Nonlinear Time Domain Research Articles

An experimental study on riser hand-over operation between an installation vessel and an FPSO in regular waves

Experimental and numerical studies were performed on the hand-over operation of a riser between an installation vessel and an FPSO. A series of model tests were conducted in the Ocean Engineering Basin of KRISO. In the model test, a riser truncation model was introduced considering the limited depth of the basin and pit diameter. In addition, a nonlinear time-domain numerical simulation was performed considering two-body interaction effects. The experimental data were directly compared with the simulation results in terms of vessel motion and wire tension under two load transfer conditions. The results show that two floating bodies during the riser hand-over operation experience significant hydrodynamic interaction. Under the low load transfer condition, the snapping phenomenon was clearly observed in the PIW tension. The discussion focuses on the effects of the two-body interaction, riser truncation, load transfer stages, and wave conditions.

Time-domain signal analysis of dielectric response of nonlinear SDBD thruster in near space

The nonlinear time domain response signals of surface dielectric barrier discharge (SDBD) are the basis for studying the energy loss of SDBD thruster. This paper is based on the construction of a double layer lumped parameter circuit model in solid dielectric and discharge plasma regions; based on virtual instrument technology, a test device for AC dielectric characteristics of a nonlinear SDBD thruster was built to obtain the time domain signals of AC voltage and response current. According to the characteristic spectral curve of the voltage and the response current signal in the time domain, the response current is decomposed into resistive current (conduction current) and capacitive current (relaxation current) by an appropriate algorithm. The experimental results show that the response current in the discharge plasma region is mainly the capacitive current, and the peak capacitive current is about 2.9 times of the peak resistance current; Relaxation planned loss is the main form of energy loss in the discharge plasma region. Due to space charge limiting current effect and space charge saturation effect, the static and dynamic resistance of discharge plasma region have platform area and negative resistance characteristics respectively; Both static and dynamic capacitance have negative capacitor characteristics.

Transient Response Sensitivity Analysis of Localized Nonlinear Structure Using Direct Differentiation Method

Based on the direct differentiation method, sensitivity analysis of transient responses with respect to local nonlinearity is developed in this paper. Solutions of nonlinear equations and time-domain integration are combined to compute the response sensitivities, which consist of three steps: firstly, the nonlinear differential equations of motion are solved using Newton–Raphson iteration to obtain the transient response; secondly, the algebraic equations of the sensitivity are obtained by differentiating the incremental equation of motion with respect to nonlinear coefficients; thirdly, the nonlinear transient response sensitivities are determined using the Newmark-β integration in the interested time range. Three validation studies, including a Duffing oscillator, a nonlinear multiple-degrees-of-freedom (MDOF) system, and a cantilever beam with local nonlinearity, are adopted to illustrate the application of the proposed method. The comparisons among the finite difference method (FDM), the Poincaré method (PCM), the Lindstedt–Poincaré method (LPM), and the proposed method are conducted. The key factors, such as the parameter perturbation step size, the secular term, and the time step, are discussed to verify the accuracy and efficiency. Results show that parameter perturbation selection in the FDM sensitivity analysis is related to the nonlinear features depending on the initial condition; the consistency of the transient response sensitivity can be improved based on the accurate nonlinear response when a small time step is adopted in the proposed method.

Design of a Robust Coordinated Power Oscillation Damper for Use with Large-Scale Wind Energy System Connected to a Multimachine Power System

