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NTNU Wave energy colloquia:

Comparison of Control Strategies for Wave Power Converters

February 17th, 2006

Jørgen Hals

CeSOS/NTNU

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Outline

Passive loading Reactive control Latching

Analytic results Numerical results

Control strategies for apoint absorber

Comparisons

Conclusions

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Control strategy for wave energy conversion

Why do we need control? What are the alternatives? How much do we gain? Which requirements are imposed on the machinery in terms of

capacity and efficiency?

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Example study of heaving sphere Semisubmerged Radius a=5 m Eigen period T0 = 4.34 s < Twave.

Amplitude restriction s ≤ 0.6 a = 3 m, constant stiffness No friction Sinusoidal incoming wave Linear theory

Figure 1: The object of the study: A sphere of radius a and vertical deviation s from its equilibrium position.

Reference:Hals, Bjarte-Larsson and Falnes: Optimum reactive control and control by latching of a wave-absorbing semisubmerged heaving sphere, OMAE 2002

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Strategies explained

Passive loading

(Optimum) reactive control Latching

Amplitude Not optimal Optimal Not optimal

Phase Not optimal Optimal Optimal

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Control strategies

Reactive control Control by latching Passive loading

Figure 2: The vertical excursion of the sphere for three different control strategies: Reactive control (red), control by latching (blue) and passive loading (black). The wave period T is 9 s and the wave amplitude is 0.5 m

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Load impedance and instantaneous power flow for passive loading and reactive control

Passive loading Reactive control

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Latching control

Position locked when velocity is zero Release to align velocity and force

Numerical solution of equation of motion

Variation of load and latching instant to find best values.

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Absorbed energy with control

Increased average absorption

Increased instantaneous power

Power inversion

Figure 3: Accumulated absorbed energy, for three different control strategies: Reactive control (red), control by latching (blue) and passive loading (black). The wave period T is 9 s and the wave amplitude is 0.5 m.

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Reactive power for optimum control (1)

Figure 4: Reactive power (dashed curve) and converted power (fully drawn curve) for the case of optimum reactive control. The wave period is T = 9 s.

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Reactive power for optimum control (2)

Figure 5: Reactive power (upper curves) and converted power (lower curves) for the case of optimum reactive control. Values are given for three wave periods T = 6, 9 and 12 s, as shown by the fully drawn curve, the broken line and the dotted line, respectively.

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Absorbed power, comparing strategies (1)

Figure 6: Maximum absorbed power Pu versus wave amplitude |A| with reactive control (fully drawn curve), latching control (dashed curve) and passive loading (dotted curve). The wave period T is 9 s.

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Absorbed power, comparing strategies (2)

Figure 7: Maximum absorbed power Pu versus wave amplitude |A| with reactive control (fully drawn curve), latching control (dashed curve) and passive loading (dotted curve). The wave period T is 12 s.

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Summary

Numerical example: Semisubmerged sphere in sinusoidal wave

Quantitative comparison of control strategies Passive loading as reference Reactive control

• Theoretically optimal for unconstrained motion• Reactive power • High instantaneous power• Power inversion • Highly efficient machinery is crucial

Latching control • Slightly reduced power output • Moderate instantaneous power • No power inversion • Efficiency less crucial