A method for comparing wave energy converter conceptual designs based on potential power capture

doi:10.1016/j.renene.2017.09.005

Renewable Energy

Volume 115, January 2018, Pages 797-807

https://doi.org/10.1016/j.renene.2017.09.005 Get rights and content

Highlights

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Introduced mechanical circuits to solve impedance matching problem for infinitely complex WECs.
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Reproved Falnes’ optimal PTO force equations for SRPAs using mechanical circuits.
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Introduced master-slave relationship between the geometric and PTO force parameters.
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Introduced the WEC canonical form as phenomenological equivalent architecture.
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Applied mechanical circuits to Korde’s WEC architecture and developed new insights.

Abstract

The design space for ocean wave energy converters is notable for its divergence. To facilitate convergence, and thereby support commercialization, we present a new simple method for analysis and comparison of alternative device architectures at an early stage of the design process. Using Thévenin's theorem, Falnes crafted an ingenious solution for the monochromatic optimal power capture of heaving point absorber devices by forming a mechanical impedance matching problem between the device and the power take-off. However, his solutions are limited by device architecture complexity. In this paper, we use the mechanical circuit framework to extend Falnes' method to form and solve the impedance matching problem and calculate the optimal power capture for converter architectures of arbitrary complexity. The new technique is first applied to reprove Falnes' findings and then to assess a complex converter architecture, proposed by Korde. This work also provides insight into a master-slave relationship between the geometry and power take-off force control problems that are inherent to converter design, and it reveals a hierarchy of distinct design objectives unbeknownst to Korde for his device. Finally, we show how application of the master-slave principle leads to the reduction in the dimensionality of the associated design space.

Section snippets

Background

Ocean waves are a vast, high-density renewable energy resource. The IEA estimates annual global wave energy potential of 29,500 TWh [1], which represents approximately 150% of annual global electricity demand [2]. In spite of this tremendous potential, there is currently no commercial deployment of a Wave Energy Converter (WEC) and, as is typical of a pre-commercial sector, proposed WEC conceptual designs vary widely [3], [4], [5]. This divergent design space exists, in part, due to the absence

Theory

Circuit methodologies originate from network theory in which physical systems are described in topological form as edges connected between nodes [22], [23]. Mathematical representation comes by means of associating constitutive equations expressing the physics for each edge. Circuits in which the substitution, superposition, and the reciprocity theorems hold are categorized as linear, satisfy the uniqueness criteria, and are suitable for simplification through application of Thévenin or

Methods

In this section we explore the potential of the mechanical circuit technique by progressively modelling more complex WEC architectures and determining the expressions for $Z_{i}$ and ${\hat{F}}_{P T O_{C l a m p}}$ as a precursor to the power analyses of Section 4. We start with a rederivation of Falnes' result for the intrinsic impedance of a heaving SRPA device. The SRPA system topology is then perturbed through addition of a new damper element representing linear viscous friction in parallel with the PTO. A perturbed

Discussion

To generalize our findings, we explicitly note Thévenin's theorem was successfully applied to all three WEC architectures described in Section 3 regardless of topological complexity, yielding the canonical form represented by Fig. 2e. In the following section, we now use these algebraic equations for $Z_{i}$ and ${\hat{F}}_{P T O_{C l a m p}}$ from Section 3 to build analytical expressions for $P_{U_{M a x}}$ that can be mined to establish important design principles applicable to linear WEC architectures. In the case of Falnes'

Conclusions

To be a competitive form of renewable energy, WEC conceptual design convergence must be achieved and further research efforts need to focus on areas with promising performance. To encourage the identification of WEC architectures which support this goal, a systematic methodology using the mechanical circuit framework has been proposed which builds on the fundamental contributions of Falnes to optimal PTO force control already widely accepted in the wave energy community. Through generalizing

Acknowledgments

We would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada, Natural Resources Canada, and the Pacific Institute for Climate Solutions in funding this research. Personal gratitude goes to Dr. Helen Bailey, Dr. Scott Beatty, and Mr. Alexandros Dimopoulos for various helpful discussions in formalizing the theoretical basis for this work.

