Norwegian University of Science and Technology NTNU Phase Control Techniques and their implementation on Wave Energy Converters Torkel Bjarte-Larsson CeSOS Norwegian University of Science and Technology NTNU Trondheim, Norway

Outline Practical implementation Phase control: Physical explanation Resonance turning Continuous control: Reactive Discrete control: Latching Phase control: Physical explanation Electric analogy (reactive) Mathematical condition (reactive) Numerical results for wave-power absorption by heaving semisubmerged sphere. Power conversion by laboratory model.

Two conditions for absorbing maximum power The oscillation velocity must be in phase with the excitation force. The amplitude of the oscillation must be adjusted to the optimum value. (The absorbed power is equal to the power reradiated into the sea).

Resonance turning The natural period of the device should at all times be turned to the period of the wave. Changing the mass of the oscillating body by pumping water in and out of ballast tanks. The buoy reacting against an internal mass by stiffness modulation.

Continuous control During the mid 1970s it was purposed independendently by Salter and by Budal to apply control engineering for optimising the oscillatory motion of a wave-energy converter in order to maximise the energy output. For the practical implementation it was proposed to use a controllable power take-off device, for instance a combined generator-and-motor or turbine-and-pump. Reference: Budal, K. And Falnes, J., 1977. Optimum operation of improved wave-power converter. Marine Science Communications, Vol 3, pp 133-150. Salter, S.H., Jeffery, D.C., and Taylor, J.R.M., 1976. The architecture of nodding duck wave power generators. The Naval Architect, pp 21-24

Continuous control The energy used by the motor should not be considered as lost, since it has been used so that the converter is able to produce more energy in the future (later in the wave period).

Continuous control of double acting piston This system allows continuous control of the velocity of the piston. But requires that the motor/pump is able to handle a very large flow.

Hydraulic power take-off for latching control Here, we have a sketch of the whole hydraulic machinery for power production and control, witch can be placed inside the buoy. Here we have the cylinder - piston pump. It pump oil through a check valves,, into a high pressure gas accumulator witch can be used as a energy storage. Her we have a low pressure gas accumulator, and oil can flow out of this check valve. This is a hydraulic motor which use the pressure difference to produce useful power. And here we have a gas accumulator and a controllable valve that is used for phase-control of the motion of the buoy. In small wave where w want to absorb much energy we control the WEC so it give the phase of the velocity and excitation force is the same. In large wave we deley the phase, to protect the machinery. Bølgeenergiomformeren er utstyrt med et hydraulisk maskineri som blir brukt for å produsere nytte energi, og som styrer amplituden og fasen til bevegelsen til bølgeenergiomformeren. Det hydrauliske maskineriet består av en sylinder-pumpe, fire gassakkumulatorer, to passive likerettende ventiler, og en styrbar ventil og en hydraulisk moter. Systemet var foreslått av Kjell Budal.

Electromagnet for latching and hydraulic power take-off Her er et nærbilde av pumpen som benyttes for energiuttak. Som jeg nevnte innledningsvis sa kan man tenke seg å låse flottøren ved å stenge forbindelsen mellom pumpen og reservoarene. Men siden at låsing av flottørbevegelsen på en liten laboratoriemodell må skje veldig raskt, siden flottøren svinger veldig fort på en liten modell, så brukes det elektromagneter som holder fast to jernskinner som er festet til flottøren for å få til styring med fastholding. PICT0015.JPG Hydraulisk pumpe benyttes for energiuttak Låsemekanismen for fasestyring består av jern skinner som går gjennom luftgapet til en elektrisk magnet.

Wave and heave motion of power buoy Optimal phase at resonance Phase control by latching t or by reactive control 6EWTEC 2005-08-31 TB-L&JF/NTNU

Phase control and amplitude control Instead of the terms phase control and amplitude control the terms reactive control and load control are used. Amplitude control is also termed resistive control. When both phase and amplitude of the oscillation are controlled, the term complexconjugate control is also used. Optimum control include both phase control and amplitude control.

