# Techno-Economic Modelling of Tidal Energy Converter Arrays in the Tacoma Narrows

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. DTOcean Overview

- Selecting the location of the OECs and calculating the energy produced;
- Designing the transmission network for the electricity generated by the OECs;
- Designing the station keeping requirements of the OECs in the chosen locations;
- Planning the installation of the OECs and array infrastructure;
- Planning the maintenance of the OECs over the lifetime of the array and recording any energy lost due to failure.

**CAPEX**,

**OPEX**and

**AEP**are the annual capital expenditures, operational expenditures and energy productions, respectively, over the lifetime of the plant. $\mathrm{NPC}$ is the net present cost, given by

#### 2.2. Tidal Current Energy Extraction

#### 2.2.1. Streamlines

#### 2.2.2. Hub Height Adjustment

#### 2.2.3. Rotor Yaw Angle

#### 2.2.4. Wake Interactions

#### 2.2.5. Array Yield

#### 2.2.6. Combination of Velocity Fields

## 3. Case Study

#### 3.1. Geography and Geology

^{−1}. The deployment area chosen was the area with the highest power density as reported in [21]. The location of the reference model relative to nearby infrastructure and population centres is shown in Figure 7.

^{−1}while the limit of TEC survival was defined by the ‘shock’ failure mode where the maximum thrust coefficient is combined with 2.85 m s

^{−1}currents. Additionally, long term, representative environmental values are required for calculating the logistical operations. Five years of continuous, concurrent data were available in the public domain, with wind data collected from the anemometer located on the NDBC C-MAN ‘WPOW1’ station in West Point, Washington and current data originating from predictions for the NOAA ‘PUG1527’ sensor station, located within the Narrows. It has been shown in [38] that the occurrence of waves which are large enough to have any impact on the design or operation of the arrays is extremely unlikely. Given that the impact of waves was also not considered in [22] and that no routine measurements are taken within the Tacoma Narrows, all wave values used by DTOcean were set to zero.

#### 3.2. Tidal Energy Converter

^{−1}and a cut-out velocity of 3 m s

^{−1}. The power coefficients of the rotors were reverse engineered from the power curve shown in [22], Figure 3-7. No thrust data was available, so momentum theory was used to estimate the thrust coefficients, by numerically calculating the axial induction factors corresponding to the power coefficients, assuming the axial induction factor is restricted to the range $[0,1/3]$. The thrust coefficients follows accordingly. The power and thrust coefficient curves are shown in Figure 12.

#### 3.3. Project Design and Economics

^{−1}and, to ensure consistency, the penetration rate for gravel cobble stratum used in the DTOcean simulations was set to 2 m h

^{−1}(from 5 m h

^{−1}). All other techniques available for installation of piles were disabled.

^{−1}. In [22] a calendar-based strategy was used to maintain the TECs over the lifetime of the array. It suggests the RM1 device would require two maintenance actions (to service the rotor and power take-off (PTO)) annually per TEC while there would be no failures to the electrical network (due to the burial of cables). As detailed in [25], DTOcean can simulate a calendar interval-based maintenance model for the TEC sub-systems, based on the failure rate, $\lambda $. Defining the mean time to failure (MTTF) as $\mathrm{MTTF}={\lambda}^{-1}$, and assuming that sub-systems exhibit perfect reliability prior to their given MTTF, the probability of failure of a sub-system before time t is:

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

B | blockage ratio |

${C}_{k\left(i\right)}$ | coefficient of undisturbed turbulence kinetic energy for rotor i |

${C}_{k\left(i\right)}^{l}$ | coefficient of undisturbed turbulence kinetic energy for rotor i at iteration l |

${C}_{T}$ | rotor thrust coefficient |

${C}_{U}$ | coefficient of undisturbed hub velocity |

${C}_{U\left(i\right)}$ | coefficient of undisturbed hub velocity for rotor i |

${C}_{U\left(ij\right)}$ | coefficient of undisturbed hub velocity for rotor i subject to rotor j |

${C}_{U\left(i\right)}^{l}$ | coefficient of undisturbed hub velocity for rotor i at iteration l |

