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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

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  • ReceivedDec 19, 2017
  • AcceptedJun 11, 2018
  • PublishedJul 18, 2018

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 CPTOvalues 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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