4th International Conference on Ocean Energy, 17 October, Dublin

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On the tidal resource of the Pentland Firth

T.A.A. Adcock1, S. Draper2, G.T. Houlsby1 and A.G.L. Borthwick3

1 Department of Engineering Science, University of Oxford, Parks Road, Oxford, United Kingdom E-mail: thomas.adcock@eng.ox.ac.uk

2 Centre for Offshore Foundation Systems, University of Western Australia Crawley, 6009, Australia.

3 Department of Civil and Environmental Engineering, University College, Cork, Ireland

Abstract

The Pentland Firth is believed to be one of the most promising locations for the extraction of energy from tidal streams, and so is one of the sites being studied as part of the PerAWaT project commissioned by the Energy Technologies Institute. In this paper we investigate numerically the hydrodynamics of the Pentland Firth using a discontinuous Galerkin, depth-averaged shallow flow model. Drag exerted on the flow by a tidal turbine (or array of turbines) is modelled by a local enhancement to the bed friction in the shallow flow model. The turbine drag and the inviscid limit to the useful energy which may be extracted are calculated using linear momentum actuator disc theory, using realistic values of wake induction factor and blockage ratio. The predictions are compared with results from simplified models of energy extraction from a tidal channel available in the literature.

Keywords: tidal stream resource, Pentland Firth,

1. Introduction The Pentland Firth is the strait of water connecting

the North Sea to the Atlantic Ocean, between the North of Scotland and the Orkney Islands. It is well known for its very fast tidal streams, which can exceed 5 m/s at spring tide. As such, the Pentland Firth is one of the most important candidate sites for tidal stream energy devices. Various locations within the strait have been licenced for development by the Crown Estates [1].

A number of estimates of the resource of the Pentland Firth have been made. Several of these [2-4] use the undisturbed kinetic energy flux, despite the fact that this has been shown to be unrelated to the power potential of a channel [5]. An alternative approach based on the energy currently dissipated in the channel [6] has also been shown to be flawed [7]. Table 1

summarises various published estimates of the resource.

In the present paper, a numerical model of the tidal dynamics in the region is used to model the flow through the Pentland Firth. We then model the change in flow due to drag imposed by tidal devices (at various locations) and find the value of drag which maximises the power extracted. We also consider an upper limit to the power that might be generated by using an idealised representation of real tidal turbines.

Study Predicted power Comments

Black & Veatch [2] ~1 GW (average)

Percentage of kinetic energy flux

ABPmer [3] 620 MW (average)

Percentage of kinetic energy flux

MacKay [4] 10 GW (average)

Percentage of kinetic energy flux

Salter & Taylor [6]

40 GW (peak)

Natural energy dissipation

Table 1 Estimates of the tidal stream resource of the Pentland Firth

2. Numerical model The numerical model used herein is the

discontinuous Galerkin version of ADCIRC [8-9]. This solves the shallow water equations commonly used for modelling tidal flows. Figure 1 shows the extent of the computational domain. A full validation is given in [10]. The predictions are in good agreement with the available measurements, providing confidence that the model is sufficiently accurate for the type of resource assessment presented in this paper.

The presence of tidal turbines is modelled using an equivalent bed friction in the same way as [11].

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Mainland Scotland

Pentland Firth

Figure 1 Computational domain used in simulation of flow through the Pentland Firth. The colours indicate the water depth. Red indicates depths less than 140 m. Dark blue (within computational domain) indicates water depth greater than 1400 m.

3. Extractable power 3.1 Entire Pentland Firth (M2 only) First we consider the maximum power that may be

extracted from the Pentland Firth when the model is forced solely with the dominant M2 tidal components. To extract maximum power from the channel, devices are placed across the entire channel [12]. We initially consider devices placed at transect A as shown in Figure 2. This is achieved by introducing a ‘strip’ of uniform bed friction, of width 735 m (although the power potential will be insensitive to the width around this value) along transect A.

