration

EMEC - European Marine Energy Centre

OPEX - Operating Expenditure

WEC - Wave Energy Converter

1.0 – Introduction

This dissertation is aiming to provide a critical analysis of whether the wave energy resource can provide a significant contribution to long term energy demands, and more specifically, the renewable energy sector. The evaluation consists of analysis of a current devices in operation, methods of determining where to place a device, theoretical outputs, and assessing if wave energy will be a major energy source in future. To fully comprehend what happens in sizing and deploying a wave energy device, a series of calculations and analyses are performed to determine if this resource is being exploited to its maximum potential, and if not, discover the causative reasons why. This dissertation will also identify what can be done to push wave power from an underperforming resource, to the forefront of renewable energy generation in the United Kingdom.

1.1 – Waves

Waves are induced from the action of wind blowing across the surface of the ocean, and are not to be confused with tides. The difference between waves and tides is that waves are formed as mentioned previously, whereas tides are formed due to the gravitational pull of the Moon and Sun acting on large bodies of water. When these waves vary in an up and down motion, usually parallel to the other waves, this is known as a “swell” (What is wave energy? — Brightside, n.d.). In great distances offshore, where the water depth is large (deep water is usually classed as 50 metres or more in the wave energy sector), wind travels great distances across the ocean surface. The energy from the wind is transferred into the formation of waves.

In deep ocean, wavelengths are long, and can be defined as a function of the period of the wave. For large bodies of water, with long uninterrupted spaces for wind to blow across the surface, these waves have an extremely low frequency, therefore a high period, and hence a long wavelength. As a wave approaches nearshore, frequencies increase and wavelengths decrease, which implies a loss of capturable wave power. Due to this it is more commonplace to place a wave device in deep water.

1.2 – Capturing Wave Energy

Wave energy devices are used to transfer the energy in the motion of waves into a useful energy resource. The general premise of a wave energy device is a mechanical method of converting wave energy to electricity, either placed at the surface of a large body of water or submerged. These are then required to be moored in place, and connected to mainland or nearshore by lengthy underwater cables. Although there are many mechanical methods to gather wave energy, including those currently in the testing phase too, the devices can be simplified to be placed into 3 different categories;

  • Devices that “ride” the surface of offshore waves ((IEA-RETD), 2012) (Wave & tidal projects : EMEC: European Marine Energy Centre, 2016)
  • Buoy-like structures that operate due to 3-dimensional motion relative to the waves (Wave & tidal projects : EMEC: European Marine Energy Centre, 2016)
  • Submerged paddle-like structures that convert 2-dimensional wave motion into electricity ((IEA-RETD), 2012)

The methods of converting wave energy are explained later in the dissertation, along with the advantages and disadvantages of each type, and comparisons are made to other “successful” renewable energy sectors with the aim to discover if wave energy extraction is worth the pursuit. It is to be noted that the scope of this dissertation will mainly focus in deep water wave energy, as opposed to nearshore solutions.

1.3 – The Problem with Wave Energy

Although many wave devices and sites are currently in the proposal or construction stage around the UK, at the time of writing this dissertation, there are only 7 operating wave energy sites within British waters generating electricity, most with a site capacity of less than 1 MW. When compared to the number of operating offshore wind farms around the UK (in excess of 25, each with a site capacity that ranges from 4 to 630 MW (Offshore Wind Electricity Map, n.d.)), one must question why wave power is not being exploited in the same manner.

The issue that is often mentioned when talking about wave energy is that for a global resource, it seems vastly underused, underfunded and underpublicized, especially in the United Kingdom. As an island nation with the might of the Atlantic Ocean to the west, one would find it hard to believe that further strides have not been made into this field of renewable energy.

On face value alone, wave energy is too costly when compared to other solutions, and the capacity to generate a large amount of electricity simply is not available at this moment in time. Consequently, some of the questions this dissertation will answer is what is holding wave energy back as a substantial renewable energy source, what measures are currently being taken to change this, and what can realistically be accomplished in future done to help with this change?

1.4 – The Scope of Work

This dissertation will aim to analyse and evaluate the past, current and future situations of the wave resource within the renewable energy sector. However, limitations are to be encountered within this dissertation, whether they be set by the scope of the dissertation itself, or the boundaries that research within the field pose. For example, some means of gathering wave energy are relatively new technologies when compared to other renewable sources. Therefore, data regarding output that is on a timescale (e.g. monthly power output as opposed to quoted site capacity) is often not open-source, and for companies working in this area it is within their interest to keep this information private. Hence, all commercially sensitive data regarding data suppliers and equipment has been anonymised.

As there are so few operating wave power sites within the UK, not accounting for the testing sites, the scope of this dissertation has been widened to include sites located all over British waters at certain points, so it is possible evaluate areas where information is freely available and where wave power devices are numerous.

The vast majority of wave devices are situated in deep water, a few kilometres from mainland. Certain devices operate closer to shore in shallower depths, for instance some paddle-like structures. The scope of this dissertation is limited in the way that certain devices work. For instance, comparing the power output of one device which rides atop waves in deep water to a seafloor paddle-like device would prove to be an ineffective comparison, due to what each device “feels” if placed in the same location. In deep water the particle motion reduces the deeper you get, reducing the effectiveness of the paddle device. A comparison of how different mechanisms react in different scenarios must be made, but can yet again be limited by the available data.

Due to the recent nature of the devices available, it is not only gaining the data that limits the scope of this dissertation, but the length of time which the data regarding wave energy devices goes back also. Hindcast data is often freely available and open-source for various locations around the UK, stretching back years and decades at a time. However, matching device data to this hindcast data is difficult, since recordings from devices may only stretch back a few years at most, with the earliest data only available from when they were commissioned. This limits the scope of the dissertation and must be accounted for.

2.0 – Literature Review

Within this dissertation, attempts are made to discover the limitations in the current methods of wave power generation, discover what drives the feasibility in the construction and deployment of these schemes in the United Kingdom, and analyse what can potentially be done to push wave power to the forefront of renewable energy in British waters. This is done through analysis of existing literature and exploiting the gaps discovered in existing research. In the latter stages of this project, an evaluation of a selected sites that has the potential for deployment of wave power generation over a specific time period will be conducted based from research found in literature and other calculations.

2.1 – Initial Reading

Offshore wave power can be defined as the conversion of energy from waves in areas of water depth usually at 50 meters or greater into useful electricity to supplement the demands of the current energy usage in modern society ((IEA-RETD), 2012). Wind blowing across the ocean surface induces waves, and when offshore these waves vary in what is called a “swell” (What is wave energy? — Brightside, n.d.).

There are various methods of converting energy from waves into electricity, and around the UK there are 3 varieties which are the most common out of the sites that are commissioned or under development. These devices are often attenuators, point absorbers, and oscillating wave surge converters.

Attenuators are long, linear, semi-submerged modular floating devices which are placed in parallel to the wave direction, and generate electricity by the relative motion of one module to another through a complex design of hydraulic rams and generators. These devices look as though they are “riding” the wave surface, and can often exceed 100 meters in length ((IEA-RETD), 2012) (Wave & tidal projects : EMEC: European Marine Energy Centre, 2016). Two of these devices are situated in the waters off the coast of the Orkney islands, both produced by Pelamis and owned by EMEC, producing a meagre 0.75MW each. It is worth noting that Pelamis has now gone into administration, and financial viability is another topic that will be discussed later within this dissertation.

Off the coast of Cornwall there are 2 operating point absorber devices, with another 3 in the development phase, mainly owned and developed by Wave Hub. Point absorber devices work by one of either the three-dimensional or two-dimensional motion of a floating buoy-like structure mechanically connected to a base either moored or anchored to the sea floor (EMEC, 2016). These schemes are much smaller in size than attenuators usually are, and the operating point absorbers produce an even smaller amount of power with a maximum site capacity of 0.24MW and 0.165MW respectively.

