Development of a modified stochastic subspace identification method for rapid structural assessment of in‐service utility‐scale wind turbine towers

The strong drive to harness wind energy has recently led to rapid growth of wind farm construction. Wind turbine towers with increased sizes and flexibility experience large vibrations. Structural health monitoring of wind turbines is proposed in the wind energy industry to ensure their proper performance and save maintenance costs. This study proposes a system identification method for vibration‐based structural assessment of wind turbine towers. This method developed based on the stochastic subspace identification method can identify modal parameters of structures in operating conditions with harmonic components in excitations. It benefits wind turbine tower structural health assessment because classical operational modal analysis methods can fail as periodic rotation excitation from a turbine introduces harmonic disturbance to tower structure response data. The effectiveness, accuracy and robustness of the proposed method were numerically investigated and verified through a lumped‐mass system model. The method was then applied to an in‐service utility‐scale wind turbine tower. The field testing campaign and modal parameter identification as well as structural assessment results were presented. Copyright © 2017 John Wiley & Sons, Ltd.     

Collapse analysis of wind turbine tower under the coupled effects of wind and near‐field earthquake

In this paper, the pattern of wind turbine tower collapse as a result of the coupled effects of wind and an intense, near‐field earthquake is investigated. The constitutive relation of the tower cylinder steel is simulated via a nonlinear kinematic hardening model, and the specific value of each parameter in the constitutive model is provided. A precise model of the tower structure coupled with the blade is created using a nonlinear, finite element method. This method is compared with the results from a static pushover test of a small cylindrical tower to validate the finite element modeling method in this research. Two earthquake wave sets are selected as inputs. One contains 20 near‐field velocity pulse‐like ground motion waves with various pulse periods; the other contains 20 ordinary far‐field ground motion waves. A wind turbine tower with a hub height of 60 m is selected as an example for analysis. The dynamic response of this tower as a result of the coupled effects of the two ground motion wave sets and a transient wind load is calculated using nonlinear time‐history analysis. The calculation results shows that the average horizontal displacement of the tower top as a result of the near‐field velocity pulse‐like ground motion is 33% larger than the case with far‐field ground motion. Finally, the seismic collapse vulnerability curve of this wind turbine tower is calculated. The seismic collapse capacity of the tower is evaluated, and the seismic collapse pattern of the tower is analyzed.     

Identification in closed‐loop operation of models for collective pitch robust controller design

To achieve load reduction and power optimization, wind turbine controllers design requires the availability of reliable control‐oriented linear models. These are needed for model‐based controller design. Model identification of wind turbine while operating in closed loop is an appropriate solution that has recently shown its capabilities when linear time‐invariant controllers and complicated control structures are present. However, the collective pitch control loop, one of the most important wind turbine loops, uses non‐linear controllers. Typically, this non‐linear controller is a combination of a linear controller and a gain scheduling. This paper presents a new algorithm for identification in closed‐loop operation that allows the use of this kind of non‐linear controllers. The algorithm is applied for identification the collective pitch demand to generator speed of a wind turbine at various operating points. The obtained models are presented and discussed from a control point of view. The validity of these models is illustrated by their use for the design of a linear fix robust controller. The performance based on simulation data of this linear controller is similar to that obtained with simulations based on a linear controller with gain scheduling, but its design and implementation is much simpler. Copyright © 2012 John Wiley & Sons, Ltd.     

Markovian power curves for wind turbines

This paper shows a novel method to characterize wind turbine power performance directly from high‐frequency fluctuating measurements. In particular, we show how to evaluate the dynamic response of the wind turbine system on fluctuating wind speed in the range of seconds. The method is based on the stochastic differential equations known as the Langevin equations of diffusive Markov processes. Thus, the fluctuating wind turbine power output is decomposed into two functions: (i) the relaxation, which describes the deterministic dynamic response of the wind turbine to its desired operation state, and (ii) the stochastic force (noise), which is an intrinsic feature of the system of wind power conversion. As a main result, we show that independently of the turbulence intensity of the wind, the characteristic of the wind turbine power performance is properly reconstructed. This characteristic is given by their fixed points (steady states) from the deterministic dynamic relaxation conditioned for given wind speed values. The method to estimate these coefficients directly from the data is presented and applied to numerical model data, as well as to real‐world measured power output data. The method is universal and is not only more accurate than the current standard procedure of ensemble averaging (IEC‐61400‐12) but it also allows a faster and robust estimation of wind turbines' power curves. Copyright © 2007 John Wiley & Sons, Ltd.     

