System Modeling and Power Optimization of a Point Absorber Wave Energy Converter

Abstract

A conventional approach to evaluating the performance of a wave energy converter (WEC), including point absorbers, is to represent the power dissipated in the electrical domain using an equivalent electrical damping coefficient. However, realistic WECs are complex systems comprised of various constituent components: (i) a wave energy capture structure, such as a single- or two-body buoy, (ii) a mechanical energy transmission mechanism, usually referred to as a gear system, and (iii) an electromagnetic generator for converting kinetic energy into electricity. Here, we show that utilizing an electrical damping constant is not sufficient to fully capture the dynamics of these systems, and optimizing output power based on this metric as an independent variable does not yield the true maximum.

In general, the design of a WEC involves sophisticated processes, which have traditionally been iterative and sequential, focusing separately on individual objectives. This approach often leads to suboptimal solutions because it neglects the coupling effects and interdependencies among subsystems. In contrast, an engineering (control) co-design method simultaneously considers the dynamics of the entire system to maximize overall energy conversion, ensuring that design rules for one subsystem align with the objectives of others, thereby enhancing system performance. While several studies have explored various aspects of co-design in WECs, comprehensive methodologies, and generalized principles remain limited in the literature. This limitation comes from the focus of these studies on specific numerical examples of wave converters, which might have been selected differently and could potentially lead to different conclusions.

In light of these challenges, this paper aims to develop a comprehensive model that captures the physical properties (e.g., equivalent mass, mechanical damping coefficient, generator inductance and resistance) and the coupled interactions of all subsystems, paving the way for analytically investigating and maximizing overall system performance. Addressing this challenge is critical for ensuring efficient energy harnessing in real-world applications and is the primary objective of the paper. In addition, the findings can provide a general and robust framework for optimizing the generated power of WECs, significantly aiding the co-design process.

In this paper, we focus on the dynamics of a point absorber WEC driven by regular wave excitation. We analytically determine the maximum possible power that can be harvested for a specific geometry of a single-body buoy structure. Furthermore, we demonstrate that these geometric dimensions and other system components can be optimized independently to maximize output power under given ocean wave conditions. The upper bound of power is expressed as a function of an effective figure of merit for the WEC, combining electromagnetic transducer coupling and parasitic losses. Our findings indicate that for complex systems with multiple energy conversion stages, such as WECs, the gradient descent method is more suitable for optimizing objective variables compared to the impedance matching principle. In such cases, although the latter is widely used in the literature, it does not yield the global maximum power delivered to the load. We derive analytical solutions for system parameters, including the complex load, mechanical transmission, and generator moment of inertia.