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Academic Study: Matching Renewable Electricity Generation with Demand: Full Report

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3 Electricity Generation

Wind, waves and tidal-currents have the potential to generate significant amounts of electrical energy. The nature and geographical distribution of the resource needs to be well understood for the successful design and implementation of energy converters. The characteristics of the machines that are likely to be to able to make a major contribution to energy production by the year 2020 must be established.

3.1 Onshore-wind Energy

3.1.1 Resource Characteristics

Wind is the result of the uneven heating of the earth's surface by the sun. Besides the pressure gradient and gravitational forces, the wind is also strongly influenced by the Coriolis force (due to the earth's rotation), the inertia of air and its friction with the earth's surface. Locally, the wind is further modified by topography and coastlines as well as by weather conditions.

The wind-speed varies over time, with seasonal and diurnal patterns. Figure 3.1 shows the wind-speed measurements of a wind turbine on Orkney during the year 2003. In Scotland the wind-speeds in summer are generally lower than in winter. Wind-speed also varies from one year to another, with a ten year period generally being considered to be representative of the local wind climate. Wind blowing across a large land mass is influenced by the daily solar radiation cycle, particularly during summer, creating a rise in wind-speeds around midday. There are also short-term variations or turbulences with timescales from seconds to minutes.

Figure 3.1 Wind-speed measurement at an onshore location

Figure 3.1 Wind-speed measurement at an onshore location.
Location: Burgar Hill, Orkney; 60 m measurement height; 4 hour averages.

The factors that influence wind-speed generally also influence direction. In Scotland the prevailing wind is from the south-west. The statistical variation of wind-speed and direction can be graphically represented by a wind rose (see Map 06). Because of the friction between wind and the earth's surface, the wind-speed increases with height above ground level. For neutral stratification of the atmosphere the profile was approximated by the logarithmic power law taking into account the surface roughness length z0:

formula, (3.1)

where v( z r) is the wind-speed at reference height z r and v( z) the wind-speed at height z. Values for the surface roughness vary from 0.0002 m for a calm open sea, to 1 m for large cities.

3.1.2 Resource Assessment

The most comprehensive estimation of the UK onshore-wind resource was done by Newton & Burch (1992), Burch et al (1992), and Burch & Ravenscroft (1992) using the mesoscale numerical wind-flow model NOABL. A similar approach based on the 'Wind Atlas Analysis and Application Program' WAsP from Risø National Laboratory in Denmark was used for this study. The program extrapolates wind measurements horizontally and vertically to estimate the local wind climate. The models are based on flows in the atmospheric boundary layer and take into account orography, surface roughness, and obstacles. ('Orography' strictly refers to the study or description of mountains, but is used in the context of wind energy to refer to the description of height variation across any area of land.) In order to compute the wind climate in each onshore 1 km2 cell, the study area was first divided into a series of twenty-one overlapping 100 km by 100 km wind simulation areas as shown on Map 06.

OrographyWAsP needs surface elevation maps with height contours. The former were derived from Ordnance Survey Panorama vector tiles. They were assembled into 120 km by 120 km maps; the calculations were carried out for the central 100 km by 100 km region (Map 06). Due to restrictions in computing power, the resolution of height contours had to be increased to 50 m. Horizontally, the contours were allowed to deviate at most 50 m from the Ordnance Survey data. To improve the results of the final analysis, high resolution maps with 10 m horizontal and vertical resolution were used in the 10 km by 10 km area around wind measurement sites.

Surface roughness Using the GIS, surface roughness information for Scotland was derived from the European land cover database CORINE CLC90 which has a resolution of 250 m. Roughness was assigned to each landscape type, with the few 'NO DATA' squares (missing information in the database) set to 0.01m (short grass). An average value was then calculated for each square kilometre, except for areas around wind measurement sites where a resolution of 250 m was retained.

ObstaclesWAsP can take into account the influence of trees or buildings that are near to the meteorological instruments. 360 degree photographic panoramas were sourced for wind measurement sites. These were evaluated along with 1:10,000 OS raster maps to determine the effects of obstacles. As available wind data is already corrected in a rather crude way for these effects, and as these correction factors are not always known for historical datasets, the data was used as delivered by the Met Office with no additional obstacles modelled in WAsP.

Atmospheric data Hourly wind-speed, wind direction, and maximum gust records for 24 meteorological stations across Scotland were purchased from the Met Office. The period of time covered was 1994 through 2003, except for South Uist, Skye Lusa and Port Ellen which have missing records at the beginning. The majority of the record sets (21 out of the 24) were obtained to represent the wind climate within each of the 100 km by 100 km wind simulation areas. The other three records were used for backup. The stations are shown in Table 3.1 and on Map 06. All values are either from measurements at 10 m above ground level (agl) or were corrected to this height. Wind direction is represented from true-north in multiples of ten degrees. Wind-speed and gust data are stored as integer values in knots. The Met Office was not able to provide estimates for the data quality before the purchase. Where data was missing for up to three subsequent hours it was interpolated. For larger gaps it was predicted from one or two neighbouring stations. Some stations, in particular Strathallan, Eskdalemuir, and Dunstaffnage had large numbers of records with zero wind-speed due to sheltered or less sensitive anemometers. These records were recalculated including data from two neighbouring stations.

The met station assigned to each of the twenty-one 100 km by 100 km simulation areas provided the wind source data for modelling (Table 3.1 and Map 06). WAsP was used to calculate the average wind-speed at 80 m height for each square kilometre within a simulation area. Neighbouring areas overlapped by ten kilometres so that scaling factors for each area could be calculated and used to smooth transitions at the boundaries and to improve the overall consistency. As a result, the transitions were reduced to below 3% except between Orkney and Shetland where a higher difference was justified by the differing wind climates.