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Wave Energy Converters (WECs) with optimised geometries and control systems have been developed in recent years to advance marine energy technologies towards commercialisation. In particular, a number of WEC hull geometry optimisation studies have been performed, due to the high cost reduction potential associated with the device structure. However, no standard and consistent method has been established for this purpose. For example, different optimisation formulations (single-objective and multi-objective), have been used, applying different optimisation algorithms. Additionally, a range of objective functions have been employed, where power maximisation has been represented through a variety of metrics, and cost minimisation expressed with diverse cost proxies. The goal of this study is to address the challenge of finding a suitable optimisation problem formulation with single-objective or multi-objective implementations, and the respective objective functions, that support the exploration of shapes that reduce the levelised cost of energy. Results show that submerged surface area cost proxies are more suitable for this purpose than volume-based cost proxies. Results from a multi-objective optimisation formulation can provide a good understanding of the solution space, whereas results from single-objective studies can be used for seeding these multi-objective optimisation approaches.
Modelling of operation and optimum design of a wave power take-off system with energy storage
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Citation Excerpt :
Today in this field are operating more than a hundred companies, farms are installed and connected to the grid, more than a thousand patents are approved [7] and the estimated installed power is predicted up to 240 GW h in 2050, according to a study by Carbon Trust. Till now, there is no agreement in the most efficient way of harnessing wave potential, except from codes related with some standards, i.e. [8] and many methods for comparison have been proposed, i.e. [9]. The principals of function for a device operating in the sea, therefore in a six degrees-of-freedom environment, are different among researchers and companies.
Wave energy is claimed to be the most powerful source of renewable energy and at the same time an area of research with many prospects for development. The subject of the present analysis is a case study of a heaving wave energy converter harnessing and storing wave energy to an onshore hydroelectric plant through water pumping. During the first phase the system variables of wave amplitude and period are fixed as the characteristics of an Airy Theory-based model. Construction parameters are optimized by evolutionary algorithms, incorporated in EASY software with two objective functions: the total investment cost and the flow rate in the reservoir. The following dynamic analysis is performed depending on the optimum set of parameters but also is constrained by criteria of operation. A maximum capture width ratio of 45% for a standard harmonic wave is achieved, which is comparable with other WECs' performance. Sensitivity tests for the free design parameters of the mechanism are also carried out. For a more realistic scenario of sea states, a specific area's wave time series provided the yearly corresponding duration curves and a second optimization analysis is performed. The attainable average efficiency (stored energy) of the system was almost 20%, showing high sensitivity of the absorbed power on the sea state. In order to increase the annual energy absorption and storage of a single device at real sea conditions, a mechanism for real-time adjustment of the piston pump diameter to better comply with varying wave characteristics, is proposed and modelled. The design of the modified system is optimized again to demonstrate its improved performance and efficiency, which is about 30% higher than the initial design.
On establishing generalized analytical phase control conditions in two body self-reacting point absorber wave energy converters
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It is widely suggested that step gains in wave energy converter power capture performance must be realized to achieve economic viability. One method of fulfilling power capture gains is to invoke resonant conditions between the device and the incoming ocean wave. However, a general method that can establish the prerequisites for achieving resonant conditions in an arbitrarily complex wave energy converter architecture is nonexistent.
In this work, we present an analytical procedure, built on the mechanical circuit framework, for identifying the resonant conditions of an arbitrarily complex wave energy converter architecture. To demonstrate the procedure, we select three complex two body point absorber devices as a case study, each with a geometry controllable feature set. Through invoking resonant conditions in each architecture, we illustrate how the choice of topology has significant influence on the power capture characteristics of the WEC device. Selecting the highest performing architecture, we then reveal how the analytical equations can be applied to promote technology innovation by supplying design criterion prior to locking down the WEC design. Finally, we apply the analytics within a numerical case study and present a hierarchy describing the incremental performance improvements realized through implementing steps in control complexity for this device.
On establishing an analytical power capture limit for self-reacting point absorber wave energy converters based on dynamic response
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Citation Excerpt :
For more complex heaving WEC architectures, once the mechanical circuit representation is established, application of Kirchhoff’s [17,41] conservation laws and Thévenin’s [17,42] equivalent circuit theorem can transform the circuit representation into a canonical form that is common to all WEC architectures. The technique is limited to linear frequency domain representations of the WEC dynamics, but within this limit it allows Falnes’ impedance matching technique [15,40], which is based on the canonical form, to be applied to WECs of infinite topological complexity [10]. Fig. 2 illustrates the function of an inerter.
To be a competitive supply of renewable energy, the power capture performance of ocean wave energy converters must improve. This requires that wave energy converter designers identify and invest resources to develop devices that exhibit a strong Technology Performance Level early in the development process. We contend that completing this identification process at the conceptual design stage requires a generalized method to establish the power capture upper bound for any given wave energy converter architecture. This upper bound must reflect simultaneous implementation of both optimal geometry control and power take-off force control – components known to be essential to optimizing performance but difficult to envision for complex WEC architectures.
In this work, we develop and demonstrate a procedure, built on the mechanical circuit framework, to identify this upper bound for a self-reacting point absorber with an inertial modulation mechanism performing the geometry control. We illustrate how the analytical procedure generates generic design guidance, required to achieve the bound, without committing to a specific technology. We follow by formally introducing a new technology into the wave energy community, the inerter, capable of implementing the design guidance to enact the required geometry control. Finally, we apply the analytics within a numerical case study of a previously published wave energy converter configuration, and compare the power capture production of that device to one with equivalent hydrodynamics, but with the new geometry control feature set suggested by the new analytical procedure. Our analysis reveals the potential for a ten-fold increase in power capture even under stringent relative displacement constraints.
Incorporating Mooring Dynamics into the Control Design of a Two-Body Wave Energy Converter
2023, Journal of Marine Science and Engineering
Comparison of Advanced Control Strategies Applied to a Multiple-Degrees-of-Freedom Wave Energy Converter: Nonlinear Model Predictive Controller versus Reinforcement Learning
2023, Journal of Marine Science and Engineering

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View full text

A method for comparing wave energy converter conceptual designs based on potential power capture

Highlights

Abstract

Section snippets

Background

Theory

Methods

Discussion

Conclusions

Acknowledgments

Renew. Energy

Appl. Ocean. Res.

Ocean. Eng.

Appl. Ocean. Res.

Int. J. Mar. Energy

Ocean. Eng.

J. Sound. Vib.

Ocean. Eng.

Ocean Energy Systems: Annual Report 2015

Key World Energy Statistics (KWES): 2016

WEC technology readiness and performance Matrix–finding the best research technology development trajectory

Wave energy utilization: a review of the technologies

Renew. Sustain. Energy Rev.

Numerical Modelling of Wave Energy Converters: State-of-the-art Techniques for Single Wec and Converter Arrays

A resonant point absorber of ocean-wave power

Nature