Abstract
Chaotic behavior is highly influential of a system's dynamics and directly affects its performance, raising the question if it is a desirable state or not depending on the user's goal. Studies thus far investigating the relationship between chaotic behavior in power take-off (PTO) systems in wave energy converters (WEC) are limited and evaluated in regular, single frequency waves. This is typically done to reduce the complexity of the dynamics, however evaluation in a sea state where multiple frequencies are present is necessary to fully understand the systems behavior when subject to a realistic environment. The pendulum PTO displays chaotic behavior and has been found to yield a higher power output in regular, single frequency waves when in a stable vs chaotic state. The investigation in this paper is then to address the question of whether this behavior is present when simulated in an irregular sea state. This would allow for control strategies used in chaos theory to be applied to the system to maximize power output by moving the system to a stable state. The toolbox WEC-Sim along with the MoorDyn library were used to simulate a PTO WEC with a catenary mooring system, based on the dimensions of NDBC 3 meter buoys. Chaos is defined in this work through the identification of chaotic attractors – an attractor made up of a chaotic orbit that also attracts a set of initial values that has a nonzero area in the plane (has an attractor basin). As the traditional Poincaré map is used for a single frequency, a modified use of the tool was applied to verify the chaotic hypothesis. One modification included the resulting Poincaré map when summing the three most prevalent frequencies during a simulation. The other studied the evolution of Poincaré maps throughout the simulation. This was achieved by identifying the most prevalent frequency in certain time ranges and creating a Poincaré map for that respective time range, in the end creating a 3D Poincaré map. Findings conclude that multiple simulation runs of the system with a combination of differing pendulum weights, radius arms, designs, and sea state spectrums, significant wave heights and peak periods lacked a chaotic attractor. This was viewed by the Poincaré map sample points filling in the area of the phase space rather than remaining close in pattern as simulation time lengthened, or when another initial condition in the attractor basin was used, as one would expect with any attractor. It was concluded that chaotic behavior as defined was not present in the pendulum PTO when evaluated in irregular sea states.