The Reference Model (RM) project developed six marine energy converter concepts using a sequential design methodology, which, while widely adopted in the industry, often overlooks interactions between system components, resulting in suboptimal designs. One such example is the Reference Model 3 (RM3), a two-body point absorber wave energy converter (WEC). An assessment using the Technology Performance Level (TPL) revealed that RM3’s low power-to-cost ratio, partly due to expensive steel construction, limits its techno-economic performance. This study aims to redesign RM3 by reducing its scale and employing control co-design to integrate WEC and Power Take-Off (PTO) dynamics, constraints, and cost considerations within an optimization framework. We demonstrate the limitations of RM3’s current PTO design and explore the benefits of scaling down to enhance techno-economic viability by lowering material costs. Using WecOptTool, we conduct a parameter sweep over gear ratios and spring stiffnesses for various Commercial Off-The-Shelf generators in irregular wave conditions. Our findings emphasize the importance of aligning PTO components with WEC dynamics, showing that control co-design and strategic scaling can improve RM3’s power-to-cost ratio. This study presents a transferable example of applied control co-design for other WECs, supporting early-stage developers in their design decisions.

Researchers are exploring adding wave energy converters to existing oceanographic buoys to provide a predictable source of renewable power. A ”pitch resonator” power take-off system has been developed that generates power using a geared flywheel system designed to match resonance with the pitching motion of the buoy. However, the novelty of the concept leaves researchers uncertain about various design aspects of the system. This work presents a novel design study of a pitch resonator to inform design decisions for an upcoming deployment of the system. The assessment uses control co-design via WecOptTool to optimize control trajectories for maximal electrical power production while varying five design parameters of the pitch resonator. Given the large search space of the problem, the control trajectories are optimized within a Monte Carlo analysis to identify optimal designs, followed by parameter sweeps around the optimum to identify trends between the design parameters. The gear ratio between the pitch resonator spring and flywheel are found to be the most sensitive design variables to power performance. The assessment also finds similar power generation for various sizes of resonator components, suggesting that correctly designing for optimal control trajectories at resonance is more critical to the design than component sizing.

A “bolt-on” wave energy converter is designed to provide power for sensors on an existing oceanographic buoy. The narrow-banded pitch/roll response of the target oceanographic buoy lends itself to a tuned-resonator design, for which we suggest a novel “pitch resonator” wave energy converter concept. Using a pseudo-spectral method, the performance of the proposed wave energy converter is modeled in the range of sea states expected to be present at the target deployment location to study the effect of flywheel inertia on performance. The results show that the system can marginally meet the desired power demands, but suggest that related design concepts may be worth consideration.

The open-source WecOptTool was developed to make wave energy converter (WEC) control co-design accessible. WecOptTool is based on the pseudo-spectral method which is capable of efficiently dealing with any linear or nonlinear constraints and nonlinear dynamics by solving the WEC optimal control problem in the time domain using a gradient based optimization algorithm. This work1 presents a control co-optimization study of the AquaHarmonics Inc. heaving point absorber WEC sized for ocean deployment to solve practical industry design problems. Components such as the specific type of generator, the hull shape, and the displaced volume are pre-determined. We co-optimize the WEC’s mass versus mooring line pretension in conjunction with the controller. The optimization is subject to the power-take-off (PTO) dynamics and the rated constraints of the components. In particular, the continuous torque rating is implemented as an explicit constraint, a novel approach for WEC optimization. The PTO dynamics are incorporated into the optimization algorithm via a combination of first principle methods (linear drivetrain model) and empirical efficiency maps (electrical generator) represented as a power loss map. This is a practical method applicable to a variety of PTO architectures and transferable to other WECs. A discussion between using an efficiency coefficient versus a power loss map and their implication for the optimization method is presented. This application of WecOptTool represents a real world WEC by combining simplified models with empirical efficiency data. The WEC, as a dynamically coupled, oscillatory system, requires consideration of the time trajectory dependent power loss for optimizing the average electrical power. This objective function, the modelling approach, and the realistic loss terms makes the common practice of artificially penalizing the reactive power needless.

Improved power take-off (PTO) controller design for wave energy converters is considered a critical component for reducing the cost of energy production. However, the device and control design process often remains sequential, with the space of possible final designs largely reduced before the controller has been considered. Control co-design, whereby the device and control design are considered concurrently, has resulted in improved designs in many industries, but remains rare in the wave energy community. In this paper we demonstrate the use of a new open-source code, WecOptTool, for control co-design of wave energy converters, with the aim to make the co-design approach more accessible and accelerate its adoption. Additionally, we highlight the importance of designing a wave energy converter to maximize electrical power, rather than mechanical power, and demonstrate the co-design process while modeling the PTO's components (i.e., drive-train and generator, and their dynamics). We also consider the design and optimization of causal fixed-structure controllers. The demonstration presented here considers the PTO design problem and finds the optimal PTO drive-train that maximizes annual electrical power production. The results show a 22% improvement in the optimal controller and drive-train co-design over the optimal controller for the nominal, as built, device design.