齿根裂纹对风电齿轮箱高速级动态特性影响分析及其故障模式识别

针对风电齿轮箱高速级齿轮传动系统齿根裂纹扩展程度识别难题,该文提出基于广义BP神经网络（GBPNN）的齿轮传动系统齿根裂纹故障模式识别方法。构建计及齿根裂纹扩展方向与路径的齿轮副时变啮合刚度解析模型及风电齿轮箱高速级齿轮-轴-轴承耦合的多自由度动力学模型,分析不同齿根裂纹扩展程度对系统振动特征的影响规律,并利用GBPNN对齿根裂纹故障模式进行识别。研究结果表明：齿轮故障振动周期冲击信号将沿着传动轴进行传递,但传动轴柔性会使其幅值产生明显的衰减;利用GBPNN并结合各轴段节点处振动加速度的峰值、峭度、统计矩阵参数以及方差,可有效实现对齿轮齿根裂纹故障模式的识别。     

Application of gray relational analysis to k-means clustering for dynamic equivalent modeling of wind farm

Considering the characteristics of dynamic gray correlation among operational conditions of wind turbines, an innovative clustering method for dynamic equivalent modeling of wind farms (WFs) based on the dynamic gray cluster algorithm is proposed. The proposed method is used to determine the number and composition of equivalent wind turbine (WT) groups that can be used to represent a WF. Based on an analysis of auto-correlation coefficients among the various monitoring items of a supervisory control and data acquisition (SCADA) system for a WT, the time span of clustering samples is determined. Then, a correlation matrix of the clustering samples is constructed by using the dynamic gray relational analysis method. Finally, WTs are divided into groups by analyzing the abovementioned correlation matrix by using the k-means clustering algorithm, and WTs belonging to the same group are considered equivalent to one turbine to realize dynamic equivalent modeling of WFs. The method is demonstrated on a WF comprising 22 WTs connected to an IEEE 39 bus test system. Dynamic responses of the proposed model for the WF are compared against the response of the detailed model and other models for various scenarios. The comparison results show that the proposed dynamic equivalent model can describe the dynamic response characteristics of a WF with accuracy similar to that of the detailed model, and the proposed model is simpler and has lower computational complexity.     

Performance modelling for wind turbines operating in harsh conditions

This paper presents a new method of online wind turbine performance modelling (recursive parameter estimation) that addresses the nonlinearity associated with wind turbine performance characteristics. A sliding linearization algorithm is implemented to track changes in the turbine operating environment. A multivariate polynomial approximation of the turbine power coefficient is developed to produce a linear process model approximating the operating wind turbine. The estimated model parameters are recursively calculated to compensate for changes in both the turbine operating environment and the condition of the wind turbine. The algorithm models both the steady‐state and dynamic wind turbine performance throughout the entire operating range, producing a continuously valid turbine linearization with applications in gain scheduling and turbine performance optimization. Copyright © 2016 John Wiley & Sons, Ltd.     