Area

SW corner Northing (m)

SW corner Easting (m)

Associated Met station

Backup Met station

Scaling factor

1

1,150,000

390,000

Sella Ness

0.926

2

1,060,000

380,000

Lerwick

0.955

3

970,000

300,000

Kirkwall

0.820

4

880,000

80,000

Stornoway

0.983

5

880,000

170,000

Altnaharra

Aultbea

1.056

6

880,000

260,000

Wick

0.959

7

790,000

50,000

South Uist

0.794

8

790,000

140,000

Skye Lusa

0.971

9

790,000

230,000

Kinloss

Aviemore

1.011

10

790,000

320,000

Dyce

0.938

11

700,000

50,000

Tiree

0.811

12

700,000

140,000

Dunstaffnage

Tulloch Bridge

0.967

13

700,000

230,000

Strathallan

Tulloch Bridge

0.971

14

700,000

320,000

Leuchars

1.012

15

610,000

50,000

Port Ellen

0.853

16

610,000

140,000

Machrihanish

0.866

17

610,000

230,000

Salsburgh

0.848

18

610,000

320,000

Charterhall

0.943

19

520,000

140,000

West Freugh

0.908

20

520,000

230,000

Dundrennan

0.942

21

520,000

320,000

Eskdalemuir

0.967

Table 3.1 Onshore wind simulation areas.

The final results were compared to the NOABL dataset which was scaled from 45 m to 80 m height using roughness information. Overall the initial results of the WAsP calculations were about 5% higher than those of the NOABL studies referred to above. This difference is consistent with the findings of Halliday et al (1995). Comparison of the results with wind and production data from operational wind turbines in the Shetland, Orkney and Borders areas led to the adoption of the final scaling factors above which also compensate for WAsP's resource overestimation in mountainous terrain. Figure 3.2 and Map 06 show the calculated average wind speeds at 80 m agl across Scotland for 1994 through 2003. According to the DTI (2004b), wind speeds during the years 2000 to 2003 were observed to be lower than the long-term average. Note that wind speeds in the 'low' category for Scotland in Figure 3.2 are still higher than those at many Central European sites.

Figure 3.2 Onshore-wind resource map

Figure 3.2 Onshore-wind resource map.
Results based on WAsP simulations with data from 21 met stations.

3.1.3 Energy Converter

When an air mass with velocity v and density r (standard value: 1.225 kg/m3 at +15ûC) passes through the rotor of a horizontal axis wind turbine with area A, power coefficient c P (maximum 0.593) and an overall efficiency h, then the extracted power may be calculated from

formula. (3.2)

The basic characteristics of the chosen reference wind turbine were as follows:

  • Horizontal axis, 3-bladed, upwind design;
  • 2.5 MW rated power, variable-pitch blades, variable rotational speed;
  • 80 m rotor diameter and 80 m hub height;
  • Rotor alignment by active yawing through 360°;
  • 25 m/s cut-out wind speed.

Figure 3.3 shows the power curve of the machine (adapted from a Nordex N80/2500 turbine).

Figure 3.3 Reference onshore 2.5 MW wind turbine

Figure 3.3 Reference onshore 2.5 MW wind turbine.
(a) Curves of wind input and output power against wind-speed; (b) Table of generated power against wind speed.

Three of these turbines were placed in a 1 km2 cell, giving 7.5 MW per km2 installed capacity. For calculation of the indicative lifetime production cost, average project costs of 600 £/kW were assumed for Scotland with 8% of this amount representing nominal grid connection costs. Actual grid connection costs were estimated from GIS cost distance as described in Section 2.3.8. Land rental was assumed to reduce annual revenues by 2%. Insurance was set to an annual fee of 1% of capital expenditure and O&M costs were 0.55 p/kWh (e.g. EWEA 2004).

3.1.4 Generation

The average wind-speed assigned to each 1 km2 cell of the onshore-wind resource map allowed an initial selection of potential sites for wind generation. Inappropriate sites were filtered out by reference to absolute and consultation constraints (discussed in Section 2.2) including:

  • Natural and cultural heritage sites;
  • Aviation and radar interference areas;
  • Cities, towns and villages; lakes; cells with an average slope greater than 15%.

For the remaining 1 km2 cells the lifetime production cost was calculated. This figure included the grid connection cost and, in the case of the islands, a share of the undersea cable connection. The cells were ranked according to the lifetime production cost and groups of the 'cheapest' (for example the cheapest 1,500 MW out of all of the onshore wind generating capacity) were selected for scenario calculations. Time-series of wind-generated power were needed for all potential onshore sites. The first stage of this process was to use the WindFarmer program from Garrad Hassan to compute a flow matrix for each cell of interest. This matrix transforms 'input' wind-speeds and directions at the associated met station (at 10 m agl) to 'output' wind-speeds (at 80 m agl) at the 1 km2 cell. The time-series of wind-speed for each selected cell was then generated from the Met Office time-series data.

Wind-speed time series were converted to power time series using the power curve shown in Figure 3.3. The generated power for each cell had to be reduced in order to allow for the following factors.

High wind cut-out To avoid damage or excessive wear, onshore wind turbines are generally designed to be shut down in wind-speeds that exceed 25 m/s. Turbulences and gusts can force the operation of the cut-out procedure, but as the study was based on hourly wind data this could not be accurately modelled. Each Met Office hourly wind data record included the maximum gust that occurred during the hour. However, this is measured at 10 m height whereas the wind turbine hub height is 80 m and generally many kilometres away. Extrapolating the gust values for the height difference and for the distance would not have been meaningful. A compromise used here was to trigger shut-down when a wind-speed of 25 m/s was reached and then wait subsequently until it fell below 22 m/s before re-starting generation. From the data used in the study, a wind-speed of 25 m/s at 80 m hub height was exceeded in Scotland for an average of 19 hours per turbine per year and the subsequent average waiting time for cut-in was 9 hours per year. Assuming a 35% plant capacity factor, the corresponding annual production losses were estimated to be 0.6% and 0.3%, respectively.

Downtime Onshore-wind turbines in projects in Europe are now commonly available (generating or waiting for sufficient wind-speed) for 98% of the time. For the remaining 2% of time they are either awaiting or undergoing repair or they are shut-down for scheduled maintenance. Equivalent production losses of 2% were used in the study.

Electrical losses Transformers and low voltage interconnections within a wind park typically cause losses from 2 to 3%. The lower number was used for the study. Losses for the grid connection were not considered, as feed-in at remote corners of the network can actually reduce transmission losses by supplying electrical energy locally.

Wake losses On average, individual turbines in wind farms spend some time in the wake of other turbines and therefore intercept less wind. Flat terrain causes wakes to propagate a long distance down-wind and the wake losses to other machines can approach 8%. Scotland's hilly terrain helps to 'mix' and re-energise the wind so that this effect is reduced. In the study, wake losses were taken into account by reducing power output linearly in proportion to turbine density. The density was defined by the number of occupied cells within a 5 km by 5 km square. The reduction was set to zero if only the centre cell was occupied (3 turbines in total) and to 7.5% if all 25 cells were occupied (75 turbines in total).

