The Development of Power Matrices
A power matrix is a highly effective info-graphic tool used in wave resource assessments. It is the result of many different areas of research and development and shows, not only to engineers and scientists but to the layperson as well, an approximation of the energy in the ocean, the power captured by a wave energy converter (WEC), and the efficiency of the WEC in this environment. It allows for the transfer of the performance of a WEC in a known sea state to many locations around the world as long as the sea-states have the same statistical description. To say the least, it is a powerful tool that shows a certain level of progress and development towards a fully realized ocean resource assessment.
For the WCWI, a power matrix represents the convergence of our many different areas of research. The numerical SWAN model outputs are combined with detailed and dynamic models of the WEC’s control systems as well as the fluid interactions between the WEC’s physical presence and the ocean waves. Simulations run in ProteusDS™ with all of this prior information and models then give an unparalleled view of the performance and effectiveness of various WEC’s in the oceans off the coast of western Canada. A summary of this research and development data is contained within the power matrix and all of its derivatives.
Figure 1 is a default histogram for a hypothetical location in the SWAN numerical model. The values in each bin represent the total hours of occurrence for a sea-state in the simulated year.
The power matrix shown in Figure 2 is for a hypothetical WEC device and shows the instantaneous energy this device can harvest from a given sea state; as would be expected the sea states with more energy-per-meter of wavefront show up as deeper red (larger magnitude). The values in each cell represent the percent contribution of instantaneous power per sea-state to the total power for all tested sea-states. Some cells are left blank to represent the decision to not run simulations in sea-states for which the latent wave power is low or the hours of occurrence are low.
The instantaneous power is then further analysed using the histogram to get an average yearly power harvest in watt-hours, as seen in Figure 3, which is then converted to percentage of total watt-hours captured for a year. The spectrum shifts on this third chart due to the total time of occurance of a given sea state in the yearly histogram. An interesting point is that this hypothetical device gets most of its energy from lower energy states due to their likelihood of occurance.
With all of this information an iterative procedure can now occur in which each step in the matrix generation can be refined and further expanded. A very practical and easy to understand engineering iteration would be the physical optimization of the WEC in order to further tune it to the ocean climate off of the west coast of Canada. Alternatively, a more scientific and fundamental investigation might be into the effects the statistics used to describe a multi-peaked sea-state have on the values seen in these power matrices.