energies

Article Optimising the Operation of Tidal Range Schemes

Jingjing Xue , Reza Ahmadian * and Roger A. Falconer

Cardiff School of Engineering, Cardiff University, Cardiff CF24 3AA, UK * Correspondence: [email protected]



Received: 3 July 2019; Accepted: 23 July 2019; Published: 25 July 2019


Abstract: Marine renewable energy, including tidal renewable energy, is one of the less exploited sources of energy that could contribute to energy demand, while reducing greenhouse gas emissions. Amongst several proposals to build tidal range structure (TRS), a tidal lagoon has been proposed for construction in Swansea Bay, in the South West of the UK, but this scheme was recently rejected by the UK government due to the high electricity costs. This decision makes the optimisation of such schemes more important for the future. This study proposes various novel approaches by breaking the operation into small components to optimise the operation of TRS using a widely used 0-D modelling methodology. The approach results in a minimum 10% increase in energy output, without the inclusion of pumping, in comparison to the maximum energy output using a similar operation for all tides. This increase in energy will be approximately 25% more when pumping is included. The optimised operation schemes are used to simulate the lagoon operation using a 2-D model and the differences between the results are highlighted.

Keywords: tidal range structure; tidal lagoons; marine renewable energy; optimisation of operation schemes; pumping

1. Introduction

With improvements in environmental awareness globally, emission levels of CO2 are expected to decrease by reducing reliance on fossil fuels, and further development in renewable energy. The UK government aims to produce 15% of its total energy from renewable resources by 2020, which corresponds to approximately 35% of the UK’s electricity demand [1–3]. Marine renewable energy (MRE) is one of the emerging renewable energies being explored further. Currently, 0.5 GWh of commercial marine energy generation capacity is in operation and another 1.7 GWh is under construction, with most of this accounted for tidal range [4]. It has been suggested that the tidal range resources of the UK is able to deliver 25 GW theoretically [5]. A number of TRS have been proposed around the UK, particularly in the Severn Estuary and Bristol Channel, with these estuaries being located in the South West of the UK, as shown in Figure1. Swansea Bay Lagoon is one of these projects, which has been one of the world’s first tidal lagoon power plants [6]. It was granted planning permission by the UK Department of Energy and Climate Change (DECC) in June 2015 [7] and was positively supported by the independent Hendry Review of tidal lagoons, commissioned by the UK government and published in January 2017 [8]. However, the cost of electricity has been found to be an issue [9] and the UK government Business and Energy Secretary Greg Clark said that the £1.3bn project was not good value for money, despite claims to the contrary by the developers Tidal Lagoon Power [10]. There have been different values reported for the cost of electricity. The general figure quoted for the levelised cost of electricity (LCOE) is reported to be £150/MWh [11], while the consumer cost over the lifetime of the project is reported to be £25.78/MWh [12]. This reemphasises the need for further optimisation of tidal range structures to enable such projects to produce competitive energy costs.

Energies 2019, 12, 2870; doi:10.3390/en12152870 www.mdpi.com/journal/energies Energies 2019, 12, 2870 2 of 23 Energies 2019, 12, x FOR PEER REVIEW 2 of 23

Figure 1. Lagoons proposals of tidal range structure ( (TRS)TRS) in the Severn Estuary and Bristol Channel (from GoogleGoogle Map).Map).

TidalTidal range structure ( (TRS)TRS) creates creates an an artificial artificial head difference difference across the scheme and generatesgenerates energy usingusing thisthis head head di difference.fference. The The schemes schemes could could be be operated operated to generateto generate energy energy during during flood flood tide (floodtide (flood generation), generation), ebb tide ebb (ebb tide generation), (ebb generation) and on, bothand ebb on and both flood ebb tides and (two-wayflood tides generation). (two-way Onegeneration). of the key One aspects of the ofkey the aspects operation of the of operation such schemes of such is schemes the head is di thefference head difference at the time at when the time the schemewhen the would scheme be programmed would be programmed to start generating to start energy generating and when energy generation and when stops generation (further details stops on(further the operation details on of the TRS operation is provided of TRS in Sectionis provided2). Therefore, in Section TRS 2). Therefore can be operated, TRS can in be various operated ways in forvarious each ways type offor operation each type scheme, of operation i.e., for scheme, flood, ebb,i.e., for or two-wayflood, ebb generation,, or two-way and generation, this operation and willthis influenceoperation thewill basin influence water the level basin and water discharge level transferred and discharge between transferred the impoundment between the and impoundment open waters, and thereforeopen wate affrs,ecting and thetherefore energy affecting generated. the 0-D energy models generated. have been 0-D widely models used have in designingbeen widely TRS used and particularlyin designing in TRS initially and optimising particularly the in operation initially optimising of such schemes the operation [13–16]. of Fundamental such schemes theoretical [13-16]. researchFundamental was carriedtheoretical out inresearch this field was by carried Prandle out in in the this 1980s field [17 by]. EightPrandle dimensionless in the 1980s parameters[17]. Eight weredimensionless defined to parameters provide a formulationwere defined for to theprovide design a formulation characteristics for and the energydesign calculations,characteristics using and fourenergy key calculations, assumptions using that afourffect key the energyassumptions predictions. that affect For example,the energy the predictions. energy generation For example, starts andthe stopsenergy at generation the same prescribed starts and minimum stops at the head, same i.e., prescribedηmin, which minimum can affect head, the energy i.e., ηmin output, which significantly. can affect Aggidisthe energy and output Benzon significantly. used a 0-D model Aggidis to evaluate and Benzon the energy used a (electricity) 0-D model generation to evaluate in the relation energy to varying(electricity) trends generation in energy in demand relation [ 13to ].varying They optimised trends in drivingenergy headsdemand based [13] on. They the sizeoptimised and number driving of turbines,heads based which on varies the size with and the number barrage and of turbines,/or lagoon which dimensions varies and with characteristics. the barrage and/or These studies lagoon havedimensions demonstrated and characteristics. that the 0-D approach These studies has significant have demonstrated preliminary design that potentialthe 0-D forapproach all types has of tidalsignificant impoundments. preliminary design potential for all types of tidal impoundments. However, Angeloudis et et al. al. showed showed that that 0- 0-DD models models can can overestimate overestimate the the energy energy predictions predictions by byup upto 40% to 40% when when compared compared to toprediction prediction based based on on more more sophisticated sophisticated and and accurate accurate 2 2-D-D numerical models [18, [18, 1919]].. TheyThey concludedconcluded thatthat thethe 0-D0-D approach overestimation is relative to the size of the scheme. They They suggested suggested that that 0-D 0 predictions-D predictions are only are reliable only reliable for design for optimisation design optimisation at the preliminary at the stagepreliminary and need stage to beand complemented need to be complemented by more sophisticated by more sophisticated 2-D models. It2- shouldD models. be noted It should that allbe threenoted studiesthat all havethree used studies constant have used driving constant and minimum driving and generation minimum heads generation throughout heads the throughout operation, i.e.,the operation, for all spring i.e. and, for neapall spring and flood and andneap ebb and tides. flood Based and ebb on thetides. authors’ Based extensive on the authors’ literature extensive review, Ahmadianliterature review, et al. [ 15Ahmadian] and Yates et al. et al.[15] [14 and] have Yates separately et al. [14] discussed have separately the concept discussed of variable the concept driving of andvariable minimum driving generation and minimum heads generation for each operation heads for period, each operation namely halfperiod, a tide, namely and highlightedhalf a tide, and the highlighted the potential improvements achievable by implementing variable driving and minimum

Energies 2019, 12, 2870 3 of 23 potential improvements achievable by implementing variable driving and minimum generation heads. More recently, Angeloudis et al. also took advantage of a gradient-based method for the optimisation of flexible operation heads [16]. Research on using pumping to increase energy generation has been limited and was mainly carried out using a constant driving and minimum generation head throughout. Yates et al. used an unlimited pumping head and constant generating head to study the influence of turbining and pumping efficiencies in a 0-D model [20]. They found that the overall energy could improve by about 17% if pumping was included in a two-way generation scheme using constant values for turbine and pump efficiencies. Furthermore, Douglas et al. showed that pumping could increase energy generation by approximately 10% [21]. Their results were consistent with the findings of Aggidis and Benzon [13]. However, they used the same hill-chart for both the energy generation and pumping phases, with a scaled down maximum energy output. With lack of detailed information, they also assumed a combined efficiency during the pumping phase. In the literature, there are a very limited number of studies for the case of pumping, with the majority of studies using a constant pumping head and constant starting and ending head difference for the schemes, with virtually no research being undertaken into measuring the pumping efficiency. Consequently, adding flexible operating heads for the whole tidal cycle, including pumping with flexible operating heads, is another novel aspect being investigated in this study. This paper focuses on facilitating the development of TRS by using a novel approach that includes splitting the operation for each tidal cycle up into smaller components and optimising the operation of Energies 2019, 12, x FOR PEER REVIEW 4 of 23 TRS, in order to generate the maximum energy and therefore reduce the cost of the energy generation. Flexibleturbines operationin order to was generate implemented energy and with continues variable until operational the head heads difference and optimisedacross the impoundment using various combinationis no longer adequate of tides and for efficient utilising energy a 0-D model. generation, The optimisedi.e., reaching outcomes the ending were head further Heeimproved towards the by consideringend of ebb tide. pumping Near the with end more of ebb optimised tide, the operational sluice gates characteristics are opened to in empty order the to increasebasin, until energy the generation.water levels The across results the were impoundment then compared embankment using a more are sophisticatedalmost the same. 2-D unstructured Following this grid step, model, the namelyflood-holding the depth phase integrated begins by velocities closing andthe turbines solute transport and sluice (DIVAST gates until 2-DU) the model, head withdifference the di ffiserences higher betweenthan the starting energy outputhead during and performance flooding, i.e. being, Hsf. highlightedThis is followed from by the the predictions flood generation obtained phase, for the where 0-D andthe turbines 2-D models. are operated again to generate energy. When the head difference is smaller than ending head, namely H , the sluice gates are again opened to raise the water levels inside the impoundment. 2. Tidal Range Schemesef The filling phase now stops and the ebb holding phase starts again, when the water levels across the 2.1.impoundment No-Pumping embankment Operation reach the same levels and the water level outside the impoundment starts falling again with the ebbing tide falling again with the ebbing tide. This can be seen as a periodicXia etprocess, al. [22] which showed repeats that the itself two throughout most effective each operational cycle. A schematic schemes of are the ebb-only two-way and generation two-way generation.scheme is illustrated Therefore, in Figure this study 2b. mainly focuses on these operational schemes, and schematic illustrations of them are shown in Figure2a,b, respectively.