Directionality Modern wind turbines have yaw systems which actively align the rotor to face the wind and so there are practically no losses caused by changes of wind direction.

High wind cut-out and subsequent cut-in were applied on an hour-by-hour basis in the calculation of the generation time-series. Downtime, electrical and wake losses were implemented by applying global reduction factors to the final time-series figures.

3.2 Offshore-wind Energy

3.2.1 Resource Characteristics

Compared with land, oceans have relatively smooth surfaces and so there is generally less reduction in wind-speed near to the surface. This characteristic is referred to as low wind shear. The atmosphere far offshore tends to be more stable than onshore due to the absence of large obstructions and because of lower vertical temperature gradients. Diurnal patterns of wind-speed variation are relatively flat and turbulence intensity tends to be low, so that dynamic machine loading is less and reduced tower heights may be considered. However, as a result of the less turbulent conditions, the machines in an offshore wind-farm generally need greater spacing to allow the wakes of up-wind turbines to be re-energised.

Figure 3.4 shows simulated wind-speeds at an offshore location north of Orkney derived from Met Office hindcast data. The location is only 60 km from the onshore measurement site of Figure 3.1 and the storm peaks are very similar.

Figure 3.4 Wind-speed simulation for an offshore location

Figure 3.4 Wind-speed simulation for an offshore location, based on Met Office hindcast data.
Location: 59.50°N, 2.58°W (north of Orkney); 80 m height; 3 hour values.

3.2.2 Resource Assessment

In comparison with the number of onshore Met Office stations, there are relatively few maintained offshore wind measurement points around Britain. Off Scotland there are four 'island systems' (North Rona, Sule Skerry, Foula, Muckle Holm) and a number of moored buoys. Due to the frequency of severe weather conditions and their relative inaccessibility, the datasets from these stations are much less complete than those of their mainland counterparts. Furthermore as these stations are all well to the north of the Scottish mainland, they are of little use for predicting conditions in potential offshore-wind areas such as the east coast or the Solway Firth.

Therefore the primary resource information for offshore-wind was the Met Office UK Waters Wave Model which has wind information included with the wave data. Hindcast averages of wind-speed and direction are provided eight times a day for a height of 10 m above sea level (asl). Data from 29th March 2000 through to 9th November 2004 was obtained for 95 simulation grid-points (shown on Map 08). Hindcasting is a well-established technique whereby archived weather data is later used as the input for a detailed meteorological model of weather conditions in some required area. In recent years the temporal and spatial resolution of hindcast data has greatly improved. The UK Waters Wave Model now has a spatial resolution of one-ninth of a degree of latitude by one-sixth of a degree of longitude, an area typically around twelve kilometres square. The start date of the data used for the study corresponds to the date at which the frequency of data archiving increased to allow 3-hourly hindcasts to be made.

For distances well offshore (more than 30 km from the coastline) the hindcast wind data could be directly applied to any potential wind turbine location, with interpolation between two or more points where necessary. However, the comparatively shallow waters needed for offshore-wind turbine foundations generally require them to be relatively close to the shore. At these distances from the coastline the models do not describe the wind resource robustly ( DTI 2004b).

To overcome this problem, the UK Waters hindcast offshore-wind data was used to provide input to WAsP (see Section 1.6.2) which was then able to correct for coastal discontinuity and to make more accurate predictions for nearshore locations. The local wind climate was established from 2001 through 2003 data. The 11 simulation areas, 150 km by 100 km in size, shown in Table 3.2 and Map 07 were created to cover potential offshore-wind locations around Scotland. The roughness of land areas can have a stronger influence on wind regimes over the coastal sea than the orography. As combined orography and roughness maps were readily available from the onshore-wind simulations (see Section 1.6.2), the appropriate parts were used for offshore-simulations as well. A total of 124 three-hour periods were missing within the four and a half year hindcast dataset, but these were filled by prediction from data from 'backup' meteorological stations within the simulation area (see Table 3.2).

Figure 3.3 and Map 07 show that, as with onshore-wind (Map 06), neighbouring offshore-wind simulation areas have 10 km overlaps. These again allowed calculation of scaling factors that were used to reduce transitions between areas. The resulting long-term averages compared very well with the data published in the UK Marine Renewable Energy Atlas ( DTI 2004a), with differences generally being smaller than 5%.

Area

Name

SW corner Northing (m)

SW corner Easting (m)

Simulation Grid-point

Backup Met station

Scaling factor

1

Shetland

1,070,000

370,000

59.94°N, 1.75°W

Lerwick

0.933

2

Orkney

930,000

290,000

59.50°N, 2.58°W

Kirkwall

0.858

3

Cape Wrath

950,000

150,000

59.06°N, 5.08°W

Altnaharra

0.810

4

Lewis

860,000

30,000

58.17°N, 7.58°W

Stornoway

0.781

5

Moray Firth

840,000

260,000

58.17°N, 2.58°W

Wick

0.876

6

Uist

770,000

20,000

57.28°N, 7.75°W

South Uist

0.781

7

Aberdeen

750,000

330,000

57.28°N, 1.75°W

Dyce

0.903

8

Tiree

680,000

20,000

56.39°N, 7.58°W

Tiree

0.778

9

Fife

610,000

310,000

56.39°N, 1.75°W

Leuchars

0.805

10

Islay

590,000

80,000

55.50°N, 5.92°W

Machrihanish

0.843

11

Solway Firth

500,000

160,000

54.61°N, 4.25°W

Dundrennan

0.924

Table 3.2 Offshore-wind simulation areas.

Figure 3.5 Offshore-wind resource map.

Figure 3.5 Offshore-wind resource map.
Data derived from the Atlas of UK Marine Renewable Energy Resources ( DTI 2004a).

