Nathan Tom

Demonstration of the Recent Additions in Modeling Capabilities for the WEC-Sim Wave Energy Converter Design Tool

WEC-Sim is a midfidelity numerical tool for modeling wave energy conversion devices. The code uses the MATLAB SimMechanics package to solve multibody dynamics and models wave interactions using hydrodynamic coefficients derived from frequency domain boundary element methods. This paper presents the new modeling features introduced in the latest release of WEC-Sim. The first feature discussed is the conversion of the fluid memory kernel to a state-space approximation that provides significant gains in computational speed. The benefit of the state-space calculation becomes even greater after the hydrodynamic body-to-body coefficients are introduced as the number of interactions increases exponentially with the number of floating bodies. The final feature discussed is the capability to add Morison elements to provide additional hydrodynamic damping and inertia. This is generally used as a tuning feature, because performance is highly dependent on the chosen coefficients. In this paper, a review of the hydrodynamic theory for each of the features is provided and successful implementation is verified using test cases.Copyright

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.

Balancing Power Absorption and Fatigue Loads in Irregular Waves for an Oscillating Surge Wave Energy Converter: Preprint

The aim of this paper is to describe how to control the power-to-load ratio of a novel wave energy converter (WEC) in irregular waves. The novel WEC that is being developed at the National Renewable Energy Laboratory combines an oscillating surge wave energy converter (OSWEC) with control surfaces as part of the structure; however, this work only considers one fixed geometric configuration. This work extends the optimal control problem so as to not solely maximize the time-averaged power, but to also consider the power-take-off (PTO) torque and foundation forces that arise because of WEC motion. The objective function of the controller will include competing terms that force the controller to balance power capture with structural loading. Separate penalty weights were placed on the surge-foundation force and PTO torque magnitude, which allows the controller to be tuned to emphasize either power absorption or load shedding. Results of this study found that, with proper selection of penalty weights, gains in time-averaged power would exceed the gains in structural loading while minimizing the reactive power requirement. ∗Address all correspondence to this author. INTRODUCTION Over the past year, researchers at the National Renewable Energy Laboratory have been developing a novel wave energy converter (WEC) concept that combines an oscillating surge wave energy converter (OSWEC) with active control surfaces [1, 2]. The active control surfaces may assist in tuning the hydrodynamic properties of the device to maximize power absorption and reduce loads in larger seas to increase the operational range. The concept of controllable airfoils applied to wave energy conversion has previously been explored by Atargis Energy [3], while the concept of large-scale geometric changes has been considered in the design of Weptos [4]. However, the novel WEC considered in this paper is closer in design to a bottomfixed pitching WEC in which the main body is composed of a single large rotatable body [5]; however, increasing the number of rotatable surfaces allows for greater control over the device hydrodynamics. The development of bottom fixed OSWECs has been led by Aquamarine Power’s Oyster [6], AW-Energy Oy’s Waveroller [7], and Resolute Marine Energy’s Surge WEC [8]; however, these designs consist of a fixed geometrical body and are generally not considered to be resonant devices [9]. This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 1 The success of such future WEC technologies will require the development of advanced control methods that adapt device performance to maximize energy generation in operational conditions while mitigating hydrodynamic loads in extreme seas [10]. If the structural loads can be properly controlled then future WECs can be designed with thinner steel thickness to reduce overall cost. The balancing of these objectives offers an interesting design and control challenge that is beginning to garner greater research interest [11, 12]. This multiobjective contrasts with previous works that solved the optimal control problem when focused solely on maximizing the time-averaged power (TAP). If power take-off (PTO) and structural loads are not considered in the control algorithm, then it is well known that the optimum WEC motion trajectory follows that of complex conjugate control [13], which is known to require large actuator forces and reactive power when the WEC oscillates away from the resonance frequency. The application of state-constrained optimization [14, 15] applied to WEC control has gained significant traction in recent years because it provides the ability to incorporate linear and nonlinear constraints. This optimization has been pursued using model predictive control [16–18] and pseudo-spectral methods [12, 19, 20]. Suboptimal strategies that eliminate reactive power, which include latching [21], declutching [22], and a nonlinear constraint on the direction of power flow [23], have been proposed yet still do not include a load metric in the optimization. It was shown in [12] that in regular waves moderate increases, roughly up to 50%, in TAP outpaced the growth in structural loads; however, further maximization of the TAP lead to rapid growth in structural loads, thereby reducing the cost-tobenefit ratio. This work extends the pseudo-spectral control methodology presented in [12] to irregular waves in order to determine if the same power-to-load ratios can be maintained in a more realistic sea environment. This analysis begins by introducing the hydrodynamic coefficients and mass properties of the WEC geometry used in the analysis. Next, modeling of the OSWEC timedomain pitch equation of motion is reviewed to provide the preliminaries for extension into its spectral representation. This is followed by a review of pseduo-spectral control theory, which entails the inclusion of the surge-foundation load and PTO actuator force in the optimization problem. Separate penalty weights are placed on both of the structural load contributions in an effort to provide greater control in achieving the desired performance. The effect on controller performance is observed by simulating the same sea state for combinations of penalty weights that range from maximum power absorption to minimization of structural loads. The time history of the WEC motion and PTO control torque are presented to illustrate how the increase in TAP can exceed the increase in structural loads. w