Many researchers have proposed the use of the doubly fed induction generator (DFIG)-based wind energy conversion system (WECS) in the enhancement of power system dynamic performance. However, the application of a coordinated design strategy to coordinate the DFIG and other synchronous generators in the system for the improvement of small-signal stability is rarely researched. What is more, the use of strategy with a low computational burden to enhance the robustness of coordinated strategy for the design of damping controllers is rare. A coordinated strategy in designing multiple damping controllers, including DFIG-based power oscillation damper (POD) and power system stabilizers (PSSs), is proposed in this paper. A modal participation factor is employed to find out the most effective feedback signal for the POD. A hybrid optimization algorithm based on the grey wolf optimizer (GWO) and particle swarm optimizer (PSO) is applied for parameter optimization of the damping controllers considering a multiobjective eigenvalue-based optimization problem. Modal analysis is carried out on the widely studied two-area four-generator benchmark power system to establish the theoretical viability of the proposed approach. Probabilistic analysis established on Monte Carlo simulation is then carried out to prove the robustness of the coordinated design strategy under diverse operating conditions. Nonlinear time-domain simulations are used to verify the damping performance and robustness of the proposed strategy under different operating scenarios.

Nonlinear air dynamics of a surface effect ship in small-amplitude waves

In many existing works, the seakeeping motions and air dynamics of a surface effect ship (SES) were assumed to be linear under small-amplitude waves (wave amplitude to wave length ratio ≤ 5%) to enhance the computational efficiency. However, according to SES model test results, it was found that even in small-amplitude waves, the fluctuating air cushion pressure shows significantly nonlinear effects. To precisely reveal this distinctive feature, the origin of nonlinearity was carefully investigated and the air leakage was considered as the main source of nonlinearity based on mathematical analysis in this paper. The reason is that the variance of clearance height under seals is comparable to the clearance height at equilibrium state in small-amplitude waves, which makes the air leakage area intermittently equal to zero without any harmonic variance. Therefore, an efficient partial nonlinear numerical model for the SES dynamics was proposed by combining a linear frequency-domain hydrodynamic model based on the efficient 2.5D methods with a nonlinear time-domain air dynamic model. The nonlinear parts of numerical results from the partial nonlinear model, including the fluctuating air pressure and midship accelerations, agree well with experimental results. The results demonstrate the effectiveness of the partial nonlinear model on the SES seakeeping performance prediction, and confirm that its nonlinearity mainly originates from the air leakage.

Dynamic Analysis and Active Stabilization of a Utility-Scale Grid-Connected Current-Source Inverter-Based PV System Considering Source Dynamics

This paper investigates the effects of the dynamic properties of a photovoltaic generator (PVG) on the stability of a grid-connected current-source inverter (CSI)-based photovoltaic system and presents a simple yet effective active compensator to ensure system stability. A detailed equivalent model of the PVG that considers the dynamic resistance, diffusion capacitance, series inductance, and dc cable resistance and inductance is used, and the effects of these parameters are assessed. It has been found that when the PVG operates in the constant-current region (CCR), the phase margin becomes negative in the control-to-input dynamics, which alters the stability of the dc-link current control. The change in the system dynamics when the operating point of the PVG shifts from the constant-voltage region (CVR) to CCR is verified through a detailed small-signal state-space model of the complete system. Furthermore, an active compensator is proposed to ensure stable dc-link current control operation at all operating points of the PVG. The influence of different control parameters on the integrated system dynamics is examined to determine the range of the control parameters required for stable operation. The performance of the proposed system under utility-grid fault, grid voltage parameter variation, weak grid, and changes in insolation level is also evaluated. Detailed nonlinear time-domain simulation results, using a typical utility-scale CSI-based PV system, validate the analytical results and the effectiveness of the proposed active stabilization under different operating conditions.

