Balancing Power Absorption Against Structural Loads with Viscous Drag and Power-Takeoff Efficiency Considerations

The focus of this paper is to balance power absorption against structural loading for a novel fixed-bottom oscillating surge wave energy converter in both regular and irregular wave environments. The power-to-load ratio will be evaluated using pseudospectral control (PSC) to determine the optimum power-takeoff (PTO) torque based on a multiterm objective function. This paper extends the pseudospectral optimal control problem to not just maximize the time-averaged absorbed power but also include measures for the surge-foundation force and PTO torque in the optimization. The objective function may now potentially include three competing terms that the optimizer must balance. Separate weighting factors are attached to the surge-foundation force and PTO control torque that can be used to tune the optimizer performance to emphasize either power absorption or load shedding. To correct the pitch equation of motion, derived from linear hydrodynamic theory, a quadratic-viscous-drag torque has been included in the system dynamics; however, to continue the use of quadratic programming solvers, an iteratively obtained linearized drag coefficient was utilized that provided good accuracy in the predicted pitch motion. Furthermore, the analysis considers the use of a nonideal PTO unit to more accurately evaluate controller performance. The PTO efficiency is not directly included in the objective function but rather the weighting factors are utilized to limit the PTO torque amplitudes, thereby reducing the losses resulting from the bidirectional energy flow through a nonideal PTO. Results from PSC show that shedding a portion of the available wave energy can lead to greater reductions in structural loads, peak-to-average power ratio, and reactive power requirement.