Introducing W2W power flow diagrams

 

Wave to wire (W2W) power flow diagrams are interesting because they: 

• Provide a level playing field for comparing wave energy converters (WECs).
• Describe the physics of the power capture mechanism.
• Make it clear what subset of the process is being modelled, which is useful for model design and interpretation of results. This gives insights into important work such as the US Wave Energy Prize and WECCCOMP.
• Highlight challenges specific to wave energy, which can inform design.

Overview of wave to wire (W2W) power flow diagrams

Consider the generic W2W power flow diagram above. It uses an impedance analogy across different domains: we use Maxwell's 'effort' and 'flow' parameters that multiply to give mechanical, electrical or fluid power: [F,v], [V,I], [p,Q]. There are two main components common to all WECs: 

1. The hydrodynamic body: if we simplify this into a linear problem, we can represent the effect of the hydrodynamic pressure over the body surface as an excitation force (Fe, due to the incident waves) combined with a radiation force (Frad, due to the body's motion). Typically this excitation causes an oscillating response (v, velocity).
2. The 'PTO' is where the power is 'taken off' from the mechanical power of the hydrodynamic body. The PTO results in a force (Fpto) that is felt by the hydrodynamic body and changes its motion. Power is captured by damping the velocity of the hydrodynamic body.

Power balances

Even the generic diagram above is useful for thought experiments and demonstration of basic principles. Losses (dashed red lines) and radiated power are included, which allows us to do power balances, for example:

1. PTO damping = ∞ (brakes on!): if the velocity of hydrodynamic body is zero then the excitation power is also zero.
2. PTO damping = 0: all the excitation power is returned as radiated power plus losses.

These two extremes are useful for illustrating a key insight into wave power capture: not all the loads on the hydrodynamic body will result in power capture. The wind-energy analogy is turbine thrust.

It is first necessary make the distinction between how I will use the terms 'Degrees of Freedom' (DoF) and modes of motion. In naval architecture they are equivalent, but in wave power this is not necessarily the case. In naval architecture, the six hydrodynamic modes of motion (surge, sway, heave, roll, pitch, yaw) are referenced to the vessel's longitudinal axis, Centre of Mass, and water-line. However, for WECs there are often reference axes that better suit the problem. So I will use the term 'modes' to describe forces and motions associated with these conventional body axes , and the term 'Degrees of Freedom' in the mechanics sense, to describe the independent parameters needed to completely specify a body's configuration. 

Case 1 above (PTO damping = ∞) applies to restrained modes (no DoF): an excitation force is experienced in that mode, so there is structural cost in providing reaction to that load. However, as there is no velocity, there is no power captured or lost. 

Case 2 above (PTO damping = 0) applies to unrestrained modes that are unaffected by the PTO. All the excitation power flowing through that mode will be reradiated or lost as friction. There is a structural cost in providing a reaction to hydrodynamic loads and resisting fatigue. Furthermore, there is a risk of parasitic power loss should one of these modes become coupled to a power extracting mode (e.g. parametric roll).

Technical challenges specific to wave energy

The loads experienced by the hydrodynamic body have properties that have design implications specific to wave energy:  

Properties of loads	Design implications and challenges:
High	High loads (low speeds) are costly to resist, so this requires:  gearing prior to the PTO,   and/or a hydraulic PTO
Irregular	Short timescale: ~ 1 min wave groups:  Ppeak > 10 Pmean:  Storage after PTO for smoothing over wave groups  A PTO with high efficiency at a wide range of loads  Annual climate: Pstorm>100 Ptypical   Load shedding during storms, preferably from the hydrodynamic body   Subsystem ratings and capacity factors informed by economics
Reciprocating	Rectification before the PTO is challenging due to high forces, irregular flows and controllability.   If rectification is done after the PTO you need:   Bidirectional transmission (tethers must be tensioned)  Bidirectional PTO (e.g. Wells turbine)  A PTO with high efficiency at a wide range of loads
Some don't align with power flow.	Power isn't captured from all six hydrodynamic modes. Examples include:  No motion in some modes: excitation felt but no power is captured.  Some modes unaffected by the PTO: motion but no power captured.
Directional	In most cases, response depends on wave direction.   Waves have a spread of directions, so there is an advantage to designs that can cope with power and loads from multidirectional waves.  The mean direction of deep water waves changes, so either weather-vaning or a multidirectional design is needed for structural efficiency.  Tidal flows can switch direction, interact with the waves, and influence weather-vaning.
Offset	Wave drift force (mean and slow oscillations) is always in the direction of wave travel, so there is a need to resist these loads. If there is a DoF in surge we refer to mooring loads, and if not, foundation loads.  If the direction of drift aligns with a DoF, this DoF will have an offset.  There is no buoyancy restoring force in surge, sway, or yaw. Moorings could provide a restoring force, particularly in surge.    Moorings and foundations also provide a reaction against tidal flows
Can induce resonance	In which case, reactive control is an option. This requires a PTO that:  can operate in four quadrant mode,   and has high efficiency at a wide range of loads.  Real seas have a spread of frequencies, often with more than one peak, which makes reactive control more challenging.  Response is impacted by inertia/spring in moorings, transmission & PTO  Response is impacted by the modes of motion which has implications for sloped concepts.