Optimal design of mooring systems for floating production units based on metamodel-assisted Differential Evolution

This work presents a new approach to the optimal design of mooring systems for oil & gas floating production units (FPU). The proposed optimization procedure integrates an efficient optimization algorithm, the ε-Constrained Differential Evolution, with Artificial Neural Networks (ANNs) as metamodels that evaluate the candidate solutions along the optimization loop, effectively replacing the computationally expensive Finite Element nonlinear time-domain simulations. The ANNs are trained with data from time-domain simulations of representative sample configurations. This integration of a metamodel and an optimization algorithm into a unified framework for the optimal design of FPU spread mooring systems comprises an innovative tool for such applications. Other innovative aspects include enhancements in the modeling of the optimization problem by defining design variables, objective function and constraints that are more simple, direct, and appropriate to actual taut leg and semi-taut leg configurations. A case study considering a real VLCC-sized spread-moored FPSO operating in a deep-water field is presented to illustrate the practical application of the optimization tool. The results indicate that, with virtually no human supervision, the tool can provide feasible solutions with noticeable overall cost reductions (in terms of the CAPEX of the system), and with drastic reductions of total computational requirement.

Numerical Evaluation of an Efficient Deep-Water Mooring Configuration Designed to Allow a Fast Identification of Failure Events

Abstract This work proposes a taut-leg deep-water mooring configuration with buoys, designed specifically to allow a quick and easy visual identification of the rupture of any mooring line of the system. This addresses one of the main concerns of the offshore oil and gas industry: the significant number of events of mooring line failure that has been recently observed in actual operations in deep and ultra-deep water scenarios; field experience indicates that, in current spread-mooring systems, several weeks may pass until a failure is detected. The proposed configuration also presents the additional advantages of reducing the mooring radius and the tensions on the top of the lines. The configuration is evaluated and compared with a standard taut-leg system, considering the same base case study of a typical deep-water FPSO, and using up-to-date numerical methods implemented into an in-house fully coupled nonlinear time-domain dynamic analysis tool. The results indicated that the proposed configuration provided significant improvements in the cost and performance of the mooring system, in terms of line lengths, mooring radii, tensions, and offsets; and confirmed that the buoy emerges and reaches the surface in the event of a line rupture, irrespective of the point where the line has broken. This indicates that the resulting configuration is a promising technical alternative to traditional standard taut-leg systems in deep and ultra-deep water scenarios.

Estimating Design Loads for Floating Structures Using Environmental Contours

Nonlinear time-domain simulations are often used to predict the structural response at the design stage to ensure the acceptable operation and/or survival of floating structures under extreme conditions. An environmental contour (EC) is commonly employed to identify critical sea states that serve as the input for numerical simulations to assess the safety and performance of marine structures. In many studies, marginal and conditional distributions are defined to construct bivariate joint probability distributions for variables, such as significant wave height and zero-crossing period. Then, ECs can be constructed using the inverse first-order reliability method (IFORM). This study adopts alternative models to describe the generalized dependence structure between environmental variables using copulas and discusses the Nataf transformation as a special case. ECs are constructed using measured wave data from moored buoys. Derived design loads are applied on a semisubmersible platform to assess possible differences. In addition, a linear interpolation scheme is utilized to establish a parametric model using short-term extreme tension distribution parameters and wave data, and the long-term tension response is estimated using Monte Carlo simulation. A 3D IFORM-based approach, in which the short-term extreme response that is ignored in the EC approach is used as the third variable, is proposed to help establish accurate design loads with increased accuracy. Results offer a clear illustration of the extreme responses of floating structures based on different models.

Statistical linearisation of a nonlinear floating offshore wind turbine under random waves and winds

This paper investigates the stochastic nonlinear dynamics of a floating offshore wind turbine (FOWT) in the frequency-domain under irregular waves and turbulent winds. The main sources of nonlinearities are estimated using statistical linearisation, which are calculated based on probability density functions (PDFs) between the degrees-of-freedom and the environment. The nonlinear mooring model captures the coupling between degrees-of-freedom when the platform has a mean displacement caused by the wind thrust, changing the natural frequency especially in surge. In addition, the nonlinear viscous drag loads offer an hydrodynamic damping that lead to better estimates of the responses. The nonlinear aerodynamic loads uses the relative motion experienced by the wind turbine under turbulent wind, and the concept of aerodynamic admittance function, which has not been applied yet to FOWTs, is included to capture the spatial effects of the wind turbulence. The results are benchmarked against nonlinear time-domain simulations using OpenFAST, and good agreement is obtained in terms of power spectral densities, PDFs and standard deviations. Several environmental conditions are used to explore some of the platform characteristics and salient features from the model. The main advantage of the following approach is the low computational cost, while providing reliable estimates of the response.

