Encyclopedia of Ocean Engineering

Living Edition
| Editors: Weicheng Cui, Shixiao Fu, Zhiqiang Hu

Analysis of Renewable Energy Devices

  • Zhiyu JiangEmail author
  • Wei Shi
Living reference work entry
DOI: https://doi.org/10.1007/978-981-10-6963-5_192-1



Analysis refers to the application of scientific and engineering principles and processes to reveal the properties of a system.


Renewable energy devices may operate in complex internal and external conditions, and engineering analysis is a key element of the design process. Because of the sophisticated physics associated with specific renewable energy devices, simplified analysis is often not adequate for a full understanding of the system behavior. With the advent of information and digital technologies, analysis at various fidelity levels can be achieved using simulation tools. To reduce the computational costs and to validate the accuracy of simulation tools, significant efforts have been invested from both industry and academia.

This chapter will focus on the analysis of renewable energy devices that operate in offshore environments. Such devices may experience hydrodynamic and aerodynamic load actions and have large dynamic motions and structural deformations. Figure 1 (left) presents an example of a floating wind turbine which is originally designed for the North Sea environments (Nielsen 2013). A bottom-fixed offshore wind turbine (OWT) is shown in Fig. 1 (right) which is intended for intermediate water depths below 50 m. At the design stage, dynamic response analysis must be performed to assess the power production quality, blade deflections in extreme wind conditions, platform pitch motions, mooring line dynamics, and so forth (Jiang et al. 2018).
Fig. 1

Schematic of a spar floating wind turbine and a jacket-supported offshore wind turbine

Hydrostatic Analysis

Traditionally, hydrostatic analysis deals with naval architectures including ships and offshore drilling units. To ensure safety of such floating installations, classification authorities (DNV GL 2013; ABS 2018) dictate that all offshore units have positive metacentric height in calm water position for afloat conditions and intact stability and damage stability be checked. Thus, hydrostatic analysis is also involved when renewable energy devices are supported on floating foundations. As shown in Fig. 2, a spar buoy has a simple geometry with a draft of T has hydrostatic pressure (p) acting on the submerged hull. The pressure is a function of the submerged depth. After a static heel within certain range, the buoy should be able to return to its equilibrium position with the assistance of the restoring moment created by the buoyancy and gravity forces. Details of hydrostatics can be found in Biran and Pulido (2013).
Fig. 2

Schematic of a buoy and hydrostatic pressure

Note that hydrostatic analysis can be among the first steps in dimensioning the floating platforms. Luan et al. (2016) checked the intact stability of a semisubmersible wind turbine (Fig. 3) considering the overturning moment from aerodynamic loads and the righting moment by hydrostatic pressure. As shown in Fig. 4, the area under the righting moment curve (ϕ) is relatively large compared to the area under the design overturning moment (straight line), and large safety margin is indicated. Similar analyses can also be found in the works of Lefebvre and Collu (2012) and Karimirad and Michailides (2015).
Fig. 3

Illustration of the 5-MW CSC wind turbine (Luan et al. 2016)

Fig. 4

Intact stability analysis of the 5-MW-CSC, ϕ, heeling angle; RMC, righting moment curve; DOM, design overturning moment curve (Luan et al. 2016)

Hydrodynamic Analysis

For renewable energy devices that are subjected to ocean waves and currents, hydrodynamic load can be an important source of excitation. Both viscous effects and potential flow effects (Faltinsen 1993) may play a role in determining the wave-induced loads and motions on certain types of renewable energy devices including wind turbines and wave energy converters. Figure 5 (upper) shows a vertical cylinder with diameter D that stands on the seabed, and an incident wave with wavelength of λ and wave height of H is propagating toward the cylinder. Based on Fig. 5 (lower), it is possible to judge which wave forces are of greater significance to the structure. If the cylinder is slender with large λ/D ratio, then viscous forces are prominent due to flow separation. For wind turbines supported by jacket or monopile foundations, the hydrodynamic forces acting on the foundations can often be represented by Morison’s equation (ME); see Morison et al. (1950). Suppose that the slender structure can be divided into many strips, the hydrodynamic force per unit length normal to each strip can be expressed as
$$ {f}_s=\rho {C}_M\frac{\pi {D}^2}{4}\ddot{x_w}-\rho \left({C}_M-1\right)\frac{\pi {D}^2}{4}\ddot{\eta_1}+\frac{1}{2}\rho {C}_DD\left({\dot{x}}_w-{\dot{\eta}}_1\right)\left|{\dot{x}}_w-{\dot{\eta}}_1\right| $$
where ρ is the density of seawater, D is the diameter of the slender structure, CM is the mass coefficient, and CD is the drag coefficient, \( {\dot{x}}_w \) and \( \ddot{x_w} \) are the velocity and acceleration of water particles at the strip center, and \( {\dot{\eta}}_1 \) and \( \ddot{\eta_1} \) are the velocity and acceleration of the strip. In Eq. (1), CM and CD are dependent on the Reynolds number, the Keulegan-Carpenter number, and surface roughness. Reference values are given by offshore standards (NORSOK 2007; DNV 2010). As the strip velocity and acceleration are included in Eq. (1), this equation is also applicable to moving structures. Note that although the ME has been widely applied by industry and academia, this equation ignores lift forces, slamming forces, and axial Froude-Krylov forces.
Fig. 5