3.2.3 Energy Converter

Offshore wind-turbines are in principle built in the same way as their onshore counterparts. Certain aspects such as noise emission or visual intrusion may be less critical, winds may be less turbulent, tower heights for a given capacity may be lower and it may be easier to move very large components at sea. However, the corrosive effect of the maritime environment is much higher, foundations and cable-laying are more complex and costly, and installation and access for maintenance are more demanding. At present offshore machines are largely modified onshore types, but in the future they are likely to evolve into more specialised designs. The parameters chosen for the study were:

  • Horizontal axis, 3-bladed, upwind design;
  • 5 MW rated power, variable-pitch blades, variable rotational speed;
  • 126 m rotor diameter and 80 m hub height;
  • Rotor alignment by active yawing through 360°;
  • 30 m/s cut-out wind speed.

Figure 3.6 shows the power curve of the machine (adapted from a REpower 5 MW turbine).

Figure 3.6 Reference 5 MW offshore wind turbine

Figure 3.6 Reference 5 MW offshore wind turbine.
(a) Power curve; (b) Tabulated values of generated power against wind-speed.

Only one 5 MW turbine was permitted in any 1 km2 cell, giving 5 MW/km2 installed capacity. For the indicative lifetime production cost calculations, a capital cost of 960 £/kW was assumed for a water depth of 10 m and nominal costs of grid connection. Cell-specific foundation and installation cost fractions were calculated as water depth dependent, while grid connection costs were calculated dependent on cost distance. Sea area rental was assumed to reduce annual revenues by 2%. Insurance was set to an annual fee of 1.5% of capital expenditure and O&M costs were 0.65 p/kWh (e.g. EWEA 2004).

3.2.4 Generation

The main constraint for offshore-wind developments is water depth. At present a depth of 30 m is considered to be the limit for economic feasibility. However, for sensitivity analysis up to 40 m was allowed in the scenario calculations. Map 07 shows these areas along with deeper water regions down to 40 m and 50 m. In line with Garrad Hassan (2001a) wind farms were placed at least 5 km offshore. All areas closer to the shore were therefore excluded from further analysis.

Further sites were removed due to absolute and consultation constraints including:

  • Natural and cultural heritage sites,
  • Aviation and radar interference areas,
  • Areas of very high navigational risk.

Navigational risk which was ranked 'very high' was used as an absolute constraint against placement of generating plant. 'High' navigational risk was treated as a consultation constraint to avoid constraining out some potential development in the Firth of Forth. This seems a reasonable decision because in places the coarse 10 km resolution of the navigational risk dataset tends to broaden the apparent shipping lanes. Likewise, Military Practice and Exercise Areas ( PEXA) were not considered as constraints in the study due to the lack of available guidance information.

For site selection, the average wind speeds as predicted by WAsP based on the Met Office hindcast input were used. The calculations beyond this were carried out in the same manner as for onshore-wind. Reduction factors included the following:

High wind cut-out The offshore turbine modelled had a cut-out speed of 30 m/s compared with 25 m/s for the onshore machine used in the study. It was assumed that the wind has to fall below 26 m/s before the turbine would resume operation. A high-wind shutdown is more likely to happen in the north of Scotland than in the south. On average across all of the offshore locations suggested by this study, 30 m/s at 80 m hub height was exceeded for only 0.2 hours per turbine per year with a subsequent waiting time for cut-in of 0.1 hours per year. The corresponding annual production losses were practically negligible. This result is likely to be optimistic since the hourly wind data was derived from three-hourly hindcast records which effectively mask gusts that can force a shutdown.

Downtime Availability figures for offshore wind projects were predicted to reach or exceed 94% by 2010, and so a corresponding 6% loss of production was assumed. Advances in technology and service concepts will be necessary to actually achieve this figure throughout all projects.

Electrical losses As for onshore-wind, losses in transformers and interconnections within offshore wind-parks were estimated at 2% of production.

Wake losses Low surface roughness offshore and less vertical wind movement than on land, allow wakes to propagate over comparatively long distances. The associated power losses in existing offshore wind farms have been reported to be in the range of 5% to 15%. Therefore power losses due to wakes were increased linearly from zero if only the centre cell in a 5 km by 5 km square was occupied (1 single turbine) to 10% if all 25 cells were occupied (25 turbines in total).

Directionality As with onshore wind turbines, there are no losses associated with the change of wind direction. As long as the actual wind speed is above the cut-in level, the automated yaw system of the turbine will change the nacelle's direction to always face the wind.

High wind cut-out and subsequent cut-in were implemented on an hour-by-hour basis during the calculation of generator time-series, whilst downtime, electrical and wake losses were applied in the form of global reduction factors.

3.3 Wave Energy

3.3.1 Resource Characteristics

When winds start to blow over calm water, they create waves that are small and short. If the winds continue to blow, the waves get bigger and longer and they also travel faster. A typical speed for a mid-spectrum Atlantic wave is 55 km/h (35 mph) and so it would take several days to cross the ocean from west to east. As such waves arrive in shallower coastal waters, they begin to lose energy due to friction with the sea bed and through breaking. Sea-states are highly complex, but can generally be thought of as being made up of waves of different periods, heights and directions combining together. The wind-sea interactions that are responsible for the waves seen at any point may have occurred hours or days ago and over distances of thousands of kilometres. Superimposed on top of a short-period wind-sea from local winds, there may be an old-wind sea of half-a-day ago from an adjacent sea area along with long-period swell from distant storms of several days ago.

Figure 3.7a shows the variation in wave height for a site 120 km north-west of Lewis, predicted over a one year period from hindcast data. Figure 3.7b shows the variation in wave power over a shorter period along with the corresponding hindcast wind power record for the same site. There is visible correlation between wave and wind, but there are clearly times (such as around 23rd February) when high wave power levels must be due to more distant winds. It is important to note that none of the traces shown in the figures give any indication of wave or wind direction.

Figure 3.7 Wave height and power density at 59.06°N, 8.42°W.

Figure 3.7 Wave height and power density at 59.06°N, 8.42°W.
(a) Three-hourly hindcast values of wave height in 2001;
(b) Comparison of wave and wind power density during February 2002.

Whatever the means used to record or predict a wave climate, the complexity of any particular sea-state is usually described by using a simplifying set of statistical parameters. A sea-state can then be thought of as being composed of a spectrum of regular waves of different heights, periods and directions. The two most important parameters are wave height and wave period.

The height parameter is used to represent the average of the heights of the constituent waves. In this study the root-mean-square (rms) wave-elevation parameter H rms was used. H rms is equivalent to the standard deviation of the water surface about the mean position. Oceanographers often use the parameter H s (significant wave height) which is now defined as being 4 times the H rms value.

