Tidal Power Schemes

Tidal Power Schemes David Prandle 1. INTRODUCTION Recent searches for ‘renewable’ energy sources have rekindled interest in tidal power schemes. Tidal mills have been used in many countries for centuries. However, La Rance in France, constructed in 1968, remains the only full-scale operational tidal power scheme. Extraction of tidal current energy via ‘free-standing’ devices is also under consideration (Bryden, 2006). Prandle (1984) described a simplified approach to the design of impounded estuarine tidal power schemes. Both one-way (flood or ebb) and two-way (flood and ebb) schemes were examined. Optimum dimensionless design parameters were derived based on the mean tidal amplitude, ζ, and the surface area of the enclosed basin, S. Comparisons were made between these optimised parameters and actual engineering designs for La Rance and proposed schemes in the Bay of Fundy and the Bristol Channel (Prandle, 1981). The key dimensionless parameters adopted were as follows: e fraction of maximum energy extracted, E/EMAX where EMAX = 4ρgζ2S; d duration of power production as a fraction of tidal period P; c installed capacity, as a fraction of EMAX/P; u e/c utilisation factor; q Q/QT flow through turbines: amplitude of the pre-existing estuarine flow, 2πζS/P; ge effective area of sluice gates, relative to Sζ½/(2g)½P hRAT rated turbine head, as a fraction of ζ hMIN minimum turbine operational head, as a fraction of ζ

2. OPERATIONAL SEQUENCES In one-way ebb generation the rising tide enters an enclosed basin through sluice gates and idling turbines, these gates are subsequently closed to maintain a maximum level in the basin and power is generated when a sufficient head develops on the falling tide. In two-way power generation, energy is extracted on both the rising and falling tide with sluicing occurring around the times of high and low water. A schematic representation of these two modes of operation is shown in Figures l(a) and l(b). The optimised designs were based on the following simplifying assumptions: i) the external tide is sinusoidal and of amplitude ζ, ii) water level within the basin ,surface area S constant, is horizontal, iii) flow through the turbines is at a constant rate, Q, during power generation, iv) power generation starts and stops at the same prescribed minimum head, hMIN. The maximum energy, EMAX, is extracted by emptying the basin instantaneously from high water to low water. However, turbines represent the primary cost in a tidal power scheme and hence careful compromises are necessary between maximising power output and minimising costs.

Figure 1. Schematic representation of the operational mode of: (a) a one-way ebb-generation tidal power plant; (b) a two-way tidal power plant.

Figure 2. Energy produced, e, in discharging a tidal basin between starting level z1 and finishing level z2 with a minimum starting (and finishing) head of (a) 0.2ζ and (b) 0.4ζ. Contours indicate the energy produced is a fraction of the maximum theoretically available. In two-way generation net energy production shown should be doubled to reflect the contribution from the flood phase.

Power generation For the assumptions stated above and following the introduction of dimensionless parameters, three independent parameters determine power generation, namely, (1) the starting time t1, (2) the finishing time t2 and (3) the minimum starting (and finishing) head hMIN. Figures 2(a) and 2(b) show the corresponding energy extracted e for hMIN = 0.2 and 0.4. The results show that in both modes of operation, maximum energy is extracted when the basin level is initially close to the maximum and, in the case of the two-way mode, power generation continues to the minimum level. In the one-way mode maximum energy extraction occurs when the finishing level t2 = 255°, or 30 minutes before low water (LW). The maximum contour value in the one-way mode increases from 0.25 for hMIN = 0.2 to 0.27 for hMIN = 0.4. The maximum contour values shown for the two-way mode must be doubled to take account of the second half of the cycle, thus we find a maximum value of 0.25 for hMIN = 0.2 and 0.37 for hMIN = 0.4. This latter result illustrates the sensitivity of the results for e to the parameter hMIN.

