Regime‐switching models and multiple causal factors in forecasting wind speed

This study evaluates two types of models for wind speed forecasting. The first is models with multiple causal factors, such as offsite readings of wind speed and meteorological variables. These can be estimated using either regressions or neural networks. The second is state transition and the closely related class of regime‐switching transition models. These are attractive in that they can be used to predict outlying fluctuations or large ramp events. The regime‐switching model uses a persistence forecast during periods of high wind speed, and regressions for low and intermediate speeds. These techniques are tested on three databases. Two main criteria are used to evaluate the outcomes, the number of high and low states than can be predicted correctly and the mean absolute percent error of the forecast. Neural nets are found to predict the state transitions somewhat better than logistic regressions, although the regressions do not do badly. Three methods all achieve about the same degree of forecast accuracy: multivariate regressions, state transition and regime‐switching models. If the states could be predicted perfectly, the regime‐switching model would improve forecast accuracy by an additional 2.5 to 3 percentage points. Analysis of the density functions of wind speed and the forecasting models finds that the regime‐switching method more closely approximates the distribution of the actual data. Copyright © 2009 John Wiley & Sons, Ltd.     

Generating wind time series as a hybrid of measured and simulated data

Certain applications, such as analysing the effect of a wind farm on grid frequency regulation, require several years of wind power data measured at intervals of a few seconds. We have developed a method to generate days to years of non‐stationary wind speed time series sampled at high rates by combining measured and simulated data. Measured wind speed data, typically 10–15 min averages, capture the non‐stationary characteristics of wind speed variation: diurnal variations, the passing of weather fronts, and seasonal variations. Simulated wind speed data, generated from spectral models, add realistic turbulence between the empirical data. The wind speed time series generated with this method agree very well with measured time series, both qualitatively and quantitatively. The power output of a wind turbine simulated with wind data generated by this method demonstrates energy production, ramp rates and reserve requirements that closely match the power output of a turbine simulated turbine with measured wind data. Copyright © 2011 John Wiley & Sons, Ltd.     

Turbine‐scale wind field measurements using dual‐Doppler lidar

Spatially resolved measurements of microscale winds are retrieved using scanning dual‐Doppler lidar and then compared with independent in situ wind measurements. Data for this study were obtained during a month‐long field campaign conducted at a site in north‐central Oklahoma in November of 2010. Observational platforms include one instrumented 60 m meteorological tower and two scanning coherent Doppler lidars. The lidars were configured to perform coordinated dual‐Doppler scans surrounding the 60 m tower, and the resulting radial velocity observations were processed to retrieve the three‐component velocity vector field on surfaces defined by the intersecting scan planes. The dual‐Doppler analysis method is described, and three‐dimensional visualizations of the retrieved fields are presented. The retrieved winds are compared with sonic anemometer (SA) measurements at the 60 m level on the tower. The Pearson correlation coefficient between the retrievals and the SA wind speeds was greater than 0.97, and the wind direction difference was very small (<0.1^o), suggesting that the dual‐Doppler technique can be used to examine fine‐scale variations in the flow. However, the mean percent difference between the SA and dual‐Doppler wind speed was approximately 15%, with the SA consistently measuring larger wind speeds. To identify the source of the discrepancy, a multi‐instrument intercomparison study was performed involving lidar wind speeds derived from standard velocity‐azimuth display (VAD) analysis of plan position indicator scan data, a nearby 915 MHz radar wind profiler (RWP) and radiosondes. The lidar VAD, RWP and radiosondes wind speeds were found to agree to within 3%. By contrast, SA wind speeds were found to be approximately 14% larger than the lidar VAD wind speeds. These results suggest that the SA produced wind speeds that were too large. Copyright © 2013 John Wiley & Sons, Ltd.     

基于季节指数调整的循环神经网络风速时间序列预测

提出一种基于季节指数调整的神经网络风速预测方法.针对历史风速之间的非线性关系,运用神经网络非线性拟合能力并结合季节性指数调整对风速时间序列进行预测.通过时序图法和增广Dickey-Fullerd检验法判断时间序列的平稳性,结果表明该序列为非平稳序列.这种不稳定性说明时间序列中可能包含趋势、季节性、循环和不规则成分的一种...     

