W2W Top Trumps

 

W2W power flow starts getting interesting when applied to specific examples of WEC. I've chosen historical examples to avoid looking like I'm giving investment advice!  We're going to play 'Top Trumps' with three very different devices: the Wave Star arm (above), Pelamis, and the LIMPET OWC.  I learnt new and surprising things while preparing this blog post. At the end I compare the electrical generators and show how 'electrical power' is very different for these three devices.

 

Wave Star arm 

 

This is a significant example which is deceptively complex. The full Wave Star concept looks like a racing rowing boat: it has a rows of arms on each side, each ending in a buoy rather than a paddle, and the central 'boat' is fixed to the sea bed by piles which allow it
to passively adjust to tidal levels (artist's impression to the right). A (nevertheless large) half-scale section (only two arms) operated for three years at a shallow-water site in Denmark. The obvious longitudinal axis of the multi-arm device is along the central supporting structure. The tank testing and numerical modelling assumed that the waves would run along the length of the device, so that the buoy excitation forces were out of phase with one another. (See for example Hansen et al where wave headings of χ = 0° and χ = 45°  were considered). For χ = 0°, the modes that move are heave and sway. These are mechanically coupled and resolve to a single DoF rotation about the joint. Note that sway is one of those modes where power is not captured: the excitation force is negligible for χ = 0°, and motion in this mode will radiate away energy without capturing any waves. For χ = 0°, there is no DoF in the direction of drift; these forces are all borne by the hinges and may result in additional friction.   

 

There is now a popular research device called the 'Wave Star arm' based on a tank test model of a single buoy. The W2W power flow diagram is at the top of the blog. This was Aalborg University's contribution to the WECCCOMP (drawing to the right).  Note that the longitudinal axis (y in the diagram) for the Wave Star arm is perpendicular to that of the full device: it is the lever arm projected onto a horizontal plane passing through the hinge (A in the diagram).  The nominal wave direction is also perpendicular to the full device as it aligns with the lever arm. So the modes that move are heave and surge, again resolved to a rotation about the joint. Unlike sway, power may be captured from surge.  

 

I was surprised to find that the research device is not a subset of the full commercial device. This is not obvious without looking at the details. The W2W power flow method can be useful for systematically reviewing a concept.  

 

Another difference to the full device was the PTO. The full Wave Star PTO used digital hydraulics. The hydraulics dealt with the high loads, and the fast digital control ensured it was efficient at part load. Hydraulics are difficult to implement at tank scale, so here the PTO was simulated with a linear generator. As this is highly inefficient at part load, the electrical power would not be representative of the digital hydraulics. Instead the mechanical power was calculated in real time from sensor measurements of the generator velocity and force. Electrical power was estimated in real time by assuming a fixed percentage of power loss (10%) across all four quadrants. Nevertheless, it was not possible to avoid the dynamics of the PTO. They found that the PTO dynamics were quite different from those assumed in the numerical model. The model assumed a unitary transfer function (infinitely fast dynamics) between the demand and applied force, while the linear motor controller resulted in large spikes and high frequency oscillations. 

 

Wave Star Arm Top Trumps 

Axes	Longitudinal axis = lever arm projected onto horizonal plane passing through the hinge.  Nominal wave direction: parallel to lever arm
Hydrodynamic DoF	1 rotational DoF: rotation about hinge
Hydrodynamic modes  (axes pass through CoM and waterline)	surge: mechanically coupled with heave, captures power  sway: restrained by hinge (no excitation for nominal wave direction)  heave: mechanically coupled with surge, captures power.   roll: restrained by hinge (no excitation for nominal wave direction)  pitch: restrained by hinge (excitation force felt in nominal wave direction; coupled to surge)   yaw: restrained by hinge (no excitation in any wave direction)
Viscous losses	Low for small motions due to circular buoy shape. Modelled in WEC-Sim as a quadratic viscous drag force.
PTO DoF	1 rotational DoF = the hydrodynamic DoF. An arrangement of hinges and levers translates this into a translation at the PTO mechanism.
PTO point of reaction	Ground (supporting frame).
Offset direction:	For nominal wave direction, in line with surge; drift results in an offset in the surge component of the buoy position. Tides not modelled.
Foundation forces	Not modelled in WECSim.  However for nominal wave direction, wave drift aligns with an excited mode; so the offset not modelled.
Pre-PTO conditioning	Translation: lever arm and hinges (which enforce a stroke limit); motion geared down to keep within PTO stroke, relatively low inertia.
PTO	A linear generator with four quadrant control and high frequency response to force demand.
PTO losses	In both tank tests and numerical models, electrical power was modelled by assuming PTO losses of 10% on the mechanical power flows.
Post-PTO conditioning	Smoothing (Digital hydraulics) not modelled in tank or simulation for WECCCOMP