Importance of mass, viscous, and diffraction forces on marine structures (Faltinsen 1993)

Hydrodynamic analysis of monopile-type wind turbines using the ME can be found in Veldkamp and Van Der Tempel (2005), Shirzadeh et al. (2013), and Jiang (2018). For monopile foundations supporting 10-megawatt (MW) wind turbines, the diameter can reach 10 m (Velarde 2016), and the ME is not necessarily applicable for short waves. For jacket-type wind turbines, the tubular members have relatively small diameters. For example, the maximum leg diameters of traditional jackets supporting 5-MW wind turbines generally do not exceed 2 m (Chen et al. 2016; Dong et al. 2011). Thus, the hydrodynamic loads are drag-dominated for extreme waves, and the ME is well-suited for the analysis. Shi et al. (2013a, b) performed dynamic loads analysis of jacket-type wind turbines extensively and applied the ME during the hydrodynamic analysis. The ME has also been considered in the hydrodynamic analysis of floating platforms including spar buoy (Jonkman 2007; Jiang et al. 2013b), tension leg platform (Bachynski and Moan 2012), as well as mooring systems (Kvittem et al. 2012).

For floating renewable energy devices supported by large-volume structures, the diffraction effects are important, and potential flow theory is often used. Potential flow theory is realized numerically through the panel method (boundary element method), which solves the boundary-value problem for the interaction of wave-waves with prescribed motions in finite and infinite water depth (Lee 1995). Figure 6 schematizes a two-body wave energy converter which produces power using the relative heave motion between the torus and the float. A panel model is shown of the submerged parts. For a low-order panel method, the velocity potential is constant over the panel, and the diagonal length of the panel mesh is recommended to be below 1/6 of the smallest wavelength analyzed (DNV 2010). Potential theory assumes ideal flow and ignores viscous effects. For floating structures with sharp corners, viscous effects may be more important, and Morison-type elements can be applied in time-domain simulations to complement the potential-flow solution. Kvittem et al. (2012) adopted this approach for a semisubmersible wind turbine with heave damping plates.
Fig. 6

Schematic of a two-body wave energy converter and the panel model (Muliawan et al. 2013a)

The panel method is a frequency-domain approach applicable to weakly nonlinear hydrodynamic problems. If there is highly nonlinear interaction between waves and floating bodies, analytical approaches (Faltinsen et al. 2004), the time-domain boundary element approaches (Schløer et al. 2016; Salehyar et al. 2017), or computational fluid dynamics methods (Li and Yu 2012) can be used. Chella et al. (2012) presented an overview of the wave impact forces on OWT substructures. Saletti (2018) studied the bottom slamming phenomenon for a combined wind and wave energy converter.

Additionally, a wave theory must be involved to calculate the wave kinematics which is closely correlated with the hydrodynamic loads. The linear wave theory, or the airy wave theory (Airy 1841; Craik 2004), is the simplest solution for the flow field and is only applicable for small-amplitude waves. Figure 7 shows the applicability of various wave theories. Here, H denotes wave height, T is wave period, d is water depth, and L0 is wavelength. Details on wave kinematics can be found in Dean and Dalrymple (1991).
Fig. 7

Applicability of wave theories (Sarpkaya 2010)