Atmospheric stability‐dependent infinite wind‐farm models and the wake‐decay coefficient

We extend the infinite wind‐farm boundary‐layer (IWFBL) model of Frandsen to take into account atmospheric static stability effects. This extended model is compared with the IWFBL model of Emeis and to the Park wake model used in Wind Atlas Analysis and Application Program (WAsP), which is computed for an infinite wind farm. The models show similar behavior for the wind‐speed reduction when accounting for a number of surface roughness lengths, turbine to turbine separations and wind speeds under neutral conditions. For a wide range of atmospheric stability and surface roughness length values, the extended IWFBL model of Frandsen shows a much higher wind‐speed reduction dependency on atmospheric stability than on roughness length (roughness has been generally thought to have a major effect on the wind‐speed reduction). We further adjust the wake‐decay coefficient of the Park wake model for an infinite wind farm to match the wind‐speed reduction estimated by the extended IWFBL model of Frandsen for different roughness lengths, turbine to turbine separations and atmospheric stability conditions. It is found that the WAsP‐recommended values for the wake‐decay coefficient of the Park wake model are (i) larger than the adjusted values for a wide range of neutral to stable atmospheric stability conditions, a number of roughness lengths and turbine separations lower than ～ 10 rotor diameters and (ii) too large compared with those obtained by a semiempirical formulation (relating the ratio of the friction to the hub‐height free velocity) for all types of roughness and atmospheric stability conditions. © 2013 The Authors. Wind Energy published by John Wiley & Sons, Ltd.     

The k‐ϵ‐fP model applied to wind farms

The recently developed k‐?‐f_P eddy‐viscosity model is applied to one on‐shore and two off‐shore wind farms. The results are compared with power measurements and results of the standard k‐? eddy‐viscosity model. In addition, the wind direction uncertainty of the measurements is used to correct the model results with a Gaussian filter. The standard k‐? eddy‐viscosity model underpredicts the power deficit of the first downstream wind turbines, whereas the k‐?‐f_P eddy‐viscosity model shows a good agreement with the measurements. However, the difference in the power deficit predicted by the turbulence models becomes smaller for wind turbines that are located further downstream. Moreover, the difference between the capability of the turbulence models to estimate the wind farm efficiency reduces with increasing wind farm size and wind turbine spacing. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of log‐of‐power extremum seeking control for wind turbines using large eddy simulations

The extremum seeking control (ESC) algorithm has been proposed to determine operating parameters that maximize power production below rated wind speeds (region II). This is usually done by measuring the turbine's power signal to determine optimal values for parameters of the control law or actuator settings. This paper shows that the standard ESC with power feedback is quite sensitive to variations in mean wind speed, with long convergence time at low wind speeds and aggressive transient response, possibly unstable, at high wind speeds. The paper also evaluates the performance, as measured by the dynamic and steady state response, of the ESC with feedback of the logarithm of the power signal (LP‐ESC). Large eddy simulations (LES) demonstrate that the LP‐ESC, calibrated at a given wind speed, exhibits consistent robust performance at all wind speeds in a typical region II. The LP‐ESC is able to achieve the optimal set‐point within a prescribed settling time, despite variations in the mean wind speed, turbulence, and shear. The LES have been conducted using realistic wind input profiles with shear and turbulence. The ESC and LP‐ESC are implemented in the LES without assuming the availability of analytical gradients.     

Short‐term forecasting of surface layer wind speed using a continuous random cascade model

This paper describes a statistical method for short‐term forecasting (1–12 h ahead) of surface layer wind speed using only recent observations, relying on the notion of continuous cascades. Inspired by recent empirical findings that suggest the existence of some cascading process in the mesoscale range, we consider that wind speed can be described by a seasonal component and a fluctuating part represented by a ‘multifractal noise’ associated with a random cascade. Performances of our model are tested on hourly wind speed series gathered at various locations in Corsica (France) and the Netherlands. The obtained results show that a better modeling of the noise term based on cascade process enhances the forecast; furthermore, there is a systematic improvement in the prediction as compared with reference models. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of variability and predictability of large‐scale wind energy in The Netherlands