基于遗传算法的汽轮机非线性调节系统的参数辨识研究

简要介绍了遗传算法应用于参数辨识的基本思想，并将其应用于汽轮机非线性调节系统的参数辨识，结果表明，采用遗传算法可准确地辨识系统中死区，限幅等非线性发生部位和参数，辨识结果准确可靠，相对误差在2%以内，与传统的辨识方法相比，具有辨识精度高，收敛速度快的优点，结合计算机仿真，可以实现系统的性能预测，控制优化，状态监测与故障诊断。     

Modelling micro‐turbines using Hammerstein models

The Hammerstein model configuration, which includes a nonlinear static block followed by a linear dynamic block, is applied to model the static and dynamic characteristics of a micro‐turbine. The parameters in the model can be extracted from the measurements of physical engines or from the simulations of physics‐based models. In this paper, a nonlinear model is used to assist in the dynamic performance of the micro‐turbine when connected to the grid as a distributed generator. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment of dynamic substructuring of a wind turbine foundation applicable for aeroelastic simulations

Dynamic vibration response of a wind turbine structure is examined. Emphasis is put on the dynamic interaction between the foundation and the subsoil, since stiffness and energy dissipation of the substructure affect the dynamic response of the wind turbine. Based on a standard lumped‐parameter model fitted to the frequency response of the ground, a surface foundation is implemented into the aeroelastic code FLEX5. In case of a horizontal stratum overlaying a homogeneous half‐space and within the low frequency range, analyses show that a standard lumped‐parameter model provides an accurate prediction of the frequency‐dependent foundation stiffness. The generalized stiffness matrix of the substructure is found to be in a reasonable agreement with the corresponding values based on a Guyan reduction scheme. In addition, experimental findings based on traditional and operational modal techniques on a Vestas V112‐3.3 MW wind turbine installed on drained soil clearly indicate that the energy dissipation related to the lowest eigenmode is described accurately in the aeroelastic simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Two new engineering models are presented for the aerodynamic induction of a wind turbine under dynamic thrust. The models are developed using the differential form of Duhamel integrals of indicial responses of actuator disc type vortex models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator disc model. The new dynamic‐inflow engineering models are verified against the results of a Computational Fluid Dynamics (CFD) model and compared against the dynamic‐inflow engineering models of Pitt‐Peters, Øye, and Energy Research Center of the Netherlands (ECN), for several load cases. Comparisons of all models show that two time constants are necessary to predict the dynamic induction. The amplitude and phase delay of the velocity distribution shows a strong radial dependency. Verifying the models against results from the CFD model shows that the model based on the linear actuator disc vortex model predicts a similar performance as the Øye model. The model based on the nonlinear actuator disc vortex model predicts the dynamic induction better than the other models concerning both phase delay and amplitude, especially at high load.     

水轮机调节系统被控对象模型辨识

建立了水轮机调节系统被控对象的非线性模型,用递推最小二乘法(RLS)对被控对象进行参数辨识。仿真实验证明,该模型与被控对象模型相吻合、过程简单、效果良好、易于实现编程。基于此对控制参数进行了优化,改善了系统的动态品质。具有实用价值。     

基于改进粒子群算法的水轮机调速系统建模

针对电力系统稳定计算分析软件中水轮机调速系统模型过于简单、粗略的问题,建立了水轮机调速系统非线性模型,并提出参数实测与改进的粒子群智能优化算法结合的模型辨识方法,获得了调速器模型参数、水轮机-引水道模型参数.现场实测数据的模型仿真结果验证了该模型辨识方法的准确性,该模型优于电力系统稳定计算软件中的模型,更符合实际.     

Model‐independent periodic stability analysis of wind turbines

In this work, a new method is proposed for the stability analysis of wind turbines. The method uses input–output time histories obtained by conducting virtual excitation experiments with a suitable wind turbine simulation model. Next, a single‐input/single‐output periodic reduced model is identified from the recorded response and used for a stability analysis conducted according to the Floquet theory. Since only input–output sequences are used, the approach is model independent in the sense that it is applicable to wind turbine simulation models of arbitrary complexity. The use of the Floquet theory reveals a much richer picture than the one obtained by widespread classical approaches based on the use of the multi‐blade coordinate transformation of Coleman. In fact, it is shown here that, for each principal mode computed by the classical approach, there are in reality infinite super‐harmonics of varying strength fanning out from the principal one at multiples of the rotor speed. The relative strength of each harmonic in a fan provides for a way of measuring how periodically one specific fan of modes behaves. The notion of super‐harmonics allows one to justify the presence of peaks in the response spectra, peaks that cannot be explained by the classical time‐invariant analysis. The Campbell diagram, i.e., the plot of system frequencies vs. rotor speed, is in this work enriched by the presence of the super‐harmonics, revealing a much more complex pattern of possible resonant conditions with the per‐rev excitations than normally assumed. Copyright © 2014 John Wiley & Sons, Ltd.     