(a) (b)

Figure 2. SchematicSchematic representation representation of of the the operational operational schemes: schemes: (a) O (ane) One-way-way ebb ebbgeneration; generation; (b) a (twob) a- two-wayway tidal tidalpower power plant. plant.

2.2. Including Pumping The total energy generated by a tidal range scheme can be potentially increased by taking advantage of pumping, at high and low water. If the turbines are also designed for pumping, there will not be any significant increase in the cost of the scheme. However, pumping could also bring additional environmental benefits [23], as well as generating more energy. In practise, pumping is introduced during the holding phases. In the ebb-only generation mode, the objective is to raise the water level inside the basin to a maximum by pumping when the water level difference across the impoundment embankment is small. This generates a bigger head

difference Hps, and in turn more energy when the seaward water level falls with the ebbing tide. For the two-way generation scheme, pumping during ebb generation will be similar to pumping for the

ebb-only scheme. Pumping will be used to lower the water levels Hpe inside the basing during the flood-holding phase. This will generate a higher head difference during the flood generation phase. Pumping is economically feasible when the combined efficiency losses of pumping and generation are offset by the gained energy output as a result of an increased head difference. Schematic illustrations for ebb-only and two-way generation with pumping are illustrated in Figure 3a,b, respectively.

Energies 2019, 12, 2870 4 of 23

Starting at a high tide, ebb-only generation starts with a holding stage where both the turbines and sluice gates are closed and there is no flow between the outside sea and the impounded water body. Therefore, the impounded basin water level stays at around high tide, while the seaward water level recedes with the tide. Ebb generation phase commences when the head difference between the water level inside and outside the basin, referred to as Hse herein, is large enough to generate energy efficiently through opening only the turbines. This ebb generation phase then continues until the head difference across the impoundment embankment is not sufficient to generate energy efficiently, referred to as Hee herein. At this time, the second holding phase commences, with both the turbines and sluice gates being closed. The downstream water levels are then raised again with the flooding tide and the filling phase starts by opening both sluice gates and turbines (without generating energy) when the seaward water levels are higher than the water level inside the basin. This filling stage is followed by a holding phase for the next cycle when the water levels reach almost the same level, both inside and outside of the impoundment close to high tide. A schematic of the ebb generation scheme is illustrated in Figure2a. For two-way generation and starting from the ebb holding phase, where both the sluice gates and turbines are closed, the holding phase continues until the head difference across the impoundment embankment is large enough for efficient generation, in other words, reaching a starting head for ebb tides of Hse. This stage of the ebb generating phase starts by operating the turbines in order to generate energy and continues until the head difference across the impoundment is no longer adequate for efficient energy generation, i.e., reaching the ending head Hee towards the end of ebb tide. Near the end of ebb tide, the sluice gates are opened to empty the basin, until the water levels across the impoundment embankment are almost the same. Following this step, the flood-holding phase begins by closing the turbines and sluice gates until the head difference is higher than the starting head during flooding, i.e., Hsf. This is followed by the flood generation phase, where the turbines are operated again to generate energy. When the head difference is smaller than ending head, namely Hef, the sluice gates are again opened to raise the water levels inside the impoundment. The filling phase now stops and the ebb holding phase starts again, when the water levels across the impoundment embankment reach the same levels and the water level outside the impoundment starts falling again with the ebbing tide falling again with the ebbing tide. This can be seen as a periodic process, which repeats itself throughout each cycle. A schematic of the two-way generation scheme is illustrated in Figure2b.

2.2. Including Pumping The total energy generated by a tidal range scheme can be potentially increased by taking advantage of pumping, at high and low water. If the turbines are also designed for pumping, there will not be any significant increase in the cost of the scheme. However, pumping could also bring additional environmental benefits [23], as well as generating more energy. In practise, pumping is introduced during the holding phases. In the ebb-only generation mode, the objective is to raise the water level inside the basin to a maximum by pumping when the water level difference across the impoundment embankment is small. This generates a bigger head difference Hps, and in turn more energy when the seaward water level falls with the ebbing tide. For the two-way generation scheme, pumping during ebb generation will be similar to pumping for the ebb-only scheme. Pumping will be used to lower the water levels Hpe inside the basing during the flood-holding phase. This will generate a higher head difference during the flood generation phase. Pumping is economically feasible when the combined efficiency losses of pumping and generation are offset by the gained energy output as a result of an increased head difference. Schematic illustrations for ebb-only and two-way generation with pumping are illustrated in Figure3a,b, respectively. EnergiesEnergies 20192019,, 1212,, x 2870 FOR PEER REVIEW 5 5of of 23 23

(a) (b)

FigureFigure 3. 3. SchematicSchematic representation representation of ofthe the operational operational mode mode (including (including pumping) pumping) of: (a of:) One (a)-way One-way ebb- generation;ebb-generation; (b) a (twob) a-way two-way tidal tidalpower power plant. plant. 3. Swansea Bay Lagoon 3. Swansea Bay Lagoon Swansea Bay is located in the South West of the United Kingdom and constitutes part of the Swansea Bay is located in the South West of the United Kingdom and constitutes part of the South Wales coastline. As a part of the Bristol Channel, the tidal range in the bay often exceeds South Wales coastline. As a part of the Bristol Channel, the tidal range in the bay often exceeds 10 m 10 m [24], which makes it a suitable location for a tidal range scheme. The Swansea Bay Tidal Lagoon [24], which makes it a suitable location for a tidal range scheme. The Swansea Bay Tidal Lagoon was was proposed by tidal lagoon power (TLP) in 2004 [25]. The proposed lagoon wall would be 9.5 km proposed by tidal lagoon power (TLP) in 2004 [25]. The proposed lagoon wall would be 9.5 km long, long, creating a lagoon area of about 11.5 km2. The scheme would have an energy-generating life of creating a lagoon area of about 11.5 km2. The scheme would have an energy-generating life of 120 120 years and would consist of 16 bulb turbines, each of diameter 7.2 m, and with an installed capacity years and would consist of 16 bulb turbines, each of diameter 7.2 m, and with an installed capacity of 320 MW [7]. The area of the sluice gates would be approximately 800 m2 and the lagoon was of 320 MW [7]. The area of the sluice gates would be approximately 800 m2 and the lagoon was designed to be operated using the two-way generation [24,25] as outlined above. Based on the most designed to be operated using the two-way generation [24, 25] as outlined above. Based on the most recent report published by TLP [7], the annual energy generated is predicted to be 530 GWh per year. recent report published by TLP [7], the annual energy generated is predicted to be 530 GWh per year. 4. Modelling Methodology 4. Modelling Methodology 4.1. 0-D Modelling 4.1. 0-D Modelling 4.1.1. 0-D Model Setup 4.1.1. 0-D Model Setup A typical 0-D backward difference model was developed to solve the continuity equation. The new upstreamA typical water 0-D levels backward inside difference the impoundment model was ( Zdevelopedup,i + 1) at to any solve point the incontinuity time can equation. be calculated The newaccording upstream to both water the upstreamlevels inside water the levels impoundment at the previous (Zup,i time+ 1) at step any (Z pointup,i) and in time the downstreamcan be calculated water accordinglevels (Zdn,i to), both as follows: the upstream water levels at the previous time step (Zup,i) and the downstream water levels (Zdn,i), as follows: Q(H) + Qin Z + = Z + ∆t (1) up,i 1 up,i A Q(H) + Qin Z = Z + ∆t (1) where ∆t denotes the time step; Qin isup the,i + 1 inflowup,/ioutflowA to the lagoon through sources other than through the TRS, e.g., a river or outflows; A is the wetted plan surface area of the lagoon and Q(H) is the where ∆t denotes the time step; Q is the inflow/outflow to the lagoon through sources other than total discharge through the turbinesin and sluices and which will be discussed further in Section 4.1.2[ 19]. through the TRS, e.g., a river or outflows; A is the wetted plan surface area of the lagoon and Q(H) In the absence of substantial wetting and drying, the plan surface area A is generally assumed to is the total discharge through the turbines and sluices and which will be discussed further in Section be a constant value in 0-D models [17]. However, due to extensive flooding and drying in some regions 4.1.2 [19]. of Swansea Bay, this plan surface area of the impoundment could change significantly through the In the absence of substantial wetting and drying, the plan surface area A is generally assumed tidal cycle. The overview location of the Swansea Bay Lagoon is shown in Figure4[ 26], and Figure5 to be a constant value in 0-D models [17]. However, due to extensive flooding and drying in some illustrates the plan surface area of the lagoon for different impounded water levels (relatively to regions of Swansea Bay, this plan surface area of the impoundment could change significantly Ordnance Datum), which is calculated based on the bathymetry of the area inside the lagoon as shown through the tidal cycle. The overview location of the Swansea Bay Lagoon is shown in Figure 4 [26], in Figure 12. The variable wetted plan surface area, which is a function of the impounded water level and Figure 5 illustrates the plan surface area of the lagoon for different impounded water levels as shown in Figure5, is used in this study. (relatively to Ordnance Datum), which is calculated based on the bathymetry of the area inside the The model simulations were compared to published 0-D results in order to first validate the model. lagoon as shown in Figure 12. The variable wetted plan surface area, which is a function of the The model was set up with conditions reported by Petley and Aggidis [24], namely Hse = 3.0 m and impounded water level as shown in Figure 5, is used in this study. Hee = 1.0 m. The annual energy generated was predicted to be 472.89 GWhr, which is within 10% of the value reported by Petley and Aggidis [24] and Angelidous and Falconer [27].

Energies 2019, 12, 2870 6 of 23 Energies 2019, 12, x FOR PEER REVIEW 6 of 23 Energies 2019, 12, x FOR PEER REVIEW 6 of 23

Figure 4. Overview of the project elements [24]. Figure 4. Overview of the p projectroject elements [[24]24]..