Oscillating wave surge converters are relatively new to British waters, with only one in operation and producing 0.8MW, also owned by EMEC and situated in the Orkney islands. However, another scheme is currently in the development phase which has a relatively large site capacity of 200MW, which if commissioned and designed to produce this value, would make it the largest wave energy site in the UK in terms of electricity produced. These converters operate by directly capturing wave energy. A paddle connected to a pump has waves push against it, moving the paddle in a forwards and backwards two-dimensional motion whilst connected to a generator to convert to electrical power ((IEA-RETD), 2012).

2.2 – Detailed Reading

It is often thought of that cost and economic viability is the major limiting factor in determining whether a wave power scheme will be commissioned and operational. Yet to truly understand what drives these schemes, looking at the factors that determine initial and ongoing cost and yield of the site must be delved into.

Waves are a natural source of power and thus the power that can be converted into electricity will vary. The power can be determined by wave height, speed, direction and a number of other factors which cannot be controlled. Looking at a paper which analyses the global resource of wave power, the impression gained is that variation (for example monthly or seasonally) of waves is a decisive factor in deciding where devices are located and the financial returns of the wave sites (Reguero, Losada, & Mendez, 2015). In this paper, it is stated that the variability in wave energy may not be as simple as monthly, but on a much longer time scale, i.e. yearly – interannual variability, a variability which as of yet has not been considered in depth for generation via offshore wave.

The study stated above considers the effects these timescales may have on the viability of the installation of wave power devices and climate variations on a larger scale. The findings state that large scale climate patterns, of which the North-Atlantic Oscillation would be most applicable to wave power, would influence the conditions that wave power devices would experience and thus in turn affect the generated electrical output (Reguero, Losada, & Mendez, 2015).

The North-Atlantic Oscillation (NAO) is a climatic variation which affects regions ranging North America all the way across to Europe, including the United Kingdom (Reguero, Losada, & Mendez, 2015). The NAO consists of a yearly varying index, which is either positive or negative at any one time, and can have huge implications in terms of weather and climate patterns in the affected areas.

When in the positive phase, westerly winds increase and alters the position of the jet stream to a near linear direction from North America to Europe, bringing with it stronger and more frequent storms, and in the UK produce storm-like winter conditions. When in the negative phase, the pressures that dictated the conditions stated for positive NAO are reversed. This in turn means that Europe and the UK have a higher probability of calm winters (North Atlantic Oscillation, 2016). Predicting what phase the NAO will be in often difficult, and the implications on long term viability on offshore wave power could be vast. Although the NAO phase is difficult to predict, it often stays in one phase for a period of a few years at a time.

What this means for the study of evaluating the offshore wave resource is that the installation of a device cannot be thought about purely in the short term. For instance, if a potential wave site has its theoretical output evaluated in a period of particularly negative NAO phase, when waters are calmer around the UK, then the project may not be considered economically viable if seen to not be producing an acceptable amount of energy, and thus dictate whether the site is commissioned.

This work provides an interesting avenue of research, but the paper looks at these climate effects on a global and continental scale, and does not tend to focus too much on small scale areas that this dissertation will be looking at. Looking at how these large-scale variations in climate affect smaller scale areas is an aspect of research to be conducted. For instance, how will the NAO affect a portion of the UK coastline which is sheltered from the Atlantic, like North-East Scotland, and could this in turn determine if devices can be deployed in these locations?

When one looks at the current wave energy sites around the United Kingdom, it immediately becomes obvious that there are no large-scale wave farms present. In fact, this is true for almost the entire planet. Wave farms are few and far between. The Agucadoura Wave Farm, situated 5 kilometres off the coast of Porto, Portugal, was the world’s first wave farm, and consists of 3 Pelamis wave attenuation devices, each over 120 metres in length. This wave farm has a peak capacity of 2.25MW and had an initial cost of $115million (around £75million at the conversion rate in 2008) (Age, n.d.). Performing a simple calculation to gain a ratio of capacity to cost, a value of 0.03W/£ is produced.

Now compare this value to one of a UK offshore wind farm. The Kentish Flats offshore wind farm is installed off the coast of Whitstable, Kent, and consists of 30 wind turbines with a total peak capacity of 90MW, installed at an initial cost of £105million (Kentish Flats – 4C Offshore, 2016). Performing the same calculation as above gives the ratio of 0.86W/£. That is nearly 30 times the value of the wave farm.

Obviously, this basic calculation does not take into account maintenance costs and the other expenditures that the sites would cost over their respective lifetimes, but it gives an impression as to why wind farms are vastly more popular than wave farms. You could argue that this is a bad comparison due to the difference in capacity sizes, but wave farms with large capacity simply do not exist, and one could argue that it is since wave farms cost so much compared to alternatives at face value.

The paper “The economics of wave energy: A review” looks at how this less developed sector of renewable energy has become such an expensive area to delve into, and whether wave power has an economic future (Astariz & Iglesias, 2014). This study states that it is difficult to estimate some costs of wave energy because the technologies are so recent, and also cites these new developments as one of the reasons why wave power is so expensive.

Initially, the paper reveals that the larger capacity wave energy converter that are installed, the lower the ratio of cost to capacity is. This document is useful for the topic of this dissertation as it provides an insight into costs that one might not consider having an implication on design and deployment. For example, part of this study is of the opinion that wave power may be costly at this moment in time due to the resource being relatively new to the market when compared to other renewable energy resources, implying that a certain premium is placed upon wave power devices due to their rarity. Of course, this is one reason among many for why wave power tends to be rather expensive, but it offers alternative avenues of thought when evaluating the resource as a whole.

In the latter stages of this dissertation a basic analysis of wave conditions using existing environmental site data will be performed to determine if an alternative location for a device deployment is suitable. Certain challenges that can be identified from this include:

  • What devices should be modelled? There is a substantial number of wave devices in the market, from large scale models funded by huge companies, to smaller devices that have been developed recently. Deciding which devices to study will define certain parameters of analysis.
  • What range of conditions should be chosen to study? The nature of wave energy is that the resource can be altered in any number of parameters including wave height, frequency, speed, and other factors such as temperature, despite the turnout of electrical generation being considered reliable. These factors will determine output from the device, as well as the suitability of certain devices for conditions which model a probable event at a location. Deciding what conditions to assess is dependent on the environmental data that is freely available.
  • How will this research be different? Studies have been conducted before to assess the conditions in which a new device will be placed, as it is an essential portion of the design process. What will this dissertation discover that has not already had in-depth analysis?

The questions above provide challenges that require research in previous methods of simulation of wave devices. The article “Design, simulation, and testing of a novel hydraulic power take-off system for the Pelamis wave energy converter” (Henderson, 2005) looks at the power take-off system for a Pelamis wave attenuation device, which includes both physical laboratory tests as well as simulations, looking for efficiency measurements as results.

Reading this article, one can spot a few similarities between the method they employed and the method to be used in this dissertation. In section 4, it is stated that the simulations described in this article were used both in the design process and to verify predictions. A part of this process was the “prediction of average power capture at specific sites”, and this sub-section of specific site conditions will be of particular interest when applied to the site analysis conducted in this dissertation.

Linear controls and hydrodynamics were assumed for the Pelamis simulation, which allowed other conditions to be varied, and power capture and “survivability” were measured as outputs initially. The advantage of simulation is that it cuts the expensive cost of a physical model and testing, yet keeping certain parameters constant may not be a realistic representation of what is happening to a wave energy converter (WEC) when placed in an actual site location.