 

 

Shore-based Oscillating Wave Column (OWC)

 

 

 

Anyone who has seen a blow-hole at the beach will understand the general principle of an Oscillating Water Column (OWC). The diagram above shows the general layout for a shoreline OWC. Here the hydrodynamic body is a body of water enclosed in a cassion.  It has a resonant response so the top of the water column moves with a greater amplitude and a different phase to the wave passing the entrance. Fixed shore-based OWCs are generally in shallow waters, with the following implications:  

• The horizonal motions of waves are greater than the vertical motions.  
• Wave shoaling means that there is a narrower range of wave directions.  
• The tidal range will impact the still water line, and hence the hydrodynamic response. 
• Wave breaking puts the device in a very energetic location, and so the cassion has challenging and expensive structural requirements. 
• The ability to house the PTO onshore has O&M advantages.  

 

OWCs generally have a pneumatic transmission. The air above the water column in the cassion is compressed by the water column below it. The air volume changes and I use the term 'pulsation' to describe this. The air chamber volume equals the cassion volume minus the water column volume. The PTO acts on the water column as a pressure on the surface. The associated power is described by the air chamber pressure and volume flow rate.  

 

The air is ducted into a turbine which drives a generator. Some designs (e.g. Mitriku) have a bi-pass valve that is activated by a pressure threshold. This is a load limiting feature with economic advantages. There is typically a pneumatic turbine that generates torque in one direction from air flow in both directions. The rectified power flow allows the use of conventional unidirectional electrical generator.   

 

We will consider the LIMPET prototype that was installed in the Isle of Islay. It was a follow-up to a smaller university-led prototype which had a vertical water column. The LIMPET introduced several design changes in response to learnings from the earlier prototype: 

• 
  The column was inclined at 40°, which allowed it to capture in both surge and heave. This greatly increased power capture potential due to strong horizonal wave motions in shallow water, bringing the water column resonant period closer to that of the waves.  
• The inclination also intended addressed one of the DoF that dissipates power: longitudinal sloshing (think bath tub). The entrance to the chamber was narrowed with to reduce longitudinal sloshing.  
• The other power-dissipating DoF is transverse sloshing, which increases with cassion width.  The Limpet had three separate collectors to reduce this.  
• There was a concern about water entering the turbine duct, so the cross-sectional volume of the cassion was increased near the duct to cause a non-linear relationship between water column height and volume.   

Note that the three separate collectors would allow differences in the water column heights if a wave crest approached from an angle. The three chambers were connected at the top at the same volume of air, so they felt each other via the air pressure. This was a potential source of parasitic power leakage.  

 

 