Numerical investigation of wave-induced loads on an offshore monopile using a viscous and a potential-flow solver

Wave-induced loads on an offshore monopile were investigated using a viscous-flow solver and a potential-flow solver. Considered were only two steep regular wave trains, with the same height but different periods. The potential-flow approach relied on a weakly nonlinear time-domain solver (i.e., Green function). The viscous-flow solver used three solution schemes, namely, an Euler scheme that neglected the flow viscosity, a Laminar scheme that numerically integrated the full Navier–Stokes equations without a model accounting for the fluctuating portion of the velocity field, and a Reynolds-averaged Navier–Stokes scheme that modeled turbulent flow via a two-equation eddy-viscosity model. Numerical uncertainties of viscous-flow simulations were quantified, and computed results were validated against model test measurements. Overall, the main characteristics of wave-induced forces and bending moments were well predicted by all adopted numerical schemes. In terms of higher harmonic components, predictions only from the viscous-flow solver compared favorably to the experimental measurements, including the local free surface elevations, higher harmonic forces/moments, and the secondary wave load cycles. The effect of strong nonlinear motion of free surface on the wave-induced total loading was secondary, and the contribution from the associated viscous and turbulent effects was also very limited. Nevertheless, they attribute to the generation of higher harmonic forces/moments as well as the secondary load cycle. In addition, the effects of wave steepness on the global, first- and higher harmonic forces were addressed.

The practical effects of friction for tuned mass dampers installed in tall buildings

In real-world applications, tuned mass dampers (TMDs) possess friction that must be overcome before they will increase the total effective damping of the structure. The performance of structure-TMD systems with unintended TMD friction is investigated in this study. A nonlinear time domain model is developed, which incorporates the TMD damping due to friction, and also exhibits TMD “lock-out” if the forces of friction are not overcome, a feature that existing studies have not considered. Comparisons with full-scale measurements indicate the model adequately captures the response of a TMD with friction. A linearized equivalent mechanical model is also presented, which represents the friction as amplitude-dependent viscous damping, but this model does not capture TMD lock-out. A parametric study is conducted to assess the effect of TMD friction on the performance of TMD systems with various TMD mass ratios, structure and TMD damping ratios, and the TMD damping form (linear or quadratic). In all cases, the TMD performance decreases markedly if the baseline peak structural acceleration is not at least an order of magnitude greater than the acceleration that causes the TMD to break free. If the baseline acceleration is less than five times the break-free acceleration, the TMD motion reduction performance may be negligible, and the linearized model predictions do not agree with the nonlinear simulations. TMD lock-out produces a non-stationary system response, in which the TMD reduces the peak structural accelerations slightly more than the RMS structural accelerations.

Coordinated Wide-Area Damping Control in Modern Power Systems Embedded with Utility-Scale Wind-Solar Plants

This paper presents a coordinated wide-area damping control of power system stabilizers (PSSs), static synchronous compensator (STATCOM), and static synchronous series compensator (SSSC) for grid-forming based wind and solar PV generation resources. The main objective of this work is to enhance the damping for inter-area oscillations while maintaining the voltage and frequency in the prescribed range, taking into consideration the operational uncertainties. Better voltage and reactive power support are provided by the use of STATCOM and for additional damping, an SSSC is employed with the coordinated wide-area damping controller (CWADC). Variable-speed wind turbine control methodology strategically combined with inertia control, de-loading control, pitch angle control, and electronic rotor speed control is employed to obtain an optimum response for discontinuous generation mixes and variable wind speed. The geometric measures of controllability/observability and residues method have been utilized to choose the appropriate input control signals and optimal location of CWADC. A multi-objective salp swarm algorithm has been used to optimize the parameters of the proposed CWADC. To demonstrate the efficacy of the proposed CWADC, nonlinear time-domain simulations are performed on a modified IEEE 68-bus test system embedded with hybrid wind-solar power plants considered multiple time delays.