Sluicing The simulation of sluicing also reduces to a three parameter problem, i.e., starting time t3, finishing time t4 and minimum starting head, hMIN. In one-way mode, the problem is independent of hMIN. Iterative techniques were used to calculate the value of ge required to refill the basin in the time available. Simulations showed that the sluicing requirement increases rapidly as the finishing level approaches the maximum tidal level. Thus some compromise must be achieved between the conflicting requirements of power generation and a reasonable sluicing capacity. A finishing level of about 0.85ζ produces an acceptable sluicing capacity with ge ~ 7. In this range the sluicing capacity required in the one-way scheme is fairly insensitive to the starting level. By comparison, a somewhat smaller sluicing capacity is required in the two-way scheme with the requisite capacity reducing further as the starting level increases. In the case of the two-way scheme, further simulations were carried out with hMIN = 0.2 and hMIN = 0.4. The results showed a significant increase in the sluicing requirements, particularly when re-filling to near the maximum level. In re-filling to the suggested level of 0.85, sluicing requirements increase by up to 20% for hMIN = 0.2 and by up to 60% for hMIN = 0.4. In practice, in a two-way scheme sluicing may start up to 90 minutes before the end of generating in order to increase the available head during the next half cycle.

3. OPTIMUM THEORETICAL VALUES The component parts (a) to (f) of Figure 3 illustrate the variation of the key dimensionless parameters over a range of values of (i) hMIN and (ii) finishing level z2. The values shown all assume a full basin starting level. To illustrate the use of these diagrams consider Figure 3(c), the respective lines for varying values of hMIN terminate at the value z2 = hMIN − 1. Thus, while for z2 = 0 the utilisation factor, u, is greatest for hMIN = 0.6, in fact the maximum overall value of u is obtained for hMIN = 0.4 since in the latter case generation can continue over a longer period.

Figure 3. Component parts (a)–(f) show values obtained in discharging a tidal basin from a maximum level z1 = 1 to the finishing level z2. Values for the two-way mode in (a) and (c) have been doubled to reflect the second half of the cycle, (a) energy produced e; (b) installed capacity c; (c) utilisation factor u; (d) maximum head hMAX; (e) flow rate q; (f) duration d. Results shown for hMIN = 0.0, 0.2, 0.4 and 0.6 (as labelled). The position indicated at z2 = −0.26 in the one-way mode corresponds approximately to the finishing level for maximum energy extraction.

Energy produced, e, installed capacity, c, and utilisation factor, u Figure 3(a) shows that the energy extracted, e, increases with hMIN with the increase being more pronounced for the two-way mode. However, Figure 3(b) shows that the requisite installed capacity, c, increases in a similar fashion. Thus the ratio of e:c represented by the utilisation factor, u, in Figure 3(c) is less sensitive to hMIN. However, careful examination shows that maximum efficiency, i.e., the maximum value of u, is found for a value of hMIN = 0.4. With this value of hMIN, Figure 2 shows that the two-way scheme extracted up to 0.37 of the energy potential compared with 0.27 for the one-way scheme. Figure 3(b) shows that the installed capacity, c, required to achieve these peak values of energy extraction is 0.7 in both the one-way and two-way mode. Hence the corresponding values for the utilisation factor u (= e/c) are approximately 0.4 and 0.5 respectively as seen from Figure 3(c).

Maximum head, hMAX, and flow rate, q Figure 3(d) shows the maximum head developed during turbining, hMAX, while Figure 3(e) shows the corresponding flow rates, q. In general, the one-way mode operates at a higher head and lower flow rate than the two-way mode. For example, with hMIN = 0.4 and at maximum energy extraction, in the one-way mode hMAX = 1.2 and q = 0.4 while in the two-way mode hMAX = 0.6 and q = 0.8. Since turbine efficiency is generally low at small heads, the approximate doubling of the operating head in the one-way scheme compared with the twoway scheme is a clear advantage. A turbine is designed to operate optimally at a rated head hRAT rated flow qRAT. The turbo-generator performance curve, reproduced by Clark (1977), for a turbine with variable wicket gates and runner blades, shows that maximum power output can be maintained with an operating head in the range 1 to 1.5hRAT and a corresponding operating flow 1.0 to 0.5qRAT. Thus operating at the maximum head conditions, energy conversion is 33% more efficient than at the minimum head condition. However, one advantage in the two-way scheme is the smaller variability of the operating head over the turbining period and hence the more constant level of power generation. In one-way mode, flow rates are reduced to 0.4, whereas in two-way mode they approach the pre-existing value (q = 1) and hence produces little change to the existing tidal flushing regime.