LIMPET OWC Top Trumps  

Axes	Longitudinal axis = perpendicular to shore; parallel to still water level (tide dependent; incorrect assumptions of mean level).   Nominal wave direction: perpendicular to shore.
Hydrodynamic DoF	Three hydrodynamic bodies (sloped columns of water) each with 4 DoF:  Volume of the oscillating water column (the power capturing DoF – coupling to the power capturing DoF of the other water columns for waves approaching from an angle)   Transverse sloshing mode   Longitudinal sloshing mode  Swirl
Hydrodynamic modes  (axes pass through CoM and waterline)	Modes for each water column:  surge: mechanically coupled with heave, captures power  sway: restrained by cassion; (no excitation for nominal wave direction)  heave: mechanically coupled with surge, captures power.   roll: transverse sloshing mode; no linear excitation; a common non-linear response, doesn't capture power; a potential source of power loss.  pitch: longitudinal sloshing mode; linear excitation and hydrodynamically coupled to surge, doesn't capture power; a potential source of power loss.  yaw: swirl, no linear excitation, doesn't capture power; not a major source of losses.
Viscous losses	Significant losses due to the sloshing modes, cassion corners and throttled entrance.
PTO DoF	Power is defined by volume flow rate and pressure.  The velocity of the water columns is damped by the air chamber pressure, so the PTO has 1 DoF.
PTO point of reaction	Turbine torque resisted by turbine mounting; there are contra-rotating turbines so some of the torque would cancel; pressure drop over the pair of turbines is relative to atmospheric pressure.
Offset direction:	For nominal wave direction, drift in the direction of surge response. Shallow water effects. When the tide is turning this might cause an assymettry in the surge mode.
Foundation forces:	Cassion reacts against drift, is a pneumatic conduit (peak internal pressure of 1 bar), protects against wave breaking (frontal wave pressure of 6 bar), restrains sway, and couples heave to surge.
Pre-PTO conditioning	First stage of the transmission is the pulsating volume of the air chamber. The air chamber provides gearing and some spring due to compressibility.  The air chamber volume is coupled to the volume of the sum of the three OWCs. It has 2 DoF; both volume and pressure are required to describe the state of the air chamber.   Next there are two inline controllable isolation valves. One was controlled to act as a governor, limiting airflow gradually once the turbine speed crossed a threshold. These were also designed to enforce the grid limit of 150 kW.   They had planned to retrofit a fast-acting by-pass valve in the chamber roof to release impulsive pressures but this was not implemented (not needed due to poor power production).    The next stage is a pair of back-to-back bidirectional Wells turbines (rectification).    Due to the gearing, the inertia of the PTO and turbine is felt by the water columns. The original Limpet also tried flywheels for power smoothing, but these impeded power capture and were removed.
Post-PTO conditioning	Without the flywheels the power is irregular. A commercial concept would have needed power smoothing after the PTO.
PTO	The air chamber fed two inline contrarotating Wells turbines, each independently powering a 250kW unidirectional induction generator, run in torque mode via an inverter drive.
PTO losses	LIMPET was a grid connected prototype so the electrical power generated was measured. The incident wave power, and the power captured, was less than expected. Also the second generator captured about half the power of the upstream generator. Both generators were running at part load and PTO losses were significant.

 

The Limpet produced much less power than expected, and the paper lists several reasons for this: incorrect assumptions about the wave climate, bathymetry, and mean water level, and the unintentional change to the bathymetry by blasting away a cliff face during construction. Stepping through the design with the W2W power flow method suggests some additional reasons for the low power capture: throttling losses due to the constricted entry, parasitic losses when waves approach from an angle, and longitudinal sloshing mode leading to water ingress into turbine duct.

 

The poor performance of the second turbine also points to associated technical issues. There was a disparity between the measured electrical power and the mechanical power, calculated from measured generator speed and demand torque. The authors described this as 'unlikely', which diminished their confidence in the measured electrical power. However, there are plausible explanations for what appears to be exceptionally high losses. The turbine gen set was a novel bespoke design, and there are several indications that it was not thoroughly bench tested, such as identical control algorithms for both generators, and the only reference to turbine tests involving a significantly different design.  It is useful to be able to spot whether poor performance is intrinsic to a design or the result of under-resourced implementation.

 

 

Pelamis

 

The diagram above shows just the power flow between the first two tubes of the Pelamis. In the top trumps table below we can see just how complex the interactions between these tubes are. The hinges impose mechanical coupling between various hydrodynamic modes of motion, some of which can be controlled. In the photo to the right, it can be seen that the relative motion of the tubes is both vertical (pitch) and horizontal (yaw). Then there is also hydrodynamic coupling, which means that waves bouncing off one tube (diffraction) or created by that tube bobbing about (radiation) could travel to other tubes and excite them.

 

What is particularly interesting about this device is the hydraulic transmission and PTO, and the fact that the electrical generator is performing the function of smoothing and rectification rather than PTO. 

 

 