This paper presents a data‐driven approach for estimating the degree of variability and predictability associated with large‐scale wind energy production for a planned integration in a given geographical area, with an application to The Netherlands. A new method is presented for generating realistic time series of aggregated wind power realizations and forecasts. To this end, simultaneous wind speed time series—both actual and predicted—at planned wind farm locations are needed, but not always available. A 1‐year data set of 10‐min averaged wind speeds measured at several weather stations is used. The measurements are first transformed from sensor height to hub height, then spatially interpolated using multivariate normal theory, and finally averaged over the market resolution time interval. Day‐ahead wind speed forecast time series are created from the atmospheric model HiRLAM (High Resolution Limited Area Model). Actual and forecasted wind speeds are passed through multi‐turbine power curves and summed up to create time series of actual and forecasted wind power. Two insights are derived from the developed data set: the degree of long‐term variability and the degree of predictability when Dutch wind energy production is aggregated at the national or at the market participant level. For a 7.8 GW installed wind power scenario, at the system level, the imbalance energy requirements due to wind variations across 15‐min intervals are ±14% of the total installed capacity, while the imbalance due to forecast errors vary between 53% for down‐ and 56% for up‐regulation. When aggregating at the market participant level, the balancing energy requirements are 2–3% higher. Copyright © 2008 John Wiley & Sons, Ltd.     

Response of stall‐controlled,teetered, free‐yaw downwind turbines

Stall‐controlled, teetered, free‐yaw downwind turbines have historically experienced higher than desired peak loads due to occasional large teeter excursions when the blades are stalled. Understanding of the causes of these excursions and the potential solution have been the subject of much research in the past. This article contributes to this study in three areas. One is the development of the equations of motion for a teetered rotor with a delta‐3 angle. The solution of these equations leads to an improved understanding of the mechanics of these types of rotors and to a theory concerning how the rotor responds to different overall aerodynamic moments. A second contribution is a set of test cases to confirm the theories developed and to show how wind speed and different delta‐3 angles affect the restoring moments on the rotor and nacelle. A final contribution is an ADAMS^® analysis of the fatigue loading of the AWT‐27 under high turbulent wind speeds with different delta‐3 angles and the comparison with results of a field testing programme. Both the predictions and the field data point to the more benign response of a hub having a negative delta‐3 angle. This contradicts previous opinions but is consistent with the criteria presented in this article. Copyright © 1999 John Wiley & Sons, Ltd.     

Time series modelling of power output for large‐scale wind fleets

Simulations of power systems with high wind penetration need to represent the stochastic output of the wind farms. Many studies use historic wind data directly in the simulation. However, even if historic data are used to drive the realized wind output in scheduling simulations, a model of the wind's statistical properties may be needed to inform the commitment decisions for the dispatchable units. There are very few published studies that fit models to the power output of nation‐sized wind fleets rather than the output at a single location. We fitted a time series model to hourly, time‐averaged, aggregated wind power data from New Zealand, Denmark and Germany, based on univariate, second‐order autoregressive drivers. Our model is designed to reproduce the asymptotic distribution of power output, the diurnal variation and the volatility of power output over timescales up to several hours. For the cases examined here, it was also found to provide a generally good representation of the overall distribution of power output changes and the variation of volatility with power output level, as well as an acceptable representation of the distribution of calm periods. Copyright © 2011 John Wiley & Sons, Ltd.     

Sampling Bias on Cup Anemometer Mean Winds

The cup anemometer signal can be sampled in several ways to obtain the mean wind speed. Here we discuss the sampling of series of mean wind speeds from consecutive rotor rotations, followed by unweighted and weighted averaging. It is shown that the unweighted averaging creates a positive bias on the long‐term mean wind speed, which is at least one order of magnitude larger than the positive bias from the weighted averaging, also known as the sample‐and‐hold method. For a homogeneous, neutrally stratified flow the first biases are 1%–2%. For comparison the biases due to fluctuations of the three wind velocity components and due to calibration non‐linearity are determined under the same conditions. The largest of these is the v‐bias from direction fluctuations. The calculations pertain to the Risø P2546A model cup anemometer. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling and analysis of floating spar‐type wind turbine drivetrain