D | TEC rotor diameter |

${I}_{i}$ | turbulence intensity for rotor i |

${I}_{i}^{0}$ | undisturbed turbulence intensity for rotor i |

${I}_{i}^{l}$ | modified turbulence intensity for rotor i at iteration l |

${I}_{i}^{m}$ | modified turbulence intensity for rotor i |

${P}_{i}$ | constrained rotor power output for rotor i |

${\mathcal{P}}_{i}$ | unconstrained rotor power output for rotor i |

${U}_{i}$ | hub velocity for rotor i |

${U}_{i}^{0}$ | undisturbed hub velocity for rotor i |

${U}_{i}^{l}$ | modified hub velocity for rotor i at iteration l |

${U}_{i}^{m}$ | modified hub velocity for rotor i |

${\overrightarrow{X}}_{ij}$ | distance from rotor i to streamlines of other rotors |

${k}_{i}$ | turbulence kinetic energy for rotor i |

${k}_{ij}$ | turbulence kinetic energy for rotor i subject to rotor j |

${k}_{i}^{0}$ | undisturbed turbulence kinetic energy for rotor i |

${n}_{r}$ | number of TEC rotors |

${\psi}_{0}$ | neutral orientation of rotor |

${\psi}_{r}$ | absolute yaw angle between current and rotor |

${\psi}_{r\left(i\right)}$ | absolute yaw angle between current and rotor for rotor i |

$\rho $ | water density |

AEP | annual energy production |

CAPEX | capital expenditure |

LCOE | levelised cost of energy |

MMAEP | mechanical mean annual energy production |

OPEX | operational expenditure |

PTO | power take-off |

RVF | representative velocity field |

TEC | tidal energy converter |

## Appendix A. Resource Characterisation

**Figure A1.**28 days of near surface easterly and northerly (with respect to true North) velocities components. Measured at the NOAA Cherry Point monitoring station, in units of centimetres per second, and resampled to hourly values.

^{−1}, the default value used by DTOcean.

**Figure A2.**Probability density calculated from tidal current velocities (u and v) measured at the NOAA Cherry Point monitoring station (data shown in Figure A1). The ’slice’ shown in (

**b**) is extracted from the data between the dashed lines in (

**a**).

**Table A1.**Point values of representative velocities from the Cherry Point data (u and v), the joint probability of those velocities occurring (${\mathbb{P}}_{v}$) and the selected time step (t).

u (cm s^{−1}) | v (cm s^{−1}) | ${\mathbb{P}}_{\mathit{v}}$ | t |
---|---|---|---|

4.04 | −30.1 | 0.0104 | 12 October 2018 06:00 |

3.33 | −24.2 | 0.0238 | 08 October 2018 18:00 |

0.781 | −18.3 | 0.0491 | 27 September 2018 06:00 |

0.833 | −12.3 | 0.124 | 27 September 2018 07:00 |

0.361 | −6.40 | 0.173 | 09 October 2018 01:00 |

2.06 | −0.466 | 0.226 | 19 October 2018 07:00 |

1.78 | 5.46 | 0.185 | 12 October 2018 17:00 |

1.99 | 11.4 | 0.149 | 06 October 2018 23:00 |

0.617 | 17.3 | 0.0461 | 28 September 2018 14:00 |

1.63 | 23.3 | 0.0149 | 29 September 2018 13:00 |

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**Figure 1.**Relationships between the key software elements and user. Data is transferred between the user, database, design and assessment modules by the core. The core also sequences the execution of modules. Support modules provide functionality shared between multiple design or assessment modules, and are accessed directly. Reproduced from [25].

**Figure 2.**Process for determining the energy extracted from a given set of velocity fields. Please note that the ecological impact calculation is not addressed within this work.

**Figure 3.**Plan view of the computational grid. Although a regular grid of points with spacing $\Delta x$ and $\Delta y$ must be supplied, the domain can take a general shape by defining points outside of the delineating polygon (marked in solid black) with NaN values. Modified from [27].

