# Analysis of a Horizontal-Axis Tidal Turbine Performance in the Presence of Regular and Irregular Waves Using Two Control Strategies

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Turbine Design Overview

^{−1}. Under steady state operation, the motor torque is equal and opposite to the torque developed by the rotor blades (${\tau}_{rotor}$) when operating in the tow tank. This can be seen in the ‘swing’ equation for the scale model HATT drive train which is presented in Equation (1).

#### 2.2. Control Strategy

#### 2.3. Test Program and Procedures

#### Duration of the Tests

#### 2.4. Flow and Wave Measurements

#### 2.5. Data Processing

^{2}, deriving it from the turbine radius (r) of 0.45 m. The density of the water was considered in these calculations as 999 kg/m

^{2}. Both power (${C}_{P}$) and thrust (${C}_{T}$) coefficients are related in the results section to the tip speed ratio (TSR). This non-dimensional value defines the ratio between the blade tip speed ($\omega \times r$) and the tow velocity (V), as shown in Equation (6). The flow velocity used in these experiments was 1.0 m/s.

## 3. Results and Discussion

#### 3.1. Non-Dimensional Power Curves and Blade-Bending Moments

#### 3.2. Time Average Signal Fluctuations

#### 3.3. Frequency Domain Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BEMT | Blade Element Momentum Theory |

CFD | Computational fluid dynamics techniques |

H | Wave height |

HATT | Horizontal Axis Tidal Turbine |

HS | Significant wave height |

iq | Quadrature axis current |

PID | Proportional–integral–derivative |

PMSM | permanent magnet synchronous machine |

rpm | Revolutions per minute |

TGC | Torque generating current |

TP | Peak wave period |

TSR | Tip Speed Ratio |

VOC | Vector-oriented control |

VSC | Voltage Source Converter |

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**Figure 1.**Test setup in the CNR-INM wave-tow facility. Horizontal-axis turbine mounted on the tow carriage via stanchion with a set of ultrasonic wave probes on the left.

**Figure 2.**Rotor schematic for the 0.9 $\mathrm{m}$ HATT used for the testing (

**a**) and Wortman FX 63-137 profile used to create the turbine blade geometry (

**b**).

**Figure 3.**Surface elevation of one of the Extreme wave-tow cases, demonstrating an average wave height of 0.39 m (

**a**,

**b**) the frequency spectrum of the signal.

**Figure 4.**Surface elevation of one of the Regular wave-tow cases, demonstrating an average wave height of 0.19 m (

**a**,

**b**) the frequency spectrum of the signal.

**Figure 5.**Water surface elevation time series for the irregular wave case undertaken (

**a**,

**b**) the frequency spectrum of the signal.

**Figure 6.**Power Coefficient (${C}_{P}$)—Tip speed ratio (TSR) curve including all the test cases for both control strategies.

**Figure 7.**Thrust coefficient (${C}_{T}$)—Tip speed ratio (TSR) curve including all the test cases for both control strategies.

**Figure 8.**Average blade root bending moment coefficient (${C}_{M}$) for blade 2 (

**a**) and blade 3 (

**b**) versus tip speed ratio (TSR). Please note that there is not available for the irregular wave-tow tests.

**Figure 9.**Average turbine rotational velocity fluctuation per wave period only for torque control cases: (

**a**) the rotational velocity fluctuation range as a percentage of the mean rotational velocity for each case is presented and (

**b**) the average maximum and minimum turbine rotational velocity per wave period are indicated by the extremes of the error bars.

**Figure 10.**Average rotor torque fluctuation per wave period only for speed control cases: (

**a**) the torque fluctuation range as a percentage of the mean rotor torque for each case is shown and (

**b**) the average maximum and minimum rotor torque per wave period are indicated by the extremes of the error bars.

**Figure 11.**Average rotor thrust fluctuations per wave period only for torque control cases: (

**a**) the thrust fluctuation range as a percentage of the mean rotor thrust for each case is presented and (

**b**) the average maximum and minimum rotor thrust per wave period are indicated by the extremes of the error bars.

**Figure 12.**Average rotor thrust fluctuations per wave period only for speed control cases: (

**a**) the thrust fluctuation range as a percentage of the mean rotor thrust for each case is presented and (

**b**) the average maximum and minimum rotor thrust per wave period are indicated by the extremes of the error bars.

**Figure 13.**Average bending root moment fluctuations per wave period only for torque control cases: (

**a**) the bending root moment fluctuation range as a percentage of the mean bending moment for each blade is presented and (

**b**) the average maximum and minimum rotor thrust per wave period are indicated by the extremes of the error bars (only for blade 2).

**Figure 14.**Average bending root moment fluctuations per wave period only for speed control cases: (

**a**) the bending root moment fluctuation range as a percentage of the mean bending moment for each blade is presented and (

**b**) the average maximum and minimum rotor thrust per wave period are indicated by the extremes of the error bars (only for blade 2).