Figure 5. Wetted area versus water level. Figure 5. Wetted area versus water level. Figure 5. Wetted area versus water level. Tidal data generated from the depth integrated velocities and solute transport (DIVAST 2-DU) The model simulations were compared to published 0-D results in order to first validate the model,The without model Swanseasimulations Bay were Lagoon, compared were used to published to provide 0 the-D results downstream in order water to first levels validate in the 0-Dthe model. The model was set up with conditions reported by Petley and Aggidis [24], namely Hse = 3.0 model. The However, model it was is common set up with to use conditions nearby tidal reported gauges by in Petley the absence and Aggidis of such [24] data., namely Comparisons Hse = 3.0 of m and Hee = 1.0 m. The annual energy generated was predicted to be 472.89 GWhr, which is within them and model-predicted Hee = 1.0 m. The energy annual output energy using generated the simulated was predicted downstream to be water472.89 levelsGWhr at, which the location is within of 10% of the value reported by Petley and Aggidis [24] and Angelidous and Falconer [27]. the10% lagoon of the value and the reported Mumbles by tidalPetley gauge, and Aggidis which is[24] part and of Angelidous the UK Tide and Gauge Falconer Network [27] of. the British Tidal data generated from the depth integrated velocities and solute transport (DIVAST 2-DU) OceanographicTidal data generated Data Centre from [28 ],the were depth carried integrated out. It v waselocities noted and that solute using transport the fixed ( operation,DIVAST 2- withDU) model, without Swansea Bay Lagoon, were used to provide the downstream water levels in the 0-D Hmodel,= 3.0 without m and SwanseaH = 1.0 Bay m, andLagoon, water were levels used from to the provide Mumbles the downstream Gauging station water underestimated levels in the 0 the-D model.se However, itee is common to use nearby tidal gauges in the absence of such data. Comparisons annualmodel. energyHowever, output it is bycommon about 10%,to use compared nearby tidal to the gauges predicted in the energy absence using of such water data. levels Comparisons generated of the model-predicted energy output using the simulated downstream water levels at the location fromof the a model 2-D model.-predicted energy output using the simulated downstream water levels at the location of the lagoon and the Mumbles tidal gauge, which is part of the UK Tide Gauge Network of the of theDue lagoon to the and large the variability Mumbles intidal the tidalgauge, range which through is part a spring-neapof the UK Tide cycle, Gauge optimisation Network process of the British Oceanographic Data Centre [28], were carried out. It was noted that using the fixed operation, inBritish this studyOceanographic involves findingData Centre the most [28], w effierecient carried operational out. It was conditions noted that for using each the ebb fixed and operation, flood tide. with Hse = 3.0 m and Hee = 1.0 m, and water levels from the Mumbles Gauging station Inwith order Hse to achieve= 3.0 m this, and a rangeHee of= starting1.0 m, generationand water water levels elevations from the (H Mumbles) were considered, Gauging varying station underestimated the annual energy output by about 10%, compared to sethe predicted energy using fromunderestimated 2 m to 8 m andthe annual in 1 cm energy increments, output and by for about a range 10%, of endingcompared generation to the predicted water levels energy (H )using from water levels generated from a 2-D model. ee 0.5water m tolevels 4.5 m generated and also withfrom 1a cm2-D increments. model. Figure6a,b illustrates the contour map of energy output Due to the large variability in the tidal range through a spring-neap cycle, optimisation process excludingDue to and the includinglarge variability the impact in the of tidal flooding range andthrough drying, a spring respectively.-neap cycle, The optimisation total energy process output in this study involves finding the most efficient operational conditions for each ebb and flood tide. In whenin this flooding study involves and drying finding of the the impounded most efficient wetted operational plan surface conditions area is for neglected each ebb is and only flood 5% less tide. than In order to achieve this, a range of starting generation water elevations (Hse) were considered, varying theorder energy to achieve output this, when a range flooding of starting and drying generation is included water elevations in the model. (Hse It) were should considered, be noted thatvarying the from 2 m to 8 m and in 1 cm increments, and for a range of ending generation water levels (Hee) from optimumfrom 2 m conditionsto 8 m and arein 1 di cmfferent increments, for with and and for without a range flooding of ending drying generation as shown water in Figure levels6 a,b.(Hee These) from 0.5 m to 4.5 m and also with 1 cm increments. Figure 6a,b illustrates the contour map of energy output changes0.5 m to 4.5 in operationm and also are with caused 1 cm byincrements. feedback Figure within 6 thea,b systemillustrate whens the thecontour head map difference of energy across output the excluding and including the impact of flooding and drying, respectively. The total energy output when structureexcluding is and reduced, including and the is similar impact to of thatflooding found and by drying, Bray et al.respectively. [29] when The the dischargetotal energy was output reduced when in flooding and drying of the impounded wetted plan surface area is neglected is only 5% less than the theflooding 2-D modelling. and drying However, of the impounded these changes wetted are plan often surface ignored area when is neglected comparing is only the simulations5% less than with the energy output when flooding and drying is included in the model. It should be noted that the optimum andenergy without output flooding when flo andoding drying and drying [15]. is included in the model. It should be noted that the optimum conditions are different for with and without flooding drying as shown in Figure 6a,b. These changes conditions are different for with and without flooding drying as shown in Figure 6a,b. These changes in operation are caused by feedback within the system when the head difference across the structure is in operation are caused by feedback within the system when the head difference across the structure is reduced, and is similar to that found by Bray et al. [29] when the discharge was reduced in the 2-D reduced, and is similar to that found by Bray et al. [29] when the discharge was reduced in the 2-D

Energies 2019, 12, x FOR PEER REVIEW 7 of 23 modelling. However, these changes are often ignored when comparing the simulations with and without flooding and drying [15].

Although both Hse and Hee covered the whole range in the 0-D models, it was found that the generated energy was insignificant when Hse was between 6.5 m and 8 m and Hee between 3.5 m and 4.5 m. Hence, the contour results shown in Figure 6a,b, and for the rest of this study, only cover from 2 m to 6.5 m for Hse and from 0.5 m to 3.5 m for Hee. It can be seen that the highest energy appears in the middle region areas in these figures, which represents the operation head of Hse and H . It can also be seen that if the impact of flooding and drying is excluded, then this has a limited seEnergies 2019, 12, 2870 7 of 23 impact on the energy output for this basin, with the energy being less than 5% compared with including the flooding and drying within the impoundment.

(a) (b)

FigureFigure 6. Energy 6. Energy output: output: (a) (Wa)ith With a constant a constant impounded impounded area; area; (b) ( bwith) with impounded impounded area area varying varying with with waterwater level, level, in inwhich which the the Hse/Hee Hse/Hee denote denote the the starting/ending starting/ending generation generation water water elevations elevations..

TheAlthough year 2012 both wasH se chosenand H foree covered this study the due whole to range the availability in the 0-D of models, boundary it was conditions found that and the validationgenerated da energyta through was insignificantother projects. when In theHse optimisationwas between model 6.5 m, andusing 8 mevery and halfHee tidebetween method 3.5 mwas and implemented4.5 m. Hence, over the acontour Neap-Spring results cycle shown instead in Figure of an6 a,b,entire and year, for thedue rest to the of thishigh study, computational only cover time from required2 m to 6.5for mthe for analysisHse and over from a 0.5year. m toIn 3.5order m for to Hensureee. It canthat be the seen ene thatrgy thepredicted highest over energy this appears typical in cyclethe represented middle region the areas average in these energy figures, generated which over represents a year, the the energy operation generated head of forHse alland tidalH secycles. It can in also2012 be was seen calculated that if the and impact the ofcycle flooding with andthe values drying isclosest excluded, to the then average this has annual a limited generation impact onwas the selectedenergy as output the typical for this tidal basin, cycle. with The the predicted energy being energy less thanoutput 5% for compared all complete with includingtidal cycles the in flooding 2012 andand the drying variation within from the the impoundment. average value per tidal cycle are listed in Table 1. Only complete cycles were included,The year resulting 2012 was in chosen the first for thiscycle study starting due after to the 60.6 availability h from the of boundary start of 2012. conditions The total and predictedvalidation energy data generated through other for the projects. complete In thecycles optimisation was approximately model, using 500.4 every GWh half for tidea starting method head was

Hseimplemented of 4.0 m and over Hee a of Neap-Spring 1.0 m. The average cycle instead energy of output an entire per year, cycle due was to approximately the high computational 20.85 GWh, time withrequired the difference for the analysis between over the amaxim year. Inum order and minimum to ensure thatoutputs the energybeing over predicted 25%. overTherefore, this typical the representativecycle represented tidal cycle the average was chosen energy in generatedorder to estimate over a year,the annual the energy generation. generated The forsecond all tidal cycle cycles in thein year, 2012 which was calculated deviated andby less the than cycle 2% with from the the values average, closest was to chosen the average as the annual representative generation tidal was cyselectedcle for optimisation as the typical in this tidal study. cycle. A The coefficient predicted of energy24.377, which output is for the all proportional complete tidal time cycles of the in year 2012 forand one the complete variation tidal from cycle, the was average used value to convert per tidal the cyclepredicted are listed energy in over Table one1. Only cycle complete to the annual cycles energywere included,generated. resulting in the first cycle starting after 60.6 h from the start of 2012. The total predicted energy generated for the complete cycles was approximately 500.4 GWh for a starting head Hse of 4.0 m and Hee of 1.0 m. The average energy output per cycle was approximately 20.85 GWh, with the difference between the maximum and minimum outputs being over 25%. Therefore, the representative

tidal cycle was chosen in order to estimate the annual generation. The second cycle in the year, which deviated by less than 2% from the average, was chosen as the representative tidal cycle for optimisation in this study. A coefficient of 24.377, which is the proportional time of the year for one complete tidal cycle, was used to convert the predicted energy over one cycle to the annual energy generated. Energies 2019, 12, 2870 8 of 23

Table 1. Energy generation per cycle for the 0-D model.

Starting Ending Time Energy Relative Starting Ending Time Energy Relative Cycle No Cycle No. Time (h) (h) (GWh) Deviation (%) Time (h) (h) (GWh) Deviation (%) 1 60.60 421.50 19.69 5.57 13 4284.40 4619.60 22.62 8.46 − 2 421.50 781.80 20.44 1.96 14 4619.60 4991.40 19.03 8.75 − − 3 781.80 1130.10 21.36 2.42 15 4991.40 5341.20 22.31 6.99 4 1130.10 1489.50 19.86 4.77 16 5341.20 5699.40 19.72 5.42 − − 5 1489.50 1824.90 21.81 4.60 17 5699.40 6061.40 21.43 2.76 6 1824.90 2197.50 19.06 8.59 18 6061.40 6445.60 21.84 4.75 − 7 2197.50 2534.10 22.57 8.24 19 6445.60 6804.80 19.20 7.92 − 8 2534.10 2892.90 19.15 8.14 20 6804.80 7165.80 23.58 13.09 − 9 2892.90 3241.80 23.30 11.76 21 7165.80 7512.20 18.29 12.29 − 10 3241.80 3612.30 18.55 11.04 22 7512.20 7873.20 23.83 14.29 − 11 3612.30 3924.60 22.17 6.32 23 7873.20 8221.20 19.26 7.63 − 12 3924.60 4284.40 17.98 13.77 24 8221.20 8568.60 23.39 12.16 −

4.1.2. Energy and Discharge Calculation The discharge through the turbines and, subsequently, the energy generated could be calculated using a Hill Chart. The Hill Chart for the Andritz Hydro double-regulated bulb turbine is shown in Figure7 and this relationship was used in this study [ 30]. The flow through the sluice gates was estimated as follows [29,31]: p Q = CdA 2gH (2)

where Cd is the discharge coefficient, a dimensionless factor of an orifice or valve, used to characterise the flow behaviour, and a suggested scalar with a magnitude of 1.0 was utilised in the study [29,30]; A is the sluice gate area (m2) and H is the head difference across the impoundment wall, calculated as EnergiesZ 2019Z , 12. , x FOR PEER REVIEW 9 of 23 up,i − dn,i

FigureFigure 7. 7. AndritzAndritz Hydro Hydro three three-blade-blade low low head head bulb bulb turbine turbine unit [31] [31]..

