# Control Parameters Optimization of Accumulator in Hydraulic Power Take-Off System for Eccentric Rotating Wave Energy Converter

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. ERWEC System

#### 2.1. Mechanical Structure of ERWEC

#### 2.2. Principle of Hydraulic PTO

#### 2.3. Physical Model of Hydraulic PTO System

## 3. Experimental Process and Result

#### 3.1. Control Strategy of Hydraulic Accumulator

_{w}is the oscillating time, A(t

_{w}) and T(t

_{w}) are the disturbances of oscillating angle amplitude and oscillating period, respectively. Both A(t

_{w}) and T(t

_{w}) are imprecise terms produced by artificial excitation, which can be used to simulate the motion of the pendulum with uncertain disturbance and analyze the energy conversion effect of the hydraulic PTO system.

- When the pressure value monitored by pressure transmitter 17 (a) reaches the trigger pressure p, the controller generates a trigger signal to open the electromagnetic switch valve. After delay time t, the electromagnetic switch valve will be opened, and the accumulator begins to release the accumulated energy. Then, Step (2) is executed.
- After the electromagnetic switch valve remains open for the time of open state duration dt, Step (3) will be executed.
- To determine whether the pressure value is higher than p repeatedly. If the pressure value is still higher than p, repeat Step (2). Otherwise, Step (4) will be performed.
- To close the electromagnetic switch valve, the accumulator will switch to the state of energy accumulation. Repeat Steps (1–3) successively after the pressure value reaches p.

_{i}, p

_{i}

_{−1}are the power at time i and i−1, respectively, n is the number of time intervals, ${\overline{p}}_{t}$ is the average output power defined in Equation (2), and p

_{e}is the power fluctuation index. The difference in output power reflects the continuous change in output power. It has the capacity of capturing periodic stability of output power approximating a square wave. Therefore, Equation (3) is used to reflect the characteristic of stability.

#### 3.2. Influence of Trigger Pressure on Output Power

#### 3.3. Influence of Delay Time on Output Power

#### 3.4. Influence of Open State Duration on Output Power

#### 3.5. Analysis of Experimental Results

## 4. Selection of Optimal Control Parameters

#### 4.1. Experimental Samples Based on Optimal Latin Hypercube Sampling

#### 4.2. Sensitivity Analysis of Output Power

#### 4.3. Optimization of Control Parameters

_{t}and S

_{t}are the parents and descendants of sizes N at the tth iteration. The population of the offspring R

_{t}is 2N after combining P

_{t}and S

_{t}. Moreover, F

_{1}, F

_{2}… are the non-dominated fronts, and t

^{max}is the maximum evaluation number. A detailed description of NSGA-III can be found in [29,30]. In the multi-objective optimization algorithm of this study, the size of the population was set as 200, and the evaluation number was set as 12,000. The Pareto frontiers of optimal solution sets for control parameters of the hydraulic accumulator were calculated, as presented in Figure 21. Part of the solution sets are shown in Table 4.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) The schematic representation of ERWEC, (

**b**) 3D schematic diagram of wave energy device, and (

**c**) 1:5 scaled model.

**Figure 2.**The schematic diagram of hydraulic PTO, 1—hydraulic cylinder for eccentricity regulation, 2—spring, 3—piston rod, 4—eccentric rotor, 5—relief valve, 6—electromagnetic switch valve, 7—electric generator, 8—hydraulic motor, 9—flowmeter, 10—proportional flow control valve, 11—oil tank, 12—filter, 13—ball valve, 14—speed increase gearbox, 15—hydraulic pump, 16—check valve, 17—pressure transmitter, and 18—hydraulic accumulator.

**Figure 5.**The output power time history curve when the electromagnetic switch valve is always in the open state.

**Figure 8.**Time histories of pressure transmitters 17 (a) (solid line) and 17 (b) (dash-dotted line).

**Figure 9.**The average values of output power and power fluctuation index under different trigger pressure conditions.

**Figure 11.**The average output power and power fluctuation index under different delay times (trigger pressure is 3.5 MPa).

**Figure 13.**The average output power and power fluctuation index under different delay times (trigger pressure is 4 MPa).

**Figure 15.**The average output power and power fluctuation index under different open state durations (trigger pressure is 3.5 MPa).

**Figure 17.**The average output power and power fluctuation index under different open state durations (trigger pressure is 4.0 MPa).