Several of these design requirements can be collectively called conditioning. Different WEC designs apply gearing, rectification, smoothing, load shedding or translation at different points. The generic diagram above shows that there can be conditioning before and after the PTO. 

What is included in a WEC model ?

Wave to wire models are widely used in design and optimisation of WECs. It is useful to be able to decode what subset of the wave to wire process is being modelled. 

It is interesting that the order in which power flows through the subsystems also reflects the R&D process. In general, higher stages of development tend to model more of the system. This rule of thumb extends to the era of the research: Falne's work in the 70s didn't consider mooring forces or PTO losses; in fact only recently has there been consensus around the significance of including PTO losses. 

Numerical models (simulations)

In early stage research (TRL 2-4), simulations focus primarily on the response of the hydrodynamic body to waves. In the diagram above, the grey box shows the typical scope of a numerical model. There is a high degree of variation in what is included in models. It is not uncommon to neglect the losses and dynamics associated with fluid viscosity, tides, moorings, power conditioning, or power capture. Various pitfalls associated with excluding too much from the scope include: 

• An overestimation of the awesomeness of reactive control.
• Neglecting spring or inertia associated with the moorings, transmission, or PTO could impact the estimates of the dynamic system response. 
• Assumptions about the shape of the hydrodynamic body may not apply in situations where this is changed by tides or drift.
• Design of physical systems could be informed by the simplified numerical model, e.g. example the Wave Energy Prize costed in the structure of the hydrodynamic body, but not the foundation loads, which would have disadvantaged self-referencing concepts.

Tank tests (TRL3 –6)

In the diagram above, the blue box shows the typical scope of physical models tested in a tank. The viscous, mooring, transmission and PTO losses are built in to the experimental model. This can be problematic as Froude-scaling and component availability often result in higher power losses than in the full scale system. As a result there are common approaches to dealing with these losses and dynamics, some of which could result in the tank tests being a less faithful representation of the full scale device:

• The general advice is to eliminate as many transmission losses as is practical.
• Avoid viscous losses on the hydrodynamic body: Professor Salter used to talk about a 'sucked toffee' shape. 
• Typically the impact of tide height and tidal stream aren't modelled in early development. There are a few tanks that can model the interaction of tidal streams and waves, and this can be useful to sense check field trial designs. 
• Often the mooring design hasn't been done in early stage research. Even if the mooring configuration is known, wave tank depth is not Froude scaled. If station-keeping is separate from the PTO, then typically a stiff mooring is chosen. This also avoids sensor cables being janked around.
• The transmission may not be a Froude-scaled version of the real system. In fact it may be entirely unrepresentative, for example:
• a pneumatic transmission (e.g. OWC), which does not Froude scale, so an additional large-volume air chamber is required,
• A pneumatic preload for a tether again doesn't Froude scale and is sometimes implemented by a motor,
• Practical constraints may limit where the PTO can be housed: it may not be possible to fit a PTO inside a buoy cavity; it may be desirable to derisk a project by avoiding a submerged PTO. In such cases, it is common to mount a PTO on the tank-side and transmit power via a pulley on the tank floor. It is then challenging to avoid unrepresentative transmission behaviour, including friction (those transmission losses again), spring and inertia (which can change dynamic response), and non-linear artefacts (eek) such as backlash or tether tangle.
• Reducing PTO losses at tank scale is an ongoing challenge. The practical work around is to measure the power going into the PTO, e.g. the mechanical shaft power of a turbine or electrical motor. There is now a growing consensus that representing PTO losses is critical for modelling WEC control. For example the WECCCOMP modelled a PTO efficiency of 90%. At higher TRLs a higher fidelity PTO model might be used.

Field trials - not grid connected:

The green box shows the typical scope of early field trials (TRL 6-8). These tend not to be grid connected, even if they generate electricity. The power is used to charge batteries, or is dumped as heat in a resistor. In some cases the conditioning step to achieve grid quality electricity is omitted. It is possible to model smoothing as a percentage efficiency applied to the electrical power, however there are some details that would be better represented in a higher resolution model:

• Instantaneous storage capacity: this depends on the control of the power drawn from reservoirs
• Sub-system sizing/rating e.g. of the storage reservoir, can impact the instantaneous storage capacity.
• In some systems, the damping that can be applied by the PTO depends on reservoir capacity, e.g. hydraulic or pneumatic PTO. This severely limits the controllability of the first stage of the PTO, and it then becomes coupled to the control of the second stage. The digital hydraulics used by Pelamis and WaveStar were an effective work-around.

The jump between tank testing and these first field trials is clear from the W2W power flow diagram. This is the first time that the key sub-systems are integrated, that the effects of the PTO, moorings and tides are represented to a useful accuracy. Nevertheless, early field trials often have many unrepresentative aspects. For example, a 'work-up' routine may prevent operation in large sea-states; or the deployment site may be in a sheltered spot that has its own quirks.

Field trials- grid connected

Results from grid-connected sea trials are a lot more 'bankable', in that it is hard to ignore subsystems that have losses and complexity and costs. On the other hand, first of a kind projects are never economically optimised, so estimates of LCOE should be considered a starting point on a technology learning curve. Collecting data on power at different stages of the W2W is useful for modelling sub-system or control improvements, or optimisation of relative ratings.

 

Credits

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