Pipeline Model Fidelity for Wave Energy System Models

Ocean wave energy conversion plants that use hydraulic power take-offs (PTOs) have been configured so that the working fluid must travel a significant distance (of several hundred to a few thousand meters) from the wave energy converter (WEC) located offshore to equipment onshore. With the pulsatile flow generated by the WEC having a peak period in the range of 3 to 12 seconds, the wavelengths of the excited pressure waves approach the length of the pipelines themselves. By the standards for modeling pipelines presented in popular fluid power and related textbooks, the system models for these plants should include distributed parameter models of the pipeline dynamics that capture the pressure wave delay effects. This work tests the importance of pipeline model fidelity for wave energy conversion plants. Simulations have been conducted of a simple but representative hydraulic PTO for wave energy conversion and incorporate several common lumped and distributed parameter pipeline models for comparison. These results are used to show the degree to which model fidelity effects several design metrics that are especially useful in the preliminary design phase of system development. The pipeline models used include: 1) a short line model that includes lumped resistive effects only, 2) a medium line model that also includes lumped inertial and capacitive effects for a single pipeline segment, 3) a long line model that uses repeated, lumped parameter line segments to approximate the distributed parameters of a real pipeline, 4) a simple method of characteristics solution to the one-dimensional momentum and continuity equations assuming a fixed wave speed, and 5) a discrete free-gas cavity model augmenting the simple method of characteristic pipeline model. The results suggest a relaxed standard for modeling pipelines in the case of this type of system, in which case, the recommended model is easily implemented in variable time step solvers and CAD software such as Simscape Fluids and can be used within the WEC-Sim modeling framework developed by the National Renewable Energy Lab.