联合循环机组的数学模型及其参数辨识研究

联合循环电站由于其复杂的控制系统和强耦合的非线性关系,其数学模型非常复杂,开展联合循环机组的建模和参数测试研究具有重要的学术意义和工程应用价值。本文提出了适用于电网一次调频和稳定性分析的联合循环电站模型,采用改进最小二乘参数辨识方法对某400MW联合循环机组的模型参数进行了辨识,采用辨识的参数进行了仿真分析并与机组运行的实测数据进行了对比,两者能够很好地吻合,证明了所提出模型和辨识方法的有效性,为联合循环电站的一次调频和动态特性分析奠定了基础。     

Modeling,simulation and control of a wind turbine with a hydraulic transmission system

A complete mathematical model of a hydraulic transmission concept for use in wind turbines is presented. The hydraulic system transfers the power from the nacelle to ground level. The main focus has been to develop a model that takes into account the most important dynamics affecting the wind turbine and the hydraulic transmission system involved, such that the model can be used to analyze the dynamic feasibility of a hydraulic transmission concept. Further, dynamic analysis of a hydraulic transmission system for wind turbines is investigated. The nonlinear dynamic model is developed in MATLAB Simulink. Analytical calculation of natural periods of a linearized model corresponds well with simulations of the overall system. A valve control system is proposed to reduce pressure and power fluctuations at operation both below and above the rated wind speed for the wind turbine. Further, a blade pitch control system based on an aerodynamic power estimator is proposed for operation above the rated wind speed. System simulations for one case below and one case above the rated wind speed show that the dynamic response of the overall system is stable and that the wind turbine variables are within typical ranges for conventional variable speed wind turbines with mechanical transmission. Copyright © 2012 John Wiley & Sons, Ltd.     

基于自适应竞争聚类的多输人多输出热工过程模糊辨识

针对多输入多输出（MIM0）热工过程的非线性、强耦合、变工况及参数时变等特点,提出了一种基于系统输入输出数据和模糊自适应竞争聚类的模型辨识新方法．该方法首先依据系统的各个典型运行工况,使用模糊自适应竞争聚类对输入输出数据进行聚类划分,并对T—S模糊模型进行结构辨识,以确定系统的模型结构和参数;然后采用最小二乘递推算法对模型后件参数进行辨识,同时对结构辨识参数进行精确修正．将所提出的模型辨识方法用于锅炉一汽轮机非线性系统的模型辨识,仿真结果验证了该方法的有效性．     

Optimization‐based load reduction during rapid shutdown of multi‐megawatt wind turbine generators

This paper describes an optimization‐based approach to reducing extreme structural loads during rapid or emergency shutdown of multi‐megawatt wind turbine generators. The load reduction problem is cast into an optimal control formulation, and a simple, low‐order model is developed in order for this optimization problem to be tractable in reasonable time using state‐of‐the‐art numerical methods. To handle the variations in wind speed and turbulence inherent to wind turbine operation as well as the presence of model mismatch, a real‐time optimization strategy based on fast sensitivity updates is also considered, whose online computational burden is limited to the repeated solution of quadratic programs that are designed offline. The low‐order model and both the open‐loop and closed‐loop optimal control strategies are validated against a high‐fidelity model in the simulation environment Bladed ? for an industrial 3 MW wind turbine. Under favorable shutdown scenarios, i.e. when the wind turbine is operating properly and the actuators and sensors are not faulty, large reductions of the first compressive peak and subsequent compressive/tensile peaks of the tower load pattern are obtained at various above‐rated wind speeds compared with normal pitch control shutdown. Extension to more challenging shutdown scenarios are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.