This paper studies the drivetrain dynamics of a 750 kW spar‐type floating wind turbine (FWT). The drivetrain studied is a high‐speed generator, one‐stage planetary, two‐stage parallel and three‐point support type. The response analysis is carried out in two steps. First, global aero‐hydro‐elastic‐servo time‐domain analyses are performed using HAWC2. The main shaft loads, which include the axial forces, shear forces and bending moments, are obtained in this integrated wind–wave response analysis. These loads are then used as inputs for the multi‐body drivetrain time‐domain analyses in SIMPACK. The investigations are largely based on comparisons of the main shaft loads and internal drivetrain responses from 1 h simulations. The tooth contact forces, bearing loads and gear deflections are the internal drivetrain response variables studied. The comparisons are based on the mean values, standard deviations and maximum values extrapolated using a 10 ^{? 5} up‐crossing rate. Both operational and parked conditions are considered. The investigation consists of three parts. First, the responses are compared between the FWT and its equivalent land‐based version. Second, the contributions from the main shaft loads (shear forces, axial forces and bending moments) and nacelle motions are investigated individually. Third, an improved four‐point support (4PT) system is studied and compared against the original three‐point support system for the FWT. The results show that there are general increases in the standard deviations of the main shaft loads and internal drivetrain responses in the FWT. In addition, these increases are a result of the increased main shaft loads in the FWT, especially the non‐torque loads. Last, the 4PT system, when applied to a FWT drivetrain, significantly reduces the tooth contact forces and bearing loads in the low‐speed stage, but this result comes at the expense of increased main bearing radial loads. Copyright © 2013 John Wiley & Sons, Ltd.     

Short‐term spatio‐temporal prediction of wind speed and direction

This paper aims to produce a low‐complexity predictor for the hourly mean wind speed and direction from 1 to 6 h ahead at multiple sites distributed around the UK. The wind speed and direction are modelled via the magnitude and phase of a complex‐valued time series. A multichannel adaptive filter is set to predict this signal on the basis of its past values and the spatio‐temporal correlation between wind signals measured at numerous geographical locations. The filter coefficients are determined by minimizing the mean square prediction error. To account for the time‐varying nature of the wind data and the underlying system, we propose a cyclo‐stationary Wiener solution, which is shown to produce an accurate predictor. An iterative solution, which provides lower computational complexity, increased robustness towards ill‐conditioning of the data covariance matrices and the ability to track time‐variations in the underlying system, is also presented. The approaches are tested on wind speed and direction data measured at various sites across the UK. Results show that the proposed techniques are able to predict wind speed as accurately as state‐of‐the‐art wind speed forecasting benchmarks while simultaneously providing valuable directional information. Copyright © 2013 John Wiley & Sons, Ltd.     

Vortex‐induced vibrations on a modern wind turbine blade

This article investigates the aero‐elastic response of the DTU 10‐MW RWT blade in deep stall conditions with angles of attack in the vicinity of 90 degrees. The simulations were conducted with the high‐fidelity fluid–structure interaction simulation tool HAWC2CFD employing the multi‐body‐based structural model of HAWC2 and the incompressible computational fluid dynamics solver EllipSys3D. The study utilizes detached eddy simulation computations and considers the three‐dimensional blade geometry including blade twist and taper. A preliminary frequency analysis of the load variations on a stiff blade showed that an inclined inflow with a velocity component along the blade axis can trigger a spanwise correlated vortex shedding over large parts of the blade. Moderate wind speeds were sufficient to generate vortex shedding with frequencies close to the first edgewise eigenfrequency of the blade. Aero‐elastic computations of the elastic blade confirmed the findings of the frequency analysis. Inflow conditions with inclination angles between Ψ = 20° and Ψ = 55° and relatively low to moderate wind speeds between V = 16 and V = 26ms^?1 were sufficient to trigger severe edgewise blade vibrations with blade tip amplitudes of several metres. The investigated inflow conditions are considered realistic and might occur when the wind turbine is idling or standing still and the yaw system is unable to align the wind turbine with the incoming wind. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental study of a small wind turbine for low‐ and medium‐wind regimes

