# Experimental and Numerical Collaborative Latching Control of Wave Energy Converter Arrays

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## Abstract

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## 1. Introduction

## 2. Control Strategies

#### 2.1. Collaborative Learning

- The central WEC detects an extremum (crest or trough).
- The central WEC calculates the wave period from the time passed since the last extremum and calculates the mean wave period for the last waves. Then it sends the “Start” (Latch event) message to all converters.
- The WECs will apply a latching time based on their policy and the mean wave period. They continuously measure their absorbed energy.
- The central WEC detects an extremum and sends a “Stop” signal.
- The WECs calculate their average absorbed power and send this information together with the applied latching time to the central WEC.
- The central WEC compares the power absorption and sends the applied latching time of the WEC which absorbed the most power together with the mean wave period to the lWECs.
- The lWECs adapt their policies based on the mean wave period and the best applied latching time.
- After the training is finished, the procedure repeats from step 3.

#### 2.2. Linear Latching Time Control

## 3. Numerical Model

## 4. Experiments

#### 4.1. Wave Sequences

#### 4.2. Simulation

#### 4.3. Wave Tank Test

#### 4.4. Differences of the CL in Numerical and Physical Tests

- The number of periods which are averaged was reduced from nine to four, as the sea states in the training wave sequence were shorter.
- The absorbed power was not considered in the learning rate.
- The quantization of the wave periods was (due to rounding issues during the scaling conversion) limited to values between 0 and 3.12 s in steps of 0.26 s (full scale equivalent).

## 5. Results

#### 5.1. Numerical Simulation

#### 5.2. Physical Scale Test

## 6. Discussion

#### 6.1. Challenges for Learning

- The periods and wave heights vary a lot between the wave crest and trough, so the mean wave period is only a rough indicator on what period the next wave will have.
- The wave height has an influence on the optimal latching time.
- The dynamic state of the WEC has an influence. A WEC might be in a better latching position compared to another because of the previous chosen latching time.

#### 6.2. The ANN Strategy

#### 6.3. Performance in the Numerical Simulation

#### 6.4. Wave Tank Test Results

#### 6.5. Comparison to Central Pattern Generator Control

## 7. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

BEM | Boundary equation method |

CL | Collaborative learning |

COAST laboratory | Coastal, ocean and sediment transport laboratory; |

Facility at the University of Plymouth containing the wave tank | |

DDE | Delayed differential equation |

g | gravity acceleration |

PTO | Power take-off |

WAMIT | WaveAnalysisMIT; Wave interaction analyzing tool |

WEC | Wave energy converter |

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**Figure 1.**The artificial neural network uses a linear activation function for the input, logistic activation function for the hidden units and a SoftMax for the output.

**Figure 2.**Flowchart of the algorithm used to detect the latch event, which is executed by the central WEC in both the numerical and the physical tests. After a maximum is detected, the central WEC waits for a decrease specified by the threshold $\epsilon $, then it sends the latch event. Then the central WEC starts waiting for a minimum. As soon as it is detected, the central WEC waits for an increase. As soon as the position is higher than the minimum plus the threshold $\epsilon $ it sends the latch event again. Then the search for a crest starts again. Short cuts (arrows in red and green) between the states ensure that the algorithm never gets stuck when overlooking an extreme.

**Figure 4.**Set-up for the wave tank test. From middle to the right: The four linear motors on the frame, the servodrives; on the table: emergency stop and control computer.

**Figure 6.**Picture sequence of latching of buoy B (second buoy from front) during collaborative learning: in the first picture the buoy is latched and significantly lower than the surrounding buoys. In picture 2 the wave crest is close to the buoy, which is released and in picture 3, it is on the same height as the other buoys. In picture 4 and 5 the buoy stays unlatched and is getting in phase with the wave again, before the latching starts again during the trough (picture 6).

**Figure 7.**The latching sequence for a latch time of $2.5$ s at a regular wave with a period of $11.5$ s and a significant wave height of $1.25$ m. Point A-C (E-G) indicate the process from detecting a maximum (minimum) until stopping the translator movement, while D (H) indicates the unlatching point.

**Figure 8.**Plot of all relevant latching times and their relationship to the optimal constant latching time: In blue, a constant latching time sweep for the evaluation wave sequence. On this curve the latching times applied by the lWEC after training (grey diamonds) and the constant latching times used by the cWECs during learning (orange) are plotted. The reference (100%) is the absorbed power of the lWEC in this wave sequence. Obtained with the numerical simulation.

**Figure 9.**The winning latching times (in orange) plotted over the time duration of the wave sequence (

**a**) and the mean wave period (

**b**). Each point represents one interval between the extremes. The latching times of the lWEC are marked as glowing blue points. Recorded during the evaluation wave sequence with one central WEC, two cWECs and one lWEC. Obtained with the numerical simulation.

**Figure 10.**The chosen latching time of the lWEC (orange circles) compared to that of the linear latching controller (blue circles). The size of the circle is proportional to the absorbed power. The yellow solid dot inside a circle states that this latching time is best. Obtained with the numerical simulation.

**Figure 11.**Power matrices of three latching strategies in relation to a constant damping, no latching strategy. Damping for all WECs was set to $70\text{}\mathrm{kNs}/\mathrm{m}$. Obtained with the numerical simulation.

**Figure 12.**Absorbed power of the three PTOs (two cWECs with 0.25 s and 1.25 s latching time and one lWEC) during the wave tank test in two sea states. Reference is the mean value of the absorbed power for all WECs for the specific sea state. The significant wave height is for all cases ${H}_{s}=1.25\text{}\mathrm{s}$. The sum is then formed by adding the absorbed power of both sea states. Obtained with experimental data.

**Table 1.**Parameters of the simulation and physical model. The latter is Froude-scaled full scale equivalent.

Parameter | Simulation | Physical Model |
---|---|---|

translator mass (${m}_{w}$) | 5000 kg | 5000 kg |

buoy mass (${m}_{b}$) | 5000 kg | 5000 kg |

buoy shape (${m}_{b}$) | cylindrical | ellipsoid |

buoy diameter (${m}_{b}$) | 3.2 m | 5 m |

stroke length (${m}_{b}$) | unlimited | 3.2 m |

PTO damping (${d}_{PTO}$) | 150 kNm/s | 63 kNm/s |

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## Share and Cite

**MDPI and ACS Style**

Thomas, S.; Eriksson, M.; Göteman, M.; Hann, M.; Isberg, J.; Engström, J.
Experimental and Numerical Collaborative Latching Control of Wave Energy Converter Arrays. *Energies* **2018**, *11*, 3036.
https://doi.org/10.3390/en11113036

**AMA Style**

Thomas S, Eriksson M, Göteman M, Hann M, Isberg J, Engström J.
Experimental and Numerical Collaborative Latching Control of Wave Energy Converter Arrays. *Energies*. 2018; 11(11):3036.
https://doi.org/10.3390/en11113036

**Chicago/Turabian Style**

Thomas, Simon, Mikael Eriksson, Malin Göteman, Martyn Hann, Jan Isberg, and Jens Engström.
2018. "Experimental and Numerical Collaborative Latching Control of Wave Energy Converter Arrays" *Energies* 11, no. 11: 3036.
https://doi.org/10.3390/en11113036