The turbine and pump efficiency can be calculated as:

Poutput ηt = (3) Ppotential

Ppotential ηp = (4) Pinput

Figure 8. Turbine efficiency calculated from Figure 7.

4.2. 2-D Modelling DIVAST 2-DU has been widely used in simulating marine renewable energy schemes in the past [33-35]. The DIVAST 2-DU model has been modified in this study to simulate lagoons, with flexible operation schemes being generated from 0-D models. The governing equations used in the DIVAST 2-DU model are outlined below. The mass conservation equation and the 2-D depth integrated momentum conservation equations in x and y directions, respectively, are given in Equations (5)–(7) and are derived by integrating the 3-D Reynolds average equations. The effects of bed friction, wind shear, the earth’s rotation, and turbulence are included in the depth-integrated momentum conservation equations [36]. Further details of the 2-D model can be found in [36,37].

Energies 2019, 12, x FOR PEER REVIEW 9 of 23

Energies 2019, 12, 2870 9 of 23

where ηt and ηp are turbine and pump efficiencies, respectively. It should be noted that although the ηt and ηp includes a variety of efficiencies, the turbine or pumping efficiency are the main losses in the tidal structure system [13], hence the other efficiencies which are outside the remit of this paper, such as generator efficiency and transformer efficiency, etc., are assumed to be 1.0 in this study; Poutput and Pinput denote the power output for the turbines and the power used during the pumping phase, respectively; Ppotential represents the potential power output of the turbines or as used in pumping. The resulting turbine efficiency obtained from the hill chart is shown in Figure8. The measured turbine and efficiency for the bulb turbines has been taken from the pervious work by Yates et al. [20]. Although the efficiency of turbines and pumps efficiency might be different before/after generating/sluicing phases, the primary direction of half of the turbines in the ebb direction and the other half in the flood direction have been considered herein. This is a very common approach adopted in the industry as confirmed through a certain number of studies published in the far-field modelling [18,24,27,32]. The difference in the turbine efficiency between Figure8 and the measured data [20] is under reasonableFigure 7. Andritz control, Hydro mirroring three-b thelade reliability low head bulb of the turbine Hill Chartunit [31] used. in this study.

Figure 8. Turbine efficiency calculated from Figure7. Figure 8. Turbine efficiency calculated from Figure 7. 4.2. 2-D Modelling 4.2. 2DIVAST-D Modelling 2-DU has been widely used in simulating marine renewable energy schemes in the past [33–35]. The DIVAST 2-DU model has been modified in this study to simulate lagoons, with DIVAST 2-DU has been widely used in simulating marine renewable energy schemes in the past flexible operation schemes being generated from 0-D models. The governing equations used in the [33-35]. The DIVAST 2-DU model has been modified in this study to simulate lagoons, with flexible DIVAST 2-DU model are outlined below. The mass conservation equation and the 2-D depth integrated operation schemes being generated from 0-D models. The governing equations used in the DIVAST momentum conservation equations in x and y directions, respectively, are given in Equations (5)–(7) and 2-DU model are outlined below. The mass conservation equation and the 2-D depth integrated are derived by integrating the 3-D Reynolds average equations. The effects of bed friction, wind shear, momentum conservation equations in x and y directions, respectively, are given in Equations (5)–(7) the earth’s rotation, and turbulence are included in the depth-integrated momentum conservation and are derived by integrating the 3-D Reynolds average equations. The effects of bed friction, wind equations [36]. Further details of the 2-D model can be found in [36,37]. shear, the earth’s rotation, and turbulence are included in the depth-integrated momentum conservation equations [36]. Further details of the 2-D model can be found in [36,37]. ∂ξ ∂q ∂qy + x + = 0 (5) ∂t ∂x ∂y   " # 2 2 ∂2q ∂qx ∂uqx ∂vqx ∂ξ τxw τxb  ∂ qx ∂ qx y  + β + = fq gH + + ε2 + +  (6) ∂t ∂x ∂y y − ∂x ρ − ρ  ∂x2 ∂y2 ∂x∂y Energies 2019, 12, 2870 10 of 23

∂q ∂uq ∂vq  τ τ  2 2 2  y  y y  ∂ξ yw yb ∂ qx ∂ qx ∂ qx  + β +  = fq gH + + ε + 2 +  (7) ∂t  ∂x ∂y  x − ∂y ρ − ρ  ∂x2 ∂y2 ∂x∂y

2 1 where qx and qy represent discharges per unit width in the x- and y-axis direction, respectively (m s− ); ξ denotes the water surface elevation above datum (m); H is the total water depth (m); β represents the momentum correction factor; f denotes the Coriolis parameter, which is caused by earth rotation 1 2 (rad s− ); g is gravitational acceleration (m s− ); τxw and τyw are the surface wind stress components in 2 the x- and y-axis directions, respectively (N m− ); τxb and τyb represent bed shear stress, also in both 2 1 directions; and ε is depth averaged eddy viscosity (m s− ). The model is constructed using an unstructured computational mesh, with a “cell-centred” layout [38]. Domain decomposition is used in this study to simulate the lagoon. This formulation enables two sub-domains to be generated, which are fully detachable. In particular, the upstream sub-domain represents the lagoon impoundment, whereas the downstream sub-domain represents the rest of the Bristol Chanel and the Severn Estuary. It should be noted that both of the sub-domains are non-overlapping, and each is covered by its own triangular unstructured mesh structure. Both sun-domains are linked dynamically, according to interior open boundary conditions defined through a water level and discharge relationship, as shown in Figures7 and8, and operated over time according to the sequences illustrated in Figure2.

5. Optimisation of Swansea Bay Lagoon

5.1. Flexible Operation As outlined in the introduction, energy generation of a TRS can be increased through using a flexible head operating system. This study calculates the energy output for various starting and ending heads to identify the most optimum operation scheme for the lagoon, but it takes a novel approach by breaking down the operation into small components as follows: Operation of every single tide, from high water to the next high water, is considered separately to find the ideal starting and ending heads which produce the maximum energy output. Optimising every single tidal cycle is denoted as ET in this study. Figure9 shows three imaginary tides to demonstrate the tidal components that are used for optimisation. The optimum operation is then calculated separately for each tide A, B, and C, as shown in Figure9a. This includes running the 0-D model for the complete range of feasible starting heads for ebb tides, i.e., Hse, and flood tides, i.e., Hsf, from 2.0 m to 8.0 m with 1 cm increments and the ending heads for ebb tides, i.e., Hee, and flood tides, i.e., Hef, covering a range from 0.5 m to 4.5 m, also with an increment of 1 cm. In this method, different starting and ending heads are examined for Tide A, with the optimum starting and ending heads defined when the maximum energy for this cycle is achieved. Similarly, the best and selected operations for Tide B and Tide C are calculated in isolation, as shown in Figure9a. However, the water level inside the lagoon for the start of Tide B is the water level calculated inside the lagoon at the end of Tide A, obtained using the selected operation for Tide A. The link between the operation of the tides leads to the next approach, which is the optimisation of the operation. In this method, which is referred herein to every tidal cycle and next (ETN), the optimum operation for every cycle is decided in conjunction with the next cycle. The 0-D model is used over the same range as for the ET method to simulate the optimum operation heads, which gives the maximum energy output for two successive tides; for instance, Tide A and B as shown in Figure9a. The optimum operation will be used for the first tide of the two tides, Tide A herein, and the process is repeated for the next two tides, Tide B and C, as shown in Figure9a. This way, we consider the fact that the inner water level for the consecutive tides, e.g., Tide B, is influenced by the inner water level at the beginning of this tide or the operation of the previous tide. In other words, the energy output generated for each cycle would be affected directly by the previous cycle. Energies 2019, 12, x FOR PEER REVIEW 11 of 23

previous tide. In other words, the energy output generated for each cycle would be affected directly by the previous cycle. On the other hand, every tidal cycle could be seen as two ebb or flood-half tides, as illustrated in Figure 9b. The every-half (EH) tide model is set up to simulate the most optimised operation head for every ebb and flood half tide. In a similar manner to the ETN approach, the EH model can be used to consider the next ebb or flood half tide, which is referred to as every half-tidal cycle and next (EHN) model in this study. The rationalisation for using the next half tide in the EHN is the impact that the operation at every half tide will have on the next half tide, corresponding to the ETN approach. In the ETN method, the best operating schedule is found by considering a range of starting and ending heads, as mentioned previously. However, the next half tide is also considered in selecting the best Energiesoperation.2019, 12, 2870 11 of 23

(a)

(b)

FigureFigure 9.9. 33 SchematicSchematic illustrationillustration ofof didifferentfferent optimisationoptimisation methodologies:methodologies: ((aa)) FullFull tidetide optimisationoptimisation illustrations:illustrations: every-tideevery-tide (ET) (ET and) and every every tidal cycletidal and cycle next and (ETN) next methods; (ETN) andmethods; (b) half and tide ( optimisationb) half tide illustrations:optimisation every-halfillustrations: (EH) every and-half every (EH half-tidal) and every cycle half and-tidal next cycle (EHN) and methods. next (EHN) methods.

OnAlthough the other a wide hand, range every of tidal starting cycle couldand ending be seen heads as two were ebb considered or flood-half in tides, this study as illustrated to ensure in Figurethat all9 b.the The potential every-half scenarios (EH) tidewere model captured, is set it up was to simulatefound that the the most energy optimised generated operation was negligible head for everyfor the ebb large and anfloodd small half tide. operating In a similar head manner combinations, to the ETN as shown approach, in Figure the EH 10. model The can main be used energy to considergeneration the graphs next ebb used or in flood this halfpaper tide, are which therefore is referred focused to on as H everyse from half-tidal 0.5 m to cycle 4.5 m and and next Hee (EHN) from model2.0 m to in 8.0 this m study. for clarity. The rationalisation Figure 10 shows for typical using theenergy next generation half tide in levels the EHN for different is the impact heads that for the 10 operation at every half tide will have on the next half tide, corresponding to the ETN approach. In the ETN method, the best operating schedule is found by considering a range of starting and ending heads, as mentioned previously. However, the next half tide is also considered in selecting the best operation. Although a wide range of starting and ending heads were considered in this study to ensure that all the potential scenarios were captured, it was found that the energy generated was negligible for the large and small operating head combinations, as shown in Figure 10. The main energy generation graphs used in this paper are therefore focused on Hse from 0.5 m to 4.5 m and Hee from 2.0 m to 8.0 m for clarity. Figure 10 shows typical energy generation levels for different heads for 10 spring tides using the ET model, where low generation outside the chosen range was clear. Moreover, the maximum energy generation point, which corresponded to the best possible operation, is shown with a red cross, highlighting the changes from tide to tide due to changes in the range for two consecutive tides. Energies 2019, 12, x FOR PEER REVIEW 12 of 23

spring tides using the ET model, where low generation outside the chosen range was clear. Moreover, the maximum energy generation point, which corresponded to the best possible operation, is shown Energieswith2019 a red, 12 , cross, 2870 highlighting the changes from tide to tide due to changes in the range for two12 of 23 consecutive tides.