Wind-Photovoltaic Combined Generation with Grid Connection Using Back-to-Back Voltage Source Converters

Here, we introduce a brand - new topology, but easy and efficient, for a grid-linked windphotovoltaic (PV) cogeneration system. A permanent magnet synchronous generator-primarily based totally full - scale wind turbine is interfaced to the utility-grid through back-to-back (Bt-B) voltage-supply converters (VSCs). A PV sun generator is at once linked to the dc-hyperlink capacitor of the B-t-B VSCs. No dc/dc conversion stages are required, and subsequently the system performance is maximized. The proposed topology capabilities an unbiased most strength factor monitoring for each the wind and the PV turbines to maximise the extraction of the renewable energy. The certain small signal fashions for the system additives are evolved to look at the general stability. The effect of the utility-grid faults at the overall performance of the proposed system is likewise evaluated. Nonlinear time-domain simulation consequences below different running situations are supplied to validate the effectiveness of the proposed topology.

Dynamic analysis of a monopile-supported offshore wind turbine considering the soil-foundation-structure interaction

This paper presents a nonlinear dynamic analysis of a large diameter monopile-supported multi-megawatt offshore wind turbine (OWT) installed in sandy soil under perfectly drained conditions. A detailed three-dimensional finite element model was used in the analysis. Two sophisticated soil constitutive models (the critical state elastoplastic SANISAND model and the hypoplastic model with intergranular strain) calibrated on the same Karlsruhe fine sand are adopted. Nonlinear 10-min time-domain simulations are performed within Abaqus/Standard under stochastically simulated scenarios of environmental loadings to compare the OWT structural and geotechnical responses as predicted using the two calibrated soil constitutive models. The comparison shows that both soil models provide close structural responses at the tower top whereas notable discrepancies are observed at mudline and within the soil domain. The relevance of both soil constitutive models was demonstrated via a comparison of their results with those of a conventional elastic-perfectly plastic soil model based on Mohr-Coulomb failure criterion. Finally, this paper investigates the accuracy of two p−y formulations developed for the dynamic analysis of monopiles in sand, based on the presented numerical model.

Nonlinear broadband time-domain admittance boundary condition for duct acoustics. Application to perforated plate liners

The behavior of perforated plates at high excitation level is generally modeled by a surface impedance that depends on the rms velocity in the perforations. A time-domain admittance boundary condition (TDABC) is developed to account for this variation using a multipole model. Two formulations are considered, based on the interpolation either of the admittance or of the multipole coefficients from a data set of reference values. These TDABC are implemented in a finite-difference time-domain solver of the linearized Euler equations and are validated by comparison with experimental results on an impedance tube. Application to a two-dimensional lined duct corresponding to the reference geometry of the NASA Grazing Incidence Tube is then performed. The spatial variation of the perforated plate liner impedance is highlighted and it is shown that assuming a uniform impedance can lead to an unacceptable prediction of the liner attenuation. These results are confirmed both for a harmonic or broadband excitation.