Duration, d Figure 3(f) shows the duration of the power generation phase as a fraction of the tidal period. The duration decreases as hMIN increases, thus where peak power is required a high value of hMIN may be used, whereas for more continuous power output hMIN must be reduced. When operating at maximum efficiency the duration d = 0.55 for both modes. Table 1 summarises the above results showing optimum theoretical values for the various dimensionless parameters when operating at maximum efficiency. Recalling that the optimum value for effective sluice gate area, ge ~ 7, corresponds to refilling to a level z = 0.85, some slight reduction in the optimum values of e and u, derived for an initially full basin, may be expected.

4. PRACTICAL APPLICATIONS In any detailed design of a tidal power plant there will be numerous constraints not considered here, however, the initial assumption of a constant tidal amplitude ζ, and a constant surface area, S, are so restrictive that some comment is necessary. Variation in tidal amplitude, ζ At almost all places the time-series of tidal elevations can be closely approximated by a sinusoidal curve between successive peaks and troughs. Since tidal amplitudes typically vary by up to a factor of two between Springs and Neaps, tidal power design must reflect a compromise between maximising power output and avoiding excess generating capacity over this cycle. For a semi-diurnal tidal regime, i.e., where constituent amplitudes M2 + S2 >> O1 + K1, the amplitude variation over the Spring-Neap cycle can be approximated by (1 + a cos ωt), where a = ⅓ for a 2:1 variation and ω represents the fortnightly variation.

Table 1. Comparison of theoretical design parameters for tidal power schemes with engineering designs from the Bay of Fundy, the Bristol Channel (Flat Holm) and La Rance. Dimensional Cumberland Flat La Rance Basin Holm km2 22 86 420 m 4.25 5.0 4.0 GWh 73.1 4.3 23.4

Non-dimensional Cumberland Flat La Rance Basin Holm

Surface area S Tidal amplitude ζ Emax = 4ρgA2S TURBINES Number n 35 24 140 Rated head hRAT m 6.5 5.6 1.3 8.7 hRAT 2.3 Min. head hMIN m hMIN 2.3 1.2 0.46 Rated flow QRAT m3s−1 797 QRAT 694 275 0.40 m3s−1 Aperture rating QT 399+ 384 195* POWER OUTPUT Installed capacity c MW 1085 7980 240 c 0.57 GWh 3423 Annual output yp 9680 500 yp 0.21 Utilisation factor u u 0.37 SLUICES Number m 24 176 6 m3s−1 Rated flow QS 988 986 715 m2 Ge(mQS + nQT)/√(2g) 8387 8.6 51566 2025 ge Design specifications extracted from Owen(XXXX), Clark(XXXX) and Cotillan(XXXX). [add column showing theoretical values for two-way operation]

Theory

2.2 0.57 1.89

1.3 0.28 0.50

1.2 0.4 0.4

1.36 0.19 0.14

0.69 0.16 0.24

0.7 0.2 0.4

8.8

7

12.1

The results shown are in dimensionless form and should be readily applicable to discrete portions of the time-series. While this approach may provide a useful first study, detailed design must take account of the ordering of successive operational modes to optimise energy output. For the value of a = ⅓, designs based on the mean tidal amplitude extract 0.82 of their potential, reducing the one-way optimised theoretical value of e from 0.27 to 0.22. Designs based on Neap tidal range extract 0.44 of the ‘mean tide’ potential but the installed capacity is reduced by the same amount. Designs based on Spring Tides extract 1.06 of the ‘mean’ potential but require the installed capacity to be increased by a factor of 1.78. Thus, the Neaps design is most efficient based on the utilisation factor, u, but results in a loss of over half of the available power.