**Figure 19.**Sensitivity of average output power and power fluctuation index. (

**a**) Sensitivity of average output power. (

**b**) Sensitivity of power fluctuation index.

Component | Name | Parameter |
---|---|---|

Hydraulic pump | Displacement | 1 cc/rev |

Output pressure | 10 MPa | |

Hydraulic motor | Displacement | 2 cc/rev |

Speed increase gearbox | Speed ratio | 40:1 |

Electric generator | Rated power | 50 W |

Rated voltage | 28 V | |

Rated speed | 500 r/min | |

Accumulator | Volume | 6.3 L |

Pressure transmitter | Maximum pressure | 25 MPa |

Measurement accuracy | 0.5% |

n | p (MPa) | t (s) | dt (s) | p_{t}(W) | p_{e} |
---|---|---|---|---|---|

1 | 3.152 | 0.930 | 2.863 | 5.317 | 0.274 |

2 | 3.317 | 1.424 | 5.699 | 4.545 | 0.257 |

3 | 3.264 | 1.978 | 4.469 | 5.435 | 0.223 |

4 | 3.082 | 1.637 | 4.824 | 5.410 | 0.295 |

5 | 3.643 | 1.831 | 5.853 | 6.558 | 0.115 |

6 | 3.370 | 0.542 | 3.019 | 5.474 | 0.333 |

7 | 3.675 | 1.620 | 3.323 | 7.352 | 0.136 |

8 | 3.844 | 1.198 | 4.124 | 7.040 | 0.148 |

9 | 3.708 | 1.784 | 2.294 | 7.002 | 0.163 |

10 | 3.570 | 0.754 | 4.682 | 5.139 | 0.168 |

11 | 3.895 | 1.699 | 5.988 | 7.245 | 0.128 |

12 | 3.148 | 1.921 | 4.050 | 5.281 | 0.270 |

13 | 3.240 | 1.353 | 2.522 | 5.235 | 0.268 |

14 | 3.013 | 0.975 | 2.161 | 5.424 | 0.315 |

15 | 3.185 | 1.502 | 4.765 | 5.437 | 0.300 |

16 | 3.511 | 1.450 | 3.249 | 6.837 | 0.177 |

17 | 3.056 | 1.568 | 5.415 | 5.162 | 0.293 |

18 | 3.115 | 0.994 | 4.996 | 5.188 | 0.331 |

19 | 3.680 | 0.793 | 3.857 | 7.019 | 0.138 |

20 | 3.478 | 1.216 | 2.616 | 6.541 | 0.190 |

21 | 3.536 | 1.273 | 3.107 | 6.429 | 0.181 |

22 | 3.995 | 1.144 | 5.057 | 7.943 | 0.145 |

23 | 3.810 | 1.325 | 4.263 | 7.784 | 0.142 |

24 | 3.582 | 0.532 | 2.371 | 6.212 | 0.201 |

25 | 3.909 | 1.879 | 4.361 | 8.161 | 0.144 |

26 | 3.946 | 0.864 | 2.028 | 7.365 | 0.213 |

27 | 3.281 | 0.662 | 4.526 | 5.404 | 0.305 |

28 | 3.954 | 1.771 | 5.132 | 8.738 | 0.137 |

29 | 3.744 | 1.030 | 2.942 | 6.830 | 0.176 |

30 | 3.794 | 1.387 | 3.624 | 7.237 | 0.149 |

31 | 3.611 | 0.639 | 5.535 | 7.686 | 0.119 |

32 | 3.403 | 0.823 | 3.574 | 4.684 | 0.362 |

33 | 3.758 | 0.723 | 5.78 | 7.890 | 0.128 |

34 | 3.867 | 1.945 | 3.911 | 7.471 | 0.143 |

35 | 3.332 | 1.529 | 2.452 | 5.463 | 0.303 |

36 | 3.035 | 1.086 | 3.724 | 5.889 | 0.306 |

37 | 3.381 | 1.103 | 5.344 | 4.371 | 0.367 |

38 | 3.460 | 0.884 | 2.705 | 5.141 | 0.303 |

39 | 3.216 | 1.731 | 5.252 | 5.109 | 0.285 |

40 | 3.431 | 0.595 | 3.416 | 4.573 | 0.388 |

n | p_{t} (W) | p_{e} | ||
---|---|---|---|---|

Experiment | Prediction | Experiment | Prediction | |

6 | 5.474 | 5.202 | 0.333 | 0.317 |

30 | 7.237 | 7.326 | 0.149 | 0.142 |

n | p (MPa) | t (s) | dt (s) | p_{t}(W) | p_{e} |
---|---|---|---|---|---|

1 | 3.877 | 1.734 | 4.950 | 8.410 | 0.135 |

2 | 3.945 | 1.699 | 4.907 | 8.569 | 0.139 |

3 | 3.781 | 0.500 | 5.933 | 8.224 | 0.133 |

4 | 3.811 | 0.536 | 5.801 | 8.190 | 0.129 |

5 | 3.862 | 0.618 | 5.422 | 8.052 | 0.125 |

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**MDPI and ACS Style**

Xue, G.; Zhang, Z.; Qin, J.; Huang, S.; Liu, Y.
Control Parameters Optimization of Accumulator in Hydraulic Power Take-Off System for Eccentric Rotating Wave Energy Converter. *J. Mar. Sci. Eng.* **2023**, *11*, 792.
https://doi.org/10.3390/jmse11040792

**AMA Style**

Xue G, Zhang Z, Qin J, Huang S, Liu Y.
Control Parameters Optimization of Accumulator in Hydraulic Power Take-Off System for Eccentric Rotating Wave Energy Converter. *Journal of Marine Science and Engineering*. 2023; 11(4):792.
https://doi.org/10.3390/jmse11040792

**Chicago/Turabian Style**

Xue, Gang, Zhenquan Zhang, Jian Qin, Shuting Huang, and Yanjun Liu.
2023. "Control Parameters Optimization of Accumulator in Hydraulic Power Take-Off System for Eccentric Rotating Wave Energy Converter" *Journal of Marine Science and Engineering* 11, no. 4: 792.
https://doi.org/10.3390/jmse11040792