This article has highlighted the many complications and difficulties that come with modelling such a complex sector, and due to this complex nature it may mean that the scope of the modelling may have to be narrowed, with a larger number of control variables, and thus potentially a more unrealistic set of results when compared to a physical test. However, the stated paper delves deeply into coded model simulation of a wave device on site, a method that is not be deployed in this dissertation, yet it still provides factors that can be applied to this process.

Figure 1 – A diagram showing the wave power per m of wave crest around the shores of the United Kingdom (Gray, 2014)

It is believed that the United Kingdom is one of the best potential locations for wave energy generation in the world. The figure above (Figure 1 (Gray, 2014)) shows the spread of mean wave power around British shores. It seems almost obvious that the United Kingdom would be suitable for wave power generation, with the west coast possessing a nearly completely exposed face for the might of the Atlantic Ocean to crash against, with only Ireland acting as shelter. Figure 1 reveals that these highest areas of mean wave power appear to be the North of Scotland, and the South-West of England, which is where most of the UK’s wave power devices are located.

How wave energy devices perform in these high wave power waters will be vastly different to comparably low wave power areas. The paper “The performance of some state-of-the-art wave energy converters in locations with the worldwide highest wave power” (Rusu & Onea, 2015) analyses areas akin to those found around the UK, and areas of higher wave power around the world. The areas of analyses are also assessed on accessibility, meaning that some regions of extremely high wave power like Antarctica have been disregarded.

In the results section of this report, it finds that wave direction is an extremely important asset in wave power generation, especially on islands. This article used Madagascar as an example, which has a “swell that spreads out in all directions” reaching its shores (Rusu & Onea, 2015). The graphical results of this study show that areas that have such a variation had the lowest wave power over a 15-year interval (Figure 2, Bar AF4 (Rusu & Onea, 2015)), with Madagascar the second lowest value out of the 30 locations assessed, as well as an extremely low variation in power.

Figure 2 – A graph showing Madagascar and other wave power location power output per metre of wave crest (Rusu & Onea, 2015)

The United Kingdom, much like Madagascar, is an island situated just off a mainland continental area, and exposed on one face to a large ocean. Assessing how the wave devices and sites around the United Kingdom respond to the variation in wave properties will be vital in analysing whether there is a potential future for wave power around British shores, and this study highlights wave direction as being influential in determining output of a device. The topics covered about Madagascar, as well as the other locations, can be comparable when assessing the UK.

3.0 – The Current Situation

In the current energy climate, the drive and desire for advancements in renewable energy sources is increasing drastically. The United Kingdom set a target of 15% of all energy consumption to be generated by renewable sources by 2020 (National Renewable Energy Action Plan for the United Kingdom, 2009), whilst the EU pre-Brexit target of 27% of all energy consumption within the EU to be generated by renewable sources by 2030 (Renewable energy – Energy, n.d.).

In 2015, the UK surpassed its 2020 target, and it was the first time in British history that electrical generation from renewable sources of energy surpassed coal production, making it the second highest source of electricity in the UK at 25%, generating roughly 83.3TWh of power, second only to gas (See Figure 3) (Nicholls, 2016).

Figure 3 – A chart showing the breakdown of electricity generation in the United Kingdom in the year 2015 (Nicholls, 2016)

Within the renewable energy sector, offshore wave generation is contributing to this increase, but minimally and at an excruciatingly slow rate. Bioenergy (renewable energy produced from living organisms, e.g. wood) and wind dominate the sector, and in the offshore subsector, winds superiority over all other offshore sources of energy continues.

In 2015, offshore wind from British sources generated 17,423 GWh (gigawatt hours) (Renewable Electricity Capacity and Generation Spreadsheet, 2017). To put that into context, the average energy usage for a household in the UK is 4,648 kWh/year (Wilson, n.d.), and therefore the offshore wind farms powered the equivalent to 3.75 million households.

To compare that to offshore wave and tidal electrical generation in 2015, a meagre 2 GWh was generated (Renewable Electricity Capacity and Generation Spreadsheet, 2017). That is around 8700 times less than offshore wind produced, equating to supplying around 430 households for a year. From these basic calculations, the offshore sector clearly favours wind over wave. These numbers do not reflect the capacities for each source, just the numerical values of what was generated in 2015.

The UK’s wave resource has been estimated to have the theoretical potential for 146TWh/year that can technically be extracted, but on a realistic level only 70TWh/year can be utilized of that (UK Wave Energy Resource, 2012). The theoretical value is decreased to a realistic value to account for the areas of British waters that cannot be suitable to place wave energy devices, due to issues such as locations where construction would not be permitted, e.g. pipelines, existing underwater cables, regions protected for natural purposes, and much more.

Therefore, of that theoretical extractable energy, the UK is currently only utilizing 0.003% of what could be available. This value reveals the extent to which the resource is not being exploited. At the time of writing this dissertation, there are only 7 operating wave energy sites in the UK, all of which are individual devices as opposed to wave energy farms, with a site capacity ranging from 0.165 MW to 8 MW.

Site capacity/device capacity differs from generation in terminology. Capacity refers to the very maximum that a device or site can generate under specified ideal conditions. Generation is the amount of electricity the device has produced over a specified time period (What is the difference between electricity generation capacity and electricity generation? – FAQ – U.S. Energy Information Administration (EIA), n.d.). It is impossible for the generation of a device to exceed its capacity, and very often the generation value will not be matching the site capacity due to realistic conditions differing from the ideal conditions in which capacity was specified.

4.0 – Theoretical Background

Waves can be defined in terms of wavelength, wave speed (also known as celerity), and wave height. These properties are dependent on the environment in which the body of water is situated, such as depth of the water, as well as wind speed.

The direction of the wave must also be considered when analysing wave mechanics, as this can have a dramatic effect on the output of some devices. Logically thinking about a device which operates based on the 2-dimensional motion of waves, if the angle of the incoming wave is not perpendicular to the paddle face, then surely the output of the device will be less than the optimal output?

Firstly, the difference between energy and power should be stated, as these can and have been used interchangeably by those who do not know the definitions of either. Energy is a systems capacity to “do work”, with the units of Joules. Power, on the other hand, is defined as the rate at which energy is transferred from the system, i.e. how much energy is transferred over a specified time period, with the units being Watts, equivalent to Joules-per-second (Energy vs Power – Difference and Comparison | Diffen, n.d.).

When one looks at renewable sources, another term that is commonplace is the “kilowatt-hour (kWh)”. A kilowatt-hour is a unit of energy, not power. It can be confusing as kilowatts are power units, yet as stated above, power is a rate (joules-per-second). Therefore, once multiplied by time, the kilowatt-hour becomes a unit of energy. It simply states how much energy would be used or produced if a device was to be in operation for an hour (What is a kWh? kW and kWh explained | OVO Energy, n.d.).

4.1 – Wavelength

It is accepted that wave energy and power can be calculated from properties of the site. Published data that has been captured on site often measures wave heights (both maximum and average), wave periods, direction of the wave, depth of water at the site, and sometimes water temperature. The basic calculations of a wave provide outputs of energy and power. Often the first step when finding these values, the wavelength (λ) is required.

  λ=gT22π (1)

Equation (1) (this equation will be referred to as Eq. (1) from here on, and this format will be used for following equations) above calculates the wavelength of wave situated in deep water using wave period (T), and acceleration due to gravity (g) – which will be assumed to be 9.81ms-2 throughout this dissertation. This equation is to be used when the water is considered “deep” – when the depth of the water is greater than half the wavelength.

However, for devices that are placed closer to shore, where the criterion of deep water in not met, the approaching waves begin to “feel” the effect of the seabed, causing resistive forces. These forces tend to reduce the wavelength, and hence Eq. (2) must be used to find a value.