FigureFigure 10. 10.ET ET model model for for 10 10 tides, tides, with with the the maximum maximum energy energy point, point, i.e., i.e. most, most optimised optimised operation, operation, being shownbeing with shown a red with cross. a red cross.

OperationOperation of of the the lagoon lagoon was was optimised optimised using a a fixed fixed (non (non-flexible)-flexible) operation operation,, and and different different methodsmethods were were introduced introduced in in this this study.study. TheThe energy generated for for each each method method over over the the second second tidal tidal cycle,cycle, representing representing the the annual annual generation generation output, output, is summarisedis summarised in in Table Table2. It2. can It can be seenbe seen that that the the EHN model,EHN i.e.,model, every-half-next i.e., every-half model,-next model, gave the gave best the optimised best optimised operation, operation, resulting resulting in the in highest the highest energy generatedenergy generated [16]. The [16] energy. The generated energy generated using the using EHN the model EHN wasmodel approximately was approximately 12.5% 12.5% higher higher than for fixed-headthan for fixe operation.d-head operation. Using half Using tides tohalf operate tides to could operate improve could theimprove energy the generated energy generated by about by 1.6%, whileabout then 1.6%, including while then the including next half tidethe next only half improved tide only the improved outcome the by outcome about 0.6%. by about 0.6%.

TableTable 2. 2.Optimisation Optimisation scenarios for for second second tidal tidal cycle. cycle. Change to Fixed-Head ScenarioScenario Energy (GWh)Energy (GWh) Change to Fixed-Head Schedule Schedule Fixed-headFixed-head schedule schedule 21.321.3 - - ET modelET model 23.523.5 10.5% 10.5% ETN modelETN model 23.623.6 10.6% 10.6% OptimisedOptimised EH modelEH model 23.823.8 11.9% 11.9% EHN modelEHN model 24.024.0 12.5% 12.5%

The behaviour of impoundments operated based on different optimisation models, including The behaviour of impoundments operated based on different optimisation models, including fixed-head operation models, are compared in order to highlight the differences. Figure 11 illustrates fixed-headthe water operation levels inside models, the are impoundment, compared in order energy to highlight output, and the ditheff erences. operation Figure scheduling 11 illustrates of the the waterimpoundment levels inside for the four impoundment, neap tides, energy based output,on different and theoptimisation operation scheduling models. Comparisons of the impoundment of the formodels four neap showed tides, that based generating on different started optimisation at a lower head models. difference Comparisons on many of occasions the models for showedthe fixed that- generatinghead models. started This at acauses lower a head lower di ffpeakerence generation on many and occasions prolonged for the generating fixed-head phases. models. This This will causes be a lowermore favourable peak generation in term ands of prolongedthe integration generating of the generation phases. This into will the benational more favourablegrid [16]. Moreover, in terms of the integration of the generation into the national grid [16]. Moreover, the corresponding increase in the tidal range within the lagoon has environmental benefits, but more detailed studies are required on the potential overall environmental impacts [29,33]. By separating every tide into two every-half tides, the ETN and EHN models showed a better capability of finding a balance point between each current tide and the next tide, thus allowing for the energy generated to be more stable. It can also Energies 2019, 12, x FOR PEER REVIEW 13 of 23

the corresponding increase in the tidal range within the lagoon has environmental benefits, but more detailed studies are required on the potential overall environmental impacts [29, 33]. By separating Energiesevery tide2019, into12, 2870 two every-half tides, the ETN and EHN models showed a better capability of finding13 of 23 a balance point between each current tide and the next tide, thus allowing for the energy generated beto be concluded more stable. that It the can maximum also be concluded energy output that the obtained maximum from energy each tide output is usually obtained less from than each the total tide installedis usually capacity, less than even the total taking installed optimisation capacity, schemes even taking into consideration. optimisation schemes into consideration.

Figure 11. Operation scheduling of the impoundment, water levels inside the impoundment, and power Figure 11. Operation scheduling of the impoundment, water levels inside the impoundment, and output comparisons for four neap tides, M_fixed-head, M_ET, M_ETN, M_EH, and M_EHN represent power output comparisons for four neap tides, M_fixed-head, M_ET, M_ETN, M_EH, and M_EHN the operation schedule based on fixed head, ET, ETN, EH, and EHN models, respectively, in which 1 to represent the operation schedule based on fixed head, ET, ETN, EH, and EHN models, respectively, 3 denote sluicing, generating, and holding phase, respectively. Zlw represent the seaside water level. in which 1 to 3 denote sluicing, generating, and holding phase, respectively. Zlw represent the seaside WL_fixed-head, WL_ET, WL_ETN, WL_EH, and WL_EHN represent the basin water level based on water level. WL_fixed-head, WL_ET, WL_ETN, WL_EH, and WL_EHN represent the basin water fixed head, ET, ETN, EH, and EHN models, respectively. P_fixed-head, P_ET, P_ETN, P_EH, and P_EHN representlevel based the on power fixed outputhead, ET, based ETN, on EH fixed, and head, EHN ET, models, ETN, EH, respectively. and EHN P_fixed models,-head, respectively. P_ET, P_ETN, P_EH, and P_EHN represent the power output based on fixed head, ET, ETN, EH, and EHN models, 5.2. Optimisationrespectively. with Pumping The inclusion of pumping, using the pumping efficiency discussed in Section 4.1.2, was also 5.2. Optimisation with Pumping considered in the optimisation models developed as a part of this study, namely the ET, ETN, EH, and EHNThe inclusion models. of The pumping, letter ‘P’ using has been the pumping added to efficiency the abbreviation discussed for in each Section model 4.1.2, toshow was also the inclusionconsidered of in pumping. the optimisation As a result, models the developed models including as a part pumping of this study, were: namely Every-tide-pump the ET, ETN, model EH, (ETPand EHN model), models. every-tide-next-pump The letter ‘P’ has model been added (ETNP to model), the abbreviation every-half-pump for each model model (EHP to show model), the andinclusion every-half-next-pump of pumping. As modela result (EHNP, the models Model). including The same pumping range of startingwere: Every heads,-tide namely-pumpH se modeland H(ETPsf, were model), chosen every from-tide 2.0-next m to-pump 8.0 m, model with a(ETNP 1 cm increment,model), every and-h alsoalf-p theump ending model heads, (EHP namelymodel), Handee andeveryH-efh,alf being-next from-pump 0.5 model m to 4.5(EHNP m, with Model). a 1 cm The increase. same range These of starting models heads, also included namely aH widese and range Hsf, ofwere flexible chosen pumping from 2.0 heads m to in8.0 order m, with to capturea 1 cm increment, many feasible and scenario,also the ending including heads, a pumping namely H startingee and head,Hef, being i.e., Hfromps, from 0.5 m 0.0 to m 4.5 to m, 2.0 with m, with a 1 acm 1 cmincrease. increase; These a pumping models also ending included head Ha pewide, from range 0.0 mof toflexible 2.0 m, pumping also with heads 1 cm increase,in order to with capture all pumping many feasible variations scenario, being consideredincluding a atpumping the end starting of each operatinghead, i.e., scenario.Hps, from 0.0 m to 2.0 m, with a 1 cm increase; a pumping ending head Hpe, from 0.0 m to 2.0 m,The also optimisation with 1 cm results increase, of the with operation all pumping for various variations models being including considered pumping at the are end shown of each in Tableoperating3. There scenario. is no particular cost considered in the pumping simulations. However, the amount of electricityThe optimisation used for pumping,results of includingthe operation pumping for various efficiency models as shownincluding in [ 20pumping], was deduced are shown from in theTable total 3. There electricity is no particular generation cost to calculateconsidered the in netthe electricitypumping simulations generated.. However, It can be the seen amount that the of EHNPelectricity model, used which for pumping, is every-half-next-pump including pumping model, efficiency produces as theshown best in optimised [20], was operating deduced schedule,from the resultingtotal electricity in approximately generation 27.2% to calculate more energy the net output electricity in comparison generated. to aIt fixed-head can be seen operation that the without EHNP pumping.model, which The di isff erencesevery-half between-next-p theump models model, introduced produces in the this best study optimised are consistent operating with the sch resultsedule, withoutresulting including in approximately pumping, as27.2% shown more in Table energy2. These output results in comparison from the 0-D to model a fixed suggests-head operation that the optimisation schemes including pumping can increase the potential of the lagoon for energy generation by about 15% without any significant extra costs. Energies 2019, 12, x FOR PEER REVIEW 14 of 23 without pumping. The differences between the models introduced in this study are consistent with the results without including pumping, as shown in Table 2. These results from the 0-D model suggests that the optimisation schemes including pumping can increase the potential of the lagoon Energiesfor energy2019, generation12, 2870 by about 15% without any significant extra costs. 14 of 23

Table 3. PPumpingumping optimisation scenarios for the second tidal cycle. Change to Fixed-Head ScenarioScenario Energy (GWh)Energy (GWh) Change to Fixed-Head Schedule Schedule Fixed-headFixed-head schedule schedule 21.321.3 - - ETP modelETP model 26.726.7 25.5% 25.5% ETNPETNP model model 26.726.7 25.5% 25.5% OptimisedOptimised EHP modelEHP model 27.027.0 26.7% 26.7% EHNPEHNP model model 27.127.1 27.2% 27.2%

6. 2 2-D-D Modelling

6.1. Model Setup To accurately simulate the tidal flowflow and energy prediction for Swansea Bay Lagoon, the entire Bristol Chanel and Severn Estuary, which encompasses the lagoon are areaa and covers an area of about 2 55805805 km 2,, is is modelled modelled in in this this study. study. The The seaward seaward open open boundary boundary data are obtained from the National Oceanographic Centre Centre [15] [15.]. Average Average river river inputs inputs were were included included as point as point sources sources in the in model. the model. The Thebathymetry bathymetry was wasprovided provided by EDINA by EDINA Digimap Digimap and and was was used used to tobuild build the the mesh mesh in in this this study study [39] [39].. Model decomposition was used used to to model model the the lagoon lagoon [22, [22, 2929]] and the domains were linked using the hydraulic structures,structures, i.e.,i.e.,the the turbines turbines and and sluice sluice gates gates [29 [29]]. The. The wind wind stress stress is assumedis assumed to beto 0be and 0 and the theManning Manning roughness roughness coeffi cient, coefficient, which representswhich represents the bed friction the bed in estuarinefriction in and estuarine riverine andstudies, riverine is set studies,to 0.02 in is this set study,to 0.02 which in this has study been, which calibrated has been to be calibrated a reliable valueto be a in reliable the 2-D value model in [ 40the]. 2 The-D model [40]only. The conserves model mass only throughconserves the mass turbines through and the sluice turbines gates, and which sluice is considered gates, which to beis considered sufficient for to the be purposesufficient of for this the study. purpose The lagoonof this representation,study. The lagoon model representation, bathymetry around model the bath lagoon,ymetry and around validation the pointslagoon are, and shown validation in Figure points 12 ,are along shown with in a Figure satellite 12, image along as with the a background. satellite image as the background.