Variation in surface area, S In two of the most attractive tidal power sites in the Bay of Fundy, Cumberland Basin and Minas Basin, on Spring tides the surface area at high water is about three times greater than at low water. Hence, some additional tests were made for a basin in which the surface area varied linearly by a factor of 4 to 1 between high and low water. Using the value of S at mean water level for converting to dimensionless parameters, the energy extracted in the one-way ebb mode increased by around 10%, the installed capacity increased by a similar amount leaving the utilisation factor more or less unchanged. Similar changes were found for the twoway mode but, assuming symmetric operation, changes on the ebb generation are effectively counter-balanced by changes on the flood. This small effect of a variable surface area found for the one-way mode may be attributed to the centring of the generation period around the time of mean water level. However, sluicing may occur over a wider range of tidal conditions and thus might be expected to be more

sensitive to changes in S. Tests were carried out with the same four-fold linear variation in S. In the one-way scheme, sluicing capacity increased by about 50% for the ebb generation and decreased by about 40% for flood generation. In the two-way scheme sluicing capacity at high water increased by more than 100% while at low water the decrease exceeded 50%. Hence the operational mode in a two-way scheme with variable S should be asymmetric to reflect the variation in sluicing capacity at high and low water.

5. COMPARISON WITH DETAILED ENGINEERING DESIGNS Table 1 shows the essential parameters for three tidal power schemes, Cumberland Basin in Fundy, the Flat Holm barrier in the Bristol Channel and La Rance. The dimensionless form of these parameters is compared with ‘optimum’ values obtained from the theoretical analyses described above. The optimisation criterion in this theoretical study was the maximisation of energy output consistent with a minimal investment in installed capacity. It should be noted that the scheme at La Rance operates in both one-way and two-way modes whereas the comparison here is made with theoretical values applying to the one-way mode.

Power output The values of surface area, S, apply to mean sea level and the tidal range ζ to the mean tidal amplitude. The maximum potential energies available, EMAX are in the ratio 5.4 : 17 : 1 for the three schemes Cumberland Basin : Flat Holm : La Rance. The equivalent ratios for annual power output, Y, (706 e EMAX), are 6.8 : 19.4 : 1, thus the more recent designs aim to extract a slightly higher percentage of the available energy than achieved at La Rance. The corresponding ratios for installed capacity, c are 4.5 : 33.2 : 1. Comparing Cumberland Basin with La Rance, in the former case a slightly higher percentage of available energy is extracted, i.e., 6.8:1 compared with the ratio 5.4: 1 for EMAX, for a lower ratio of installed capacity, 4.5:1. This apparent improved efficiency of the Cumberland Basin scheme may be related to the more constant value of the tidal range at this site. Comparing Flat Holm with La Rance, the higher percentage of energy extracted in the former case, i.e., 19.4:1 relative to the ratio 17:1 for EMAX, may be attributed to the much higher level of installed capacity indicated by the ratio of 33.2:1. In dimensionless terms the power output, e, from all three schemes lie in the range 0.16 to 0.21 in close agreement with the theoretical value of 0.2. However while the values of the installed capacity, c, at Cumberland Basin, 0.57, and La Rance, 0.69, are in good agreement with the theoretical value of 0.7; the value at Flat Holm, 1.36, is approximately double the theoretical value. In consequence the utilisation factor of 0.14 at Flat Holm is much less than the theoretical value of 0.4.

