Optimal control of wave energy converters
A wave energy converter and method for extracting energy from water waves maximizes the energy extraction per cycle by estimating an excitation force of heave wave motion on the buoy, computing a control force from the estimated excitation force using a dynamic model, and applying the computed control force to the buoy to extract energy from the heave wave motion. Analysis and numerical simulations demonstrate that the optimal control of a heave wave energy converter is, in general, in the form of a bang-singular-bang control; in which the optimal control at a given time can be either in the singular arc mode or in the bang-bang mode. The excitation force and its derivatives at the current time can be obtained through an estimator, for example, using measurements of pressures on the surface of the buoy in addition to measurements of the buoy position. A main advantage of this approximation method is the ease of obtaining accurate measurements for pressure on the buoy surface and for buoy position, compared to wave elevation measurements.
1. A method for extracting energy from water waves, comprising:
providing a wave energy converter comprising a buoy in water having heave wave motion;
estimating an excitation force of the heave wave motion on the buoy;
computing a control force from the estimated excitation force using a dynamic model, wherein the model comprises
constructing a Hamiltonian as a function of buoy states, wherein the Hamiltonian is a linear function of the control force and wherein the control force comprises a singular arc,
computing partial derivatives of the Hamiltonian with respect to the buoy states and the control force, and
computing the control force at which the partial derivatives vanish; and
applying the computed control force to the buoy to extract energy from the heave wave motion.
2. The method of claim 1 , wherein the buoy states comprise a heave position and a heave velocity of the buoy.
3. The method of claim 2 , wherein the buoy states further comprise a radiation state.
4. The method of claim 1 , wherein the excitation force is estimated from a wave elevation in front of the buoy.
5. The method of claim 1 , wherein the excitation force estimated from one or more pressure measurements on a surface of the buoy and a heave position of the buoy.
6. The method of claim 1 , wherein the buoy comprises a cylindrical buoy or a spherical buoy.
7. A wave energy converter for extracting energy from water waves, comprising:
a buoy in water having heave wave motion,
a controller for computing a control force, wherein the controller:
estimates an excitation force of the heave wave motion on the buoy;
computes a control force from the estimated excitation force using a dynamic model, wherein the model:
constructs a Hamiltonian as a function of buoy states, wherein the Hamiltonian is a linear function of the control force and wherein the control force comprises a singular arc,
computes partial derivatives of the Hamiltonian with respect to the buoy states and the control force, and
computes the control force at which the partial derivatives vanish; and
an actuator for applying the computed control force to the buoy to extract energy from the heave wave motion.
8. The wave energy controller of claim 7 , wherein the buoy states comprise a heave position and a heave velocity of the buoy.
9. The wave energy controller of claim 8 , wherein the buoy states further comprise a radiation state.
10. The wave energy controller of claim 7 , wherein the excitation force is estimated from a wave elevation in front of the buoy.
11. The wave energy controller of claim 7 , wherein the excitation force estimated from one or more pressure measurements on a surface of the buoy and a heave position of the buoy.
12. The wave energy controller of claim 7 , wherein the buoy comprises a cylindrical buoy or a spherical buoy.