Representative Structural Thickness (RST) and Characteristic Capital Expenditure (CCE)

In order to compare the potential cost of energy between wave energy conversion (WEC) devices at low Technology Readiness Levels (TRLs), the ACE metric was created as a proxy for Levelized Cost of Energy (LCOE) (see blog post from June 11). The Characteristic Capital Expenditure (CCE) portion of the ACE metric is determined by the following equation:

Characteristic Capital Expenditure (CCE) = Total Surface Area (m2) x Representative Structural Thickness (m) x Density of Material(s) (kg/m3) x Cost of Manufactured Material per unit Mass ($/kg) for all applicable materials.

Representative structural thickness, or RST, is the most crucial of these variables, and is described below.

What is RST?

RST is used to determine the total structural mass when multiplied by the surface area of the device. The RST can be visualized as a single uniform thickness that is obtained by melting down all of the structural components of a WEC then “casting” the shape of the WEC with a constant wall thickness – the RST. This means that all stiffeners and support structures are “lumped” together. A simple representation of the RST is shown below with a flat plate. The original structure includes a grid of stiffeners with a thin hull. That same quantity of material is then represented by a solid plate with the thickness given by the RST.

Plate Thickness

What is considered in determining RST? How is it calculated?

The following components determine RST:

1. Structural Mass

The structural mass of the device accounts for the mass of any and all load bearing structures that are critical to the power conversion path. This includes:

  • Any structure that interacts with the wave environment
  • Any supporting structures used to resist forces in the power conversion chain central to the load path/force flow path
  • Any significant load bearing foundation components

2. Simplified Surface Area

The surface area that is multiplied by the RST is a simplified representation of the WEC device. All stiffeners and support members that do not directly contribute to the power conversion path are excluded. The following examples show how the geometries of two U.S. Department of Energy reference models have been simplified for the RST calculation (reference model reports and documentation can be accessed at In the first example (point absorber) the surface area (faces in green) is simplified by not including external stiffeners and only accounting for one side of any thin plates. In the second example (oscillating water column), the surface area excludes all external stiffeners and only one surface of any thin plate is considered.




How do we calculate RST?

The overall methodology that is used to calculate the RST for all contestants is the same. At the most basic level, the device geometry and wave interactions are used to estimate hydrostatic, hydrodynamic, PTO and structural loads. The loads are calculated using widely used empirical formulas as well as NREL offshore models and first principle approximations where existing standards and guidelines do not exist. These loads are fed into structural models that calculate stresses using existing offshore guidelines and standards. The diagram below represents the process that will be used to calculate the RST for each WEC.


What are RST Tables?

As described in Appendix D of the official Wave Energy Prize Rules (5.26.15 R1), each WEC will be assigned an RST Table by September 15, 2015. This table will include the RST value calculated based on the above process, along with additional RST values that represent different load cases. These additional RST values can be used by the Prize judges during the competition to alter the final RST value depending on results from and performance in the 1/50th and/or 1/20th tank tests. For devices that utilize more than one material, an RST table will be supplied for each material.

Why RST?

Now that we’ve described what RST is and how it’s calculated, you’re probably asking yourself, why is the Wave Energy Prize using RST instead of the actual structural design? This simple answer is to maintain consistency during the competition. Every contestant will have a structural mass that is estimated using similar standards and design guidelines, allowing lower TRL devices to be judged against high TRL devices without bias. This also allows for a quicker analysis because devices with similar geometry and similar wave interactions will be viewed as structurally similar devices.

What is Manufactured Material Cost?

Referencing back to the equation for CCE, the last critical variable is manufactured material cost (MMC). This value represents the total cost to manufacture the materials used in the WEC at full production scale. Therefore, the MMC includes the raw material cost, any fabrication, forming, assembly, etc. In addition to the RST tables, the Prize judges will be given a table that includes a range of MMC values that will allow the judges to address designs that have high or low complexity, which will result in a higher or lower MMC value.


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