  λ=gT22πtanh⁡(kd) (2)

This equation is often an iterative process, as while depth to the seafloor (d) can be easily measured, the wavenumber (k) is a function of wavelength – which is the desired outcome (Eq. (3)).

  k=2πλ (3)

4.2 – Wave Energy and Power

Once wavelength is determined, the energy and power of the wave can be calculated. The total mechanical energy of a wave per unit width of crest (E) is given by the sum of its kinetic energy and potential energy (Eq. (4)).

  E=Ek+Ep (4)

It should be noted that the values of energy, kinetic energy (Ek) and potential energy (Ep) are all values that represent energy per unit of wave width, and for one wavelength. Kinetic energy is calculated by the integration of differential elements multiplied by the horizontal and vertical particle velocities (u and w) squared over one whole wave length and the entirety of the depth to the seabed (Sorenson, 2006) (Eq. (5)), which when integrated once the velocity values have been entered simplifies down to Eq. (6). Again, please note that the coordinate system of these calculations dictates that x is positive in the direction of which the waves propagate, and z is positive in the vertical axis rising upwards perpendicular to the static water level. Here, “H” is the height of the wave.

  Ek=∫0λ∫-d012ρdxdz(u2+w2) (5)
  Ek=ρgH2λ16 (6)

Potential energy is derived from the subtraction of the potential energy of the mass of static water from the potential energy of the wave form (Eq. (7)). The surface elevation is denoted as a function of x where the time (t) is set to zero, this therefore simplifies η (which is a function of both x and t) and hence further simplifies the potential energy equation down to Eq. (8) (Sorenson, 2006).

  Ep=∫0Lρgd+ηd+η2dx-ρgλd(d2) (7)
  Ep=ρgH2λ16 (8)

Eq. (6) is notably the same as Eq. (8), therefore the total mechanical energy per unit width for one wavelength, Eq. (4), can be displayed as:

  E=Ek+Ep=ρgH2λ8 (9)

As both kinetic and potential energy vary at different positions along a wave crest, it is worth considering the average energy per unit of surface area (

E̅) in the equation below (Sorenson, 2006).

  E̅=Eλ=ρgH28 (10)

As stated earlier, power is the rate at which energy is transferred, and wave power is the measure of wave energy per unit time when transmitted in the direction of wave propagation, and this is what a wave power device depends on. The power induced by a wave (P) is from the change in dynamic pressure, and horizontal components in particle velocity (Sorenson, 2006).

  P=ρgH2λ16T1+2kdsinh2kd=E2T(1+2kdsinh2kd) (11)

This equation can be simplified in notation into the equations below (Eq. (12) and Eq. (13)), and this notated form has been utilized in the methodology of this dissertation, where “n” is a constant.

  n=12(1+2kdsinh2kd) (12)
  P=nET (13)

As “n” is a function of depth, its value tends to increase as the water gets shallower, from around 0.5 to a maximum value of 1. Due to most wave energy generation devices being placed offshore, the depth to the seabed is high, meaning the value of “n” is closer to 0.5 (Sorenson, 2006). These devices are usually placed in a fixed geographical location, so the effects of distance between wave crests altering as one approaches the shore due to coastal actions, for example shoaling, are ignored for the purposes of this dissertation.

5.0 – Analyses of the Wave Power Resource

The calculated aspects of this dissertation rely on open-source data regarding the wave properties of sites where wave energy devices are deployed, as well as the generous nature of the companies which develop such devices, of which have wished to remain anonymous given the sensitive nature of the information. For the main example, the site data was taken from the historical sources provided by Wave Hub, and provided by a developer whom is testing a wave energy device at Wave Hub. Wave Hub is a site located off the north coast of Devon where clients can test and monitor the outputs and efficiency of their technology (Wave energy and tidal energy test site in Cornwall, n.d.).

The site data from Wave Hub that applies specifically to the outputs given from the device, that shall be named “Point Absorber 1 (PA1)” from here on for the purposes on anonymity, is of half hourly readings starting on 19/12/2015 at 12:30pm through to 16/01/2016 at 12:30pm, therefore spanning 29 days’ worth of measurements. Being a point absorber, PA1 converts wave power into output by the three-dimensional motion of a floating buoy-like structure mechanically connected to a base moored to the sea floor (Wave devices: EMEC: European Marine Energy Centre, 2016). This ability to transfer wave energy from three-dimensional motion means the direction of the wave has a decreased effect on power output compared to that of attenuators and oscillating wave surge converters. Data collected from the site consists of average wave heights (H), maximum wave heights (Hmax), peak wave periods (TP), mean wave periods (Tz), peak wave direction, and the temperature of the sea.

Large portions of this dissertation will focus on the data provided by Wave Hub and the company working on the PA1 device, and its comparisons to other renewables sectors. Output data from devices has proven hard to acquire, as due to the relatively new nature of recent wave power technologies companies are often reluctant to share data that could prove to be sensitive and commercially damaging if discovered by rival firms. Despite this, vast amounts of deductions can be gleaned from what few sources of data have been provided for research purposes within this dissertation.

5.1 – Power Analyses of Wave Hub

Firstly, wavelength was to be calculated from the data provided. The location at which PA1 was fixed has a constant depth of around 50 metres, which is safe to assume is deep water, so Eq. (1) provided a wavelength value in metres. Eq. (1) was to be favoured over use of Eq. (2) here because the wavelength values produced by Eq. (1) corresponded to the statement that water is deep when the depth is greater than half of the wavelength.

However, for confirmation Eq. (2) was also used, but in an iterative manner due to the inclusion of wavenumber “k” and its relationship to wavelength (stated in Eq. (3)), and the values output were identical to 4 decimal places. This is due to the fact that as the value of depth increases, the value of “tanh(kd)” in Eq. (2) approaches 1. The time period value taken to use in these equations was the mean wave period “Tz”, in order to provide an average across the half hourly intervals.

Once average wavelength values for each interval were calculated from the given site data, kinetic energy, potential energy, total energy per unit width per wavelength, and wave power per wavelength could be calculated using Eq. (6, 8, 9 and 11). Of course, the values of most interest, being energy and power, are average values for all waves across that half hourly period. Therefore, to find the total energy and total power of the wave for that time, one would have to know how many waves the data was collected from during each half hour average.

To work out the number of waves in each half hour slot, an equation was derived. Taking the mean wave period Tz, which has the units of seconds, the desired value can be calculated. Multiplying thirty minutes into the units of seconds, and then dividing by the mean wave period gives an estimated value of the number of waves within each half hourly slot (Eq. (14)).

  Number of waves per half hour=30×60Tz (14)

Of course, Eq. (14) is based entirely from the value of mean wave period, which is an average across each half hourly interval for the site data provided by Wave Hub. Using this value implies that the spread of the wave periods may not be accounted for in the output value of number of wavelengths. For instance, the mean wave period on 16/01/2016 at 11:00am was 5.1 seconds. Yet the peak wave period value for this interval was 7.1 seconds, a whole 2 seconds longer than the average, which might not seem like a lot but the peak wave period value is 39% larger than the mean. Hence taking the mean wave period in equation 14 assumes that all the waves across the entirety of that half hour at 11:00am had a period of 5.1 seconds, therefore the number of waves should be taken as a relatively accurate estimation.

Having a known number of waves then meant that it was possible to multiply these values by the energy per wavelength and power per wavelength for each interval, providing an output value that equates to the total energy of the waves throughout each half hourly interval (EInterval), and the total power of the waves throughout each half hourly interval (PInterval) (Eq. (15) and Eq. (16)).

