NTNU%20Wave%20energy%20colloquia:%20Comparison%20of%20Control%20Strategies%20for%20Wave%20Power%20Converters

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NTNU Wave energy colloquiaComparison of
Control Strategies for Wave Power Converters

• February 17th, 2006
• Jørgen Hals
• CeSOS/NTNU

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Outline
Control strategies for a point absorber
Passive loading
Reactive control
Latching
Analytic results
Numerical results
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 a5 m
• Eigen period T0 4.34 s lt Twave.
• Amplitude restriction s 0.6 a 3 m, constant
  stiffness
• No friction
• Sinusoidal incoming wave
• Linear theory

Reference Hals, Bjarte-Larsson and Falnes
Optimum reactive control and control by latching
of a wave-absorbing semisubmerged heaving sphere,
OMAE 2002
Figure 1 The object of the study A sphere of
radius a and vertical deviation s from its
equilibrium position.
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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