# Optimisation of Control Algorithm for Hydraulic Power Take-Off System in Wave Energy Converter

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## Abstract

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## 1. Introduction

## 2. System Description

#### 2.1. Physical Test Setup

#### 2.2. Non-Linear Model

## 3. Optimal PTO Torque

#### 3.1. Resistive Case

#### 3.2. Reactive Case

## 4. Wave Power Extraction Algorithms

#### 4.1. Resistive Case

- All valves closed at all times—reference case.
- Switching only occurs at position endpoints (no velocity).
- Switching can be done continuously throughout the PTO movement.

#### 4.2. Reactive Case

#### 4.3. Generator Torque Strategy

## 5. WPEA Performance

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Simple illustration of the power take-off in the PTO housing, note that point B is the same as in Figure 1. Blue and red line colors indicates low and high pressure respectively.

**Figure 6.**Heat map showing the optimal value of ${C}_{PTO}$ and the corresponding absorbed power as a function of different wave periods. Wave input: Regular with height of 0.5 m.

**Figure 7.**Damping and spring constants to achieve resonance and maximum power at different wave period.

**Figure 9.**The optimal torque, the applied torque and the estimated possible torques for the three WPEAs at a system pressure of 115 bar during a regular wave with a height of 0.35 m and a period of 5 s.

**Figure 10.**Actual PTO torque and ideal PTO torque for the high-pressure path-aided reactive strategy measured with a system pressure of ~115 bar. Wave input: Regular with a height of 0.35 m. and a period of 6.5 s.

**Figure 12.**Average power over different system pressures with x-marked optimal motor torque control algorithm. Wave input: Irregular Wave.

**Figure 13.**Frequency sweep comparison of resistive WPEAs versus reactive with pressure-dependent generator control. Wave input: regular wave of 0.35 m at varying periods.

**Figure 14.**Measurements of absorbed and Generator power as a function of systems pressure using different WPEAs. Wave input: Irregular Wave.

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## Share and Cite

**MDPI and ACS Style**

Andersen, N.E.; Mathiasen, J.B.; Carøe, M.G.; Chen, C.; Helver, C.-E.; Ludvigsen, A.L.; Ebsen, N.F.; Hansen, A.H.
Optimisation of Control Algorithm for Hydraulic Power Take-Off System in Wave Energy Converter. *Energies* **2022**, *15*, 7084.
https://doi.org/10.3390/en15197084

**AMA Style**

Andersen NE, Mathiasen JB, Carøe MG, Chen C, Helver C-E, Ludvigsen AL, Ebsen NF, Hansen AH.
Optimisation of Control Algorithm for Hydraulic Power Take-Off System in Wave Energy Converter. *Energies*. 2022; 15(19):7084.
https://doi.org/10.3390/en15197084

**Chicago/Turabian Style**

Andersen, Niklas Enoch, Jakob Blåbjerg Mathiasen, Maja Grankær Carøe, Chen Chen, Christian-Emil Helver, Allan Lynggaard Ludvigsen, Nis Frededal Ebsen, and Anders Hedegaard Hansen.
2022. "Optimisation of Control Algorithm for Hydraulic Power Take-Off System in Wave Energy Converter" *Energies* 15, no. 19: 7084.
https://doi.org/10.3390/en15197084