Nonlinear Time-domain Simulation Research Articles

Unmanned Floating Object Transportation Applying Multiple Dynamic Positioning Tugboats: A Novel Cooperative Control Algorithm

Abstract To promote the automation and intelligence of marine floating object transportation, this paper proposes a cooperative consensus control algorithm for multiple unmanned dynamic positioning (DP) tugboats to transport an unactuated floating structure object using cables. The major concept of present algorithm is to implement a leader-follower formation strategy among distributed tugboats, with the aim of effectively maneuvering the object by adjusting the relative position between the virtual leader and the object in a reasonable manner. A cooperative consensus controller is integrated into the feedback controller of each tugboat local DP system in order to facilitate cooperative coordination among tugboats in a formation. A customized DP system, which incorporates the radial basis function neural network supervisor control into the DP controller design and introduces nonlinear disturbance observer into the low-frequency motion state observer design, is proposed to address cable tension disturbances, and thus, the tracking performance of the DP tugboat is improved. Full-scale nonlinear time domain simulations are performed under variable environmental conditions, verifying the effectiveness of the proposed automatic towing control scheme.

A new metamodel for predicting the nonlinear time-domain response of offshore structures subjected to stochastic wave current and wind loads

Offshore structures are subjected to stochastic loads from wave, current, and wind. A long-term response analysis is important for evaluating the structural safety; however, it is computationally demanding to perform the large number of nonlinear time-domain simulations. Metamodeling is an attractive prospect, but there are two existing obstacles to overcome. First, existing metamodels are mostly confined to a single sea state and are unable to predict the response for different wave directions. Second, for floating systems, the inputs are usually vessel loads/motions, which are a priori unknown. This paper develops a new metamodel framework for accurately predicting the time series response under short-term uncertainties from the stochastic process, and seven long-term variables, namely the significant wave height, spectral period, wave direction, and speeds and directions of current and wind. The exogenous input is based only on the environmental variables, which can be predefined. The proposed metamodel is implemented on a floating system and used to predict the time series of riser stress, the extreme stress response and fatigue damage. Four cases with increasing number of long-term variables are tested. Excellent agreement is found between the metamodel prediction and numerical simulation even for the most critical case with all variables included.

Dynamic Stabilization of a Centralized Weak Grid-Tied VSC System Considering PV Generator Dynamics

This paper addresses the instabilities and dynamic interactions in a centralized vector-controlled voltage-source converter interfacing a single-stage utility-scale photovoltaic (PV) generator to a high-impedance grid system. The dynamic resistance of the PV generator is considered, and effective active stabilization methods to guarantee the entire system's stability are proposed. Further, a complete state-space linearized model is developed, and different operating conditions alongside the maximum-power operation (MPO) are considered, such as fixed-voltage operation (FVO) and fixed-current operation (FCO). It is found that with the change of the PV generator operation from the FVO or MPO to the FCO region under the weak grid and nominal dc-link capacitance conditions, the dominant eigenmodes are relocated to the open-right-half-plane of the S-plane. This eventually induces inevitable high- and low-frequency oscillation instabilities. Further, it is found that medium-frequency oscillation instability is induced in the FVO region under a weak grid and reduced dc-link capacitance conditions. Active compensators are proposed to reduce the interaction dynamics and stabilize the entire system by reshaping the converter transfer functions; hence, the Nyquist stability criterion is maintained. Finally, detailed nonlinear time-domain simulation results are provided, showing the effectiveness of the proposed method in preserving the system's stability under a wide range of operation conditions.

An adaptive wide-area neuro-fuzzy based controller for variable frequency transformer in damping inter-area oscillations

Due to the dynamic, non-linear, and complex character of large-scale power networks, prolonged inadequately damped low frequency oscillations may develop, leading to loss of synchronisation of generating units. Flexible AC transmission controller when equipped with an appropriate additional damping mechanism offers substantial damping in mitigating these oscillations. In this context, a smart flexible transmission device namely variable frequency transformer (VFT) is integrated into a multimachine power system network to effectively damp low-frequency oscillations. An adaptive model free neuro-fuzzy inference system (ANFIS) based damping controller is developed for VFT in order to damp inter-area oscillations. The ANFIS is a resilient and intelligent system that combines fuzzy logic and neural network capabilities with attributes like robustness, adaptability, speed, and flexibility. The proposed damping controller, which provides additional damping proportionate to the frequency variation, was included into the VFT’s power loop. The controller input is determined as the center-of-inertia difference of generator rotor speeds and is a remote signal delivered by a wide-area measuring system. Depending on the observability of crucial modes, participation factor (PF) investigation is used to extract the appropriate feedback signal, which provides details on the overall the system’s dynamics. The ANFIS-based scheme for the VFT is designed to impart sufficient damping qualities to the critical modes of the examined system under a variety of operating conditions. Using extensive non-linear time-domain simulations and eigenvalue analysis, the effectiveness of the suggested technique was evaluated on a popular 2-area, 4-generator, 11-bus test system.

