# The Potential for Tidal Range Energy Systems to Provide Continuous Power: A UK Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Case Study

- (a)
- (b)
- (c)

## 3. Methodology

#### 3.1. Hydrodynamic Model of the Irish Sea

#### 3.2. Modelling Tidal Power Plants

- Water level data: Ambient tidal elevations ${\eta}_{o}$ (m) in each power plant location are extracted from outputs of the 2D Irish Sea model, harmonically reconstructed for a given duration at any point in time (Figure 3).
- Surface plan area data: In applying the three tidal power plant basins to the computational mesh as subdomains, the manner in which the water surface plan A (m${}^{2}$) changes with basin free surface elevation ${\eta}_{i}$ (m) is determined for each tidal power plant (Figure 3). This provides a simplified means to represent intertidal regions.
- Hydraulic structure parameterisations: Given operation mode and water elevations inside ${\eta}_{i}$ and outside ${\eta}_{o}$ the basin, head difference $H\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{\eta}_{i}-{\eta}_{o}$ (m), flow rate Q (m${}^{3}$ s${}^{-1}$) and power output P (MW) through the turbines and sluices can be calculated where applicable. This allows energy yield E (MWh) to be determined.
- Control schedule: Based on either time intervals or specific head differences, the control schedule determines how the tidal power plant will shift between the different operation modes (holding, generating and sluicing in the ebb and flood phases) [5].

#### 3.3. Control Schedule Optimisation

- EM-I: Energy maximisation, inflexible.
- EM-F: Energy maximisation, flexible.
- CG-I: Continuous generation, inflexible.
- CG-F: Continuous generation, flexible.

#### 3.3.1. Energy Maximisation (EM)

#### 3.3.2. Continuous Generation (CG)

#### 3.4. Economics

- Hourly Variable Market (HVM), $p{\left(t\right)}_{HVM}$ (£/MWh): This market is applied to reflect the value in providing power during periods of high demand. A price signal is derived from the Nord Pool N2EX market for the year 2018 [51]. The price of electricity changes hourly, with the tidal power system only needing to generate over the whole hour in question for valid market trading. While Nord Pool requires a constant rate for each hour, it is assumed that all energy generated by the power plant system in this hour is sold.
- Baseload Market (BM), $p{\left(t\right)}_{BM}$ (£/MWh): This market considers a constant supply of electricity over the course of a day. Nord Pool does not regulate a UK-based baseload market [51]. Analysis of Ofgem baseload contract prices [52] reveals that monthly averages over a ten-year period are similar to equivalent monthly averages on the hourly Nord Pool N2EX market (HVM), albeit at a slight increase [51]. The employed BM data does therefore not directly reflect a historic price signal, but instead encompasses an averaging of the HVM price signal. Daily $p{\left(t\right)}_{BM,D}$, weekly $p{\left(t\right)}_{BM,W}$ and monthly $p{\left(t\right)}_{BM,M}$ averages are tested.

#### 3.5. Optimisation Cases

- Default, $\delta $: In the event of continuous generation not being permissible over a tidal cycle, the algorithm defaults to the system’s secondary priority. Defaulting the cycle to maximise energy, as with $\delta $ = EM-I or $\delta $ = EM-F, considers a commitment to increasing the economic gain from that particular cycle. Meanwhile, $\delta $ = CG-I might prioritise phasing the system in a better position to attempt continuous generation in the next cycle.
- Cut-off power, ${P}_{c}$(MW): Employing a cut-off power ${P}_{c}$ recognises that, if only low levels of minimum cumulative power output $\wedge P$ are possible, it might not be worthwhile pursuing continuous generation. It also acknowledges that the required shift in ${t}_{h,e}$ and ${t}_{h,f}$ from the default might be large enough that the energy output is significantly reduced. ${P}_{c}$ values of 0 MW, 75 MW, 150 MW, 225 MW, and 300 MW are tested in the CG-F algorithm.

## 4. Results

#### 4.1. Performance of System

- Total energy output, ${E}_{T}$ (TWh/year).
- Number of “CG days” in which a continuous supply of energy is achieved.
- Energy output on CG days to be traded on the Baseload Market, ${E}_{BM}$ (TWh/year), determined by the cumulative minimum power output $\wedge P$ of that day.
- Average $\wedge P$ annually, $\overline{\wedge P}$ (MW).
- Average $\wedge P$ on CG Days only, ${\overline{\wedge P}}_{CG}$ (MW).
- Average power output peaks on all days, $\overline{\vee P}$ (MW).
- Average power output peaks on CG days only, ${\overline{\vee P}}_{CG}$ (MW).