Figure 12. SwanseaSwansea Bay Lagoon region and bathymetry as included in the d depthepth i integratedntegrated v velocitieselocities and solutesolute transporttransport (DIVAST(DIVAST 2-DU)2-DU) model.model.

Unstructured models including and excluding the lagoon were set up over the computational domain using different different grid sizes. A finer finer mesh without Swansea Bay Lagoon was refined refined to 50 m in the location location of of the the lagoon lagoon to give to give a higher a higher resolution resolution around around the lagoon the lagoon site. The site. computational The computational domain domainconsisted consisted of 59,410 of unstructured 59,410 unstructured triangular triangular cells, 117,377 cells, nodes, 117,377 and nodes 176,787, and elements. 176,787 The elements. calculation The calculationof the discharges of the through discharges the turbines through and the sluice turbines gates and were sluice coupled gates with were a ramp coupled sinusoidal with function a ramp sinusoidalto provide function a smooth to relationship provide a smooth between relationship the operation between regime the modes operation [41]. regime modes [41].

6.2. Model Validation Validation of the models were carried out using available field measurements in the DIVAST 2-DU model without Swansea Bay Lagoon in the year of 2012. In particular, the models were calibrated against water levels and velocity magnitudes and directions measured at five different offshore Energies 2019, 12, x FOR PEER REVIEW 15 of 23

Validation of the models were carried out using available field measurements in the DIVAST 2- DU model without Swansea Bay Lagoon in the year of 2012. In particular, the models were calibrated against water levels and velocity magnitudes and directions measured at five different offshore locations, shown in Figure 12, using seabed mounted Aquapro acoustic doppler current profilers (ADCPs) by Aberystwyth University as a part of the Smart Coast Project [42]. For brevity, three points representing the Western, Central, and Eastern parts of the Bay, namely L2, L3, and L5, are shown here. Figures 13–15 show the comparisons between observed and predicted water levels, and depth average velocity magnitudes and directions, respectively. It is clear that the 2-D model overestimates the water levels by roughly 0.2 m at high tide (HW) and 0.5 m at low tide (LW), compared with the observed ADCP data. The discrepancies between the measured and observed current speeds are limited, as shown in Figure 14, and this is thought to be due to inaccuracies in the representation of the wind effects, recently changed bed elevations, and a constant bed friction [38]. The root mean square error (RMSE) and the R-squared (R2) of differences between the predicted and measured water levels and current speeds at all three validation sites are included in Table 4. The RMSE and R2 values are calculated according to the formulations given in Equations (8) and (9):

∑n (P − O )2 RMSE = √ i=1 i i (8) n Energies 2019, 12, 2870 15 of 23 2 n n n n(∑i=1 PiOi) − ∑i=1 Pi ∑i=1 Oi locations, shown in FigureR2 = 12 , using seabed mounted Aquapro acoustic doppler current profilers(9) (ADCPs) by Aberystwyth University√[n ∑n asP a2 part− (∑ ofn theP ) Smart2][n ∑n CoastO 2 Project− (∑n [O42)].2] For brevity, three points ( i=1 i i=1 i i=1 i i=1 i ) representing the Western, Central, and Eastern parts of the Bay, namely L2, L3, and L5, are shown here. whereFigures n 13 denotes–15 show the the number comparisons of time between steps during observed the andsimulation predicted period, water and levels, Pi andand depthOi represent average thevelocity predicted magnitudes and observed and directions, terms at respectively. time step i, respectively. It is clear that the 2-D model overestimates the water levelsThe by relatively roughly 0.2small m atRMSE high and tide high (HW) R2 and values 0.5 mindicate at low good tide (LW),correlation compared between with the the predicated observed andADCP measured data. The values discrepancies with the errors between in the the predicted measured water and levels observed being current less than speeds 0.15. are Hence, limited, it can as beshown concluded in Figure that 14 the, and model this agrees is thought well towith be the due observed to inaccuracies data and in, thetherefore representation, can be reliably of the windused toeff modelects, recently the key changed hydrodynamic bed elevations, parameters and of a constantelevations bed and friction velocities [38]. over the domain of interest.

(a)

Energies 2019, 12, x FOR PEER REVIEW 16 of 23 (b)

(c)

FigureFigure 13. 13. TypicalTypical comparison comparison of of observed observed and and predicted predicted water water levels levels at at L2 L2 ( (a),), L3 L3 ( (b)),, and L5 ( c).

(a)

(b)

(c)

Figure 14. Typical comparison of observed and predicted current speed at L2 (a), L3 (b), and L5 (c).

Energies 2019, 12, x FOR PEER REVIEW 16 of 23

(c)

EnergiesFigure2019, 12 13., 2870 Typical comparison of observed and predicted water levels at L2 (a), L3 (b), and L5 (c). 16 of 23

(a)

(b)

(c)

FigureFigure 14. 14. TypicalTypical comparison comparison of of observed observed and and predicted predicted current current speed at L2 ( a), L3 ( b)),, and L5 ( c).

The root mean square error (RMSE) and the R-squared (R2) of differences between the predicted and measured water levels and current speeds at all three validation sites are included in Table4. The RMSE and R2 values are calculated according to the formulations given in Equations (8) and (9): s Pn 2 = (Pi Oi) RMSE = i 1 − (8) n

 2  P  P P   n n P O n P n O  2  i=1 i i i=1 i i=1 i  R =  −  (9)  r    Pn Pn 2 Pn Pn 2   n P 2 P n O 2 O  i=1 i − i=1 i i=1 i − i=1 i

where n denotes the number of time steps during the simulation period, and Pi and Oi represent the predicted and observed terms at time step i, respectively. Energies 2019, 12, 2870 17 of 23 Energies 2019, 12, x FOR PEER REVIEW 17 of 23

(a)

(b)

(c)

FigureFigure 15. 15. TypicalTypical comparison comparison of of observed observed and and predicted currentcurrent directiondirection from from North North at at L2 L2 (a (),a L3), L3 (b ), (band), and L5 L5 (c). (c).

Table 4. Analysis of measured and predicted data at L2, L3, and L5. Table 4. Analysis of measured and predicted data at L2, L3, and L5. 2 No NoLocation Location Latitude Latitude Longitude Longitude Terms Terms RMSE RMSE RR2 WaterWater Level Level (m) (m)0.111 0.111 0.9970.997 1 1L2 L251°31.78′51 N◦ 31.780030 N°58.90036′ W◦58.96 0 W VelocityVelocity (m/s) (m /s)0.055 0.055 0.8320.832 WaterWater Level Level (m) (m)0.136 0.136 0.9970.997 2 2 L3 L351°33.56′51 N◦ 33.560030 N°56.30032′ W◦56.32 0 W VelocityVelocity (m/s) (m /s)0.031 0.031 0.7740.774 WaterWater Level Level (m) (m)0.147 0.147 0.9970.997 3 3L5 L551°31.82′51 N◦ 31.820030 N°51.20035′ W◦51.25 0 W VelocityVelocity (m/s) (m /s)0.017 0.017 0.7870.787

GridThe dependencyrelatively small assessment RMSE and was high carried R2 values out indicate and it was good found correlation that thebetween models the werepredicated not dependentand measured on the values grid withsize. theThere errors was in only the a predicted slight difference water levels in the being water less levels than 0.15.between Hence, the itcoarse can be andconcluded finer meshes. that the The model main agreesreason wellfor this with is thought the observed to be datadue to and, the therefore,differences can in bethe reliably surface usedslope to ∂ξ gradients,model the i.e. key, the hydrodynamic term of gH parametersin Equations of ( elevations6) and (7), andas a velocitiesresult of differences over the domain in the ofbathymetry interest. ∂x and asGrid a result dependency of interpolation assessment based was on carried different out grid and itsizes. was found that the models were not dependent on the grid size. There was only a slight difference in the water levels between the coarse and finer

Energies 2019, 12, 2870 18 of 23

Energies 2019, 12, x FOR PEER REVIEW 18 of 23 meshes.Energies 2019 The, 12 main, x FOR reason PEER REVIEW for this is thought to be due to the differences in the surface slope gradients,18 of 23 The water levels∂ξ and currents during ebb and flood generation are shown in Figures 16 and 17, i.e., the term of gH ∂x in Equations (6) and (7), as a result of differences in the bathymetry and as a resultrespectively.The of interpolation water These levels results and based currents are on consistent diff erentduring grid withebb sizes. andprevious flood studiesgeneration [18] are and shown give furtherin Figure confidences 16 and 17, in respectively.utilisingThe waterthe modelThese levels forresults and the currents purposeare consistent duringof energy with ebb generation andprevious flood generationstudiesprediction. [18] are and shown give further in Figures confidence 16 and 17 in, respectively.utilising the model These for results the purpose are consistent of energy with generation previous studiesprediction. [18] and give further confidence in utilising the model for the purpose of energy generation prediction.

(a) (b)

Figure 16. Water level( a(a)) and current (b) streamlines during the flood generating(b) mode in the 2-D FigureFiguremodel. 16.16. WaterWater level level (a (a) )and and current current (b ()b streamlines) streamlines during during the the flood flood generating generating mode mode in the in 2 the-D 2-Dmodel. model.