Cooperative control for automatic towing operation by multiple DP tugboats with fully unknown model parameters

This paper presents a cooperative consensus control scheme for multiple unmanned dynamic positioning (DP) tugboats to transport an unactuated floating object through cables, aiming to promote the automation and intelligence of marine towing operation. The scheme implements a leader-follower formation strategy among distributed tugboats, maneuvering the object by adjusting the position of the virtual leader in a reasonable manner. To ensure the formation configuration, a cooperative consensus controller is integrated into the feedback controller of each tugboat local DP system. In addition, a customized model parameter-free DP system is proposed to enhance the tracking performance of a single tugboat, addressing the challenges of full unknown model parameters and large cable tension disturbances. The proposed automatic towing control scheme is verified through full-scale nonlinear time domain simulations under variable environmental conditions and formation configurations, demonstrating its effectiveness.

Stochastic analysis of the nonlinear dynamics of oscillating water columns: A frequency domain approach

This paper investigates the first and second-order stochastic responses of oscillating water columns (OWCs) under random waves. The OWCs’ nonlinear dynamics are computed in the frequency domain, where sources of nonlinearities are replaced by equivalent polynomial terms up to second order by minimising their difference in a mean-square sense. This procedure is known as the statistical quadratisation (SQ) technique. In such an approach, the linear and quadratic coefficients are obtained using an iterative procedure and non-Gaussian distributions based on Gram–Charlier expansions, and the dynamics are solved using the Volterra theory. The results are compared against a statistical linearisation model (SL), and nonlinear time-domain simulations (TD) to illustrate the capabilities of the method. The result demonstrated an excellent agreement for the first and second-order motions of the water column obtained using statistical quadratisation compared to nonlinear time-domain simulations in terms of spectral response and probability distribution. Along with the good accuracy, the statistical quadratisation has the advantage of being approximately two orders of magnitude faster than nonlinear time-domain simulations. For the proposed systems, the nonlinearity from the variable mass system (inertial type) is shown to be the most important source of second-order effects driving the oscillating water column dynamics based on the environmental conditions and drafts investigated in this work.

Performance evaluation of microgrid with extreme learning machine based PID controller

The enhanced penetration of the renewable energy sources (RES) is dependent on microgrid (MG) to a power system is impact stability of the system due to a variation in dynamic properties of the MG from a traditional generator. As a result, analyzing the new issues with dynamic stability and controlling the operation of the power system in the connection of rising MG penetration becomes critical. This paper contains a MG system with renewable energy assisted, superconducting magnetic energy storage (SMES) storage and an extreme learning machine (ELM) based proportional integral derivative (PID) controller. The effect of renewable-based MG penetration on a dynamic stability and control of the multi machine multi area system under varied operating situations is comprehensively investigated in this study. Non-linear time-domain simulations and several performance indicators are used to evaluate the controller's ability with the different MG penetration percentages under various disturbances and operational conditions.

Performance evaluation of microgrid with extreme learning machine based PID controller

The enhanced penetration of the renewable energy sources (RES) is dependent on microgrid (MG) to a power system is impact stability of the system due to a variation in dynamic properties of the MG from a traditional generator. As a result, analyzing the new issues with dynamic stability and controlling the operation of the power system in the connection of rising MG penetration becomes critical. This paper contains a MG system with renewable energy assisted, superconducting magnetic energy storage (SMES) storage and an extreme learning machine (ELM) based proportional integral derivative (PID) controller. The effect of renewable-based MG penetration on a dynamic stability and control of the multi machine multi area system under varied operating situations is comprehensively investigated in this study. Non-linear time-domain simulations and several performance indicators are used to evaluate the controller's ability with the different MG penetration percentages under various disturbances and operational conditions.