Aerodynamic and Aeroelastic Analysis

For renewable energy devices that are exposed to wind loads, analysis of wind effect is indispensable. Wind turbines are particularly designed to harness the kinetic energy from the wind, and modern wind turbine blades are long and slender. For horizontal-axis wind turbines (HAWTs), the longest blade announced approaches 90 m for an 8-MW wind turbine (LM Wind Power 2018). Such flexible blades may experience large deformation under the combined effect of wind excitations, centrifugal forces, gravitational forces, and control actions. Aerodynamic analysis helps to understand the behavior of the airflow and the forces acting on the blades and the performance of the wind turbine. The classical blade element moment (BEM) was initially proposed by Glauert (1983) and modified for wind turbine analysis. The basic assumption of the BEM theory is that the force of a blade element is solely responsible for the change of axial momentum of the air which passes through the annulus swept by the elements, and there is no radial interaction between the flows through contiguous annuli (Burton et al. 2011). BEM can be used to calculate the steady loads, the thrust, and the power of HAWTs. A simple BEM algorithm to find the axial and tangential induction factors is presented in Hansen (2008). A BEM algorithm with improved convergence rate is presented in Ning (2014). The classical BEM needs to be corrected by Prandtl’s tip loss factor and Glauert correction to get reasonably good results, as compared to the measurements. Due to unsteadiness of the wind seen by the rotor, the classical BEM cannot realistically capture the aeroelastic behavior of wind turbines, and the unsteady BEM method should be considered. The unsteady BEM, albeit still efficient, considers the time behavior of loads and power by the dynamic wake model and the dynamic change of angle of attack by the dynamic stall model (Hansen 2008). Further, physical phenomena like wake meandering can also be incorporated as engineering corrections to BEM (Larsen et al. 2013).

The BEM theory considers uniform pressure distribution across a rotor plane. Unlike BEM, the generalized dynamic wake (GDW) method, also known as the acceleration potential method, allows for a more general distribution of pressure across a rotor plane and includes inherent modeling of the dynamic wake effect, tip losses, and skewed wake aerodynamics (Moriarty and Hansen 2005). However, the GDW method was developed for lightly loaded rotors at high wind speeds, and the induced velocities are small relative to the mean inflow velocity. Detailed descriptions of the GDW theory can be found in Pitt and Peters (1980) and Suzuki (2000).

Over the past decades, computational fluid dynamics (CFD) has been widely used in aerodynamic analysis of rotors, and actuator disc and actuator line methods are special types of CFD methods (Hansen and Aagaard Madsen 2011). Krogstad and Eriksen (2013) presented a summary of different computational methods that were applied to predict the performance and wake development of a tested model wind turbine. De Vaal et al. (2014) used the actuator disc model to study the effect of surge motion of a floating wind turbine on rotor thrust and induced velocity. Wen et al. (2018) applied the free vortex method to study the power coefficient overshoot of a floating wind turbine in surge oscillations.

Aeroelastic analysis refers to the type of analysis that deals with the interaction between the inertial, elastic, and aerodynamic forces when the structure is exposed to a fluid flow. For commercial wind turbines, stall-induced vibrations and classical flutter are two categories of instabilities that have been observed for stall- and pitch-regulated wind turbines, respectively. Hansen (2003, 2007) presented a state-of-the-art review on aeroelastic stability analysis of wind turbines.

Integrated Dynamic Analysis

A complex renewable energy system may comprise structural components, mechanical parts, electrical devices, and control systems. Modeling and simulation of such systems can be achieved by using numerical methods such as multibody simulation (MBS) or finite element method (FEM). Integrated dynamic analysis of renewable energy devices under external load conditions is usually performed in the time domain and provides global and structural responses. For OWTs, the integrated dynamic analysis is also addressed as aero-hydro-servo-elastic analysis (Jonkman et al. 2008) as aerodynamics, hydrodynamics, servo dynamics, and structural dynamics are involved in the analysis. Figure 8 illustrates the computational flowchart of an integrated dynamic analysis in the HAWC2 program (Larsen 2009). As shown, user-specified control actions including mechanical system faults can be added to the main program via external dynamic-link libraries (DLLs) written in a programming language. For HAWTs, blade pitch control and generator torque control are also achieved through DLLs. There exist many engineering challenges with regard to modeling complexity, coupling of different submodules, nonlinear responses, and time-domain efficiency; see Butterfield et al. (2007).
Fig. 8

Modularized computational flowchart for floating wind turbine simulation (Jiang et al. 2013a)

Global motions and structural responses are two main aspects of concern. The global motions refer to the horizontal displacement and rotation of structural members or bodies. For floating wind turbines, rigid body motions of the floating platforms under dynamic loading can provide insights into system dynamics. Nielsen et al. (2006) conducted dynamic response analysis of the floating wind turbine concept HYWIND under wind, wave, and current conditions and compared the simulated and experimental decay tests of tower pitch angle. Pereya et al. (2018) analyzed the nacelle acceleration and platform pitch motion of the TetraSpar floating wind turbine. Such global motion responses, albeit not stated explicitly, can form design constraints for drivetrain components. Kurniawan et al. (2012) performed modeling and global motion analysis of a pitching wave energy converter and discussed dynamics of such a system with different hydraulic components. Muliawan et al. (2013b) conducted dynamic response analysis of a combined wind-wave energy converter and uncovered positive synergy between the two floating bodies by global motion analysis. Shi et al. (2016) developed an ice load force module for an aero-hydro-servo-elastic program and identified important response characteristics of a monopile-type wind turbine under combined ice and wave loads. From an integrated dynamic analysis, structural responses are available. To ensure structural integrity of renewable energy devices, the structural responses need be checked against possible failure modes including fatigue and ultimate limit states. Dong et al. (2011) checked the long-term fatigue damage of tubular joints of a jacket-type OWT (see Fig. 1 right) after performing integrated dynamic analysis. Jiang et al. (2015) analyzed the short-term fatigue damage of mooring lines of a floating wind turbine during shutdown. Wei et al. (2014) calculated the structural capacity of jacket support structure of an OWT under extreme wind and wave loading.