The results of an experimental assessment of a small prototype battery charging wind turbine designed for low‐ and medium‐wind regimes are presented. The turbine is based on a newly designed axial flow permanent magnet synchronous generator and a three‐bladed rotor with variable twist and taper blades. Overspeed control is performed by a furling mechanism. The turbine has the unique feature of being capable of operating at either 12, 24 or 48 V system voltage, requiring no load control in any case. In the 48 V configuration, the system is capable of providing 2 kWh day^?1 for an average wind speed as low as 3.5 m s^?1 and an air density of 85% of the standard pressure and temperature value. The experimental assessment has been conducted under field conditions with the turbine mounted on a 20 m guy‐wired tubular tower. The experimental power curves are shown to be in good agreement with a detailed aerodynamical and electromechanical model of the turbine for non‐furling conditions and for wind speeds above the theoretical cut‐in speed. In the case of the rapidly spinning load configurations, a finite power production at wind speeds below the theoretical cut‐in speed can be observed, which can be explained in terms of inertia effects. During the measurement campaigns with high loads, we were able to observe bifurcations of the power curve, which can be explained in terms of instabilities arising in situations of transition from attached to separated flow. A full experimental C_p(λ)‐curve has been constructed by operating the turbine under different load conditions and the findings are in good agreement with a variable Reynolds‐number blade‐element momentum model. The three proposed system configurations have been found to operate with a high aerodynamic efficiency with typical values of the power coefficient in the 0.40–0.45 range. Copyright © 2009 John Wiley & Sons, Ltd.     

First and second order Markov chain models for synthetic generation of wind speed time series

Hourly wind speed time series data of two meteorological stations in Malaysia have been used for stochastic generation of wind speed data using the transition matrix approach of the Markov chain process. The transition probability matrices have been formed using two different approaches: the first approach involves the use of the first order transition probability matrix of a Markov chain, and the second involves the use of a second order transition probability matrix that uses the current and preceding values to describe the next wind speed value. The algorithm to generate the wind speed time series from the transition probability matrices is described. Uniform random number generators have been used for transition between successive time states and within state wind speed values. The ability of each approach to retain the statistical properties of the generated speed is compared with the observed ones. The main statistical properties used for this purpose are mean, standard deviation, median, percentiles, Weibull distribution parameters, autocorrelations and spectral density of wind speed values. The comparison of the observed wind speed and the synthetically generated ones shows that the statistical characteristics are satisfactorily preserved.     

Hindcasting hourly wind power across Scotland based on met station data

This paper presents methods and results from a study where long‐term wind measurements at 10 m above ground level from meteorological stations across Scotland were used to hindcast both average and hour‐by‐hour local wind speeds. For this, Scotland was divided into 21 simulation areas each containing a meteorological station. The Wind Atlas Analysis and Application Program (WAsP) was then used—well outside its specified range for both distance and area slope—to predict the wind climate at 80 m above ground level on a square kilometre basis. With further processing, time series of wind speed were derived for selected locations. Based on wind turbine power curves it was then possible to derive time series of power which were applied in power system analysis and used to study the degree of matching between renewable generation and electricity demand. This paper focuses on the creation of the onshore wind speed and power time series for areas of interest in Scotland. Copyright © 2007 John Wiley & Sons, Ltd.     

Simulating Feedback Linearization control of wind turbines using high‐order models

As wind turbines are becoming larger, wind turbine control must now encompass load control objectives as well as power and speed control to achieve a low cost of energy. Due to the inherent non‐linearities in a wind turbine system, the use of non‐linear model‐based controllers has the potential to increase control performance. A non‐linear feedback linearization controller with an Extended Kalman Filter is successfully used to control a FAST model of the controls advanced research turbine with active blade, tower and drive‐train dynamics in above rated wind conditions. The controller exhibits reductions in low speed shaft fatigue damage equivalent loads, power regulation and speed regulation when compared to a Gain Scheduled Proportional Integral controller, designed for speed regulation alone. The feedback linearization controller shows better rotor speed regulation than a Linear Quadratic Regulator (LQR) at close to rated wind speeds, but poorer rotor speed regulation at higher wind speeds. This is due to modeling inaccuracies and the addition of unmodeled dynamics during simulation. Similar performance between the feedback linearization controller and the LQR in reducing drive‐train fatigue damage and power regulation is observed. Improvements in control performance may be achieved through increasing the accuracy of the non‐linear model used for controller design. Copyright © 2009 John Wiley & Sons, Ltd.