#### 4.2. Income

## 5. Discussion

#### 5.1. Continuous Generation Potential

#### 5.2. Economics

#### 5.3. Optimisation Methodology

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

TLP | Tidal Lagoon Power Ltd. |

CfD | Contract for Difference |

CBL | Colwyn Bay Tidal Lagoon |

MB | Mersey Tidal Barrage |

WSL | West Somerset Tidal Lagoon |

EM-I | Energy Maximisation Optimisation, Inflexible |

EM-F | Energy Maximisation Optimisation, Flexible |

CG-I | Continuous Generation optimisation, Inflexible |

CG-F | Continuous Generation optimisation, Flexible |

HVM | Hourly Variable Market |

BM | Baseload Market |

CG Days | Continuous Generation Days |

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**Figure 2.**Unstructured mesh and computational domain including elevation data sampling locations for validation against BODC tide constituent data. ${R}^{2}$ correlation coefficient and Root Mean Square Error ($RMSE$) are computed between model and gauge data ${M}_{2}$ and ${S}_{2}$ tide constituent amplitude $\alpha $ (m) and phase $\varphi $ (${}^{\circ}$).

**Figure 3.**Ambient tidal elevations ${\eta}_{o}$ (m) in three scheme locations for (

**a**) spring and (

**b**) neap tides, and (

**c**) the relationship between basin surface plan area A (km${}^{2}$) and basin elevation ${\eta}_{i}$ (m) in the corresponding tidal power plants.

**Figure 4.**Power output P (MW) and basin elevations ${\eta}_{i}$ (m) of the tidal power plants. Example 1 indicates a scenario where the holding periods ${t}_{h,e}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{t}_{h,f}=$ 2 h for each scheme. Examples 2–4 display BG-F optimised schedules, applying different examples of “default” $\delta $, defined as the operation schedule reverted to when cut-off power ${P}_{c}$ (MW) cannot be achieved in the CG-F case. Daily minimum power $\wedge P$ (MW) determines the power sold on the Baseload Market (BM), indicated with red.

**Figure 5.**Hourly Variable $p{\left(t\right)}_{HVM}$ and corresponding Baseload Market price signals (£/MWh). $p{\left(t\right)}_{BM,D}$, $p{\left(t\right)}_{BM,W}$, $p{\left(t\right)}_{BM,M}$ refer to daily, weekly and monthly averaging respectively. The displayed snapshots indicate (

**a**) the entirety of 2018, and periods where (

**b**) $p{\left(t\right)}_{BM,D}$ and (

**c**) $p{\left(t\right)}_{BM,M}$ would be financially advantageous.

**Figure 6.**Annual (705 tidal cycles) energy results of optimisation cases from Table 3: total energy output ${E}_{T}$ (TWh/year), total Baseload Market output ${E}_{BM}$ (TWh/year) and number of days where $\wedge P$ > 0 MW.

**Figure 7.**Temporal operation characteristics of the tidal power plant system in applying flexible controls to optimise towards continuous generation, with $\delta $ = EM-I, an inflexible energy maximisation default (CG-I${}_{EM-I,{P}_{c}}$). For all three power plants,

**(a)**indicates holding periods ${t}_{h,e}$ and ${t}_{h,f}$ per tidal cycle

**(b)**the tidal range each cycle and

**(c)**daily cumulative minimum power output $\wedge P$ (GW).

**Figure 8.**Temporal operation characteristics of the tidal power plant system in applying flexible controls to optimise towards continuous generation, with $\delta $ = EM-F, a flexible energy maximisation default (CG-I${}_{EM-F,{P}_{c}}$). For all three power plants, (

**a**) indicates holding periods ${t}_{h,e}$ and ${t}_{h,f}$ per tidal cycle (

**b**) the tidal range each cycle and (

**c**) daily cumulative minimum power output $\wedge P$ (GW).

**Figure 9.**Temporal operation characteristics of the tidal power plant system in applying flexible controls to optimise towards continuous generation, with $\delta $ = CG-I, an inflexible baseload generation default (CG-I${}_{CG-I,{P}_{c}}$). For all three power plants, (

**a**) indicates holding periods ${t}_{h,e}$ and ${t}_{h,f}$ per tidal cycle (

**b**) the tidal range each cycle and (

**c**) daily cumulative minimum power output $\wedge P$ (GW).

**Figure 10.**How scaling $\alpha $ of the Baseload Market electricty price $p{\left(t\right)}_{BM}$ (£/MWh) affects income both exclusively in the Baseload Market (BM), and in combination with the Hourly Variable Market (HVM). l-r is $\delta $ = EM-I, $\delta $ = EM-F, and $\delta $ = BG-I default cases.

