Controller methods used for WECs including OWCs

Much of control design for WECs is concerned with the response of devices which respond smoothly across a range of frequencies, with one particular resonant period dominating the motion. (A review is given in Freeman et al. (2014).) For an OWC-WEC with closely packed columns, the internal water surface displacements will not change smoothly with frequency, but will be sensitive to period. Thus, control for such an OWC-WEC is likely to be different to that established for WECs with a smooth response.

The distinctions between smooth and latched control

One of the difficulties in WEC control is that sometimes power must be added to the system so as to increase the overall energy taken out. This means that the PTO equipment must allow for bidirectional power flow, which increases the cost of the PTO equipment and also may increase the fatigue cycling and thus the likelihood of failure. One way around this is to latch the WEC. This involves stopping the motion at the extreme point, which is when velocity is zero and thus no work is required. Some time later, the WEC is released and the power converted during its return in direction is greater than if the WEC were allowed to move freely. Clearly the key variable for control then becomes the moment at which unlatching occurs (Hals et al. (2011)).

In an OWC-WEC, this latching strategy requires a little alteration (Lopes et al., 2009). Instead of latching a fixed mass buoy, the air chamber is cut off from the surrounding atmosphere by moving a shut-off valve into position very quickly. The mass of air within the chamber will then remain the same while the water around it is acted upon by the wave around the column. This leads to a greater pressure difference between chamber and surroundings, and thus greater air flow once the valve is reopened.

There are some difficulties with this set-up. The valve must not require a lot of energy to move, or to fix in place. The air pressure may fluctuate due to compressibility, which is seen at small scales in Lopes et al. (2009). The large fluctuations in pressure negate the beneficial effect of the latching. The turbine is entirely deprived of air-flow during large fractions of the wave cycle, so its inertia must be made very large, and its design must avoid stall and air-flow separation which could damage the blades. Also, the power taken out will not be so smoothed, which could have implications for the price of the electricity from the WEC, due to the variability and potential energy storage requirements.

Control in the frequency domain

Returning to the electrical SHO impedance matching discussion of Section 1.2.2, it is possible to find a mathematically optimal control solution for smooth control. Following Falnes (2002b), it may be stated that the speed of WEC motion is proportional to the excitation force, F (ω) and to the intrinsic impedance of the WEC, ZW EC(ω) and its PTO,

ZP T O(ω), such that

F (ω) = (ZW EC(ω) + ZP T O(ω)) U (ω) (1.32)

In order to increase the converted energy, total power conversion across the frequency domain should be maximised. This leads Falnes (2002b) to

Z_{P T O}ideal(ω) = Z_{W EC}∗ (ω) (1.33)

where Z_{W EC}∗ (ω) is the complex conjugate of ZW EC(ω).

The ideal PTO settings are thus of the same magnitude as the intrinsic impedance, but with a 90◦phase shift. In the OWC case, the ZP T O includes the impedance due to the

chamber pressure, turbine and generator. ZW EC is the hydrodynamic impedance only.

In order to convert the maximum energy, therefore, the WEC must be able to have control operating at the different frequencies at any moment, and must be able to foretell

the excitation force, f (t), into the future, as F (ω) has information based on frequency which necessarily must extend to future waves.

Tuning requires that the reference setting, based in some way on the Z_{W EC}∗ , must be converted into settings for the real system. Fundamentally, the “damping” value must be converted into something in reality.

Control of multiple units

If there are the five OWCs described in Chapter 2, they interact in the sense that the water moves differently around each individual purely owing to the presence of the others, whether they are converting energy or not. Other multiple unit formations are possible, for example, a spaced array of single buoys, some line of pitching flaps, or some attenuators along a coast line. Thus if the interactions between the WECs may be understood, then the PTOs may be controlled so that the greatest energy is converted (Westphalen et al., 2011).

Presumably the objective is to extract the maximum energy from the group overall. If the WEC which sees the wave front first extracts the maximum energy that it can, those behind it may find that they are operating at low efficiencies and thus not converting very much energy. In effect, each WEC is an agent in a free market. This does not necessarily lead to a good overall energy conversion. Also, WECs deployed as free agents do not share wave information that might be able to improve performance in the others.

Considering the breakwater OWCs again, it might be beneficial under certain wave conditions in the breakwater to switch off some of the WECs according to their linked motions - increasing the motion in the ones which are on and getting them to work in an efficient range. Looking to economics or biomimicry may also be of benefit in having the WECs work together. It could be possible to give each individual simple rules and a little information about the others - such as occurs in flocks and shoals. Such an approach was taken by Mundon (2006) for a buoy-WEC.

Another alternative is one in which there is a master controller which gives each WEC specific instructions. However, the time delay in getting these instructions to each WEC could be a considerable hindrance.

A likely scenario is one in which there is a high level controller that gives objectives to each WEC’s controller based on the amount of energy available at the site of each one, and it is up to the low level controllers to select options to achieve these objectives.

1.4.4 The purpose of OWC-WEC control and considerations for controller