**Figure 4.**Calculation steps for determining the velocities and turbulence kinetic energies of the array TECs subject to wake interactions. The original process shown in (

**a**) was updated for this work, as shown in (

**b**).

**Figure 5.**Distance ${\overrightarrow{X}}_{ij}({s}_{1},{s}_{2})$ for TEC rotor i relative to the streamline of rotor j, where ${s}_{1}$ is the distance along the streamline to the shortest orthogonal projection from rotor i and ${s}_{2}$ is the distance from i to the point of intersection. If more than one orthogonal projection exists, then the projection with the minimum ${s}_{1}$ is selected.

**Figure 6.**Comparison of the mean coefficient of velocity, $\overline{{C}_{U}}$, for the 0-th iteration of the DTOcean tidal hydrodynamics model and the converged value (ordered by the converged value). The simulation included 19 TECs with 30 RVFs.

**Figure 7.**Location of the RM1 reference model deployment area within the Tacoma Narrows, WA, U.S.A., relative to nearby medium and large cities.

**Figure 8.**Bathymetry, deployment area extents and energy export infrastructure for the Tacoma Narrows DTOcean model.

**Figure 9.**Comparative relative frequency histograms of [22], Figure 3-5 and all points within the Delft3D simulation of the Puget sound ($\tilde{U}=3ms-1)$. The comparison prior to scaling is shown in (

**a**) and following scaling in (

**b**).

**Figure 11.**RM1 device schematic (adapted from [22], Figure 3-2 with permission.)

**Figure 12.**Coefficients of power (${C}_{P}$) and thrust (${C}_{T}$), with respect to current velocity magnitude, for the RM1 device rotors.

**Figure 15.**50 TEC DTOcean simulation installation phases Gantt chart. Please note that time categories (such as waiting time) are aggregated and may occur at different intervals than shown.

**Table 1.**Simulation scope and modelling assumptions of the DTOcean software. Reproduced from [25].

OEC types | Floating or bottom fixed wave or tidal |

Mixed OEC types | Single type per simulation |

Maximum number of OECs | 100 |

Maximum deployment depths | 80m for tidal, 200m for wave |

Sedimentary layers | Single or multi-layered strata |

Electrical network types | Single substation, single export cable |

Foundation types | Gravity, piles, anchors, suction caissons, shallow |

Mooring types | Catenary or taut |

Logistics | Single port, one vessel per operation |

Maintenance strategies | Corrective, calendar-, or condition-based |

**Table 2.**Description of modules provided by the DTOcean software. Reproduced from [25].

Name | Category | Purpose | Local Optimisation Strategy |
---|---|---|---|

Array Hydrodynamics | Design | Locate OECs and calculate their power generation per sea state | OECs positioned for maximum power output |

Electrical Sub-Systems | Design | Design electrical network suited to the OEC and export cable characteristics and calculate losses | Minimise cost per unit energy |

Moorings and Foundations | Design | Design foundations and moorings (if appropriate) subject to array requirements and extreme conditions | Minimise cost |

Logistics | Support | Calculate vessel and equipment requirements, costs and durations for installation or maintenance phases | Minimise cost within a maximum time limit |

Installation | Design | Schedule the installation of all requested design phases | Minimise cost within a maximum time limit per phase |

Reliability | Support/Assessment | Combine components networks into reliability metrics for major sub-systems | Not applicable |

Economics | Support/Assessment | Calculate absolute or probabilistic costs for each design stage | Not applicable |

Maintenance | Design | Schedule the maintenance activity over the array lifetime and record yearly costs and energy production | Minimise logistics cost subject to the maintenance strategy and maximum time limit |

Environmental Impact | Assessment | Assess the environmental impact of the array design | Not applicable |

Mass | 219.37 tonnes |

Height | 30 m |

Length | 6 m |

Width | 6 m |

Submerged volume | 433 m^{3} |

Hub height | 30 m |

Rotor diameter | 20 m |

Rotor separation | 26 m |

Rated power | 1.1 MW |

Deployment depth | 45–67.5 m |

Unit cost | 1.96 × 10^{6} € |

**Table 4.**RM1 CAPEX contributions from externalities in 1 × 10

^{6}Euro (converted from U.S. dollars at the rate of 1 $ = 0.85 €).