**Figure 11.**Tidal range power plant system daily income upon trading in baseload markets I${}_{BM}$ and hourly variable markets I${}_{HVM}$ (I${}_{BM}$ + I${}_{HVM}$ = I${}_{T}$). Displayed results are from CG-F${}_{CG-I,0}$ control schedule, which yields the highest baseload energy E${}_{CG}$ of all optimisation cases. Percentage difference between daily averaged baseload price and the weekly and monthly equivalents is provided.

Power Plant: | (a) Colwyn Bay Tidal Lagoon | (b) Mersey Tidal Barrage | (c) West Somerset Tidal Lagoon |
---|---|---|---|

Notation | CBL | MB | WSL |

Number turbines | 125 [37] | 28 [32] | 960 [32] |

Number sluices | 40 [37] | 10 | 300 |

Turbine diameter (m) | 7.35 | 8 [32] | 3.12 [32] |

Turbine power output (MW) | 20 [32] | 25 [32] | 3.12 [32] |

Installed capacity (MW) | 2500 | 700 | 2995.2 |

Operation mode | Bi-directional | Bi-directional | Bi-directional |

Basin area (km${}^{\mathbf{2}}$) | 192.8 | 61.5 | 89.7 |

Mean tidal range (m) | 6.77 | 7.65 | 8.27 |

${\mathbf{M}}_{\mathbf{2}}$tidal phase (${}^{\circ}$) | 315.3 | 328.3 | 171.1 |

**Table 2.**Summary of optimisation cases applied in this study. Unless classed as “Flexible”, inflexible holding periods are presented in the following order: CBL ${t}_{h,e}$, CBL ${t}_{h,f}$, MB ${t}_{h,e}$, MB ${t}_{h,f}$, WSL ${t}_{h,e}$, WSL ${t}_{h,f}$.

Optimisation Case | Objective Functional | Holding Periods (h) | Default $\mathit{\delta}$ | Cut-off Power ${\mathit{P}}_{\mathit{c}}$ (MW) |
---|---|---|---|---|

EM-I | Energy maximisation | 1.77, 1.65, 2.74, 2.14, 2.74, 2.19 | N/A | N/A |

EM-F | Energy maximisation | Flexible | N/A | N/A |

CG-I | Continuous generation | 1.00, 1.00, 3.00, 3.00, 3.00, 3.00 | N/A | N/A |

CG-F${}_{EM-I,0}$ | Continuous generation | Flexible | EM-I | 0 |

CG-F${}_{EM-I,75}$ | Continuous generation | Flexible | EM-I | 75 |

CG-F${}_{EM-I,150}$ | Continuous generation | Flexible | EM-I | 150 |

CG-F${}_{EM-I,225}$ | Continuous generation | Flexible | EM-I | 225 |

CG-F${}_{EM-I,300}$ | Continuous generation | Flexible | EM-I | 300 |

CG-F${}_{EM-F,0}$ | Continuous generation | Flexible | EM-F | 0 |

CG-F${}_{EM-F,75}$ | Continuous generation | Flexible | EM-F | 75 |

CG-F${}_{EM-F,150}$ | Continuous generation | Flexible | EM-F | 150 |

CG-F${}_{EM-F,225}$ | Continuous generation | Flexible | EM-F | 225 |

CG-F${}_{EM-F,300}$ | Continuous generation | Flexible | EM-F | 300 |

CG-F${}_{CG-I,0}$ | Continuous generation | Flexible | CG-I | 0 |

CG-F${}_{CG-I,75}$ | Continuous generation | Flexible | CG-I | 75 |

CG-F${}_{CG-I,150}$ | Continuous generation | Flexible | CG-I | 150 |

CG-F${}_{CG-I,225}$ | Continuous generation | Flexible | CG-I | 225 |

CG-F${}_{CG-I,300}$ | Continuous generation | Flexible | CG-I | 300 |

**Table 3.**Energy and power output results of all optimisation cases over 705 tidal cycles (≈1 year). CG-F subscript indicates associated $\delta $ and cut-off power ${P}_{c}$ (MW). Days where continuous generation is achieved are indicated as CG Days, as well as the associated proportion of the total energy ${E}_{T}$ (TWh/year) to be traded in the idealised baseload market ${E}_{BM}$ (TWh/year). $\overline{\wedge P}$ and ${\overline{\wedge P}}_{CG}$ (MW) indicate average daily minimum cumulative power output over the year and exclusively on CG Days, respectively, while $\overline{\vee P}$ and ${\overline{\vee P}}_{CG}$ (MW) show equivalent daily average power peaks. The combined installed capacity of the power plant system is 6195.2 MW.