The period parameter is used to represent the average of the periods of the constituent waves. In this study the energy period parameter T e was used because it has a robust definition. The T e of a spectrum of waves having a certain H rms and power density is equivalent to the period of a regular wave that has the same values of H rms and of power density. This is useful because the power density of a spectrum of waves is generally easy to calculate.

A curve can be drawn for any measured sea-state to show how energy is distributed across the wave frequency spectrum. Such spectra can also often show the relative contribution of swell (at low frequencies) or local wind-sea (higher frequencies). With a long fetch and steady wind conditions, it is possible to estimate the wave spectrum from knowledge of wind-speed by using parametric spectra such as the Pierson-Moskowitz or the Jonswap.

Wave recording buoys are often equipped to measure horizontal surge and sway motions as well as heave motions so that wave directionality can be calculated. Swell from a distant source may have a very narrow angular range whereas locally generated waves may approach from a wide range of angles as winds shift and change speed.

The power density of a wave is proportional to the square of its height multiplied by its period. If r is the density of water (1,025 kg/m3) and g the acceleration due to gravity (9.81 m/s2), then the wave power density in deep water (in watt per metre of wave crest) is given by:

formula. (3.3)

As an example, a sea-state with H rms = 1 m and T e = 10 s has a power density of nearly 79 kW/m.

3.3.2 Resource Assessment

Off Scotland, the areas that have historically been of most interest as potential wave energy generation sites are in the Atlantic approaches to its western coasts, because these areas are at the ends of very long fetches that stretch out in the directions of the prevailing wind systems.

Early UK wave energy researchers used data from Ocean Weather Ship 'India' which kept more or less permanent station in the deep Atlantic, 700 km west of the Western Isles, from 1947 to 1975. Estimates of the overall average power density at that location varied between 80 kW/m (Leishman & Scobie 1976) and 91 kW/m (Mollison, Buneman and Salter 1976). Crabb (1978) later reported systematic calibration errors in the 'India' data and reduced the mean figure to 78 kW/m.

In 1976, in response to interest in wave energy generation, the Institute of Oceanographic Sciences ( IOS) began a wave measurement programme by installing a 'waverider' buoy about 18 km west of South Uist in 42 m depth. The long-term average wave power density was estimated at 48 kW/m (Crabb 1982).

These assessments were for specific areas and gave no explicit indication of the general wave climate. Winter (1980) used two years of data from the Met Office depth-dependent wave-forecasting model to hindcast directional wave power climates around the western approaches to the UK from Land's End to Shetland and also in the Moray Firth. He found close agreement between the Met Office model and the IOS measurements made at South Uist.

In 1992 Queen's University Belfast made calculations of the UKshoreline and nearshore wave energy resource using a Met Office wave prediction model. Included in the study were 14 representative locations to the west of the UK and Ireland and one location to the east of Shetland. Five of the locations were in areas of relevance to the present study and were modelled for the period February 1983 to July 1986.

The wave energy resource data used by Garrad Hassan (2001a) in their assessment of Scotland's renewable resource was interpolated from data for 29 offshore grid points that was obtained from the Norwegian company Oceanor. The data covered a period of nine years and was derived in part from information and techniques developed under 'Eurowave', a collaborative European research project during the 1990s. The interpolation process used for the Garrad Hassan work also used inshore waters data produced by the Queen's University Belfast project referred to above.

The calculations in the present study were based on Met Office hindcast data that recently became available with improved temporal and spatial resolution. The UK Waters Wave Model, referred to in Section 1.7.2 above, has a spatial resolution of 1/9th degree latitude by 1/6th degree longitude (each record thus represents conditions in an area of about twelve kilometres square), and a time-resolution of 3 hours. Data from 29th March 2000 through to 9th November 2004 was obtained for 95 simulation grid-points shown in Map 08.

Source

IOS
(1976-1978)

Winter
(1977-1979)

QUB
(1983-1986)

GH
(1992-2000)

UoE
(2000-2004)

Fair Isle

-

-

-

50.5

37.5

Islay

-

-

29.3

27.7

16.0

Malin Head

-

-

53.1

54.9

30.0

North Rona

-

-

-

60.4

45.0

NW (DB2)

-

57

75.8

65.8

43.5

Shetland (DB3)

-

45

66.9

52.0

39.0

South Uist

48

52

71.6

56.4

45.0

Table 3.3 Comparison of average wave power density (kW/m) estimates from various sources.

IOS: Institute of Oceanographic Sciences (Crabb 1982); Winter (1980); QUB: Queen's University Belfast (1992); GH: Garrad Hassan (2001a); UoE: University of Edinburgh (present study).

Table 3.3 compares wave power estimates for 7 locations, taken from the studies discussed above, with values from the present study. It is notable that the latter figures are lower than those of the other studies. With the exception of Garrad Hassan (2001a) the studies were based on 3 or 4 years, time periods too short to establish a long-term wave climate, and some variation was to be expected. According to the classic work of Pierson and Moskowitz (1964) the wave power density of a fully developed sea is proportional to the 5th power of wind-speed and so the wave resource is very sensitive to year-to-year variations in wind climate. According to the DTI (2004b), wind-speeds during the years 2000 to 2003 were observed to be significantly lower than the long-term historical record. They quantify the windiness of the period as 93.6% of the long-term value, which on a simple 5th power analysis would correspond to wave power density levels being 72% of the longer term value. This could explain the relationship between previous estimations and the present calculations.

Figure 3.8 Comparison of measured and simulated rms wave elevation values

Figure 3.8 Comparison of measured and simulated rms wave elevation values.

Measurement: three-hourly at the European Marine Energy Centre on Orkney; data courtesy of EMEC Ltd. Simulation: derived from Met Office hindcast data for the nearest grid-point. Distance between EMEC buoy and grid-point: 9 km.

Variations in the UK wave climate may also be linked to the North Atlantic Oscillation, but a brief comparison has found no clear correlation. The wave resource values calculated for the study are in very close agreement with the wave power densities published in the Atlas of UK Marine Renewable Energy Resources ( DTI 2004a) which derive from the same Met Office data. Figure 3.8 compares wave heights calculated from the Met Office hindcast data with buoy measurements from a nearby location for the month of November 2003. There is good agreement, particularly between the average values for the month.