Item | 10 TEC Array | 50 TEC Array |
---|---|---|

Sound barrier | 3.92 | 3.92 |

Maintenance vessel purchase | 12.3 | 12.3 |

Design and site assessment | 4.21 | 4.21 |

Contingency & profit margin | 15.9 | 25.8 |

Environmental | 4.67 | 5.17 |

Total | 41.0 | 51.4 |

**Table 5.**RM1 annual OPEX contributions from externalities in 1 × 10

^{6}Euro (converted from U.S. dollars at the rate of 1 $ = 0.85 €).

Item | 10 TEC Array | 50 TEC Array |
---|---|---|

Insurance | 1.00 | 1.00 |

Environmental | 0.81 | 0.50 |

Total | 1.81 | 1.50 |

DTOcean | RM1 | |
---|---|---|

MMAEP (MWh) | 32,505.50 | 27,272 |

Network efficiency (%) | 99.5 | 100 |

Array capacity factor (%) | 33.5 | 28.3 |

DTOcean | RM1 | |
---|---|---|

MMAEP (MWh) | 183,736.51 | 136,360 |

Network efficiency (%) | 94.2 | 100 |

Array capacity factor (%) | 35.9 | 28.3 |

10 TEC Array | 50 TEC Array | |
---|---|---|

Mean annual number of operations | 20.08 | 101.9 |

Mean array availability (%) | 99.92 | 99.83 |

Mean lifetime energy production (TWh) | 0.65 | 3.58 |

Number of TECs | RM1 | DTOcean Most Likely | DTOcean 95th Percentile Range |
---|---|---|---|

10 | 34.612 | 36.69 | 36.27–37.00 |

50 | 17.34 | 20.34 | 19.71–21.19 |

**Table 10.**LCOE share per cost category comparison for 10 TECs (in 1 × 10

^{−2}€/kWh where 1 $ = 0.85 €). RM1 values extracted from [22], Tables 3-14, 3-15, and most likely LCOE used for DTOcean.

Cost Category | RM1 | DTOcean |
---|---|---|

TEC | 8.925 | 7.4 |

Electrical network | 5.1 | 0.65 |

Moorings and foundations | 0 | 2 |

Installation | 4.335 | 2.3 |

Externalities (CAPEX) | 5.882 | 15.49 |

Maintenance | 3.91 | 3.44 |

Externalities (OPEX) | 6.46 | 5.41 |

**Table 11.**LCOE share per cost category comparison for 50 TECs (in 1 × 10

^{−2}€/kWh where 1 $ = 0.85 €). RM1 values estimated from [22], Figures 3-27, 3-28, and most likely LCOE used for DTOcean.

Cost Category | RM1 | DTOcean |
---|---|---|

TEC | 7.99 | 7.54 |

Electrical network | 1.105 | 0.21 |

Moorings and foundations | 0 | 1.6 |

Installation | 1.955 | 2.11 |

Externalities (CAPEX) | 2.635 | 3.96 |

Maintenance | 2.21 | 4 |

Externalities (OPEX) | 1.445 | 0.92 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Topper, M.B.R.; Olson, S.S.; Roberts, J.D.
Techno-Economic Modelling of Tidal Energy Converter Arrays in the Tacoma Narrows. *J. Mar. Sci. Eng.* **2020**, *8*, 646.
https://doi.org/10.3390/jmse8090646

**AMA Style**

Topper MBR, Olson SS, Roberts JD.
Techno-Economic Modelling of Tidal Energy Converter Arrays in the Tacoma Narrows. *Journal of Marine Science and Engineering*. 2020; 8(9):646.
https://doi.org/10.3390/jmse8090646

**Chicago/Turabian Style**

Topper, Mathew B. R., Sterling S. Olson, and Jesse D. Roberts.
2020. "Techno-Economic Modelling of Tidal Energy Converter Arrays in the Tacoma Narrows" *Journal of Marine Science and Engineering* 8, no. 9: 646.
https://doi.org/10.3390/jmse8090646