On-board monitoring and estimation of lateral accelerations through extreme value theory

Lateral accelerations experienced on-board of ships with high initial stability, especially in beam waves and at low speed, can be a source of risk for people and cargo. In the present paper, an on-board system that informs the crew on the actual situation of the vessel is described. The system monitors the lateral acceleration and estimates the extreme values that could occur in the short-term.A mid-sized stern trawler typical of the Galician fleet (Spain) has been selected to test the system. Fishing vessels are susceptible to dangerous dynamic phenomena in waves due to their hull form, loading conditions, size and operational profile. The vulnerability of the vessel has been confirmed by the application of the excessive acceleration failure mode, one of the Second Generation Intact Stability Criteria. Results have shown that the operability criterion for lateral acceleration is exceeded in many sea states.The on-board system has been tested against weakly non-linear time domain simulations and time series from experimental tests conducted at the University of A Coruña (Spain) towing tank. The estimated extreme values are close to the ones experienced, confirming the ability of the system to identify potentially dangerous situations.

A QUASI-Z-SOURCE Converter Using a Single-Stage Switched-Inductor Boost DC-DC Converter

Abstract: This paper introduces a new topology, yet simple and efficient, for a grid-connected wind-solar cogeneration system. A permanent magnet synchronous generator-based full-scale wind turbine is interconnected to the utility grid. The dc-link capacitor has been utilized to directly interface a photovoltaic solar generator. No dc/dc conversion stages are required, and hence, the hybrid system is simple and efficient. Moreover, the proposed topology features an independent maximum power point tracking for both the wind and the solar generators to maximize the extraction of renewable energy. This paper presents a quasiZ-source inverter (qZSI) that is a new topology derived from the traditional Z-source inverter (ZSI). The qZSI inherits all the advantages of the ZSI, which can realize buck/boost, inversion and power conditioning in a single stage with improved reliability. In addition, the proposed qZSI has the unique advantages of lower component ratings and constant dc current from the source. All of the boost control methods that have been developed for the ZSI can be used by the qZSI. One of the more commonly used techniques is the incremental conductance method. In this paper, an improved particle swarm optimization- (IPSO-) based MPPT technique for photovoltaic system operating under varying environmental conditions is proposed. Basically, an Artificial Neural Network (ANN) based approach is utilized to automatically detect the global maximum power point of the PV array by using a preselected number of power measurements of the PV system. The approach of linearly decreasing scheme for weighting factors and cognitive and social parameters is modified. The proposed control scheme can overcome deficiency and accelerate convergence of the IPSO-based MPPT algorithm. Detailed small-signal models for the system components are developed to characterize the overall stability. The influence of the utility-grid faults on the performance of the proposed system is also investigated. Nonlinear time-domain simulation results under different operating conditions are presented to validate the effectiveness of the proposed topology.

Multiscale EMC Modeling, Simulation, and Validation of a Synchronous Step-Down DC-DC Converter

The proliferation of power electronics in automotive and industrial applications raises compliance challenges in meeting electromagnetic compatibility (EMC) regulatory standards. In this work, we develop a robust multiscale system-level modeling and simulation methodology for predicting CISPR 25 conducted emission (CE) and radiated emission (RE). The method is based on a novel two-stage process. In the first stage, the IC model is generated either by non-linear time-domain simulation using a device-level physics model or oscilloscope measurements if a prototype is available. In the second stage, the IC model waveforms are used in a simulation environment comprising 3D full-wave frequency domain analysis and specially prepared macro-models for the laboratory equipment. Silicon validation of CISPR 25 EMC measurements on a “low-EMI,” high-performance DCDC automotive/industrial synchronous step-down converter is presented to validate the integrity of the predictive modeling methodology. Good correlations between modeling and EMC-certified testing laboratory emission measurements are achieved (i.e., within +/- 3dBuV for CE and +/- 6dBuV for RE). As a result, the predictive EMC modeling methodology can be implemented, early in the design cycle, to ensure first-pass EMC-compliant design.