Turbines Some explanation for the high value of installed capacity in the Flat Holm scheme can be found from the large values shown for the turbine parameters at this site. The rated head, hRAT, has a value of 2.2 at Flat Holm compared with 1.3 for Cumberland Basin and La Rance and a theoretical value of 1.2. The minimum head for turbining, hMIN, is also larger at 0.57

Table 2 Representative characteristics of tidal power schemes across a range of estuarine sizes. Shape, depth and breadth ∝ x0.8, L = 2460D5/4/ζ½ and current amplitude based on synchronous theory, Prandle (2004). DEPTH Length Breadth Surface area Power extracted ge/cross-section Energy extracted/Dissipation

D L = 2460D5/4/ζ½ 2 × D / 0.013 B L / 1.8 0.8ρgζ2S/P

m km km km2 MW (ζ = 2 m) (ζ = 4 m) 7S/P(ζ/2g)½/A (ζ = 2 m) (ζ = 4 m) (0.2EMAXP)/(0.5ρgAζU cos θ) (ζ = 2 m) (ζ = 4 m)

32 16 132.4 55.7 2.46 1.23 180.9 38.1 127 27 508 107 0.22 0.20 0.32 0.27 0.42 0.57 0.53 0.78

8 23.4 0.62 8.06 5.6 23 0.16 0.23 0.88 1.11

4 9.8 0.31 1.69 1.2 4.8 0.14 0.20 1.15 2.04

than the values 0.46 and 0.28 for Cumberland Basin and La Rance respectively and is almost 50% larger than the theoretical value of 0.4. Correspondingly the flow rate, q value of 1.89 for Flat Holm greatly exceeds the theoretical value of 0.4 whereas the values at Cumberland Basin, q = 0.4, and at La Rance, q = 0.5 are in close agreement with the theoretical value. Two advantages follow from this high level of installed capacity at Flat Holm. One is the capability of supplying larger power outputs over smaller time intervals, a particular advantage in meeting daily demand peaks whenever the tidal phasing is appropriate. Secondly, the efficiency of the scheme should increase towards spring tides when the additional capacity can be usefully employed.

Sluices Table 1 shows the sluicing capacity for the Flat Holm scheme is also somewhat larger, at ge = 12.1, than the theoretical value of 7 whereas the other schemes, at ge = 8.6 and 8.8, both agree closely with the theoretical value.

6. ENVIRONMENTAL IMPACTS AND SMALL-SCALE TIDAL POWER SCHEMES Traditionally, proposed tidal power schemes focused on large bays or estuaries with high tidal ranges producing power of the order of 1000 MW comparable with nuclear, gas, oil or coal stations. The current quest for renewable energy widens interest to much smaller-scale schemes. While, the dimensionless approach described here allows designs to be readily scaled down, it is useful to provide explicit indications of the range of power outputs and the associated environmental impacts. Table 2 shows power outputs for depths, D, (at the mouth) of 4, 8, 16 and 32 m for tidal amplitudes, ζ, of 2 and 4 m. The table assumes a synchronous estuary morphology, i.e., breadths and depths varying with × 0.8 and tidal lengths L = 2460D5/4/ζ½ as indicated by Prandle (2004). A side slope of 0.013 was assumed based on the analysis of 96 UK estuaries by Prandle (2006). This study also shows that some 40% of these estuaries have D < 4 m, while 75% have D < 8 m. Moreover since the mean value of ζ was close to 2 m, it is clear from Table 2 that the power availability for most UK estuaries is less than 10 MW.