Optimisation | CG | ${\mathit{E}}_{\mathbf{BM}}$ | ${\mathit{E}}_{\mathit{T}}$ | $\overline{\wedge \mathit{P}}$ | ${\overline{\wedge \mathit{P}}}_{\mathbf{CG}}$ | $\overline{\vee \mathit{P}}$ | ${\overline{\vee \mathit{P}}}_{\mathbf{CG}}$ | $\overline{\vee \mathit{P}}-\overline{\wedge \mathit{P}}$ | ${\overline{\vee \mathit{P}}}_{\mathbf{CG}}-{\overline{\wedge \mathit{P}}}_{\mathbf{CG}}$ |
---|---|---|---|---|---|---|---|---|---|

Function | Days | (TWh/year) | (TWh/year) | MW | MW | MW | MW | MW | MW |

EM-I | 0 | 0.00 | 12.18 | 0 | N/A | 3439.6 | N/A | 3439.6 | N/A |

EM-F | 0 | 0.00 | 13.20 | 0 | N/A | 3528.8 | N/A | 3528.8 | N/A |

CG-I | 200 | 2.08 | 11.39 | 237.3 | 433.1 | 3179.8 | 3891.0 | 2942.5 | 3457.9 |

CG-F${}_{EM-I,0}$ | 218 | 2.76 | 11.05 | 315.5 | 528.2 | 3040.5 | 3630.3 | 2725.0 | 3102.1 |

CG-F${}_{EM-I,75}$ | 209 | 2.73 | 11.06 | 312.1 | 545.1 | 3040.8 | 3669.0 | 2728.7 | 3123.8 |

CG-F${}_{EM-I,150}$ | 194 | 2.67 | 11.09 | 304.3 | 572.3 | 3044.6 | 3729.5 | 2740.3 | 3157.0 |

CG-F${}_{EM-I,225}$ | 174 | 2.50 | 11.17 | 285.6 | 599.1 | 3063.4 | 3793.8 | 2777.8 | 3194.7 |

CG-F${}_{EM-I,300}$ | 140 | 2.19 | 11.31 | 250.0 | 651.9 | 3111.2 | 3891.5 | 2861.2 | 3239.6 |

CG-F${}_{EM-F,0}$ | 206 | 2.63 | 11.55 | 299.8 | 531.1 | 3286.7 | 3645.6 | 2986.9 | 3114.5 |

CG-F${}_{EM-F,75}$ | 173 | 2.22 | 11.80 | 253.9 | 535.6 | 3331.2 | 3658.9 | 3077.3 | 3123.3 |

CG-F${}_{EM-F,150}$ | 102 | 1.27 | 12.36 | 145.3 | 520.0 | 3413.9 | 3650.4 | 3268.6 | 3130.4 |

CG-F${}_{EM-F,225}$ | 18 | 0.26 | 12.98 | 29.1 | 590.5 | 3515.4 | 3752.6 | 3486.3 | 3162.0 |

CG-F${}_{EM-F,300}$ | 6 | 0.11 | 13.09 | 12.0 | 730.8 | 3529.3 | 3902.8 | 3517.3 | 3172.0 |

CG-F${}_{CG-I,0}$ | 242 | 2.94 | 11.08 | 335.8 | 506.5 | 3071.5 | 3600.7 | 2735.7 | 3094.1 |

CG-F${}_{CG-I,75}$ | 233 | 2.92 | 11.09 | 333.5 | 522.4 | 3074.1 | 3636.5 | 2740.6 | 3114.1 |

CG-F${}_{CG-I,150}$ | 224 | 2.89 | 11.10 | 330.0 | 537.7 | 3077.2 | 3676.3 | 2747.2 | 3138.6 |

CG-F${}_{CG-I,225}$ | 209 | 2.80 | 11.13 | 320.0 | 558.8 | 3082.6 | 3716.9 | 2762.6 | 3158.1 |

CG-F${}_{CG-I,300}$ | 203 | 2.72 | 11.15 | 310.0 | 557.4 | 3090.2 | 3731.7 | 2780.3 | 3174.4 |

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**MDPI and ACS Style**

Mackie, L.; Coles, D.; Piggott, M.; Angeloudis, A.
The Potential for Tidal Range Energy Systems to Provide Continuous Power: A UK Case Study. *J. Mar. Sci. Eng.* **2020**, *8*, 780.
https://doi.org/10.3390/jmse8100780

**AMA Style**

Mackie L, Coles D, Piggott M, Angeloudis A.
The Potential for Tidal Range Energy Systems to Provide Continuous Power: A UK Case Study. *Journal of Marine Science and Engineering*. 2020; 8(10):780.
https://doi.org/10.3390/jmse8100780

**Chicago/Turabian Style**

Mackie, Lucas, Daniel Coles, Matthew Piggott, and Athanasios Angeloudis.
2020. "The Potential for Tidal Range Energy Systems to Provide Continuous Power: A UK Case Study" *Journal of Marine Science and Engineering* 8, no. 10: 780.
https://doi.org/10.3390/jmse8100780