Pelamis (P1) Top Trumps 

Axes	Longitudinal axis = the length of the device  Nominal wave direction (χ = 0°): in line with the length of the device (head-seas).   Self-weather-vaning to align with principle wave direction.
Hydrodynamic DoF	A line of 4 tubes, connected by 3 joints, each of which has 2 hinge DoF:  6 DoF for the first tube + 2 hinge DoF for each subsequent tube = 12 DoF.  The hinge DoFs have orthogonal axes inclined in the transverse direction, so that each hinge DoF is resolved into a combination of pitch and yaw.    There is mechanical cross-coupling between many of the DoF of adjacent tubes.  There is also hydrodynamic cross-coupling as diffracted and radiated waves could excite neighbouring tubes.
Hydrodynamic modes  (axes pass through CoM and waterline)	surge: Tube 1: Hydrodynamically coupled to tube 1 pitch which captures power.   Tube 2: Restrained mode.  sway: Tube 1: Not excited for nominal wave direction. Excited by waves in other directions. Mechanically coupled to both of the tube 2 hinge modes (via tube 2 yaw). There is no buoyancy restoring force in this mode. Tube 2: Restrained mode.  heave:  Tube 1: Mechanically coupled to both of the tube 2 hinge modes (via tube 2 pitch); captures power. Tube 2: Restrained mode.  roll: Both tubes: Not excited for nominal wave direction. Excited by waves in other directions (e.g χ  = 90°), does not capture power.  pitch: Tube 1: Excited in head-seas. Mechanically coupled to both of the tube 2 hinge modes; captures power. Control determines the degree of coupling to tube 1 yaw. Tube 2: A component of both hinge DoFs. Mechanically coupled to heave and pitch of tube 1.  yaw: Tube 1: not excited in head-seas, and radiated waves do not capture power. Can be excited when tidal stream or waves approach tube at an angle, with increased yaw resulting in an increased incident wave angle. There is no buoyancy restoring force in this mode; restoring force is provided by coupling to pitch.  Mechanically coupled to both of the tube 2 hinge modes.  Control determines the degree of coupling to tube 1 pitch.  Tube 2: a component of both hinge DoFs. Mechanically coupled to sway and yaw of tube 1.
Viscous losses	Low viscous losses due to streamlined profile.
PTO DoF	The PTO DoF are the joint DoF, and they damp the relative rotational velocity of the joints. Separate control of each hinge gives control over the axis of relative rotation. When the tubes pitch relative to the tube in front, the resonant period is lower than the wave period. However, when a combination of pitch and yaw is chosen, this raises the resonant period to that of the waves, resulting in more power capture.
PTO point of reaction	The device is self-reacting so the tubes resist the PTO forces.  The PTO force has an equal and opposite reaction in the neighbouring tube.
Offset direction:	For nominal wave direction (head seas), the drift force is in the surge direction. Tides could impact weather-vaning; hence wave direction.
Foundation forces	The slack mooring resists the drift forces and surge forces due to coupling with pitch, a power capturing mode. The mooring is attached to the front tube, so it passively weather vanes. This is influenced by both the tidal stream and principle wave direction.
Pre-PTO conditioning	The oscillating hinge rotation is geared to a higher speed shaft. The gearing increases the impact of the transmission and PTO inertia on the tube dynamics.
PTO	The PTO is an Artemis digital hydraulic pump, which offers four quadrant control. The output is pressurised hydraulic fluid.
PTO losses	The volume of fluid flow can be controlled digitally to ensure high efficiency over a wide range of loads.
Post-PTO conditioning	High and low pressure accumulators store the captured power between wave groups.  A unidirectional hydraulic generator is then used to output a steady voltage with slow ramps in response to changing accumulator levels. Together these two subsystems rectify and smooth the power.

Comparing these examples – what is the electrical generator doing? 

 

These examples highlight that electrical generators can do different jobs in different WECs:  

• In the Wave Star arm, the generator is the PTO. There is minimal pre-PTO conditioning, so the generator velocity is slow, reciprocating and highly irregular.  
• In the OWC, the generator is also the PTO. There is significant pre-PTO conditioning, so the generator velocity is fast, unidirectional and irregular.  
• In the Pelamis however, the generator is fed from the captured power stored in high and low pressure accumulators. These accumulators provide the post-PTO conditioning functions of storage, rectification and gearing, so the generator velocity is fast, unidirectional and smooth. 

One reason for highlighting this is that representing PTO losses is important when modelling advanced control. The distinction between mechanical and electrical power is often used as a short-hand for describing whether these losses have been modelled. Here we see it is more important to distinguish between the input and output power of the PTO. 

 

Another reason for highlighting this is that it can help for making like-for-like comparisons between different types of WEC. Comparing the electrical power generated is not a level playing field if one is comparing the unrectified fluctuating power coming from a PTO (the most common practice) with power that has been rectified and smoothed.

 

Credits

This blog was written as a first step in generating material for the AIM-WEC project, at the University of Heriot Watt.  

Wave Star C artist's impression from Hansen et al

Wave Star arm photo from Faedo et al

LIMPET cross-section from Boake et al  

Pelamis: Orkney Renewable Energy Forum