Interaction Dynamics and Active Suppression of Instability in Parallel Photovoltaic Voltage-and Current-Source Converters Connected to a Weak Grid

Parallel operation of power electronic converters is becoming popular in utility-scale photovoltaic (PV) systems. However, the literature does not cover the interaction dynamics and stabilization of parallel PV-based voltage- and current-source converters (VSC and CSC) connected to a weak grid. To fill in this gap, this article characterizes the dynamic interactions among the parallel PV-based VSC and CSC systems considering the effects of the PV source dynamics, grid strength, operating point variation, and control parameters. A detailed small-signal model of the parallel system is developed and used to characterize the dynamic interactions using eigenvalue and input/output impedance-based analyses. The study showed that undesirable converters interactions are yielded, the dc-links stability is reduced, and the parallel system cannot inject 1.0 p.u. of active power at unity short-circuit ratio (SCR). Therefore, an active stabilization approach is proposed for the parallel VSC-CSC system to reduce the interactions, improve stability, and facilitate 1.0 p.u. of active power injection at unity SCR. Detailed nonlinear time-domain simulations and real-time simulation results verified the accuracy of the analytical results and the effectiveness of the proposed stabilization method under a wide range of operating conditions.

Dynamic response of a SWATH vessel for installing pre-assembled floating wind turbines

New and efficient installation concepts which can reduce the cost of developing an offshore wind farm are of particular interest. This paper explores a promising concept using the small water-plane area twin-hull vessel (SWATH) to install pre-assembled wind turbines (OWT) onto floating spar foundations. A focus is placed on the hydrodynamic performance of the SWATH and the response analysis of the coupled SWATH-spar system. Firstly, the numerically calculated difference-frequency wave force effect and damping forces of the original SWATH were verified with experimental data. Secondly, the original SWATH was modified to satisfy the criteria of weight-carrying capacity and hydrostatic stability. Thirdly, a multibody numerical model for the SWATH-spar system was developed, in which the hydrodynamic and mechanical couplings between the SWATH and a spar were considered. The SWATH is equipped with a dynamic positioning system to counteract the slow-drift wave force effects. The nonlinear time-domain simulations were carried out for the mating stage when a wind turbine is lifted above the spar foundation. Based on the analysis of statistics of the relative displacement and velocity of the tower bottom and the spar top, the installation concept with SWATH is found to be of decent performance. Finally, recommendations are provided for future research on this concept, which contributes to developing next-generation installation concepts for bottom-fixed and floating wind farms.

Enhancement of inter‐area oscillation damping by wide‐area controlled hydropower plants

This paper examines how the combined use of hydro governors and a wide-area damping controller (WADC) can improve the damping of inter-area oscillations in power systems. Such oscillations can endanger the stability of power grids, thus damping them is a high priority for transmission system operators (TSO). To ensure that low-frequency oscillations decay as fast as possible, a modal linear quadratic Gaussian (LQG) is proposed as a wide-area controller approach. Using the 10-machine New England Test System, the combined application of the WADC in hydropower plants via generator excitation as well as via the hydro governor is examined for their effectiveness in terms of damping capability. In order to minimize the number of essential PMUs in power systems for the model-based WADC, the residue-based input/output signal selection method is applied. To increase the robustness against large disturbance faults, the generator voltage as additional signal is utilized for the WADC. For controller performance and robustness, the verification has been done under various operating points, tie-line failures as well as different PMU delays. The successful damping of the inter-area oscillation by means of wide-area controlled hydropower plants has been also demonstrated through a nonlinear time domain simulation.

Interconnection of hybrid AC/DC grids of arbitrary strengths using supplementary bus-voltage feedforwards

This article proposes an intuitive methodology to analyse and mitigate system-level interactions in hybrid ac/dc networks interconnecting ac grids of arbitrary strengths, and especially weak grids. In particular, the challenge of interconnecting such grids is posed as an interaction problem in which the mechanism can be analysed explicitly through the unique ac/dc interaction functions. Then, it is demonstrated how these interaction functions can be manipulated to mitigate ac–ac, ac–dc, and dc–dc interactions simultaneously through a simple augmentation of the classic vector current control structure. The augmented loop adopts supplementary bus-voltage feedforwards from the ac and dc-sides. Significant improvements over the classic structure are demonstrated for an high voltage dc-link connecting two ac grids with arbitrary grid strengths particularly a very weak ac connection. It is shown how these supplementary loops provide a more inclusive and flexible solution to contradictory requirements on existing control, with a thorough system outlook. In addition, it is shown that the augmented loop is also beneficial for system dynamics when the grid is strong than without it. The analysis is carried out in the frequency domain, and performance is validated with nonlinear time-domain simulations.

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.

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.

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.