Philosophy

The DEXAWAVE converter was inspired by the wave extraction system developed and patented in 1980 by the famous inventor Sir Christopher Cockerell. The Cockerell Raft consisted of two buoyant pontoons hinged together and dampened by a hydraulic power take-off system.
This was a simple and ingenious solution for extracting energy from the ocean waves, but unfortunately it never came into production. 

Analysis of the Cockerell Raft showed a relatively low efficiency and a short life expectancy. In the DEXAWAVE converter the basic construction of the Cockerell Raft is reconfigured and simplified, so that only the two-pontoon and hydraulic system concepts from the original technology are used. DEXAWAVE is developing a new Wave Converter technology, focusing on low cost, good life expectancy and minimal maintenance requirements. This new breed of Wave Energy Converter is patented, and based on modern, advanced materials and innovative technical solutions. One of the important solutions is full software control of the power take-off system.  

Cockerell's Raft was based on the principle that a flat pontoon, when turned out of its balance point, will attempt to regain its balance with a force of 44 % of its total mass.
The maximum force is exerted when the pontoon is fully lifted out of the water at one end. 

By placing the buoyancy and mass at the outer ends of the pontoon, the force can be optimized against material consumption, so the balancing force is now 50 % (instead of 44 %) of the total mass. This also reduces the material consumption relative to a flat pontoon.
 
Each DEXAWAVE pontoon consists of two tubular floats, connected using a rigid link, for optimal weight distribution. Looking at the DEXAWAVE converter, it may initially appear that there are four pontoons. However, the tubular floats are connected in pairs, so that there are effectively only two pontoons. 

Showing the transmission of forces in the DEXAWAVE converter during ¼ of a wave cycle.
mp stands for megapond (1000 kg of buoyancy) 

The force generated can both compress and expand the hydraulic cylinder, allowing for double-stroke power take-off. If the force is extracted on the outer perimeter of the tilting pontoon, the force is 44 % (or 50 %) of the total weight or buoyancy of the pontoon. The outer perimeter has a relatively large movement, and yields a weak force for the hydraulic system. It is therefore beneficial to reduce the power take-off perimeter, as shown on the diagram. The movement is reduced, but the force is increased proportionally. Since energy is force x movement (Newton's second law), the energy in Nm (Newton meters) is constant.  
 
The 44 kg of force shown is for a flat, 100 kg pontoon, while an optimized 100 kg pontoon gives 50 kg of force, and thus a little bit more energy output. Every wave with a height above the lifting limit will start the movement of hydraulic fluid in the system and generate electricity. The energy uptake is 0.44*M*Hd. M is the weight of the pontoon. The weight (in Newtons) is the pontoon's mass in kg multiplied by 9.8 m/s2 (the gravitational force). Hd is the wave height above the pressure threshold of the hydraulic system (where the converter starts to pivot).  
NOTE: this formula is not intended for energy calculation, but is given to explain how energy is generated.  
 
For wave heights below Hd, the converter is rigid and does not pivot. The “slope” of the wave forces part of the converter under the water, but the force from the partially-submerged pontoon's buoyancy is not enough to achieve the power take-off system's hydraulic working pressure (typically 160 to 200 bar).  
 
If the wave height is above Hd, the partially-submerged pontoon's buoyancy is sufficient to achieve the power take-off system's hydraulic working pressure and the converter pivots, forcing hydraulic fluid through the power take-off system. The hydraulic fluid flows through a pump, so that its energy can be extracted at the pump's shaft. From the amplitude of movement the volume of pressurized hydraulic fluid that will be driven through the pump can be calculated. From the period time for the waves, how many times this will happen per minute can be calculated. These two calculations can be combined give a flow, in liters per minute. Using the data sheet of the pump, the flow can be directly transformed into kWh per minute. Multiply the result by 60 to get the average produced power, in kW, for the applied wave data.

1 kW shaft power	4 liters per minute
1 kWh power	about 240 liters

We assume that each pontoon weighs 2 tonnes (2000 kg), and has a buoyancy of 2 tonnes (as in the drawing above). The break-in wave height (which makes the hydraulic fluid flow) is assumed to be 20 cm. The actual wave height is 60 cm, with period of 3 seconds. Each wave will generate a lifting power of 50 % of 2 tonnes = 1 tonne (= 9.80 kN). We use a power take-off radius of 1:4, which gives us 4 tonnes = 39 kN force. The outer diameter movement is 50 cm (60 cm – (20cm/2)), so the inner PTO (power take-off) radius is 12.5 cm.   At this point we can directly calculate the wave energy, since we have force in kilo Newtons, and movement in meters. This gives us energy in kJ per wave.  
 
