Dynamic modelling and design of various robust sliding mode controls for the wind turbine with estimation of wind speed

The main propose of this paper is extracting the maximum efficiency from variable speed wind turbine, which is modelled as an electromechanical system with two masses dynamics. The maximum efficiency can be obtained by tracking the optimal rotor speed, which is controlled by the generator torque as the input. One of the most important information that is required for designing of the control system is the measurement of the effective wind velocity. In this paper, a new ANFIS-based method for estimating the effective wind velocity is developed. The aerodynamic torque has a direct relationship with the power coefficient. So in this paper, power coefficient of WindPACT 1.5 MW turbine as a function of tip speed ratio (TSR) and blade pitch angle is considered. Then, three control methods based on high order sliding mode controllers are examined. The rotor speed and the wind velocity are the only variables required in the design of second and third order sliding mode controllers. FAST (Fatigue, Aerodynamics, Structures and Turbulence) is valid software that offers a fairly complete model of the wind turbine. Results of this paper are validated using FAST. Performance of the designed controllers is compared in terms of the generator torque and desired rotor speed tracking. Finally, the doubly fed induction generator (DFIG) is controlled such that the objectives of reactive power minimization and tracking the desired generator torque are achieved. Two main hindrances in designing the control systems are the uncertainties and the lack of sufficient information on measurements. Therefore robust performance of designed controllers against the model uncertainties is investigated.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016     

航天器编队飞行多目标姿态快速跟踪鲁棒控制

研究了航天器编队飞行多目标姿态跟踪鲁棒控制问题．主航天器装有一个快速机动天线和一个星载相机．考虑相机对地面目标跟踪,同时考虑天线与从航天器通信的空间任务．通过引入角速度约束和姿态角约束,分别推导了相机和天线的参考姿态角、角速度和角加速度．提出期望逆系统的概念,将三维空间姿态跟踪问题转化为调节问题,简化了控制器的设计．考虑存在参数摄动和外部干扰力矩的情况,基于期望逆系统和滑模控制,设计了鲁棒姿态跟踪控制器,并利用Liapunov稳定性理论证明了控制系统的渐近稳定性．以两航天器编队飞行多目标跟踪为例进行数值仿真,结果表明所设计的控制器具有良好的鲁棒性和优越的跟踪性能．     

Advanced Control Design for Wind Turbines

In this contribution, the concept of a general design platform for control system of wind turbines is proposed. Different models of wind turbine systems are summarized, a novel control strategy for wind turbine control is proposed as a general platform for control system design. Simulation results are presented demonstrating the success of the proposed control method based on one of the chosen models for the design platform. A benchmark model (NREL) is chosen for the platform in order to adjust the control system design. Finally, the design process of control system based on the general platform is given and explained. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Net demand prediction for power systems by a new neural network‐based forecasting engine

Integration of renewable generations, such as wind and photovoltaic, into electrical power systems is rapidly growing throughout the world. Stochastic and variable nature of these resources makes some operational challenges to power systems. The most effective way to tackle these challenges is short‐term prediction of their available powers. Despite various developed methods to forecast generation of renewable resources, still they have large errors, which may lead to under/over‐commitment of conventional generators in power systems. Prediction of net demand (ND), defined as electrical load minus renewable generations, can provide useful information for accurate scheduling of conventional generators. In this article, characteristics of the time series of electric load, renewable generations and ND are analyzed, and a new hybrid prediction strategy is presented for direct prediction of ND. The training mechanism of the proposed forecasting engine is composed of a new stochastic search method and Levenberg–Marquardt learning algorithm based on an iterative procedure and greedy search. The suggested prediction strategy is tested on different real‐world power systems and its obtained results are compared with the results of several other forecast methods and published literature figures. These comparisons confirm the validity of the developed forecasting strategy. © 2016 Wiley Periodicals, Inc. Complexity 21: 296–308, 2016     

A dynamic wind farm aggregate model for the simulation of power fluctuations due to wind turbulence