(a) (b)

FigureFigure 17.17.Water Water level level(a ()a )(a and) and current current (b) streamlines(b) streamlines during during the ebb the generating ebb generating(b) mode inmode the 2-Din the model. 2-D model. 7. ComparisonFigure 17. Water between level 2-D (a) andand 0-Dcurrent Models (b) streamlines during the ebb generating mode in the 2-D model. 7. Comparison between 2-D and 0-D Models 7.1. Under Constant Operation Head 7. Comparison between 2-D and 0-D Models 7.1. Under0-D and Constant 2-D model Operation predictions Head were compared, in order to validate the 0-D model predictions. It was also noted earlier that no extra momentum transfer was added in the DIVAST 2-DU model 7.1. Under0-D and Constant 2-D model Operation predictions Head were compared, in order to validate the 0-D model predictions. It as a result of the flow through the turbines, as the main purpose of this study has been focused on was also noted earlier that no extra momentum transfer was added in the DIVAST 2-DU model as a optimising0-D and the 2 operation-D model predictions head to maximize were compared, the energy in generation, order to validate with more the detail0-D model being predictions. given in [43 It]. result of the flow through the turbines, as the main purpose of this study has been focused on Thewas 2-Dalso simulations noted earlier were that carried no extra out momentum with constant transfer operating was added heads in of theH DIVAST= 4.6 m 2 and-DUH model= 1.9 as m, a optimising the operation head to maximize the energy generation, with morese detail being givenee in [43]. whichresult were of the the flow values through from the the most turbines, optimal as theconstant main operation purpose headof this in studythe 0-D has model. been Simulations focused on The 2-D simulations were carried out with constant operating heads of H = 4.6 m and H = 1.9 m, wereoptimising conducted the operation over the typicalhead to spring maximize and the neap energy tidal cycles,generation, i.e., the with second morese cycledetail as being shown givenee in Table in [43]2,. which were the values from the most optimal constant operation head in the 0-D model. Simulations inThe order 2-D simulations to provide awere representative carried out estimatewith constant of the operating annual output heads of yield. Hse = Figure 4.6 m 18anda–c H showsee = 1.9 the m, were conducted over the typical spring and neap tidal cycles, i.e., the second cycle as shown in Table 2, waterwhich levels,were the water values head from diff erence,the most discharge optimal constant through theoperation turbines head and in sluices the 0-D gates, model. power Simulations output, werein order conducted to provide over a representativethe typical spring estimate and neap of the tidal annual cycles, output i.e., the yield. second Figure cycle 18 aas– cshown shows in the Table water 2, inlevels, order water to provide head a difference, representative discharge estimate through of the the annual turbines output and yield. sluices Figure gates, 18 a power–c shows output the water, and levels,energy waterin the head2-D and difference, the 0-D models, discharge respectively. through the The turbines duration and of generation sluices gates, per power tide and output energy, and in energy in the 2-D and the 0-D models, respectively. The duration of generation per tide and energy in

Energies 2019, 12, 2870 19 of 23

andEnergies energy 2019 in, 12 the, x 2-DFOR PEER and theREVIEW 0-D models, respectively. The duration of generation per tide19 and of energy23 in the typical cycle are summarized in Table5. It can be seen that there is good regression between thethe 0-D typical and 2-Dcycle models. are summarized The energy in Table predicted 5. It can usingbe seen the that 0-D there model is good in regression this study between overestimated the the0 predictions-D and 2-D models. relative The to the energy 2-D predicted model by using approximately the 0-D model 7.5%. in this These study are overestimated consistent with the the overestimationpredictions relative of about to 7% the reported 2-D model for by a similar approximately 0-D predictions 7.5%. These for arean independent consistent with study the [18]. overestimation of about 7% reported for a similar 0-D predictions for an independent study [18]. Therefore, the 0-D model is considered as a reliable tool for energy estimation for the preliminary design Therefore, the 0-D model is considered as a reliable tool for energy estimation for the preliminary stages and implementation during optimisation, which requires a large number of runs. The main design stages and implementation during optimisation, which requires a large number of runs. The reasonmain for reason the di forfferent the different values ofvalues the energyof the energy generated generated between between the 0-D the and0-D and 2-D 2 models-D models is the is the impact fromimpact hydrodynamics from hydrodynamics associated associated with a more with accurate a more accurate prediction prediction from the from 2-D the models. 2-D models. As mentioned As above,mentioned the upstream above, the water upstream level iswater calculated level is fromcalculated a continuity from a continuity equation equation (Equation (Eq (1))uation in the(1)) formerin model,the former while model the latter, while model the latter applies model the applies mass conservation the mass conservation equation equation and the and 2-D the depth 2-D integrateddepth momentumintegrated conservation momentum conservation equations (Equations equations (Eq (5)–(7)).uations (5)–(7)).

(a)

(b)

(c)

FigureFigure 18. 18.2-D 2-D and and 0-D 0-D model model comparisonscomparisons between: between: (a ()a W) Waterater level level and and power power output, output, in which in which WL_0-D,WL_0-D, WL_2-D WL_2-D and and Zlw_0-D,Zlw_0-D, Zlw_2 Zlw_2-D-D denote denote the the basin basin water water level leveland seaside and seaside water level water in 0 level-D in 0-Dand and 2-D 2-D models, models, respectively. respectively. P_0-D P_0-Dand P_2 and-D denote P_2-D the denote power the output power in 0 output-D and in2-D 0-D models, and 2-D models,respectively; respectively; (b) water (b) waterhead difference head diff erence and energy and energygenerated, generated, in which in DH_0 which-D, DH_0-D, DH_2-D DH_2-Dand andEnergy_0 Energy_0-D,-D, Energy_2 Energy_2-D-D denote denote the water the water head headdifference difference and energy and energygeneration generation in 0-D and in 0-D2-D and 2-Dmodels, models, respectively; respectively; and and (c) (cdischarge) discharge through through the thesluice sluice gates gates and andturbines, turbines, in which in which QTB_0 QTB_0-D,-D, QTB_2-D and QSL_0-D, QSL_2-D denote the discharge through turbines and sluice gates in 0-D and QTB_2-D and QSL_0-D, QSL_2-D denote the discharge through turbines and sluice gates in 0-D and 2-D, respectively. 2-D, respectively.

Energies 2019, 12, 2870 20 of 23

Table 5. Energy generation comparison between 0-D and 2-D models.

Averaged Duration of Generating in Every Average Energy Generated in the Half Tide of the Typical Cycle (h) Typical Cycle (Gwh) 0-D model 1.9 21.3 2-D model 1.9 19.7 change 0% 7.5% −

7.2. Energy Comparison with Flexible Optimisation Scenarios The DIVAST 2-DU model was then modified to run using a flexible operation, derived from the 0-D models. Moreover, the DIVAST 2-DU was also modified to include pumping, with a flexible pumping operation being obtained from the 0-D model simulations, in which the upstream and downstream were linked dynamically with the pumping volume over each time step being added to the linked cell. A flexible pumping efficiency was used in this section [20]. The 2-D model was implemented to assess the performance of the various 0-D models developed in this study, namely the ET, ETN, EH, and EHN models. It should be noted that the Hse and Hee in the fixed-head scheme were similar to the previous section and were set to 4.6 m and 1.9 m, respectively. Tables6 and7 summarise the energy estimates and their changes compared to fixed-head operations, using various flexible optimisation schemes in the 2-D and 0-D models and without and with pumping, respectively. The 2-D model results support the 0-D model results and highlight that the optimisation schemes could bring more than a 15% increase to the energy generated using fixed-head operation without pumping. This increase is about 30% when pumping is included. Finally, the energy generation predicted using flexible 0-D models were in very good agreement with those predicted using the 2-D models under the same conditions, with the difference between the 0-D and 2-D model predictions being lower for the flexible models. This highlights that the 0-D model is also a reliable tool for energy estimation, including flexible operation and pumping at preliminary stages and as an optimisation tool requiring a large number of runs.

Table 6. Comparison of optimisation scenarios without pumping.

Energy (GWh) Change to Fixed-Head Difference between 2-D Scenario Schedule 2-D (%) and 0-D Energy 2-D Model 1 0-D Model Prediction (%) Fixed-head schedule 19.7 21.3 - 7.5% − ET model 22.7 23.5 15.6% 3.2% − ETN model 22.8 23.6 15.7% 3.2% Optimised − EH model 22.8 23.8 15.8% 4.3% − EHN model 22.9 24.0 16.0% 4.6% − 1 as shown in Table2.

Table 7. Comparison of optimisation scenarios with pumping.

Energy (GWh) Change to Fixed-Head Difference between 2-D Scenario Schedule 2-D (%) and 0-D Energy 2-D Model 1 0-D Model Prediction (%) Fixed-head schedule 19.7 21.3 - 7.5% − ETP model 25.3 26.7 28.4% 5.0% − ETNP Optimised 25.4 26.7 29.0% 4.8% model − EHP model 25.4 27.0 29.0% 5.9% − EHNP 25.5 27.1 29.6% 5.8% model − 1 as shown in Table3. Energies 2019, 12, 2870 21 of 23

8. Conclusions In this paper, various schemes have been proposed to optimise the operation of TRS using a widely used 0-D modelling methodology and applied to the proposed Swansea Bay Lagoon. Initially, the energy output was calculated for various starting and ending heads to identify the optimum operation schemes for the lagoon. However, in estimating the optimal operation schemes, a novel approach has been adopted by breaking the operation up into small components instead of applying a fixed head for a whole tidal cycle. In turn, the optimisation results of the operation for various models, including pumping, has been adopted to further optimise more operational characteristics. These results from the 0-D models were compared with a more sophisticated 2-D model, and the differences between the energy output and performance were highlighted, as predicted from the 0-D and 2-D models, ensuring the reliability of the optimisation effects in some extent. Most notably, it has been shown that the 0-D model and 2-D models can complement one-another, particularly in enabling the number of computationally expensive 2-D model simulations to be reduced. Multi-dimensional numerical models without barrages or lagoons can provide the input water level boundary conditions for 0-D models. In return, 0-D models can support multi-dimensional models with optimised parameters for more accurate predictions. For Swansea Bay Lagoon, the results shown that optimisation using the novel approach reported herein can lead to at least a 10% increase in energy output, without including pumping, in comparison to the maximum energy output using a similar operational procedure for all the tides. This increase in energy could be as much as approximately 25% more when pumping is included. It has been shown that storm surges could affect the instantaneous power output, although the two-way generation mode of operation utilised in this study has been shown to be least influenced by storm surges [44]. This improved energy generation procedure, including operation flexibility, needs to be validated using 2-D modelling due to differences in the simplistic 0-D modelling approach compared to the more accurate 2-D model procedure. Further studies are required to evaluate the impact of storm surges and improve on the simplified 0-D modelling approach used in this study to predict the total energy generated for a spring-neap and annual cycle. The optimised operation schemes are used to simulate the lagoon using 2-D models, and the differences between the 0-D and 2-D results are highlighted. The 0-D model results are in good agreement with the hydrodynamic model predictions, since the deviation is below 10%. Additionally, simulations of the optimised operations using the 2-D model reveals an increase in energy generation of 10%–20% without pumping and 20%–30% with pumping. Hence, the results show that by using flexible operation heads, a TRS is able to improve on the energy output efficiency, particularly when taking into account the different tidal ranges at the start of every or every-half tide. With regard to the designed operational characteristics of tidal lagoons, more research should aim towards the far-field hydrodynamic impact, both with and without the combined effects of other proposed tidal lagoons and barrages in the Bristol Chanel and Severn Estuary, particularly when applying such optimisation schemes to the studied lagoon. Additional studies of particular interest could focus on the method of implementing these schemes as the operational characteristics may vary during the whole tide.