As the thrust applied by the turbines is increased, the flow through the Pentland Firth reduces. Figure 3 shows how the power extracted from the flow, averaged over the tidal cycle, varies as a function of the maximum flow rate through the strait, Qnat. The

maximum average power which can be extracted is approximately 4 GW. This would require a reduction in the flow through the Pentland Firth to 55% of the natural value. However, it is possible to extract much of the power with a much smaller disturbance (e.g. 3 GW with only a 20% reduction in the maximum flow rate).

3.2 Pentland Firth sub-channels (M2 only) A similar approach can be applied to the sub-

channels formed by the islands within the Pentland Firth (Figure 2). The power potential of these sub-channels is relevant given present plans to develop individual sites within the Pentland Firth [1]. Table 2 presents the maximum average powers which might be extracted.

It can be seen that the power available in the different channels is inter-dependent. If two sites are developed which are in ‘parallel’ then the extractable power is greater than the sum of the power from the two sites developed alone. In contrast, if two sites are developed which are upstream and/or downstream of each other, then the extractable power is less than the sum of the powers when developed from each site in the absence of the other site. Therefore, different areas in the Pentland Firth should not be developed independently, as the energy available and the optimum development strategy for each development is unknown. As well as leading to uncertainty for developers and investors, developing areas independently risks making inefficient use of the total resource of the entire site.

It can also be noted that power extracted along BCD combined is almost equivalent to A, suggesting that extracting the maximum resource is is virtually independent of the location of the devices.

Although details are not presented here, analysis of the energy from the numerical model is in excellent agreement with simplified analytical models for energy extraction from channels [13].

Figure 2 Locations of turbine fences within numerical model. Colours show the rms velocity of the M2 tidal components in m/s.

3.4 3.3 3.2 3.1 3 2.9 2.858.6

58.62

58.64

58.66

58.68

58.7

58.72

58.74

58.76

58.78

58.8

Longitude

Latit

ude

0.5

1

1.5

2

2.5

3

3.5

4

Mainland Scotland

Swona

Stroma

SouthRonaldsay

A

B

C

D

E

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Figure 3 Average power extractable from M2 tide from the Pentland Firth as a function of flow rate.

Maximum average power extracted (MW)

for selected transect Total

average power (MW) A B C D E

3943 3943

99 99

1547 1547

451 451

240 240

179 1611 1790

121 466 587

86 220 305

1513 166 1622

2401 1093 3494

213 570

248 2555 1136 3939

Table 2 Maximum average power extractable from various locations within the Pentland Firth.

3.3 Power of the spring/neap cycle The tidal dynamics of the Pentland Firth vary

significantly over the spring/neap cycle as the M2 and S2 tides move in and out of phase. On averaging the power over the daily power cycle, it is found that the maximum power that can be extracted along transect A (or BCD) at spring tide is 6.6 GW but falls to 1.8 GW at neap tide. This is in agreement with results from analysis of a simplified tidal channel over the spring/neap cycle [14]. Whilst the variation is large, it is smaller than that predicted using kinetic energy flux to model the tidal stream resource [2].

The average power over the entire spring/neap cycle is also increased, and reaches 4.4 GW (a 10% increase above the corresponding value when the M2 tide is solely considered). Again, this is in agreement with simple analytical models of energy extraction from a tidal strait [5].

Although it is possible to consider other tidal components (such as N2, K1 etc.), the additional power averaged over the entire cycle will be small (a few percent of the 4.4 GW) and so this is not analysed in detail here.

4. Available power Unfortunately, it is not possible for tidal stream

devices to convert all the extracted power to electricity. Certain inefficiencies, such as arise from the viscous flow through the turbine and generator losses, are device specific and so are not examined further here. However, the energy lost in mixing downstream of an ideal tidal turbine can be used to obtain an upper bound for the power which could be generated. This is termed ‘available’ power [15].