Environmental Impact While the power output of schemes in small, shallow estuaries is much reduced, one advantage is that the associated environmental impacts are also likely to be significantly reduced. A major concern (Prandle and Rahman, 1980) for both the Fundy and Bristol Channel schemes is the possibility of barrier constructions causing changes in tidal conditions extending hundreds of kilometres seawards of the barriers. This arises from the nearresonance of these large and deep basins. By contrast, Prandle (2006) shows that the semidiurnal resonant length of a typical estuary can be approximated by LR = 37000D½ (in metres), rendering most shallow estuaries far too short for ‘quarter-wavelength’ resonance. Moreover, such estuaries are overwhelmingly ‘friction-dominated’ as opposed to inertialdominance in Fundy and the Bristol Channel, (D < 10ζ providing an indication of this demarcation). Thus, in small, shallow estuaries tidal amplitudes are rarely significantly amplified and the responses are unlikely to change significantly due to barrier construction. A quantitative assessment of the impact of tidal power extraction on estuarine functioning is shown in Table 2 based on the ratio of the proposed energy extraction e EMAX to the (existing) upstream tidal energy dissipation, 0.5ρgAζU cos θ, where A is the cross-sectional area and θ the phase lag between ζ and U. The results show that in deeper water this ratio is close to 50% whereas in the shallowest case it exceeds a factor of two for the largest tidal amplitude. (The scaling ratio reduces to ζ2/U3, the results shown rely on the synchronous solutions which indicate that U ∝ ζ½ for F >> ω, hence the ratio increases for larger tides.) These impacts can be related to equivalent changes in the bed friction factor k. Prandle (2004) showed that, for synchronous estuaries, in shallow (frictionally dominated) water, current amplitude and estuarine length are proportional to k−½. In deep water, current amplitude is insensitive to k while estuarine length is proportional to k−1. Thus, in shallow water we might anticipate some reduction in the pre-existing power potential and a longer term (decadal) tendency for a reduction in estuarine volume. Conversely, in deeper water there will be little change to the power potential and the indicated morphological changes occur over centuries in deeper water (Prandle, 2004). Table 2 also indicates the percentage of cross-sectional area required for sluicing. This varies from 15% for the shallowest water and smaller tide to 30% in the deepest water and larger tide. This indicates that accommodating sluices should be less problematic in the smallerscale schemes. The 30% figure for the largest schemes explains why the impounding barriers are often inclined to the shortest cross section in order to accommodate both sluices and turbines. The reduction in water exchange, 60% for the indicated value of q ~ 0.4 in one-way schemes, will significantly decrease the flushing rate of suspended contaminants from the impounded basin. However, contamination levels in many estuaries are determined by leaching from historic deposits on the estuarine bed. In many cases, reduced velocities in the impounded basin will reduce this supply rate of contaminants.

Drainage and flood protection The one-way operating mode results in mean water levels in the impounded basin significantly higher than existing. Minimum levels may be close to pre-existing mean sea levels with consequent impacts on land drainage.

Tidal power barriers can be effectively used for flood protection against flooding from storm surges and exceptionally high tides. Interestingly, the possibility of incorporating tidal power extraction alongside the Thames Flood Barrier has often been suggested. With an upstream tidal length of about 40 km and Neap to Spring tidal amplitudes of approximately 2 to 4 m, Table 2 suggests available energy in the range 20 to 80 MW.

7. SUMMARY The design of tidal power schemes is synthesised in terms of optimised values for eight dimensionless parameters shown in Table 1. Operating with a minimum head of 0.4 of the tidal amplitude with an installed capacity of 0.7 of the maximum energy available (averaged over a tidal cycle), power outputs of 0.27 and 0.37 can be realised for one-way and two-way operations respectively. Table 2 translates these theoretical values into representative values for a range of estuarine sizes showing outputs ranging from a few MW in the smallest estuaries increasing to upwards of 1000 MW in the largest. Comparisons were made between the above theory and the La Rance scheme together with proposed designs in the Bay of Fundy and the Bristol Channel. Generally good agreement is found between the design parameters for Cumberland Basin, La Rance and the optimum theoretical values. The additional energy output, for the same installed capacity, in the two-way operation combined with a flushing regime closer to the undisturbed state appears to recommend this operational mode. However, the operating heads in the one-way mode may be double those in the two-way mode and hence turbine efficiency should be greater. Turbine efficiency in the two-way mode is further reduced by the basic turbine design compromises necessary to accommodate two-way flow. Thus, the theoretical advantage of the two-way scheme shown here may well be more than counter-balanced by practical engineering realities.

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