Wave data records The Met Office UK Waters Wave Model data was supplied in the '1D Integrated Variables' format for the 95 grid-points shown in Map 08. The wave information in each three-hourly record is listed as 13 spectral density values, each of which corresponds to one of the frequency bins illustrated in the spectral density histogram of Figure 3.9. The units of spectral density are such that the area of each column represents the energy at its nominal frequency, so that the sum of all columns represents the total energy in the sea-state. A second array lists the associated wave direction for each bin. The Met Office records include wind hindcast data that was used in calculating the offshore-wind resource (see Section 1.7.2), and so the 95 grid-points were chosen to give good coverage for wind as well as for waves. The record for each grid point also includes water depth.

Figure 3.9 Energy spectrum from one record of the UK Waters Wave Model '1D' data.

Figure 3.9 Energy spectrum from one record of the UK Waters Wave Model '1D' data.
The nominal frequency of each bin is shown on the second horizontal axis.

Wave data preparation The preparation of the wave data was based on work by Tucker (1991) and the World Meteorological Organization (1998). With reference to the 13 bins shown in Figure 3.9, if i is used to represent the bin number, the ith bin has nominal frequency f i, width d f i and spectral density S(f i).

Spectral moments are used in wave analysis. For the binned data, the nth spectral moment can be written as

formula. (3.4)

The rms wave elevation H rms is then found from the zeroth spectral moment as

formula. (3.5)

The energy period T e can be found from the ratio of two spectral moments:

formula. (3.6)

If ? is the density of sea water and g the acceleration due to gravity, the power density P W per metre of crest length is

formula, (3.7)

where c g(fi) is the group velocity of the wave of frequency f i in water depth h. In shallow water (depth less than half of a wavelength) this is given by:

formula. (3.8)

In Equation (3.8), k is the so-called 'wave number':

formula, (3.9)

where ? is the wavelength which depends on water depth. In deep water it is

formula. (3.10)

k can be found for any depth by an iterative solution of the following equation, using the above value of k0 as an initial guess:

formula. (3.11)

A contiguous file of 3-hour parametric records was prepared from the 1D data set for each of the 95 grid-points used in the study. For general resource estimation, average power density values based on four years of data running from 1st April 2000 to 31st of March 2004 were calculated. For the electricity generation time series, three years of data from 1st January 2001 to 31st December 2003 were used.

For the preparation of maps and site selection in the Atlantic areas of interest, power density data was interpolated in a two-stage process. The first stage consisted of interpolation from the 95 grid points down to the nominal resolution of the UK Waters Model (approximately 12 km). The second stage consisted of interpolation from that grid down to the 1 km2 cells that were used in the study.

Figure 3.10 shows the average wave power densities across Scotland according to the DTI (2004a) derived from UK Waters Wave Model data for the period 1st June 2000 to 30th September 2003. Map 08 in the Appendix shows in addition the wave power densities in areas of interest for wave power developments calculated in this study from data covering 1st April 2000 to 31st March 2004.

Figure 3.10 Wave energy resource map

Figure 3.10 Wave energy resource map.
Data derived from the Atlas of UK Marine Renewable Energy Resources ( DTI 2004a).

3.3.3 Energy Converter

The present study was concerned with notional installations having aggregate capacities at the gigawatt level. The offshore deep-water wave resource is considerably more energetic than the shoreline resource and there are more possible sites for energy conversion systems. Of the prototype deep-water wave energy devices that had recently been deployed, Ocean Power Delivery's 'Pelamis' device seemed to be the one nearest to commercial introduction. Furthermore it can be placed in a range of water depths commonly found around the Scottish coast.

Based on public domain information and after discussions with the device developer the characteristics of the 750 kW prototype were scaled up to represent anticipated future machines. The device parameters used for the study were:

  • Semi-submerged, cylindrical structure consisting of 5 segments and 4 power modules, 180 m long;
  • 1.5 MW rated power, power limitation through inherent design characteristics;
  • Water depth range 50 to 150 m;
  • Passive device alignment > ±90°;
  • Packing: 3 rows of devices with 12.5 to each 1 km2 cell (18.75 MW/km2 capacity).

Table 3.4 shows the power-matrix of the notional wave energy converter. Each entry in the matrix gives the generated electrical power in kilowatts for a particular combination of parametric wave height and period. The combinations of H rms and T e values cover the full range of values found in the data records.

Figure 3.10 Wave energy resource map

Table 3.4 1.5 MW wave energy converter power matrix.

3.3.4 Generation

The creation of power generation time-series for the wave energy devices was a two-stage process. First, a power time-series was generated for each of the 95 grid-points of the hindcast wave resource data using values of H rms and T e to interpolate values for generated power from the power-matrix of Table 3.4. This set of time-series was then used to produce interpolated time-series at each 1 km2 cell to which devices had been allocated. Inverse distance weighted values from up to four nearby grid-points were used.

Power limitation The chosen device has an inherent power limitation capability as described by the power matrix. H rms and T e combinations with blank entries in Table 3.4 did not occur in the dataset.

Downtime Once the technology is established, availabilities similar to those of offshore wind farms may be achievable. Maintenance will be carried out bi-annually in summer with little loss of production. An average 8% loss of production was assumed beyond 2010.

Electrical losses Production losses due to electrical interconnections within the wave farm were set to 2%.

Array losses The row of devices which faces the wave front will produce the highest power output. As devices are interleaved and as the attenuator type does not intercept all of the power, the array losses were set to 1%.

Directionality The nominal directional orientations for wave energy devices in each 1 km2 cell were based on the all-year average direction of maximum incident wave energy. Moorings were assumed to allow devices to swing to either side of this mean position. However, an angular-attenuation factor k was calculated by the approximation

formula (3.10)

and applied to power calculations. ? nom represents the nominal moored orientation of the device and ? ss represents the direction of the sea-state. As examples, this function gives attenuation factors of 0.8, 0.88, 0.94, 0.97 respectively for seas whose mean directions are offset at respective angles of 90°, 80°, 60° and 45°.

3.4 Tidal-current Energy

3.4.1 Resource Characteristics

Tides are long oceanic waves which cause the sea level to change over periods of roughly half a day or a day (Pugh 1987). The rising tide is known as a flood-tide with a corresponding 'mean high water' ( MHW) level. The falling tide is known as an ebb-tide with a corresponding 'mean low water' ( MLW) level. The difference between the MHW and MLW levels is the tidal range and the average is the 'mean tide level'. The latter often serves as a datum for elevation measurements.