We use actuator disc theory to represent the behaviour of tidal turbines, following Garrett & Cummins [16] whose model accounts for the blockage in the channel but not for finite Froude number effects (considered in [17]) which only have a small effect on the power produced. The turbine properties are characterised by the blockage ratio (the fraction of the channel cross-section swept by the turbines) and the thrust applied to the flow by the turbines (which is implied from our use of a uniform friction coefficient to represent the tidal devices in Section 3). Here, a relatively large blockage of 0.5 is considered. We consider this the largest blockage that is likely to be feasible and using this will give the maximum available power. The turbine properties are tuned to maximise the available power following [15]. It is assumed that the rows are spaced so that complete mixing takes place between them.

Table 3 shows the available power, averaged over the entire cycle when the model is forced with both M2 and S2 tides, for different numbers of rows extending the whole way across the strait. It can be seen that a substantial portion of the extractable power is available when only one or two rows are used, but that there is a diminishing return on the extra energy available as more rows are added.

Number of turbine rows assumed along transect

Average power available for

generation (GW) A BCD

1 1.4

2 2.0

3 2.3

1 1.9

2 2.6

3 2.9

1 3 3.2

Table 3 Available power for different turbine rows with blockage of 0.5

10 2 10 10

0.5

1

1.5

2

2.5

3

3.5

4x 109

1 Q/Qnat

Pow

er (W

)

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There is a substantial variation in the power

produced over the tidal cycle. For example, Figure 4 plots the power over a tidal cycle for the case where there are two rows of turbines located across BCD.

To extract all of this power it is necessary to size the generators and cabling to cope with a peak of 8.5 GW. However, there would be a relatively small decrease in the overall average power if power capping is employed. Assuming that the thrust on the flow remains unchanged when power is capped, then the average power over the tidal cycle can be calculated as a function of the generation capacity. This is shown in Figure 5.

Figure 4 Available power for two rows of turbines placed at BCD. Thin line shows instantaneous power. Thick line shows power averaged over a daily cycle (i.e. 24 hour centered moving average).

Figure 5 Reduction in power due to power capping. Power normalised by maximum power available. Generator capacity

normalised by generator required for maximum power. Case presented is for 2 rows of turbines at BCD.

5. Feasible power

The total power available for generation increases as more rows of turbines are added. However, the power that each turbine produces decreases. There is therefore a trade off between making use of the finite resource and having sufficient power available to each turbine to make its deployment viable. Further analysis would require detailed knowledge of the tidal device performance characteristics and of the economics of the device, and is beyond the scope of this paper. However, an indication is given here of what scale of deployment is likely to be viable.

Let us consider the metric defined by the power generated per swept area of turbine. For a tidal turbine to be viable the value of this metric must be significantly larger than for an offshore wind turbine, as the latter will be significantly cheaper due to the lower loading and easier maintenance. For a typical offshore location on the UK continental shelf, the available power per swept area varies between 0.25 kW/m2 to 1 kW/m2 [18]. By comparison, the power per swept area of a single row of tidal turbines across BCD is 7.1 kW/m2 which compares favourably to the figure for wind. However, if we are considering whether to deploy three or four rows, the extra power available from the additional row is around 300 MW. If we divide this figure by the extra area of turbines required we get 0.84 kW/m2. Thus it is very unlikely that this level of deployment will be competitive with offshore wind.

6. Conclusions

The maximum power which can be extracted from

the Pentland Firth is around 4.4 GW averaged over the entire tidal cycle. This figure is larger than the power which it will be feasible to generate. If we consider turbines which span across the entire strait, and which have a high blockage ratio, then it is unlikely that more than 2.6 GW will be available to the turbine. This is larger than the actual amount of power real turbines could generate as the analysis neglects viscous losses in the turbine and other inevitable inefficiencies in power generation.

The extractable powers of the various subchannels within the Pentland Firth are interdependent. This implies that areas within the Pentland Firth cannot be developed in isolation, but should be planned as a single development. To maximise the resource, it is necessary to place turbines across the entire channel, otherwise there is a very significant reduction in the power available as flow bypasses the turbines.

