An Oscillator Model Applied to Power Take-Off and Tuned Control for Renewable Energy

Abstract

The square-law model inspired by its electronic circuit namesake is adopted to describe the dynamics of an electromechanical system that can be used as a power takeoff subsystem in renewable power generation plants where the energy source is near-periodic reciprocation along an axis. Typical cases of such processes in the maritime environment include many types of ocean energy converters as well as several hydrokinetic energy converters that convert water current translational energy into the oscillatory motion of bluff bodies located in-stream with mechanisms like e.g. vortex-induced vibrations (VIV). In the latter case specifically, the steady fluid flow causes through a vortex pattern an in-stream bluff body, typically a cylinder outfitted oftentimes with appendages, to oscillate in a near periodic pattern. From a dynamical system perspective, this can be described as a linear or more appropriately positive feedback oscillator. The most common form of feedback oscillator is an amplifying process connected in a feedback loop with its output fed back into its input through a frequency selective filter to provide positive feedback. When the steady flow to the amplifying process is initially engaged, fluctuations and noise in the loop provide a non-zero source to get oscillations started. The noise travels around the loop and is amplified and filtered until very quickly it converges on a sine wave at a single frequency. Such dynamic behavior occurs not only in electronic circuits but also in renewable energy harvesting processes of importance to ocean engineering applications.