The moon provides the primary tidal force. It orbits the earth every 27.3 days around an axis of rotation which lies within the earth. The water masses on earth experience centrifugal and gravitational forces which tend to produce tidal-bulges, both on the side of the earth that faces the moon and on the opposite side. The shapes and phasing of the tidal bulges are complicated by the earth's daily rotation about its own axis and by the interaction of land masses and waters of varying depths. The earth-moon system and the earth rotate in the same direction, and so the earth's cycle with respect to the moon is 24 hours and 50 minutes. This is called the lunar day.

The sun has a similar influence on the water masses, with a diurnal period of 24 hours. Its enormous size is compensated by its great distance so that the solar gravitational force is about 0.46 that of the moon. When earth, sun and moon are in line (either a new or a full moon depending on their relative positions), then the forces combine to produce larger than average spring-tides. When the moon is in quadrature (half-moon), smaller than average neap-tides are produced. The basic earth-moon cycle repeats approximately every 29.5 days, or lunar month.

Tidal changes in water level are fed by very large horizontal movements of water having the same cyclic periodicity. Where the horizontal water motions are particularly pronounced, they are referred to as tidal-currents. As with the usually more apparent vertical motions, the intensities of the horizontal flows are very sensitive to the sizes of sea areas, the variations in water-depths (bathymetry) and the shapes of land masses.

Figure 3.11 shows the change of tidal-current velocities throughout a year for a site in the Fall of Warness (Orkney). The peaks during spring tides are clearly visible.

Figure 3.11 Absolute value of tidal-current velocity in the Fall of Warness (Orkney

Figure 3.11 Absolute value of tidal-current velocity in the Fall of Warness (Orkney).
Location: 59.135°N, 2.805°W, hourly values for 2003 computed with TotalTide.
• new moon; ? full moon.

In restricted areas such as channels and narrow estuaries, tidal-currents are more or less bi-directional. In more open areas of sea, the direction of flow (which may be plotted in the form of a tidal ellipse) may be complicated by factors that include the Coriolis force. Tidal-currents are sensitive to bathymetry changes and to bottom friction. In general, current velocities reduce with depth, particularly near to the sea bed. In some cases, the near sea-bed and the free surface water motions may be significantly out of phase.

Because of their dependence on astronomical constellations, tidal-currents are deterministic and can be predicted with great accuracy into the future. However, weather has some additional influence. Wind can reinforce or weaken tidal motions, and water level is influenced by changes in atmospheric pressure.

3.4.2 Resource Assessment

Tidal levels can be predicted by summing up a number of harmonic constituents, each of which corresponds to a particular astronomical influence with its own characteristic frequency. Almost 400 constituents have been identified. The prediction of tidal-currents is made still more complex by their very high sensitivity to bathymetry and landmasses. The available sources of information include:

  • Some Admiralty Charts with a resolution equal to or better than 1:200,000 contain tidal arrows indicating the direction and magnitude of the spring tide currents, sometimes for both the flood and the ebb tide.
  • More information is attached to the tidal-diamonds that feature on some Admiralty Charts. For a number of selected points that are marked with diamond symbols, a table lists the hourly velocities up to six-hours before and six-hours after high water at a reference port, for average spring and for average neap tides. The values shown on the charts are obtained from short-term measurements and are applicable five metres below the surface. An example of a tidal diamond is shown in Figure 3.12a.
  • Tidal stream atlases published by the United Kingdom Hydrographic Office ( UKHO) cover specific areas in more detail. Each atlas contains thirteen hourly charts with spot values for spring and neap tidal velocities, and arrows to indicate the general direction of the currents. Scaling of the arrows may contain further information on the velocity rate. Each of the thirteen charts in any series represents a time in hourly intervals from six hours before high water at Dover to six hours after. A small extract from an atlas is shown in Figure 3.12b.
  • The 'TotalTide' software package was designed by the UKHO for mariners and allows prediction of tidal-currents at tidal-diamond locations at any time in the past or in the future.
  • When tidal-currents are needed for an area where no measurements have been made, a complete computational fluid dynamics ( CFD) analysis could be made. Because of the amount of data required to adequately describe the bathymetry of sea areas and the shapes of land masses, such studies are usually confined to smaller areas of a few hundred square kilometres. The data in the UK Marine Renewable Energy Atlas ( DTI 2004a) is based on interleaved computer models with different resolutions. Such models perform well when given accurate boundary conditions, although at inshore locations the accuracy is generally lower. At the beginning of this project simulation models were not available at the correct resolution.
  • For definitive information on current velocities, directions and depth profiles at any location, on-site measurements must be made. These should be carried out over a complete spring and neap cycle, and the results should be corrected for the effects of weather.

Directly measured information was not available for the study and a CFD analysis of the whole Scottish coastal area was well-beyond the available time and computing resources. Neither was the dataset nor the model used to compile the UK Marine Renewable Energy Atlas ( DTI 2004a) available in the public domain. Accordingly, the tidal-current resource data used was based on UKHO information.

Figure 3.13 and Map 09 show the average spring-tide velocities across Scotland. Spring tidal-velocities of at least 2 m/s are commonly considered to be required for economic energy extraction. In collaboration with The Robert Gordon University, potential areas for tidal-current applications were identified. Where tidal-diamonds were available within a few kilometres of such a site, their data were included in the study. The phasing of some of this data, such as in the example shown in Figure 3.12a, is given with reference to sites other than Dover. In these cases the phasing was transformed to the Dover datum. In areas with no local tidal-diamonds, 'pseudo' tidal-diamonds were constructed using data estimated from the tidal stream atlases. Further spring tidal rates were obtained from Admiralty charts and from previous studies, in particular Black & Veatch (2004).

Figure 3.12 Examples for a tidal diamond and a tidal stream atlas.

Figure 3.12 Examples for a tidal diamond and a tidal stream atlas.
(a) Tidal diamond "E" on Admiralty Chart 2250 for the Fall of Warness (Orkney);
(b) Extract from tidal stream atlas NP 256 ( UKHO 1992b), 2 hours before HW Dover.

Figure 3.13 Tidal-current resource map.