  EInterval=E×Number of waves per half hour (15)
  PInterval=P×Number of waves per half hour (16)

Interval values of energy and power then opened the possibility of a comparison between what the obtainable power resource of each wave was to what was being harnessed by the device in operation at Wave Hub. Of course, it would be safe to assume that the entire resource was not being utilised at the time for a number of reasons, one major reason being that Wave Hub is a testing site, so large arrays of wave devices would not be installed there with the goal of consistently extracting the maximum amount of power as possible, but with the goal of testing if the device works, if it reaches its quoted power output, and measuring the efficiency of the device. Nevertheless, deductions can be made from comparing the Wave Hub site data to the output data of PA1.

One such comparison that is made is between the power output of device PA1 within each half hourly wave interval and the theoretical power that the wave possesses. Of course, even within high power wave climates, it would be safe to assume that the device would not be operating at the maximum quoted power output it was designed for, mainly due to the fact that PA1 is placed in a natural environment where the variables that dictate the power output cannot be controlled, unlike in a laboratory environment.

Figure 4 below shows the comparison between the theoretical wave power at half hourly intervals, and the device power output of PA1 within the same time period. From this graph, one can easily deduce that the increase in wave power leads to an increase in output due to the correlation of peaks and troughs occurring at the same time periods.

Figure 4 also reveals a limitation of device PA1. Between the dates, 01/01/2016 and 06/01/2016 the theoretical wave power reaches a maximum peak of around 9000kW. In the same period, and in the same position of the wave power spike, the output power of the device also peaked. However, device PA1 appears to plateau on output at around 230 kW, being unable to achieve a larger power output value that would correlate with the wave power spike. This plateau implies that in the wave condition, device PA1 is operating close to its maximum power output.

Figure 4 – A graph to show the comparison of theoretical wave power and device PA1 output power

PA1 is shown to be responsive to relatively rapid changes in wave power. All peaks and troughs from the device power output correspond to the theoretical power of the wave, implying a short time lag between converting power from the wave into usable output power. If wave power is to maintain a growth in the renewables sector, optimising power output from the environment which a device is situated in and a rapid response time to convert power from said environment is an ideal characteristic.

5.1.1 – Power Calculations of PA1 Wave Device

How a wave energy device converts wave power into electricity is of utmost importance, and, more specifically, how the power output is calculated based off the external conditions. In conjunction with the site data provided regarding Wave Hub, power outputs for each of those half hourly site conditions were also provided, as well as the equation used to calculate it.

It appears as though the equation for how the output power of the device, Pdevice, is calculated is mainly dependant on the height of the wave, as shown below in Eq. (17). The function limits the wave height input to a maximum of 6 metres, and the maximum power output to 170kW. Hence, the equation below only applies to waves of less than 6 metres, so if the wave height exceeded this value, the output would default to 170kW. However, this must be a limitation of the device in how it deals with large changes in wave height, as in lower wave heights, greater power outputs have been produced, as seen in Table 1 below using data from site recordings.

  Pdevice=41.415×H-14.467 (17)

Table 1 – A selection of wave environments to show how the output power of PA1 varies

Wave Height (m) Wave Period (s) Wave Energy (kJ) Wave Power (kW) PA1 Output Power (kW)
6 9 1,129,665 66,876 170.00
5 10 855,755 48,376 192.61
4 7 395,410 28,369 151.19

This equation is a simplistic straight-line-graph equation, of format “y=mx+c”, and must be assumed that the constant value of 41.415 which H is multiplied by, and the subsequent value of -14.467 that is taken from it are derived from the environmental factors, including wave period. Although the constants have been determined by the designers of the PA1 device, the above equation allows determination of how PA1 would behave in other wave environments around the UK, as will be discussed later in this section of the dissertation.

For the case of the PA1 device then, although a larger value of wave height leads to greater values of power output, the limitations of the device render it unresponsive to waves of heights larger than 6 metres, meaning that potential electrical gain is being wasted. For wave energy devices of the future to flourish, the power output of devices should mirror that of the environment, e.g. a high-power wave should lead to a large power output, not being bound by a value which limits its output.

5.1.2 – Wave Environment at Wave Hub

Having been provided site data regarding the environment at Wave Hub, it is possible to gain an insight into the typical wave conditions a device would experience if deployed at the test site. The data provided included wave periods and wave heights, and plotting the frequency of individual wave conditions would allow an identification of the most common wave scenarios. Gathering wave data is done before the design of a wave energy device, and knowledge of site conditions is of paramount importance if a wave power device is to be deployed effectively, ideally working to the greatest efficiency it could achieve. Table 3 below show the frequency of individual wave climate scenarios at Wave Hub.

As Table 3 shows, from a colour based scheme where green represent the least frequent events and red the higher frequency events, the wave period and wave height combination of 9 seconds and 6 metres respectively occurred most frequently. The Wave Hub environment at Cornwall tends to peak towards middling wave periods, in the 7 to 10 seconds’ region, and medium to higher wave height values from 3.5 up to the 6 metres area. Placing the most common wave event into Eq. (9) and Eq. (11) to find out the wave energy and wave power, after having discovered wavelength using Eq. (2), for a half hour period, the values as such are shown below in Table 2.

Table 2 – Wave energy and power for a common wave event over a half hourly period assuming wave height and period to be constant throughout

Wave Height (m) Wave Period (s) Wavelength (m) Energy (kJ) Power (kW)
6 9 124.83 1,129,665 66,876

Table 3 – A frequency table showing the number of times events of a certain wave height and wave period occurred

  Wave Period (s)

Wave Height (m)

  4 5 6 7 8 9 10 11 12
0.5 15 11 9 7 6 5 5 4 4
1 56 45 37 31 27 24 21 19 17
1.5 98 78 64 55 48 42 38 34 31
2 139 111 92 79 69 61 54 49 45
2.5 181 144 120 102 89 79 71 64 59
3   177 148 126 110 98 88 80 73
3.5     175 150 131 116 104 95 87
4       174 152 135 121 110 100
4.5       197 172 153 138 125 114
5         193 172 154 140 128
5.5           190 171 155 142
6           208 187 170 156

Comparing the power of the wave, 66,876kW, to the values shown on Figure 4 (made visible by the horizontal black line), it is obvious that this power output is in the upper bounds of what was present during the period that these values were calculated from. Within this wave power bound, using the corresponding line on the same figure, the output power of the device PA1 would be nearing the peak output levels shown by the plateauing sections of its output power line.

In contrast to the most common event, an analysis must still be made of the events which occur the least frequently, as even though these events happened few and far between, they still took place, and the device PA1 would still be subject to its conditions. As shown by Table 3, these events are the low wave height and high wave period environments of 0.5 metres and 11/12 second periods respectively. It is believed that large wave heights and long wave periods imply that a wave has a high power, as will be analysed further in this dissertation, so how would having a low wave height yet high period affect the power of the wave?

Table 4 below shows the conditions for these least frequent events. These events are under the same assumptions that Table 2 was subject to; where the power and energy values of the wave are the total values throughout a half hour time period where the stated conditions would be constant. Comparing the wave power values in Tables 4 and 2 reveals interesting snippets of information. Although the wave periods are higher in these low frequency events than in the high probability events, the wave height values are significantly less, and this decrease in wave height has had a drastic effect on the wave power.

Table 4 – Wave energy and power for infrequent wave events over a half hourly period assuming wave height and period to be constant throughout

Wave Height (m) Wave Period (s) Wavelength (m) Energy (kJ) Power (kW)
0.5 11 178.13 9159 503
0.5 12 204.83 9655 517

Such is the scale of the effect that the decrease in wave height has on the power of the wave that by decreasing the wave height by 5.5 metres, the power has decreased by a factor of 100. This decrease in wave power can be viewed on Figure 4, by the lowest red horizontal line, representing the scenario with a wave height of 0.5 metres and wave period of 11 seconds.