Analysis of Mechanical Components

For many renewable energy devices, mechanical components are widely used to transfer the energy to the generator side. Figure 9 demonstrates a three-stage gearbox of a 750-kilowatt stall-regulated wind turbine. The gearbox has one planetary stage and two parallel stages. High failure rates of gearbox components have been observed for the wind industry since its inception (McNiff et al. 1991), and analysis of mechanical components sometimes requires knowledge of both external loading conditions from the rotor side and internal conditions like friction, oil viscosity, and lubricant temperature (Harris and Kotzalas 2007). Numerical methods like FEM and MBS are useful tools for modeling the detailed setup of mechanical components and to study the internal responses under dynamic conditions. Using FEM and MBS, Xing and Moan (2013) showed that the main shaft non-torque loads can substantially contribute to the bearing loads and gear displacements. Dong et al. (2012) investigated gear contact fatigue in a wind turbine drivetrain using a decoupled analysis approach. Jiang et al. (2014a) proposed using multilevel integrated analysis for contact fatigue analysis of planetary bearings. Nejad et al. (2014, 2016) analyzed dynamic load effects of a drivetrain components and performed reliability analysis of wind turbine gears.
Fig. 9

Illustration of a wind turbine gearbox (Image source: (Jiang et al. 2014a), courtesy of National Renewable Energy Laboratory)

Hydraulic components including valves, pumps, accumulators, pipelines, and motors are also mechanical components that have been suggested for use in wave energy converters and wind turbines. Analysis of hydraulic systems often involves mathematical modeling and numerical simulations. Henderson (2006) presented both numerical simulation and laboratory tests of the hydraulic system employed in the Pelamis wave energy converter. Yang et al. (2010) investigated the wear damage in the piston ring and cylinder bore of a heaving-buoy wave energy converter. Numerical simulations of hydraulic transmission of wind turbines can be found in the works of Jiang et al. (2014b), Yang et al. (2015), Buhagiar et al. (2016), and Buhagiar and Sant (2017).

Code Verification and Validation

A multitude of design codes have been developed and extensively used for analysis of renewable energy devices. In general, many design codes adopt simplified physical representations of actual systems with reduced degrees of freedom but account for most prominent system features. Before being put into use, a new code should be verified against other state-of-the-art codes with adequate model fidelity levels or validated against experimental results. Larsen et al. (2013) showed good comparison between HAWC2 and the CFD code EllipSys3D for aerodynamic forces on a blade. Extensive benchmark work usually involves international collaboration among various academic and industrial partners. Passon et al. (2007) introduced the first international investigation and verification of aeroelastic codes for OWTs. Modeling capabilities of offshore environment, structural modeling, and rotor aerodynamics were compared among nine design codes for four different support structures. Later, code-to-code verifications were conducted of other types of foundations with an increased number of participants and additional load cases; see Jonkman et al. (2008), Popko et al. (2012), and Vorpahl et al. (2014).

Experiments at model scale or full-scale testing are other effective means of code verification. Discrepancies in results between model testing and numerical codes are not uncommon, especially for renewable energy devices that have both aerodynamic and hydrodynamic excitations, because similarity between inertia and viscous forces of the models cannot be achieved simultaneously. Li and Calisal (2010) developed numerical codes using a discrete vortex method for vertical axis tidal current turbines and verified the two- and three-dimensional codes with experiments. Preliminary verification of a wave energy converter design tool with experimental wave tank results is presented in Ruehl et al. (2014). Coulling et al. (2013) verified a numerical model constructed in the design code FAST (Jonkman and Buhl 2005) with 1/50th-scale model test data for a semisubmersible floating wind turbine system. Luan et al. (2018) compared the simulated sectional responses of a semisubmersible using a nonlinear finite element code SIMO-Riflex with the 1/30th-scale model test results.



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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Engineering SciencesUniversity of AgderGrimstadNorway
  2. 2.Deepwater Engineering Research CenterDalian University of TechnologyDalianP.R. China

Section editors and affiliations

  • Zhen Gao
    • 1
  1. 1.Norwegian University of Science and TechnologyTrondheimNorway