An important aspect related to wind energy integration into the electrical power system is the fluctuation of the generated power due to the stochastic variations of the wind speed across the area where wind turbines are installed. Simulation models are useful tools to evaluate the impact of the wind power on the power system stability and on the power quality. Aggregate models reduce the simulation time required by detailed dynamic models of multiturbine systems.In this paper, a new behavioral model representing the aggregate contribution of several variable-speed-pitch-controlled wind turbines is introduced. It is particularly suitable for the simulation of short term power fluctuations due to wind turbulence, where steady-state models are not applicable.The model relies on the output rescaling of a single turbine dynamic model. The single turbine output is divided into its steady state and dynamic components, which are then multiplied by different scaling factors. The smoothing effect due to wind incoherence at different locations inside a wind farm is taken into account by filtering the steady state power curve by means of a Gaussian filter as well as applying a proper damping on the dynamic part.The model has been developed to be one of the building-blocks of a model of a large electrical system, therefore a significant reduction of simulation time has been pursued. Comparison against a full model obtained by repeating a detailed single turbine model, shows that a proper trade-off between accuracy and computational speed has been achieved.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016     

Stochastic Modelling of Wind Speed Power Production Correlations

Based on measurements we investigate the velocity-power characteristic of a 2 MW wind turbine. We apply a stochastic analysis where we describe the evolution of the power output with a Langevin equation, with special respect to short-time fluctuations in wind speed. Standard procedures, such as the IEC 61400-12 standard, are limited due to the fact that only mean values over several minutes of wind speed and power output are considered. According to this, short-time dynamics of wind and power fluctuations are usually not taken into account. We introduce an improved method which enables us to extract these dynamics of the power characteristic from the measured data. In particular, we get the response dynamics of the power L (u (t)) via the estimation of Kramers-Moyal coefficients, describing its evolution in time (t) with a Langevin equation where we separate the power output into a relaxation and a noise part. A fixed-point analysis provides the required power characteristic. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments

Stochastic simulations applied to black-box computer experiments are becoming more widely used to evaluate the reliability of systems. Yet, the reliability evaluation or computer experiments involving many replications of simulations can take significant computational resources as simulators become more realistic. To speed up, importance sampling coupled with near-optimal sampling allocation for these experiments is recently proposed to efficiently estimate the probability associated with the stochastic system output. In this study, we establish the central limit theorem for the probability estimator from such procedure and construct an asymptotically valid confidence interval to quantify estimation uncertainty. We apply the proposed approach to a numerical example and present a case study for evaluating the structural reliability of a wind turbine.     

Spatial dependencies of wind power and interrelations with spot price dynamics

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. In particular, prices are more volatile due to the stochastic nature of wind, such that more generation of wind energy yields lower prices. Therefore, it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole. In this paper, we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas, incorporated into a supply and demand based model for the electricity spot price. This model is calibrated with German data. We find that the specific location of a turbine – i.e., its spatial dependence with respect to the aggregated wind power in the system – is of high relevance for its value. Many of the locations analyzed show an upper tail dependence that adversely impacts the market value. Therefore, a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases. This effect becomes more important for increasing levels of wind power penetration and may render the large-scale integration into markets more difficult.     

A Fokker–Planck control framework for multidimensional stochastic processes

An efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The resulting optimality system is discretized by the Chang–Cooper scheme that guarantees positivity of the forward solution. The effectiveness of the proposed computational framework is validated with a stochastic Lotka–Volterra model and a noised limit cycle model.     

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.     

An optimal investment strategy in bank management

This paper considers the application of stochastic optimization theory to asset and capital adequacy management in banking. The Basel II Capital Accord lays down regulations to control bank behaviour, and relies on regulatory ratios such as the capital adequacy ratio (CAR). In an attempt to address the problem of compliance to minimum CAR and under assumptions about retained earnings, loan‐loss reserves, the market and shareholder‐bank owner relationships, we construct a continuous‐time model of the Basel II CAR which is computed from the total risk‐weighted assets (TRWAs) and bank capital in a stochastic setting. In particular, we derive an optimal equity allocation strategy for the bank and monitor the performance of the Basel II CAR under the allocation strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Generation of strongly non-Gaussian stochastic processes by iterative scheme upgrading phase and amplitude contents

Random excitations, such as wind velocity, always exhibit non-Gaussian features. Sample realisations of stochastic processes satisfying given features should be generated, in order to perform the dynamical analysis of structures under stochastic loads based on the Monte Carlo simulation. In this paper, an efficient method is proposed to generate stationary non-Gaussian stochastic processes. It involves an iterative scheme that produces a class of sample processes satisfying the following conditions. (1) The marginal cumulative distribution function of each sample process is perfectly identical to the prescribed one. (2) The ensemble-averaged power spectral density function of these non-Gaussian sample processes is as close to the prescribed target as possible. In this iterative scheme, the underlying processes are generated by means of the spectral representation method that recombines the upgraded power spectral density function with the phase contents of the new non-Gaussian processes in the latest iteration. Numerical examples are provided to demonstrate the capabilities of the proposed approach for four typical non-Gaussian distributions, some of which deviate significantly from the Gaussian distribution. It is found that the estimated power spectral density functions of non-Gaussian processes are close to the target ones, even for the extremely non-Gaussian case. Furthermore, the capability of the proposed method is compared to two other methods. The results show that the proposed method performs well with convergence speed, accuracy, and random errors of power spectral density functions.     