The power in kW is calculated by dividing the product of force and movement by the period time, Tp.  
 
The wave power is: force (kN) * distance (m) / Tp (s)= 39 * 0.125 / 3 = 1.625 kW.  
 
We now want to calculate the output power, by taking the hydraulic system loss out of the power chain. Therefore, we use the flow of hydraulic fluid per minute as the basis for this calculation.  
 
First, we choose a suitable hydraulic cylinder for 200 bar working pressure at 39 kN. A 50 mm cylinder is adequate, and will give a 180 bar working pressure. The flow of hydraulic fluid is now calculated as r^2*pi*distance = 0,25 liters per wave. We have wave period (Tp) of 3 seconds, so this gives us 20 waves per minute. 0.25 x 20 = 5 liters of hydraulic fluid per minute. From the data sheet of the hydraulic pump, we know that it takes 4 liters per minute to generate 1kW. We have 5 liters per minute, therefore the power is: 5 / 4 = 1.25 kW. This power at the shaft of the hydraulic pump is consistent with the expected loss for the hydraulic system of 25 to 30 %.                
 
The above example is simplified, to show the mechanics used to predict the power production. There are many factors which influence the output power. For example, when power is taken out of the expanding cycle, the following contracting cycle will produce less power. Water salinity, wave direction, variance of the wave period and other factors also influence the output power. All this data can be fed into a computer model, and then run with actual wave data. This is one of the tools we use to accurately predict the output power of a DEXAWAVE converter.  
The predicted data are then compared with actual measured data from our model, and show very good consistency.

Model tests are very important, because they offer valuable verification of the theoretical computer models. The expected power production is first calculated using our computer model. Then the small scale model is transported to a protected water track, and equipped with a wave recorder. Data is recorded over a few hours, and the output power is stored along with the wave data. From these two figures we can now derive a power curve, or expected output power for modeled waves. If the results from the computer model do not match up with those from the small scale model, we evaluate the causes of the offset, and tune either the computer model or the small scale model. When the computer model gives a very good prediction of the actual power, we can scale up to a larger model.
 
The power produced by the small scale model can be observed on the scope shot, and fluctuates from 0 to 3 times the average power within a wave cycle. This will not be a problem in future full-scale implementations, as the power take-off system will absorb these fluctuations completely, and deliver a clean, stable electricity output. The measured power peaks can be integrated to give the precise average output power in Watts.  
 
The small scale model's electronics system contains a wave logger, showing the real time significant wave height (Hs) in mm. A true RMS power logger shows the power produced over a 10 second or 1 minute interval, with mW precision. The zero level (water tide level) is shown as a reference.  
 
In our experience, the more automated the test procedure is, the better the quality of the test results. For this reason, a dedicated logger is a very important part of the small scale model. 

The small scale model data can be scaled up using Froude's scaling law, which says that the output power scales up by the scaling factor s^3.5. This means every time the model is scaled up by a factor of 2, the power increases by a factor of 11. However the material consumption only grows by a factor of s^3.0. This means the material consumption per produced output power decreases as the model is scaled up.  
 
If you scale a wind turbine up by a factor of 2, you will get about 4 times the power production. However if you scale up a wave energy converter by a factor of 2, you will get about 11 times as much power. That is why small scale wave energy converters appear to be very large, compared to small scale wind turbines.
A wave energy converter can be scaled up as much as desired, as long as the wave height of its proposed location is sufficient. In practice, wave height limits the size of wave energy converters.

The optimal scale, or size, of a DEXAWAVE converter depends on the wave climate at the installed location. The significant wave height is the average of the highest 25 % of the annual wave climate. 

Wave Height	DEXA Length	DEXA Width	Output
1.5 m	20 m	8 m	13 kW
2 m	26 m	11 m	35 kW
4 m	52 m	21 m	392 kW
6 m	78 m	32 m	1620 kW