SCIENCE CHINA Technological Sciences, Volume 61 , Issue 8 : 1114-1126(2018) https://doi.org/10.1007/s11431-017-9308-9

## A feedback latching controller for two-body wave energy converters under irregular wave conditions

• AcceptedJun 11, 2018
• PublishedJul 18, 2018
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### Abstract

Latching control is considered to be an effective way to improve the energy absorption of a wave energy converter (WEC). Recently, a latching control method was realized in a hydraulic power take-off (PTO) system and was demonstrated to be effective in one-body WECs. However, the effectiveness of latching control for two-body WECs still needs to be tested. In this paper, a feedback latching controller is proposed for a conceptual two-body WEC. In this conceptual design, a permanent-magnet linear generator (PMLG) is adopted as the PTO system, and a pure water hydraulic cylinder system is designed for performing the latching control. A feedback control strategy based on the measurement of latching force is established, formulated and tested numerically under realistic irregular wave conditions. The effects of the wave peak period and the PTO damping coefficient on the effectiveness of the latching control is also investigated. The results indicate that the proposed feedback latching control is effective for improving the annual power absorption of the two-body WEC. Furthermore, compared to another latching control, the proposed control is more practical because it does not require any knowledge of the wave conditions or the dynamics of the whole WEC system.

### Funded by

the China Postdoctoral Science Foundation(Grant,No.,2017M622692)

the Fundamental Research Funds for the Central Universities(Grant,No.,2017BQ093)

the Open Foundation of the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology(Grant,No.,LP1713)

the Guangdong Provincial Department of Science and Technology(Grant,Nos.,2015A020216005,&,2015B010919006)

### Acknowledgment

This work was supported by the National Key R&D Program of China (Grant No. 2016YFC1400202), the China Postdoctoral Science Foundation (Grant No. 2017M622692), the Open Foundation of the State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology (Grant No. LP1713) and the Guangdong Provincial Department of Science and Technology (Grant No. 2015A020216005) and the Fundamental Research Funds for the Central Universities (Grant No. 2017BQ093).

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• Figure 1

(Color online) The illustration of the two-body heave system and the latching control system. (a) The model of two-body WEC; (b) a diagram of the PMLG system; (c) a diagram of the latching mechanism.

• Figure 2

(Color online) The diagram of a two-body heaving buoy WEC with a latching mechanism.

• Figure 3

(Color online) An illustration of the differences between the velocities of the feedback latching and the optimal latching strategies under conditions of regular waves.

• Figure 4

(Color online) Panel model of the two-body WEC.

• Figure 5

(Color online) The hydrodynamic parameters of the WEC for heave motion. (a) Wave force amplitude; (b) added mass; (c) radiation damping.

• Figure 6

(Color online) The wave exciting force and wave elevation of IRW8 for 0–180 s.

• Figure 7

(Color online) The wave exciting force and wave elevation of the single random wave condition.

• Figure 8

The optimal damping coefficients for regular waves.

• Figure 9

The average annual power (kW) for different PTO parameters.

• Figure 10

The absorbed power (kW) of the WEC with fixed-time latching control under different wave conditions, for different $CPTO$values and latching times. (a) IWC 6; (b) IWC 8.

• Figure 11

(Color online) The heave response of the WEC with different control strategies under the IWC 10 wave condition. (a) The heave related displacement of WEC with different control strategies; (b) the heave related velocity of WEC with different control strategies; (c) the absorption power of the WEC with different control strategies; (d) the heave displacement response of the WEC with the feedback latching control.

• Figure 12

(Color online) The velocity amplify ratio and latching time ratio of the two latching control strategies under the different irregular wave conditions. (a) Velocity amplify ratio; (b) latching time ratio.

• Figure 13

(Color online) The capture width of the WEC with different control strategies under the different irregular wave conditions in Table 2 with different PTO damping levels. (a) CPTO=1.6×105 N s m−1; (b) CPTO=2×104 N s m−1.

• Figure 14

(Color online) The amplitudes of the relative heave motion under 1-m-amplitude regular waves.

• Table 1   Parameters of the WEC
 Description Value Outer radius of the buoy (m) 3.0 Inner radius of the buoy (m) 1.5 Draft of the buoy (m) 3.5 Displacement of the buoy (t) 42.63 Radius of the heave plate (m) 6 Draft of the heave plate (m) 30 The radius of the PTO (m) 1.4 The length of the PTO (m) 4.5 Travel range of the PMLG (m) ±3
• Table 2   Characteristic wave parameters of the real wave sea state
 Wave condition number $Tpi$(s) $Hsi$(m) Ratio (%) IWC 1 1.826 0.614 1.85 IWC 2 2.530 1.147 8.54 IWC 3 3.453 1.900 9.45 IWC 4 4.401 2.758 10.89 IWC 5 5.445 3.658 12.27 IWC 6 6.478 3.398 8.66 IWC 7 7.451 2.497 14.6 IWC 8 8.330 2.073 7.03 IWC 9 9.090 1.940 5.64 IWC 10 10.606 1.746 15.83 IWC 11 12.859 1.723 3.05 IWC 12 14.751 1.813 1.56 IWC 13 17.168 2.448 0.52 IWC 14 20.922 4.889 0.12
• Table 3   Optimal latching time of fixed-time latching control for different PTO damping coefficients
 Wave conditionnumber Optimal latching time (s) CPTO=1.6×105 N s m−1 CPTO=2×104 N s m−1 IWC 1 0.00 0.00 IWC 2 0.00 0.00 IWC 3 0.00 0.00 IWC 4 0.30 0.40 IWC 5 0.70 0.90 IWC 6 1.10 1.20 IWC 7 1.30 1.60 IWC 8 1.40 1.30 IWC 9 1.40 1.20 IWC 10 1.40 1.40 IWC 11 1.50 1.30 IWC 12 1.60 1.50 IWC 13 1.50 1.70 IWC 14 1.70 1.90
• Table 4   Annual average power estimation for different control strategies of a two-body system with the optimal PTO damping condition: =1.6×
 Wave condition number Wave condition Average Power (kW) $Tpi$(s) $Hsi$(m) Ratio (%) Uncontrolled Fixed-time latching Feedback latching IWC 1 1.826 0.614 1.85 0.005 0.005 0.002 IWC 2 2.530 1.147 8.54 0.170 0.170 0.095 IWC 3 3.453 1.900 9.45 1.970 1.970 2.077 IWC 4 4.401 2.758 10.89 10.179 11.137 10.997 IWC 5 5.445 3.658 12.27 31.634 34.292 35.575 IWC 6 6.478 3.398 8.66 35.316 39.581 40.729 IWC 7 7.451 2.497 14.6 20.484 24.057 24.485 IWC 8 8.330 2.073 7.03 14.089 16.465 16.656 IWC 9 9.090 1.940 5.64 11.876 13.210 13.632 IWC 10 10.606 1.746 15.83 7.980 7.123 8.441 IWC 11 12.859 1.723 3.05 5.112 2.428 4.644 IWC 12 14.751 1.813 1.56 4.526 1.687 3.879 IWC 13 17.168 2.448 0.52 5.763 2.115 4.674 IWC 14 20.922 4.889 0.12 14.485 5.656 10.982 Annual average power (kw) 14.437 15.710 16.385

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