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System model with WEC and PTO 

System model with WEC and PTO 

Source publication
Conference Paper
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In this paper, an economic Model Predictive Control (MPC) is used to investigate the effects that arise from the model mismatch between the control and the system. It is shown that the average electrical power is affected by the modelling discrepancies, but that the performance is still acceptable. A move-blocking technique is incorporated into the...

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... and system. This shows that there needs to be a balance where the minimum control horizon is found while maintaining high performance. A cylindrical wave energy converter point absorber which is restricted to move in the heave direction is assumed in this paper. The model is based on linear wave theory. The hydrodynamic model (1), as shown in Fig. 1, consists of the hydrostatic force F h (t), the radiation force F r (t), the excitation force F e (t), controlled PTO force F P T O (t) and the non-linear viscous force F v (t). Initially in this paper, F v (t) is neglected, since it adds unnecessary complexity into the individual characteristic mismatch ...
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... is clearly shown from the waveforms in Fig. 10 that as the control horizon N c decreases, the control action across the prediction horizon becomes more disjointed and diverges from the control waveform when N c = N ; this results in the deterioration of average power. However, by incorporating a move-blocking system in the control horizon, less control variables need to be ...
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... the performance of the MPC with a perfect (matched) hydrodynamic model was investigated using a full control horizon, a reduced control horizon and a move-blocking control horizon. For all tests, a 1 m monochromatic excitation wave was used; linear constraints were assumed for WEC heave and velocity and for the PTO force. Fig. 11 shows the average electrical powers absorbed from the system when the different types of control horizons were used. When a standard reduced horizon is used with N c = 30, the average power has drastically diminished when compared to the average power results found when using a full control horizon with N c = N . However, when a ...
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... for N c < 10 show much improved power levels when compared with the standard control horizon reduction with a much greater control horizon N c . To show the serious advantages of using a move-blocking control horizon, the average optimisation solution times for the unconstrained and linearly constrained problems were recorded. As shown in Fig. 12, the difference between the solution times for constrained and unconstrained MPC is very clear. However, for both unconstrained and constrained cases Furthermore, this figure also shows the corresponding power ratio obtained for the various control horizons. The power ratio here is the ratio of the average power extracted using a ...
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... test the robustness of the system, the move-blocking technique was used on the mismatched hydrostatic system where a −20% hydrostatic stiffness coefficient was used; 1 m high monochromatic waves are used in this analysis. The resulting extracted average electrical power from the mismatched system are shown in Fig. 13. From Fig. 13 it is shown that to some degree, the inclusion of the move- blocking technique does not cause any significant difference in performance. It is only when the control horizon has been decreased to the point (N c = 10) where ∆u q (k + 2) is forced to become the same as ∆u q (k+1) that the average power starts to significantly deviate from ...
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... + 2) is forced to become the same as ∆u q (k+1) that the average power starts to significantly deviate from the average power extracted when using a full control horizon. On the other hand, when move-blocking results in a ∆u q (k +2) and ∆u q (k +1) which are equal to each other, the calculated PTO force ∆u q (k) becomes damped; this is shown in Fig. 14. This damped PTO force control action can lead to problems in satisfying the hard ...
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... Fig. 15 it is shown for a 1 m high monochromatic wave with a frequency of 0.419 rad.s −1 that the heave of the WEC and LPMG stay within the heave limitation of ±3.5 m when a control horizon of N c = 100 is used. However, when a control horizon of N c = 10 is implemented, the PTO force (Fig. 14) becomes more damped and the heave of the system ...
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... Fig. 15 it is shown for a 1 m high monochromatic wave with a frequency of 0.419 rad.s −1 that the heave of the WEC and LPMG stay within the heave limitation of ±3.5 m when a control horizon of N c = 100 is used. However, when a control horizon of N c = 10 is implemented, the PTO force (Fig. 14) becomes more damped and the heave of the system starts to exceed the heave limitation, which Time (s) could cause damage. If the control horizon N c is too low, then there is a higher chance of ∆u q (k + 2) = ∆u q (k + 1) which would degrade the systems performance. However, as stated in section. IV-A, if the control horizon N c is ...

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... WEC control systems aim to keep the buoy velocity 410 in phase with the wave force. Modelling uncertainties and input/output disturbances may introduce errors in the reference and tracking loops leading to a significant degradation of the converter efficiency (O'Sullivan and Lightbody, 2017). For the controller shown in Figure 4, the main 415 sources of modelling errors and their effect on the buoy performance are listed in Table 2. Firstly, the current value of the excitation force, ˜ F exc (t), is estimated using the Extended Kalman filter which is based on the available model of the WEC. ...
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