This low probability environment has been investigated in order to gain an understanding of how the environmental factors would affect the power of the wave, after all, it is the power of the wave that drives the generation of electricity from wave power devices such as PA1. Even though the data provided shows that these low power wave scenarios are rare, they have occurred, and hence it is worth seeing how the wave power would be affected in these climates.

However, using this data regarding frequency of events may not be a true representative of the year-round wave environment at Wave Hub. The data provided is from winter months, where the wave environment would be more severe. Higher wave heights are expected within these months, as well as a greater variation in wave heights, hence the shown values may be skewed. For a year-round time period, the power outputs in certain months may be lower than the values shown in Figure 4, due to the differing conditions from summer and winter.

For the measured time period, although the most common individual event was a wave period of 9 seconds and wave height of 6 metres, when the information is broken down into the individual dependant variables, an interesting discovery can be made in regard to which group of events are actually the most common, and hence most likely to occur, as shown in Figure 5 and Figure 6 below.

Figure 5 – Visual representation of wave period occurrences at Wave Hub

From analyses of the environmental data at Wave Hub site, it would seem that the PA1 device would thrive in this location. The wave height rarely exceeds 6 metres, yet the waves tend to be most commonly found nearing that value of wave height. Hence, the power output would be operating at close to its maximum output at this site, as deducted from both the equation and analyses in section 5.1.1 (Eq. (17)). However, as this site does not represent the entire wave environment throughout the United Kingdom, determining whether this device or devices that would operate similar to PA1 are a suitable and efficient choice shall be analyses in a latter section of this dissertation.

Figure 6 – Visual representation of wave height occurrences at Wave Hub

Figure 5 clearly shows that the most common wave period was 9 seconds, which is aligned to the most common individual event, and that higher period waves, such 11 seconds, occurred in some cases twice as much as the lower period waves, such as 5 seconds. By rearranging Eq. (11), one can form a relationship with wave power which determines if lower wave periods or higher wave periods are better environments to deploy wave power generation devices.

  P=ρgH2λ16T1+2kdsinh2kd (11)

Eq. (11) already reveals that the power of the wave, P, is greatly influenced by the wave period, and also the wavenumber “k”. The wavenumber is also dependant on the period of the wave, as is wavelength, as shown in Eq. (1) and Eq. (3). By substituting the entire equations for wavelength and wavenumber into the energy equation (Eq. (9)) and then substituting that into Eq. (13), the following relationships are formed.


Hence the proportional relationship Eq. (18) is formed:

  P∝T (18)

This relationship implies that the power of a wave is proportional to the wave period. Therefore, a higher wave period will mean the presence of a longer wavelength, a lower wavenumber, and a greater energy and power of the wave. Hence, the higher values of wave period, which tend to be more common as shown in Figure 5, are more suitable to place the PA1 wave device. The Wave Hub environment can therefore be assumed to be beneficial to the PA1 device due to the higher probability of high wave periods.

The contrast between Figure 5 and Figure 6 is that some of the occurrences of different wave heights happened almost the same number of times, whereas the chart showing wave periods has a clear wave period which occurred most frequently. The wave heights of 2.5 metres and 4.5 metres had happened almost the same number of times, and only wave heights of under 1.5 metres tend to be vastly less likely to occur.

Predicting wave heights from previous events such as Figure 6 presents would hence prove to be difficult due to the even manner in which the range of waves height occurrences are present. Using a similar method to how Eq. (18) above was derived, one can formulate a relationship which reveals how the power of a wave is dependent on the wave height. From simply looking at Eq. (11), it is easy to see how wave height affects wave power, as shown by the relationship below, Eq. (19).

  P∝H2 (19)

The above relationship reveals that changes in wave height appear to have a greater effect on the power of a wave than the wave period. An increase in wave height would yield an increase in wave energy and an increase in wave power, both by a squared factor. Therefore, the tendency of the Wave Hub environment to have a greater probability of large waves occurring is beneficial to the PA1 device, and potentially most other wave devices, due to its ability to generate electricity close to its maximum output levels.

5.1.3 – Device Behaviour at Other Locations

The European Marine Energy Centre (EMEC) is a testing site for wave and tidal energy converters, working towards similar goals as the Wave Hub sites (ABOUT US : EMEC, 2017). EMEC is based in the Orkney Islands, in the very most northern reaches of the UK. Figure (1) that is contained within the literature review shows that the power of the waves tends to be greater within the Orkney region than down in Cornwall, where Wave Hub is located. Through contacting EMEC, they have provided hourly site data from the past ten years for the purposes of this dissertation, as shown in Appendix 1A and Appendix 1B.

This site data is monitoring wave heights and wave periods every hour from their Orkney site, and has a larger number of recordings than the Wave Hub site data found in Table 3. The site-specific data for the Orkney site contains a much larger collection of wave periods, ranging from 2 seconds to 19.5 seconds, and the waves recorded have also been greater in height, with the largest wave recorded from the 10-year site data being at 11.5 metres, nearly double the highest wave found at Wave Hub.

It was stated earlier in this dissertation that the PA1 device would be more suited to environments where the wave height and period are large, and it was also discovered in section 5.1.1 that the limitations of the device mean that it would thrive in waves that have a height of roughly 6 metres. The wave environment in the Orkneys is much more varied than that of Wave Hub at first glance, and Table 5 below shows the comparisons of the power of the waves per wavelength during the most common, middle frequency and infrequent events that took place.

Table 5 – A comparison of wave events of varying frequency at EMEC and Wave Hub sites

  Frequency Wave Height (m) Wave Period (s) Energy Per Wavelength (J) Power Per Wavelength (W)
EMEC High 0.75 8.25 75132 4699
Medium 0.75 8.75 84514 5094
Low 8.25 11.75 18440626 1033439
Wave Hub High 6.00 9.00 5722418 339884
Medium 2.50 7.00 600991 43119
Low 0.50 11.00 59363 3344

From looking comparing the site data found in appendix 1A, appendix 1B, Table 3 and Table 5 one can clearly deduce that the wave environment at EMEC tends to lower wave heights over a vast range of wave periods, compared to the tendency for wave heights to be around 6 metres at Wave Hub. The Orkney site’s trend towards to the lower wave heights (usually not much greater than 3 metres) implies that the type of device that PA1 is may not be suitable for this site.

Table 5 shows that the high frequency events (where frequency is the number of times the wave event occurred in this case, not the reciprocal of wave period) at EMEC yield a low power wave, and vice versa, whereas the higher frequency events at Wave Hub provide a relatively higher wave power. For PA1 to thrive, it must be in environments where the wave height tends to 6 metres, not vastly lower or greater, hence Table 5 shows that PA1 could prove unsuitable for the Orkney site due the wave power devices’ lack of adaptability.

However, although the EMEC site tends to low wave height, there are occasions when the wave height is massive, reaching heights of up to 11.5 metres on rare incidents. If the wave height is greater than 6 metres, then PA1 would not be operating to its maximum potential. When counting the number of events that exceed 6 metres and comparing them to the number of recorded wave environments over the 10-year period, it is possible to roughly work out how often the PA1 device would not be operating to extract as much of the power of the wave as possible, based from Eq. (17).

A grand total of 87670 wave events were recorded for the EMEC site data, of which 1430 events consisted of waves of height 6 metres or greater. The implications of this are as follows; if the device PA1 was placed in the EMEC environment throughout the 10 years of wave data collection, then for a meagre 1.6% of the time it would not have been outputting power gathered from the wave to its maximum potential. Therefore, even though the EMEC site tends to lower wave heights than Wave Hub, for 98.4% of the time the PA1 device would have been generating as much electricity as it possibly could have for each wave height, implying that this type of device may in fact be well suited to such a location as the Orkneys, despite initial impressions.