Nilsson & Riedel Electric Circuits: The apparent power, or volt-amp,requirement of a device designed to convert electric energy to a nonelectric form is more important than the average power requirement. Although the average power represents the useful output of the energy converting device, the apparent power represent the volt-amp capacity required to supply the average power.

Accumulation of energy by oscillating body. reactive control latching control no control (passive) By reactive control, energy flow through the conversion machinery has to be reversed during part of the wave cycle. 6EWTEC 2005-08-31 TB-L&JF/NTNU

heaving semi-submerged sphere Theoretical (numerical) study of heaving semi-submerged sphere Diameter 2a = 10 m smax = 0.6 a = 3 m Natural heave period = 4.3 s 6EWTEC 2005-08-31 TB-L&JF/NTNU

Absorbed power (MW) from wave of period T = 9 s Amplitude (m) of incident wave latching Example: A = 0.5 m: Preact = 172 kW Platch = 137 kW Ppassiv = 24 kW 6EWTEC 2005-08-31 TB-L&JF/NTNU

A = 0.5 m, T = 9 s Absorbed energy Curve slope = instantaneous power Average slope: Preact = 172 kW Platch = 137 kW Ppassiv = 24 kW 6EWTEC 2005-08-31 TB-L&JF/NTNU

Cylinder with hemispherical bottom. Heaving buoy. Cylinder with hemispherical bottom. Arranged to slide along a vertical strut. 6EWTEC 2005-08-31 TB-L&JF/NTNU

Heaving buoy of diameter 0.14 m and natural heave frequency 1.1 Hz, tested in a wave channel 0.33 m wide. Power take-off by piston pump lifting water to an elevated reservoir. Two vertical rails may be latched by two electromagnets on the lower fixed platform. 6EWTEC 2005-08-31 TB-L&JF/NTNU

Relative absorbed power and useful power without and with phase-control versus heave/wave amplitude ratio absorbed useful Amplitude ratio |s/A| decreases by increasing the load (increasing the pump head). Curves are fits to a mathematical model. 6EWTEC 2005-08-31 TB-L&JF/NTNU

Concluding remarks. Compared to reactive control, latching control is slightly sub-optimum, but avoids the necessity for reversing the power flow. The relative benefit of applying control (reactive or latching) is strongly dependent upon the width of the resonance curve, that is, upon the size of the oscillating body compared to the wavelength. The model experiment demonstrates the need for developing a guiding system with less friction. 6EWTEC 2005-08-31 TB-L&JF/NTNU

THE END 6EWTEC 2005-08-31 TB-L&JF/NTNU

Outline: Phase control and amplitude control Reactive control (optimum) and latching control (sub-optimum). Numerical results for wave-power absorption by heaving semisubmerged sphere. Heaving vertical cylinder: Hydrodynamical parameters approximated. Power conversion by laboratory model. Concluding remarks. Jeg har tenkt til å starte med å snakke om eksperimenter på et strandlokalisert kraftverk (Artikkel C). Så fortsetter jeg med å pressentere numeriske beregninger av hydrodynamiske parametre for et flytende kraftver. Jeg vil nevne hvordan man tilnærmet kan finne estimater for de hydrodynamiske parametrene. Så vil jeg pressentere noen resultater fra eksperimenter på et flytende kraftverk. Og til slutt vil jeg konkludere. 6EWTEC 2005-08-31 TB-L&JF/NTNU

Sketch of the floating wave-energy converter rounded edge geometry Water depth h = 25 m 3.65m 10.15m 3.3m Siden at et virkelig kraftver bør ha avrundetde kanter for å minimalisere viskøse tap, brukte jeg senere progammet til å beregne hydrodynamiske parametre for avrundet geometri. 0.3m 4m 6EWTEC 2005-08-31 TB-L&JF/NTNU

Radiation resistance versus frequency in normalised units. numerical (AQUADYN) limit for  = 0 Upper curve: approximate empirical elementary-function deep-water formula. Lower curve: same formula, but with k = k() for water depth h = 25 m.