The dynamics of wave energy

The U.S. Dept. of Energy figures that harnessing just 20% of offshore wave energy at 50% efficiency would be comparable to the electrical power generated by all U.S. hydro resources in 2003.

In the quest for green energy, engineers have increasingly viewed tides and ocean waves as sources from which they can harvest energy. But there is no one single technology that has emerged as a standard for harvesting wave energy. There are several viable methods being studied. Most of them have several functions in common. These functions include a captor which collects energy from the oscillatory motion of waves, power take-off equipment which converts mechanical energy into electricity, and an anchoring system which holds the wave energy converter (WEC) in place.

For example, consider a device called the P2 from Pelamis Wave Power in the UK. Its captor is a ‘snake-like’ construction on the surface of the water consisting of several cylindrical sections joined together by hinged joints. As waves pass down the length of the machine these sections flex relative to one another. Hydraulic cylinders at each joint resist wave motion and pump fluid into high pressure accumulators. The power take-off equipment consists of a hydraulic motor powered from fluid in the accumulator. The motor turns a generator which sends electrical power to shore. The anchoring system consists of several anchors connected to a central point, plus a yaw-restraining line.

Another WEC from Ocean Power Technologies looks like a buoy. Called the PowerBuoy, its collector consists of a buoy that moves freely up and down as waves pass by. The buoy sits on a vertical shaft anchored to the ocean floor. As it rides the waves it moves hydraulic cylinders up and down to power a hydraulic motor. The power take-off includes the hydraulic motor which drives an electrical generator transmitting power via an underwater power cable. The anchoring system consists of a foundation on the seabed.

A third example is the Oyster wave device developed by Aquamarine Power in Scotland. The collector consists of a buoyant, hinged flap attached to the seabed at depths of between 10 and 15 m. The hinged flap, which is almost entirely underwater, pitches back and forth under the influence of waves. The movement of the flap drives two hydraulic pistons which push high pressure water onshore via a subsea pipeline to drive a conventional hydro-electric turbine. The power take-off consists of the hydraulic pistons and pumping mechanics. The anchoring system consists of a foundation on the seabed.

Resolving forces

All these WECs use different approaches for harvesting wave energy. But essentially, engineers analyze the dynamics of all WECs with the same approach, applying Newton's second law: Inertial force balances the forces acting over the WEC captor, or, simply, F = mA. The typical approach is to decompose forces into those from hydrodynamic and external sources. The hydrodynamic source includes the excitation force inflicted by the incident waves, the buoyancy force which comes from the variation in submergence caused by wave oscillations, and radiation force related to the pressure over the submerged surface caused by fluid displaced from device oscillations. Moreover, forces from the PTO and mooring system could also constrain the motion of the WEC.