Author Contributions: J.X. developed and set up the 0-D model for the various scenarios reported and carried out the simulations. R.A. developed the concept and supervised the project. R.A. and R.A.F. have led a wide range of research projects in tidal renewable energy and R.A.F. has advised on this project. J.X. drafted the manuscript which was refined by all authors. Funding: This research received no external funding. Acknowledgments: Jingjing Xue would like to thank China Scholarship Council (CSC) and Cardiff University for supporting this work. Conflicts of Interest: The authors declare no conflicts of interest. Energies 2019, 12, 2870 22 of 23

References

1. Falconer, R.A.; Xia, J.; Lin, B.; Ahmadian, R. The Severn Barrage and other tidal energy options: Hydrodynamic and power output modeling. Sci. China Ser. E Technol. Sci. 2009, 52, 3413–3424. [CrossRef] 2. Wikipedia. Wind Power in the United Kingdom. Available online: https://en.wikipedia.org/wiki/Wind_ power_in_the_United_Kingdom (accessed on July 2019). 3. Department of Energy Climate Change. UK Renewable Energy Roadmap. 2011. Available online: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/48128/2167- uk-renewable-energy-roadmap.pdf (accessed on 24 July 2019). 4. World Energy Council. World Energy Resources Marine Energy. 2016. Available online: https://www.marineenergywales.co.uk/wp-content/uploads/2016/01/World-Energy-Council-Marine- Energy-Resources-2016.pdf (accessed on 12 December 2015). 5. Wave and Tidal Energy: Part of the UK’s Energy Mix. Available online: https://www.gov.uk/guidance/wave- and-tidal-energy-part-of-the-uks-energy-mix#tidal-range-potential (accessed on 22 January 2013). 6. Waters, S.; Aggidis, G. A World First: Swansea Bay Tidal lagoon in review. Renew. Sustain. Energy Rev. 2016, 56, 916–921. [CrossRef] 7. Green Light for World’s First Tidal Lagoon. Available online: http://www.renewableenergyfocus.com/view/ 42607/green-light-for-worlds-first-tidal-lagoon/ (accessed on 21 July 2015). 8. Hendry, C. The Role of Tidal Lagoons. Available online: https://hendryreview.files.wordpress.com/2016/08/ hendry-review-final-report-english-version.pdf (accessed on September 2016). 9. BBC. David Cameron’s enthusiasm for Swansea Tidal Lagoon ‘Reducing’. Available online: https://www. bbc.co.uk/news/uk-wales-politics-35306084 (accessed on 13 January 2016). 10. BBC. £1.3bn Swansea Bay Tidal Lagoon Project Thrown Out. Available online: https://www.bbc.co.uk/news/ uk-wales-south-west-wales-44589083 (accessed on 25 June 2018). 11. Mohr, P.; Lloyd, A. “Levelised Costs of Power from Tidal Lagoons,” Pöyry Management Consulting (UK) Ltd. Available online: http://www.poyry.co.uk/sites/www.poyry.co.uk/files/tidallagoonpower_ levelisedcoststudy_v7_0.pdf (accessed on 31 March 2014). 12. Tidal Lagoon Power. The New Power Cost League Table2016. Availableonline: http://www.tidallagoonpower. com/wp-content/uploads/2016/09/New_Power_Cost_League_Table_2016.pdf (accessed on 24 July 2019). 13. Aggidis, G.; Benzon, D.S. Operational optimisation of a tidal barrage across the Mersey estuary using 0-D modelling. Ocean Eng. 2013, 66, 69–81. [CrossRef] 14. Yates, N. Optimising Tidal Lagoons. In Proceedings of the European Wave and Tidal Eenergy Conference 2017, Cork, Republic of Ireland, 27 August–1 September 2017. 15. Ahmadian, R.; Xue, J.; Falconer, R.A.; Hanousek, N. Optimisation of Tidal Range Schemes. In Proceedings of the 12th European Wave and Tidal Energy Conference, 27 August–1 September 2017; p. 1059. 16. Angeloudis, A.; Kramer, S.C.; Avdis, A.; Piggott, M.D. Optimising tidal range power plant operation. Appl. Energy 2018, 212, 680–690. [CrossRef] 17. Prandle, D. Simple theory for designing tidal power schemes. Water Resource 1984, 7, 21–27. [CrossRef] 18. Angeloudis, A.; Falconer, R.A.; Bray, S.; Ahmadian, R. Representation and operation of tidal energy impoundments in a coastal hydrodynamic model. Renew. Energy 2016, 99, 103–1115. [CrossRef] 19. Angeloudis, A.; Ahmadian, R.; Falconer, R.A.; Bockelmann-Evans, B. Numerical model simulations for optimisation of tidal lagoon schemes. Appl. Energy 2016, 165, 522–536. [CrossRef] 20. Yates, N.; Walkington, I.; Burrows, R.; Wolf, J. The energy gains realisable through pumping for tidal range energy schemes. Renew. Energy 2013, 58, 79–84. [CrossRef] 21. Douglas, T.H. Pumped Storage, Conference Proceedings edition; Thomas Telford Publishing: London, UK, 1990. 22. Xia, J.; Falconer, R.A.; Lin, B. Impact of different operating modes for a Severn Barrage on the tidal power and flood inundation in the Severn Estuary, UK. Appl. Energy 2010, 87, 2374–2391. [CrossRef] 23. Vieira, F.; Ramos, H. Hybrid solution and pump-storage optimization in water supply system efficiency: A case study. Energy Policy 2018, 36, 4142–4148. [CrossRef] 24. Petley, S.; Aggidis, G. Swansea Bay tidal lagoon annual energy estimation. Ocean Eng. 2016, 111, 348–357. [CrossRef] 25. Rajgor, G. Time for tidal lagoons. Renew. Energy Focus 2016, 17, 202–204. [CrossRef] Energies 2019, 12, 2870 23 of 23

26. Tidal Lagoon Swansea Bay plc. Environmental Statement Non-Technical Summary. Available online: http://www.tidallagoonpower.com/wp-content/uploads/2018/01/6.1_Environmental-Statement-Non-Tech- Summary.pdf (accessed on 24 July 2019). 27. Angeloudis, A.; Falconer, R.A. Sensitivity of tidal lagoon and barrage hydrodynamic impacts and energy outputs to operational characteristics. Renew. Energy 2017, 114, 37–351. [CrossRef] 28. BODC. Download UK Tide Gauge Network Data from BODC. Available online: https://www.bodc.ac.uk/ data/hosted_data_systems/sea_level/uk_tide_gauge_network/ (accessed on 24 July 2019). 29. Bray, S.; Ahmadian, R.; Falconer, R.A. Impact of representation of hydraulic structures in modelling a Severn barrage. Comput. Geosci. 2016, 89, 96–106. [CrossRef] 30. Baker, C. Tidal Power–Energy Engineering. Energy Policy. 1991, 19, 792–797. [CrossRef] 31. Aggidis, G.; Feather, O. Tidal range turbines and generation on the Solway Firth. Renew. Energy 2012, 43, 9–17. [CrossRef] 32. Neill, S.P.; Angeloudis, A.; Robins, P.E.; Walkington, I.; Ward, S.L.; Masters, I.; Lewis, M.J.; Piano, M.; Avdis, A.; Piggott, M.D.; et al. Tidal range energy resource and optimization Past perspectives and future challenges. Renew. Energy 2018, 127, 763–778. [CrossRef] 33. Ahmadian, R.; Falconer, R.A.; Bockelmann-Evans, B. Comparison of hydro-environmental impacts for ebb-only and two-way generation for a Severn Barrage. Comput. Geosci. 2014, 71, 11–19. [CrossRef] 34. Fairley, I.; Ahmadian, R.; Falconer, R.A.; Willis, M.R.; Masters, I. The effects of a Severn Barrage on wave conditions in the Bristol Channel. Renew. Energy 2014, 68, 428–442. [CrossRef] 35. Xia, J.; Falconer, R.A.; Lin, B. Impact of different tidal renewable energy projects on the hydrodynamic processes in the Severn Estuary, UK. Ocean Model. 2010, 32, 86–104. [CrossRef] 36. Falconer, R.A. Flow and water-quality modelling in coastal and inland water. J. Hydraul. Res. 1992, 30, 437–452. [CrossRef] 37. Ahmadian, R.; Falconer, R.A.; Lin, B. Hydro-environmental modelling of proposed Severn barrage, UK. Proc. Inst. Civ. Eng.Energy 2010, 163, 107–117. 38. Namin, M.; Lin, B.; Falconer, R.A. Modelling estuarine and coastal flows using an unstructured triangular finite volume algorithm. Adv. Water Resour. 2004, 27, 1179–1197. [CrossRef] 39. “DiGSBS250K [SHAPE Geospatial Data], Scale 1:250000, Tiles: GB, Updated: 6 September 2011, BGS, Using: EDINA Geology Digimap Service, Downloaded: 2017,” ed. Available online: http://digimap.edina.ac.uk (accessed on 6 September 2011). 40. Xia, J.; Falconer, R.A.; Lin, B. Hydrodynamic impact of a tidal barrage in the Severn Estuary, UK. Renew. Energy 2010, 35, 1455–1468. [CrossRef] 41. Xia, J.; Falconer, R.A.; Lin, B.; Tan, G. Estimation of annual energy output from a tidal barrage using two different methods. Appl. Energy 2012, 93, 327–336. [CrossRef] 42. Tidal Lagoon (Swansea Bay) plc. Hydrodynamic model update and validation report. Available online: http://www.tidallagoonpower.com/wp-content/uploads/2018/02/App-7.1-Hydrodynamic- Model-Update-and-Validation-Report.pdf (accessed on 24 July 2019). 43. Ahmadian, R.; Falconer, R.A.; Bockelmann-Evans, B. Far-field modelling of the hydro-environmental impact of tidal stream turbines. Renew. Energy 2012, 38, 107–116. [CrossRef] 44. Lewis, M.J.; Angeloudis, A.; Robins, P.E.; Evans, P.S.; Neill, S.P. Influence of storm surge on tidal range energy. Energy 2017, 122, 25–36. [CrossRef]

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