**Figure 15.**Frequency domain graphs for a regular wave-tow test at peak power condition of TSR = 3.6, i.e., 76 rpm, 15 Nm for rotor: (

**a**) torque and (

**b**) power.

**Figure 16.**Frequency domain graphs for a regular wave-tow test at peak power condition of TSR = 3.6, i.e., 76 rpm, 15 Nm for: (

**a**) thrust and (

**b**) root bending moment blade 3.

**Figure 17.**Amplitudes observed at wave frequencies of: (

**a**) power, (

**b**) rotor thrust, (

**c**) root bending moment blade 2 and (

**d**) root bending moment blade 3.

Author | Tank Type | Rotor Diameter m | Blockage Ratio % | Current/Tow Speed m s ^{−1} | Turbulence Int.% % | Wave Height m | Wave Period s |
---|---|---|---|---|---|---|---|

Barltrop et al. (2007) [8] | Tow | 0.4 | 2.49 | 0–1.2 | - | 0.10 | 1.20 |

0.10 | 1.20 | ||||||

0.10 | 1.60 | ||||||

0.10 | 1.70 | ||||||

0.10 | 2.26 | ||||||

0.02–0.14 * | 1.20 | ||||||

Gaurier et al. (2013) [6] | Flume | 0.9 | 8.8 | 0.67 | 5 | 0.16 | 2.00 |

0.67 | 0.16 | 1.43 | |||||

0.68 | 0.28 | 1.43 | |||||

Galloway et al. (2014) [7] | Tow | 0.8 | 9.4 | 0.9 | - | 0.15 | 2.00 |

0.10 | 2.00 | ||||||

Henriques et al. (2015) [5] | Flume | 0.5 | 36.9 | 0.5 | 2 | 0.04 | 0.70 |

0.08 | 0.90 |

**Table 2.**Test matrix showing the wave cases and control type used throughout the test campaign. All tests were run at 1.0 m/s.

Wave Case | Wave Height (m) | Wave Period (s) | Control Type |
---|---|---|---|

Tow-only * Speed Control Tow | N/A | N/A | Speed |

Tow-only * Torque Control Tow | N/A | N/A | Torque |

Regular wave-tow * Speed Control Wrg | 0.19 | 1.44 | Speed |

Regular wave-tow * Torque Control Wrg | 0.19 | 1.44 | Torque |

Irregular wave-tow * Speed Control Wjsp | 0.19 | 1.44 | Speed |

Irregular wave-tow * Torque Control Wjsp | 0.19 | 1.44 | Torque |

Extreme wave-tow * Speed Control Wex | 0.40 | 2.00 | Speed |

Extreme wave-tow * Torque Control Wex | 0.40 | 2.00 | Torque |

Speed/Torque Control | Tow | Wrg | Wex | Wjsp |
---|---|---|---|---|

30 rpm | 2 | |||

67 rpm | 2 | |||

76 rpm | 2 | 2 | 2 | 2 |

5 Nm | 2 | |||

10 Nm | 2 | |||

15 Nm | 2 | 2 | ||

17.6 Nm | 2 | |||

18 Nm | 3 | |||

18.8 Nm | 2 |

Parameter | Speed Control | Speed Control (Repeat) | Torque Control | Torque Control (Repeat) |
---|---|---|---|---|

Length of data (s) | 136 | 140 | 135 | 139 |

Average wave period (s) | 1.25 | 1.24 | 1.25 | 1.29 |

Maximum wave period (s) | 1.83 | 2.25 | 1.96 | 3.14 |

Minimum wave period (s) | 0.25 | 0.45 | 0.08 | 0.58 |

Average wave height (m) | 0.12 | 0.13 | 0.12 | 0.13 |

Maximum wave height (m) | 0.28 | 0.33 | 0.30 | 0.29 |

Minimum wave height (m) | 0.00 | 0.01 | 0.00 | 0.01 |

© 2019 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**

Ordonez-Sanchez, S.; Allmark, M.; Porter, K.; Ellis, R.; Lloyd, C.; Santic, I.; O’Doherty, T.; Johnstone, C.
Analysis of a Horizontal-Axis Tidal Turbine Performance in the Presence of Regular and Irregular Waves Using Two Control Strategies. *Energies* **2019**, *12*, 367.
https://doi.org/10.3390/en12030367

**AMA Style**

Ordonez-Sanchez S, Allmark M, Porter K, Ellis R, Lloyd C, Santic I, O’Doherty T, Johnstone C.
Analysis of a Horizontal-Axis Tidal Turbine Performance in the Presence of Regular and Irregular Waves Using Two Control Strategies. *Energies*. 2019; 12(3):367.
https://doi.org/10.3390/en12030367

**Chicago/Turabian Style**

Ordonez-Sanchez, Stephanie, Matthew Allmark, Kate Porter, Robert Ellis, Catherine Lloyd, Ivan Santic, Tim O’Doherty, and Cameron Johnstone.
2019. "Analysis of a Horizontal-Axis Tidal Turbine Performance in the Presence of Regular and Irregular Waves Using Two Control Strategies" *Energies* 12, no. 3: 367.
https://doi.org/10.3390/en12030367