Figure 3.13 Tidal-current resource map.
Data derived from the Atlas of UK Marine Renewable Energy Resources ( DTI 2004a).

For the study, the spring and neap tidal-current values at each site had to be transformed into three-year time-series of tidal-current velocities and directions. The first stage of this process was to produce a three-year reference time-series of tidal ranges for Dover using TotalTide. For each hour of the three-year period, the levels at the last high and low water times and those at the next high and low water times were used to calculate the short-term tidal range. This range was related to the known mean spring range of 6.0 m and the mean neap range of 3.2 m at Dover to establish the relative phasing within the spring and neap cycle. With the spring and neap tidal current velocities known for each tidal diamond, as well as the time to High Water at Dover, a velocity and a current direction could then be interpolated for each tidal diamond at every hour. Weighted tidal-current vectors from up to three diamonds were used to calculate velocity and direction at a site of interest.

3.4.3 Energy Converter

Traditionally, tidal power generation has been associated with the building of a dam or barrage at a site with sufficient tidal range and the generation of power by low-head hydro turbines either during ebb or flood or both. Because of the civil construction costs involved, and the potential impact on the environment, and in spite of there being several superb candidate sites no large plant has been built in the UK. In comparison to tidal-barrages, the direct use of tidal-currents avoids long-duration civil engineering activity and the environmental impacts are likely to be lower.

Several designs exist for tidal-current converters. At the time of writing the development of the horizontal-axis concept is more advanced than that of other proposed systems, and these machines therefore seem likely to be used for large-scale implementation in the near-future. Although there are many aspects of machine design and performance analysis that are quite distinct, horizontal-axis tidal-current machines extract power very much in the manner of wind-turbines, with the incident power being proportional to the cube of current velocity:

formula. (3.11)

The major difference is the much higher density ? of seawater (about 1,025 kg/m3) compared to air.

The key parameters for the projected 1 MW underwater turbine, which was conceived for the study, were:

  • Horizontal axis, 2-bladed, twin rotor design. 18 m rotor diameter;
  • Two 0.5 MW generators, variable rotational speed, blade pitch reversible;
  • 5 m or more clearance to the sea bed, 9 m clearance to the sea surface;
  • No yawing, but 180° blade pitch-reversal to capture bidirectional flows.

To reduce cost, the machine in the study did not have a yaw system. This requires the currents to be essentially bi-directional. Figure 3.14 shows the power curve of the machine (adapted from the MCTSeaGen design).

Figure 3.14 1 MW tidal-current turbine power curve.

Figure 3.14 1 MW tidal-current turbine power curve.
(a) Power curve; (b) Tabulated values of generated power against wind-speed.

The optimum spacing of tidal-current generators is subject to speculation and is likely to be site specific. Bryden & Couch (2004) suggest that up to 10% of the mean energy flux at a particular site could be intercepted by tidal-current generators without significantly changing the resource. Salter (2005) argues that higher fractions could be extracted from relatively long channels where the power losses already incurred by tidal-currents in overcoming bottom-friction are comparable with the energy to be extracted. For the notional machine, a minimum spacing of 1 km was assumed. When fifteen of these machines were placed along a line perpendicular to the main current direction, the lateral spacing was about 67 m. This gave an effective capacity of 15 MW per 1 km2 cell. However, this machine density was only used in the most energetic areas of the Pentland Firth. Elsewhere, the axial spacing was increased to at least 2 km.

3.4.4 Generation

Due to the limited number of potential locations, the placement of machines was based on the suitability of sites from a physical and resource perspective, rather than being based on cost. It was assumed that the machines could be installed in water depths between 30 and 50 metres. All locations with spring tide rates of 2 m/s or greater and which were close to 1 km2 in size or greater were considered. Narrow channels (such as Kyle Rhea) and lochs (such as Loch Linnhe) were excluded from the study due to the limited capacity for electricity generation at those locations (e.g. less than 5 MW).

For the 30 to 50 metre range of depths and the 2 m/s qualifying current, the total number of 1 km2 cells in Scottish waters was of the order of 100. These cells were thinned out so as to normally stay within the ten-percent extraction limit. This left 26 cells in the Pentland Firth, 15 cells in the northern Orkney area, 5 cells in Shetland, and a further 34 cells in the south-west. The latter areas are known to be less energetic, but could make a valuable contribution to a balanced generation portfolio.

Some of the sites, in particular in the Pentland Firth, experience relatively high shipping densities which will be have to be taken into account before any project developments take place. However, as with offshore-wind, it was decided to not to attempt to constrain these sites with the low-resolution navigational risk dataset.

For the selected sites, the clearance between blade tips and the mean water surface was assumed to be 9 m. With 18 m rotor diameter the hubs are then 18 m below the surface. A 1/10th power law was applied to scale down the nominal near-to-surface velocities of the resource to values appropriate to the mean depths of the turbines. Based on resource time series and the conversion characteristic, power time series were calculated for each 1 km2 cell. Further global reduction factors were applied to the turbine power output including the following.

High velocity cut-out Because of their predictability compared with winds and waves, the maximum velocities of tidal currents at any site will be known before installing the plant. Machines will be subjected to known stresses and will be designed to operate at all current velocities, probably using blade pitch-control to regulate power. Therefore a cut-out velocity was not set for the machines in the study.

Downtime The type of tidal current generator used in the study has the useful feature that its drive train can be raised above the surface of the water for maintenance. Tidal machines idle for several hours each day at slack water and the projects will be near the shore. Accordingly, access will be relatively easy and total downtime losses were set at 4% in the study.

Electrical losses As with the other technologies, the electrical losses due to interconnection within the tidal farm were set at 2% of production.

Wake losses Recent research (e.g. Bryden & Couch 2004) suggests that currents will only recombine after a long distance. In the study, wake losses of 5% were assumed. Future research is needed to obtain generally applicable figures.

Directionality Most turbine designs have no facility for yawing as tidal-currents in energetic areas are predominantly bi-directional. However tidal flow cycles usually have some small amount of angular deviation from the ideal. Within each 1 km2 cell, the turbine orientations were set to the mean current direction. Whenever the tidal-currents deviated from this axis, a cosine correction was applied to the power output of the machine. For instance, a 5° off-axis current invoked a reduction of 0.5%, while 10° caused a loss of 1.5%.