However, in terms of power output, it would seem that sites akin to Wave Hub would be more idealistic for deployment around the UK. When comparing the power output during the most frequent events, one gets the results shown below in Table 6.

Table 6 – A comparison of device output power during the most common wave event at each test site

Site Wave Height (m) Wave Period (s) Wavelength (m) Output Power (W)
EMEC 0.75 8.25 106 16.6
Wave Hub 6.00 9.00 126 234.0

As shown in the table above, the high frequency of the wave event at Wave Hub leads to almost 15 times the power output than the high frequency event found at EMEC. This low power output at the EMEC site leads to a conclusion that deploying a device similar to PA1 at said location would simply not be cost efficient, and the lead time on repayment for the device at such a location would most likely render it undeployable. Hence, it is of utmost importance for in depth site analysis to be undertaken before deployment of a wave energy device, in order to maximise the electrical generation of the device, and hence making it a possible cost effective and efficient solution to the ongoing energy demands of the UK.

5.1.4 – Capacity Factor

From testing, a singular PA1 device is quoted as having a mean power output of 62kW/hour, assuming a 37% capacity factor, as specified in the provided data. A capacity factor is defined as the average generated power of a device in kW/hour divided by the rated peak power Eq. (20) (Andrew, What does the capacity factor of wind mean?, 2014).

  Capacity Factor (%)=Average Generated Power (kWhour)Rated Peak Power (kWhour) (20)

Using the given capacity factor, it is easily calculated that the rated peak power output of device PA1 is 168kW/hour. Summing all the values of device power output for each half hourly interval, then dividing by the number of half hourly intervals produces an average generated power value of 142.4kW/hour. Therefore, as theorised from taking observations from Figure 4, device PA1 is operating close to its rated peak power, so close in fact that it is producing only 25.6kW/hour less that the peak power. Using equation 20 produces a capacity factor as seen below.

Theoretical Capacity Factor=142.4kW/hour168kW/hour=84.8%

A theoretical capacity factor of 84.8% appears to be a fantastic value, especially when compared to the quoted capacity factor of 37%. However, capacity factor is not calculated, but rather chosen as a design decision for each device (Andrew, What does the capacity factor of wind mean?, 2014). Capacity factors are chosen based upon balanced decisions to be made between capital expenditures, operating expenditures, ease of maintenance, unexpected occurrences during a devices lifetime, power output, the tariff for generated electricity, and many more factors. Offshore wind farms around the UK are currently operating on capacity factors ranging from 28.6% to 45% (Andrew, UK Offshore Wind Capacity Factors, 2017), and when the capacity factor of the PA1 device is compared to this, one can see that 37% is in the upper regions of capacity factors to the comparable renewables sector. Therefore for an operational value such as capacity factor, wave power appears to be on par with wind.

5.2 – Economic Viability of PA1 Device

Included within the data provided by Wave Hub and the PA1 device was basic estimations of various costs throughout the lifetime of a singular device, and how these costs compare to when more than one PA1 device is installed on site. Such data allows for initial calculations in judging the “lead time” one or more deployed PA1 devices would have when commissioned. The data provided shows that at brackets of increasing number of devices, certain costs will be decreased, as seen in Table 7 below. Lead time refers to the length of time taken for the value of electricity produced to equal the initial and running costs of the devices.

Table 7 – Table showing the brackets at which costs alter for the PA1 device

No° of Devices CAPEX (£) CAPEX per device (£) Annual OPEX (£) Annual OPEX per device (£)
1 850,000 850,000 150,000 150,000
3 1,800,000 600,000 200,000 66,667
5 2,500,000 500,000 300,000 60,000
60 24,000,000 400,000 1,640,000 27,333

As shown in Table 7, both the capital expenditure (CAPEX) and operating expenditure (OPEX) decrease as the number of devices placed in operation on the same site increase. The capital expenditure is a one-off payment which covers the actual purchasing of the devices, installation, and other initial costs, whilst the operating expenditure accounts for annual ongoing costs of maintenance, labour, and other potential services. Therefore, in order to be economically viable, the value of the electricity produced has to be greater than that of the operating expenditures for any profit to be made. However, the designers of PA1 have estimated that the device only has a lifetime of 15 years, and this has consequences on profitability.

With knowledge of the initial costs and operating costs, it is possible to calculate the lead time of a device, and hence predict how many devices must be installed for this particular model to prove to be economically worthwhile. By equating the sum of the capital expenditure and operating expenditure over an “

x” number of years to the annual revenue generated (ANREV) over the same number of years, one can easily calculate the time it would take for a device to start producing a profit Eq. (21).


Figure 7 – A comparison of capital expenditure, lifetime operating expenditures, and lifetime revenue generated by the PA1 device

Figure 7 above compares lifetime and capital costs to lifetime revenues. The revenue from the device is based from the mean output power provided with the data from PA1, being 62 kW/hr, and a “strike-price” of £150 per MWhr, with the term “strike-price” referring to the fixed price which the generated electricity is sold at when fed into the national grid. From the graph, it is easily determined that a single device would simply not generate the required amount of electricity in order to break even and start producing a profit during the fifteen-year lifespan of the PA1 device.

Using Eq. (21), one can calculate how long it would take for the lead time to be reached, and hence start making profit, shown in Figure 8 below. This graph reveals the lead time if the device were to be fully functional and in operation indefinitely, regardless of the fifteen-year lifespan.

Figure 8 – A graphical representation of how the number of devices affects lead time

Figure 8 has therefore revealed that one would require a minimum of 8 devices in place for the lead time to fall under the 15-year lifespan cut off point. The graph does not show data values for scenarios when a maximum of only 2 devices are in place, due to the fact that Eq. (21) produced negative values, implying that if device PA1 could in theory generate electricity indefinitely, then the operating costs would always be higher than the generated revenue, and never produce a profit. This scenario is also revealed in Figure 7, where lifetime OPEX is greater than lifetime revenue for 2 devices. The combination of these two graphs prove that a large array of at last 8 PA1 devices must be installed to produce any profit.

Referring again to Figure 7, the trendlines for the initial capital expenditure is very similar to that of the operating expenditure for the whole lifetime of the device. Lower numbers of devices have lower CAPEX prices compared to the lifetime OPEX, and higher number of devices have larger total CAPEX values than the corresponding OPEX values. Whilst the high operating cost can be dealt with gradually by the revenue generated over the period that the PA1 devices functioning, the initial capital funds required to kickstart a journey into this renewables sector may be off-putting. Figure 9 below shows the significance of the CAPEX with each device, and the percentage of the cost that this value is over the costs that are induced throughout the entirety of the PA1’s device lifetime.

Figure 9 – A visual representation of how the number of devices affects the percentage that initial financial outlay makes up of total lifetime cost

As Figure 9 clearly shows, the general trend appears to be that as number of devices increases, the higher the initial financial outlay percentage of total cost. The segment of number of devices ranging from 1 to 5 bucks this trend, but as stated earlier the PA1 device seems to be only economically viable for a minimum of 8 installed devices. In the upper bounds of this figure, the capital expenditure can account for as much as 55% of the costs throughout the 15 years of operation, and even with only 8 devices in place, the financial outlay required would still be large (see Table 8).

Table 8 – Lifetime costs and profits over lifetime for varied numbers of devices

No of Devices CAPEX (£) Lifetime OPEX (£) Total Cost (£) Profit over Lifetime (£)
8 4,000,000 5,596,380 9,596,380 179,780
16 8,000,000 8,520,060 16,520,060 3,032,260
24 12,000,000 11,443,740 23,443,740 5,884,740
32 16,000,000 14,367,420 30,367,420 8,737,220
40 20,000,000 17,291,100 37,291,100 11,589,700
60 24,000,000 24,600,000 48,600,000 24,721,200

For 8 devices to be installed, the minimum upfront capital expenditure is 4 million pounds. Wave power at this moment in time is always going to difficult to access and utilize for multitudes of people, for numerous reasons including size of device and how far they have to be placed offshore, but the enormity of this CAPEX seems to place it even further beyond the reaches of those who do not possess vast quantities of wealth.