The application of the spectral domain modeling to the power take-off sizing of heaving wave energy converters

The power take-off (PTO) system is a main component in wave energy converters (WECs), and it accounts for a notable proportion in the total cost. Sizing the PTO capacity has been proven to be significant to the cost-effectiveness of WECs. In the numerical modeling, the PTO size is normally represented by a force constraint. Therefore, to accurately evaluate the power performance of WECs with various PTO sizes, it is necessary to take the PTO force limitation, a nonlinear effect, into consideration. In this paper, a computationally-efficient spectral domain model of the PTO force saturation is developed for a heaving point absorber, and the nonlinear term is included by statistical linearization. For comparison, a frequency domain and nonlinear time domain model are implemented, and the developed spectral model is verified with the results of the nonlinear time domain model. Compared with the frequency domain model, the spectral domain model remarkably reduces the relative errors in predicting the power performance of WECs with force constraints, while the computational demand is much lower than the nonlinear time domain model. Furthermore, a case study is conducted to size the PTO capacity for reducing the levelized cost of energy (LCOE) in a chosen wave site. Three different numerical models are applied respectively. The frequency domain model could lead to a misestimate of the optimal PTO capacity, with a maximum relative error on the prediction of the annual energy production (AEP) of 24%. In contrast, the spectral domain model indicates the same optimal PTO size with the time domain modeling, and its relative errors on the prediction of the AEP are within 4.3%.

Ultrafast and Low-Threshold THz Mode Switching of Two-Dimensional Nonlinear Metamaterials.

Judiciously designed two-dimensional THz metamaterials consisting of resonant metallic structures embedded in a dielectric environment locally enhance the electromagnetic field of an incident THz pulse to values sufficiently high to cause nonlinear responses of the environment. In semiconductors, the response is attributed to nonlinear transport phenomena via intervalley scattering, impact ionization, or interband tunneling and can affect the resonant behavior of the metallic structure, which results, for instance, in mode switching. However, details of mode switching, especially time scales, are still debated. By using metallic split-ring resonators with nm-size gaps on intrinsic semiconductors with different bandgaps, we identify the most relevant carrier generation processes. In addition, by combining nonlinear THz time-domain spectroscopy with simulations, we establish the fastest time constant for mode switching to around hundred femtoseconds. Our results not only elucidate dominant carrier generation mechanisms and dynamics but also pave the route toward optically driven modulators with THz bandwidth.

A Novel Hybrid Chaotic Jaya and Sequential Quadratic Programming Method for Robust Design of Power System Stabilizers and Static VAR Compensator

This paper proposes a novel hybrid algorithm combining chaotic Jaya (CJaya) and sequential quadratic programming (SQP), namely CJaya-SQP, for solving the coordinated design problem of static var compensator (SVC) and power system stabilizers (PSSs). The CJaya serves as a global optimizer and the SQP as a local optimizer for fine-tuning the solution. In the proposed algorithm, chaotic maps are used to generate the initial solutions and control the search process. In order to prove the performance of the CJaya-SQP, a set of benchmark optimization problems is used where the results are compared with those of the basic Jaya and other recognized algorithms. The proposed optimization method is then applied for the optimal tuning of PSSs and SVC controllers in such a way that damping ratios and damping factors of the electromechanical modes are optimally improved. To illustrate the robustness of the CJaya-SQP-based coordinated PSSs and SVC controllers, the four-machine, two-area system is used. Eigenvalue analysis and nonlinear time-domain simulation vividly show that the CJaya-SQP-based coordinated controllers improve greatly the system’s dynamic stability with a robust damping of local and inter-area power oscillations.

Short-time FORM analysis for extreme roll motion prediction in beam seas

This paper presents an efficient computational method to predict extreme roll motions by the First Order Reliability Method (FORM). The method facilitates accurate estimation of the reliability index distribution by short time domain calculations. The calculations are based on the transfer function of roll motion together with an equivalent linear damping for the estimation of the most probable largest roll motion using nonlinear time domain simulations. The linearization of the damping gives rise to an inconsistency (a “time shift”) in the time series evaluation. Thus, in order to account for this nonlinear effect, when evaluating the most probable largest roll motions, a method to correct the time shift from the linear solution is proposed. Two different container ships in beam seas and zero forward speed are used to demonstrate the effectiveness of the method. It is also shown that a further reduction of computational efforts is attained by using the Karhunen-Loeve wave representation based on Prolate Spheroidal Wave Functions (PSWF).