风电场运行状况分析及优化

假设风速服从威布尔分布。1)从平均风速、平均风功率密度、年有效风小时数、理论发电量这4个指标对风电场风能资源进行了评估,得出该风电场风能资源属于"丰富区",但发电效率只有19.3%。2)一期和二期风机的平均容量系数在0.19~0.28之间,说明风机与风频匹配程度较差,若选用机型Ⅲ更好。3)通过建立随机优化模型和多目标规划模型,构建了风电场所有风机每年2次的维护方案和维修人员的值班方案,该方案较好地体现了发电经济性和值班均衡性。     

Stochastic optimal time-delay control of quasi-integrable Hamiltonian systems

A nonlinear stochastic optimal time-delay control strategy for quasi-integrable Hamiltonian systems is proposed. First, a stochastic optimal control problem of quasi-integrable Hamiltonian system with time-delay in feedback control subjected to Gaussian white noise is formulated. Then, the time-delayed feedback control forces are approximated by the control forces without time-delay and the original problem is converted into a stochastic optimal control problem without time-delay. After that, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. As an example, the stochastic time-delay optimal control of two coupled van der Pol oscillators under stochastic excitation is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.     

An index tracking model with stratified sampling and optimal allocation

This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out‐of‐sample performance. A mixed‐integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out‐of‐sample time period. As mixed‐integer program is a well‐known NP‐hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental results show that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.     

A new stabilized finite element method for optimal control for a Ladyzhenskaya model for unsteady flows

This article considers the time‐dependent optimal control problem of tracking the velocity for the viscous incompressible flows which is governed by a Ladyzhenskaya equations with distributed control. The existence of the optimal solution is shown and the first‐order optimality condition is established. The semidiscrete‐in‐time approximation of the optimal control problem is also given. The spatial discretization of the optimal control problem is accomplished by using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. Finally a gradient algorithm for the fully discrete optimal control problem is effectively proposed and implemented with some numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 263–287, 2012     

Experimental reconsideration of spatio‐temporal dynamics observed in fluid‐elastic oscillator arrays from complex system viewpoint: From vibrating pipes in heat exchangers to waving plants in agricultural fields

Transition from local complexity to global spatio‐temporal dynamics in a two‐dimensional array of fluid‐elastic oscillators is examined experimentally with an apparatus comprising 90‐1000 cantilevered rods in a wind tunnel as the Reynolds number (based on rod diameter) is increased from 200 to 900. A cluster‐pattern entropy measure is introduced as a quantitative measure of local complexity. As the intensity of interaction among neighboring elements (in this case, frequency of collisions among rods) increases, a set of the elements (in this case, a rod‐array) achieves globally better‐organized behavior. On the basis of accelerometer data, the rod impact rate versus flow velocity shows a power‐law scaling relation. Video images reveal that, initially, each rod moves individually; then clusters consisting of several rods emerge. Finally, global wave‐like motion occurs at higher flow velocities. Each wave‐like motion has its specific frequency and spatial wavelength, which vary according to wind velocity. © 2007 Wiley Periodicals, Inc. Complexity 12: 36–47, 2007     

Adaptive cooperative control of networked uncalibrated robotic systems with time‐varying communicating delays

This paper investigates the trajectory tracking control of the networked multimanipulator with the existence of time‐varying delays and uncertainties in both kinematics and dynamics. To address time‐varying delays in the communication links, a novel control scheme is established by the design of delay–rate‐dependent networking mutual coupling strengths. Besides, to handle the kinematic and dynamic uncertainties, an adaptive controller is designed. The proposed control scheme guarantees that the networked robotic system can track a commonly desired trajectory cooperatively with the strongly connected communication graph, uncertainties, and time‐varying communicating delays. A Lyapunov–Krasovskii functional is employed to rigorously prove the asymptotic convergence of both tracking errors and synchronization errors. The simulation results are provided to verify the effectiveness of the control method proposed by this paper.