A great benefit of certain sources of renewable energy is that almost anyone can be involved with them, and comparisons must be made with wave power and those of more easily accessible renewable energy sources. Whilst electrical gains from wind sources can be achieved easily on land, the stereotypical low capital cost renewable energy is solar power. Both sources can be accessed through government grants and feed-in tariffs.

The feed-in tariff is a government scheme created with the ideal of promoting small to medium scale renewable energy sources and development, where payments are made to the owner in exchange for generated electricity from their possessed renewable source (Feed-In Tariff (FIT) rates, 2017). The size of these payments is dependent on the capacity of the source, what the source is, when it is or was installed, and the energy efficiency of the home (Feed-in tariffs: get money for generating your own electricity, 2017). The feed-in tariff is a stranger to wave power, as no funding is currently granted to small-to-medium scale wave power, simply because wave power devices do not yet exist in abundance; proving that wave power is often the victim of its own large and unobtainable nature. This tariff is a privilege granted solely to wind, solar, onshore hydropower, and combined heat and power (Feed-In Tariff (FIT) rates, 2017).

Solar panels can be placed onto a homeowner’s roof for an enormously less expensive fee ranging from around £4000 to £6000, producing around 3kW of electricity (Solar Panels Cost, 2017). The capital expenditure is vastly less than that of wave power, the maintenance costs are minimal due to the small size and simplistic nature of domestic solar panels, and the estimated life span exceeds twenty years (Solar Panels Cost, 2017). Interestingly, the lead time on domestic solar panels is very much similar to that of the PA1 wave energy device, despite the vast difference in capacity size, as shown in Table 9 below.

Table 9 – Profit generated from a 4kW domestic solar panel scheme in association with the feed-in tariff (Solar Panels Cost, 2017)

Years in Operation Profit (£)
1 -5,984
5 -3,980
10 -1,960
15 60
20 2,080

At around roughly 15 years of operation, the 4kW domestic solar panel begins to produce profit, a similar lead time to that of 8 PA1 wave energy devices. Of course, Figure 8 also reveals that as you increase the number of devices, the lead time decreases, but the minimum period it will take to start producing pure profit is still around 7 years, a significant amount of time.

One could say that this a poor comparison to make. The capacity sizes of PA1 and a 4kW domestic solar panel are vastly different, the accessibility of the products is not similar at all, and the popularity of solar power in comparison to wave power is again dissimilar. However, wave power can be seen as a comparably new area of research to delve into for generating electricity. Over the last few years, the price of solar panels has decreased by over 70% (Solar Panels Cost, 2017), increasing its availability to the general public, and hence causing an increase in the number of operating domestic solar panels, contributing to the rise of renewable energy generation within the UK.

Wave Hub is a testing site for wave power generation devices, and many of the products that are in operation there are in a phase of development. This development is experiencing an acceleration, as there are minimal devices generating electricity, and the limited devices to select from driving demand. With this continued development, technologies of increasing efficiency and greater value for money will be developed.

As PA1 is a brand-new wave power device, it could be viewed as having a “premium” price; being sold at a large price due to the new nature of wave power technologies in comparison to other renewable sources. The same statement could be made about all current wave technologies, with the high initial cost often putting off clients and hence a contributing factor as to why wave power generation is considerably less popular to its renewable counterparts.

If wave power generation were to continue its increase in development and operation, fuelled by the ever-rising requirement for renewable source generated electricity as opposed to fossil fuels, then one could safely estimate that the capital expenditure required to be involved in wave power would decrease significantly over the coming years.

6.0 – Conclusion

This dissertation set out with the goal of evaluating the current climate relating to the wave energy resource, through methods of analysis of power generation, and financial viability. From this analysis, the outstanding message that is being transmitted regarding wave energy is that there are currently too many factors that weigh in opposition of wave power generation.

The current price of wave energy is simply too high when compared to that of offshore wind farms and other renewable sources of energy around the United Kingdom, and even worldwide. As with all new technologies, there is a premium placed over the pricing, and due to the relatively new nature of wave energy when compared to long-standing sources of renewable electrical generation, wave energy possesses this high pricing. This has therefore driven potential investors to choose alternative renewable sources, with offshore wind power being more popular than ever.

However, targets of reaching certain percentages of electrical generation via renewable sources of energy have been put in place both domestically and worldwide. Whilst the United Kingdom has already surpassed its target for renewable generation, the sector is going to experience a continued growth. Such a growth will affect all renewable sources of generation, including wave energy. Whilst the sector continues to expand, wave energy will gain increasing investment, and hence wave energy will develop. This development would eventually lead to a decrease in the premium that currently hinders wave energy, and hopefully deployment of wave energy devices will contribute significantly to energy demands worldwide within the coming years, as at this very moment, other sources of renewable energy simply yield more power for a vastly lower cost.

Wave power generation has also proven to be inaccessible to masses of people. Whilst other sources of energy, i.e. solar panels and wind turbines, can be privately owned and financially aided via government schemes, wave power proves to be ungainly due to the large distance the devices must be placed offshore, and the size of the devices means they cannot be “owned” by a homeowner for example, often requiring teams of people for maintenance and deployment. This issue has limited the deployment of wave power generation devices to individuals and companies of large wealth, with the ability to finance and maintain such a vast investment. Whether this issue will be solved and wave energy made to be easily accessible is an issue to be solved with time and ongoing development, as the current wave energy climate does not accommodate for such a market.

Analysing the wave energy resource does not provide any great push in the immediate positive direction of this subsector. Whilst there is no doubt that utilising this resource will one day prove to be vital due to its abundant nature, the output power of current wave energy devices proves to be one of its downfalls. The high cost and low power output drives deployment of alternative methods of capturing renewable energy that could potentially be deployed in the same location, i.e. offshore wind power, hence the high popularity of offshore wind farms, and the presence of very few wave energy farms worldwide. As wave technologies continue to develop and progress, larger power outputs are to be expected in the coming years, and this will inevitably be a great push for the deployment of increasing numbers of wave energy devices.

Although this dissertation has provided some interesting points as to the current wave energy climate, the great majority of its analysis has been regarding one type of device in particular; the PA1 device. This dissertation has been limited by the willingness of wave energy developers to provide information regarding the sites they work at and output information of the devices they are currently testing and deploying, due to the commercially sensitive nature of the data that would be analysed. Whilst the data provided by the designers of the PA1 device has been both helpful and interesting, other sources of information would have made for an improved comparison within the industry and a provided a greater insight into the current wave energy climate.

In conclusion, at the time of writing this dissertation, the reasons why anyone would choose to delve into wave energy do not outweigh those that would point potential investors to alternative sources of renewable energy. However, the new and prosperous nature of this vast resource prompts the need for greater funding, the need for greater development, and the need for greater numbers of wave power output devices, and whilst the current climate may not be desirable for this subsector of renewable energy, the ongoing and increasing demand for energy worldwide will inevitably drive a greater involvement into this exciting new resource. With recent worries regarding climate change and the depletion of fossil fuels, wave energy provides a predictable, reliable source of energy generation in an otherwise hectic sector, and the future benefits greatly outnumber the current hindrances of this up and coming renewable energy.

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Appendix 1A – EMEC Hourly Wave Event Recordings Over 10 Years

Appendix 1B – EMEC Hourly Wave Event Recordings Over 10 Years

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