Control co-design has been shown to significantly improve the performance of wave energy converters (WEC). By considering the control and WEC design concurrently, the space searched by the optimization routine is greatly expanded which results in better performing devices. Recently, an open-source WEC co-design code, WecOptTool, was released to perform control co-design research and facilitate its adoption in the community. In this study, we use WecOptTool to perform control co-optimization and uncertainty analysis of the LUPA device. The Laboratory Upgrade Point Absorber (LUPA) is a new open-source laboratory-scale WEC that provides a platform for testing new concepts, innovating control schemes, and validating numerical models. The LUPA can be adjusted to different configurations, including changing the number of bodies, the degrees of freedom (DOF), the float and spar geometry, and the diameter of the drive sprocket pulley in the power take off (PTO) system, as well as providing different control algorithms and input waves. The drive sprocket diameter influences the torque vs speed of the generator, which allows for more flexibility in operating under different wave conditions or with different control schemes. In this study we optimize the drive sprocket diameter, while considering the optimal control algorithm for each potential design, to identify the optimal diameter for electric power production at the PacWave South WEC test site. This case study demonstrates several new capabilities of WecOptTool including a multi-body multi-DOF system and multi-directional irregular waves. The PTO dynamics are modeled using first principle methods for a parametrized model of the mechanical subcomponents in combination with generator model obtained using a power-invariant Park transform. The case-study will be made available to serve as a design tool along the LUPA hardware. Users can readily use this model to perform their own design optimization prior to testing with the physical LUPA device. Finally, we use the automatic differentiation capability of WecOptTool to perform a sensitivity and uncertainty analysis of the LUPA device.

This study presents a numerical model of a WEC array. The model will be used in subsequent work to study the ability of data assimilation to support power prediction from WEC arrays and WEC array design. In this study, we focus on design, modeling, and control of the WEC array. A case study is performed for a small remote Alaskan town. Using an efficient method for modeling the linear interactions within a homogeneous array, we produce a model and predictionless feedback controllers for the devices within the array. The model is applied to study the effects of spectral wave forecast errors on power output. The results of this analysis show that the power performance of the WEC array will be most strongly affected by errors in prediction of the spectral period, but that reductions in performance can realistically be limited to less than 10% based on typical data assimilation based spectral forecasting accuracy levels.

The oscillating water column (OWC) wave energy converter (WEC) together with a self-rectifying air turbine and generator which convert alternating airflow induced by the water motion into kinetic energy and then into electric energy is a promising device for the advancement of marine renewable energy. As researchers overcome the modeling challenges of OWCs, such as the nonlinearities due to air compressibility and power take-off (PTO) dynamics, we can integrate control algorithms to improve the efficiency of the OWC. Herein, we present a nonlinear model predictive controller (NMPC) that maximizes the generated electro-mechanical power while maintaining the efficiency of a self-rectifying turbine attached to an OWC WEC. To achieve this goal, a good trade-off between maximizing generated power and turbine efficiency is found by adjusting the importance of both objectives in the computation of the control signal. Furthermore, we apply the proposed NMPC to an array of three WECs that takes into account the hydrodynamic interactions between the devices in the computation of optimal generator torque control signal.

Ocean wave energy is a renewable energy which remains too costly for large-scale electricity generation. The oscillating water column (OWC) wave energy converter (WEC) is a promising device-type with a rectifying air turbine and generator which convert alternating airflow induced by the water motion into kinetic energy then into electric energy. Applying control at each stage of energy conversion could increase the electric energy output of the device. As researchers overcome the modeling challenges of OWC, such as the nonlinearities due to air compressibility and power take-off (PTO) dynamics, we can integrate specific control algorithms to test their ability to improve the efficiency of the OWC. Herein, we present a state-space model of an array of OWC WECs restricted to heave motion with nonlinear PTO dynamics. We apply second-order sliding mode control (SMC) which commands a smooth torque signal to a direct-drive generator to maintain a reference turbine angular velocity. Because the algorithm can yield high turbine torques, we investigate a simple feed-forward relation for the control of a valve to limit the turbine airflow and discard mechanical power. We find that implementing the SMC algorithm and valve control can improve electric energy conversion most effectively in less energetic sea states.

In this paper we derive a state-space model restricted to heave motion of a full scale array of floating oscillating-water-column (OWC) wave energy converters with nonlinear power take off dynamics, taking hydrodynamic interactions between all bodies into account. The resulting state-space model is intended as a basis for accelerated development of advanced control approaches to maximize power generation. The kinetic and potential energy transferred to the air chamber causes a pressure difference, inducing unidirectional motion of a novel bi-radial turbine. This can be accurately modeled using pressure dependent turbine characteristics, taking into account the nonlinearity of the gas compressibility. The analytical model of the floating OWC is based on linear hydrodynamic coefficients, obtained using the boundary element solver ANSYS Aqwa of an equilateral triangle array of axis-symmetric floating OWCs of the Marmok-A-5 type. Finally, the system’s model time domain equations are simulated in different wave climates and an ideal active controller is applied to maximize energy conversion. For the specific implemented separation distance the resulting cross body interactions are found to be negligible in irregular compared to regular wave scenarios. The turbine rotational speed suggests investigations on discontinues nonlinear control methods before semi-global approaches are used to optimize power generation.