In this paper we have confined our study to the theoretical maximum for the magnitude of the resource. There are, of course, other considerations, such as environmental impact and structural survivability on

0 50 100 150 200 250 300 3500

1

2

3

4

5

6

7

8

9

Time (hours)

Avai

labl

e po

wer

(GW

)

0.6 0.7 0.8 0.9 10.88

0.9

0.92

0.94

0.96

0.98

1

Normalised generating capacity

Nor

mal

ised

pow

er

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tidal devices, which will be important in developing tidal sites.

Acknowledgements This work has been carried out as part of the

PerAWaT project commissioned by the Energy Technologies Institute. The second author acknowledges the support of the The Lloyd’s Register Educational Trust.

References [1] Crown Estates (2011) Wave and tidal energy in the

Pentland Firth and Orkney waters: How the project could be built. Tech. rep., prepared by BVG Associates.

[2] Black and Veatch (2005), “ Phase 2: UK tidal stream resource assessment”, Technical report. Department of Trade and Industry

[3] ABPmer (2007), “Quantification of Exploitable Tidal Energy Resources in UK Waters” commissioned by npower Juice.

[4] Mackay, D. J. C. (2009) Sustainable energy — without the hot air. UIT, Cambridge.

[5] Garrett, C. & Cummins, P. (2005); “The power potential of tidal currents in channels”. Proceedings of the Royal Society A, 461, pp.2563-2572.

[6] Salter, S. & Taylor, J. R. M. T. (2007) Vertical-axis tidal-current generators and the Pentland Firth. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 221, 181 – 195

[7] Draper, S., Houlsby, G. T. & Borthwick, A. G. L. (2012) Energy potential of a tidal fence deployed near a coastal headland. Phil. Trans. R. Soc. A. in press.

[8] Kubatko, E. J., Bunya, S., Dawson, C., Westerink, J. J. & Mirabito, C. (2009) A performance comparison of continuous and discontinuous finite element shallow

water models. J. Sci. Comput., 40(1-3), 315–339. [9] Kubatko, E. J., Westerink, J. J. & Dawson, C. 2006 hp

Discontinuous Galerkin methods for advection dominated problems in shallow water flow. Computer Methods in Applied Mechanics and Engineering, 196(1-3), 437 – 451.

[10] Adcock, T.A.A, Draper, S. and Houlsby, G.T. Tidal stream resource assessment of the Pentland Firth. In preparation.

[11] Karsten, R. H., McMillan, J. M., Lickley, M. J. & Haynes, R. D. (2008) Assessment of tidal current energy in the Minas Passage, Bay of Fundy. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 222(5), 493–507.

[12] Garrett, C. & Cummins, P. (2004) Generating Power from Tidal Currents. J. Waterway, Port, Coastal, Ocean Eng, 130, 114.

[13] Draper, S., Adcock, T.A.A., Borthwick, A.G.L. and Houlsby, G.T. An Electrical Interpretation of the Pentland Firth Tidal Stream Energy Resource. In preparation.

[14] Adcock, T.A.A., Draper, S. and Houlsby, G.T. Energy extraction from tidal straits — multiple tidal constituents and overtides. In preparation.

[15] Vennell, R. 2010 Tuning turbines in a tidal channel. J. Fluid Mech., 663, 253–267.

[16] Garrett, C. & Cummins, P. 2007 The efficiency of a turbine in a tidal channel. J. Fluid Mech., 588, 243–251.

[17] Houlsby, G. T., Draper, S. & Oldfield, M. 2008 Application of Linear Momentum Actuator Disc Theory to Open Channel Flow. Technical report 2296-08, Department of Engineering Science. University of Oxford.

[18] DTI 2004 Atlas of UK Marine Renewable Energy Resources. Tech. Rep. R.1106,Department of Trade and Industry.