A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco

Time series of then years of Hourly Average Wind Speed, HAWS, data from Tangiers station are analysed on a statistical basis by applying the Markovian process. The limiting behaviour of the Markov chain is then examined and compared to the histogram of observed wind speed. It was found that a 12×12 transition probability matrix was necessary to generate an acceptable synthetic time series. The manner in which the Markovian model can be used to generate wind speed time series are also described.Using the transition probability matrix developed from the real wind data, the synthetic wind speed time series are generated. The comparison between the real wind speed and the synthetic one shows that the statistical characteristics of wind speed are faithfully reproduced. The synthetic HAWS may be utilised as input data for any wind energy system.     

Synthesis of long-term hourly wind speed time series on the basis of European wind atlas data

A method for the synthesis of annual wind speed time series with a time resolution of 1 hour is presented. It is based upon statistical information on the wind climate given in the European Wind Atlas. The synthetic time series reproduce the monthly average daily time pattern of the site. The distribution of the synthetic wind speed data shows the correct mean value of the cubed wind speed. The site-specific variance of the wind speed and the power spectrum of the wind speed fluctuations are closely approximated. Results of time step simulations for small stand-alone wind energy systems using synthetic and measured data sets as input data show a close agreement.     

Model of a synthetic wind speed time series generator

Wind energy has assumed a great relevance in the operation and planning of today's power systems due to the exponential increase of installations in the last 10 years. For this reason, many performed studies have looked at suitable representations of wind generation for power system analysis. One of the main elements to consider for this purpose is the model of the wind speed that is usually required as input. Wind speed measurements may represent a solution for this problem, but, for techniques such as sequential Monte Carlo simulation, they have to be long enough in order to describe a wide range of possible wind conditions. If these information are not available, synthetic wind speed time series may be a useful tool as well, but their generator must preserve statistical and stochastic features of the phenomenon. This paper deals with this issue: a generator for synthetic wind speed time series is described and some statistical issues (seasonal characteristics, autocorrelation functions, average values and distribution functions) are used for verification. The output of the model has been designed as input for sequential Monte Carlo simulation; however, it is expected that it can be used for other similar studies on wind generation. Copyright © 2007 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.     

De‐trending of wind speed variance based on first‐order and second‐order statistical moments only

The lack of efficient methods for de‐trending of wind speed resource data may lead to erroneous wind turbine fatigue and ultimate load predictions. The present paper presents two models, which quantify the effect of an assumed linear trend on wind speed standard deviations as based on available statistical data only. The first model is a pure time series analysis approach, which quantifies the effect of non‐stationary characteristics of ensemble mean wind speeds on the estimated wind speed standard deviations as based on mean wind speed statistics only. This model is applicable to statistics of arbitrary types of time series. The second model uses the full set of information and includes thus additionally observed wind speed standard deviations to estimate the effect of ensemble mean non‐stationarities on wind speed standard deviations. This model takes advantage of a simple physical relationship between first‐order and second‐order statistical moments of wind speeds in the atmospheric boundary layer and is therefore dedicated to wind speed time series but is not applicable to time series in general. The capabilities of the proposed models are discussed by comparing model predictions with conventionally de‐trended characteristics of measured wind speeds using data where high sampled time series are available, and a traditional de‐trending procedure therefore can be applied. This analysis shows that the second model performs significantly better than the first model, and thus in turn that the model constraint, introduced by the physical link between the first and second statistical moments, proves very efficient in the present context. © 2013 The Authors. Wind Energy Published by John Wiley & Sons Ltd.     

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.     

Quality of wind speed fitting distributions for the urban area of Palermo,Italy

This study investigates the wind speed characteristics recorded in the urban area of Palermo, in the south of Italy, by a monitoring network composed by four weather stations. This article has two main objectives: the first one, to describe with clarity and simplicity the numerical procedures adopted to perform a preliminary statistical analysis of wind speed data, providing at the same time, the necessary mathematical tools useful to perform this analysis also without special software. The second objective is to verify if there are more suitable probability distributions able to better represent the original data respect the traditional ones. After a preliminary statistical analysis, in which the wind speed time series are split and analysed for each month and season, seven probability density functions are employed to describe wind speed frequency distributions: Weibull, Rayleigh, Lognormal, Gamma, Inverse Gaussian, Pearson type V and Burr. Shape and scale parameters for each weather station, period and distribution are provided. Their estimation is performed using the maximum likelihood method and the maximum likelihood estimators for each probability density function are provided. The quality of the data-fit is assessed by the classic statistical test Kolmogorov–Smirnov. The statistical test is used to rank the selected distributions in order to identify the distribution better fitting with the wind speed data measured in the urban area of Palermo. The Burr probability density function seems to be the most reliable statistical distribution.     

Application of Bayesian model averaging in modeling long-term wind speed distributions

Accurate estimation of wind speed distribution is critical to the assessment of wind energy potential, the site selection of wind farms, and the operations management of wind power conversion systems. This paper proposes a new approach for deriving more reliable and robust wind speed distributions than conventional statistical modeling approach. This approach combines Bayesian model averaging (BMA) and Markov Chain Monte Carlo (MCMC) sampling methods. The derived BMA probability density function (PDF) of the wind speed is an average of the model PDFs included in the model space weighted by their posterior probabilities over the sample data. MCMC method provides an effective way for numerically computing marginal likelihoods, which are essential for obtaining the posterior model probabilities. The approach is applied to multiple sites with high wind power potential in North Dakota. The wind speed data at these sites are the mean hourly wind speeds collected over two years. It is demonstrated that indeed none of the conventional statistical models such as Weibull distribution are universally plausible for all the sites. However, the BMA approach can provide comparative reliability and robustness in describing the long-term wind speed distributions for all sites, while making the traditional model comparison based on goodness-of-fit statistics unnecessary.     

An M‐Rice wind speed frequency distribution

Several known statistical distributions can describe wind speed data, the most commonly used being the Weibull family. In this paper, a new law, called ‘M‐Rice’, is proposed for modeling wind speed frequency distributions. 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 AutoRegressive Moving Average (ARMA) model where the noise term is ‘multifractal’, i.e. associated with a random cascade. This leads to the distribution of wind speeds according to the M‐Rice probability distribution function, i.e. a Rice distribution multiplicatively convolved with a normal law. A comparison based on the estimation of the mean wind speed and power density values as well as on the different goodness‐of‐fit tests (the Kolmogorov–Smirnov test, the Kuiper test and the quantile–quantile plot) was made between this new distribution and the Weibull distribution for 35 data sets of wind speed from the Netherlands and Corsica (France) sites. Accordingly, the M‐Rice and Weibull distributions provided comparable performances; however, the quantile–quantile plots suggest that the M‐Rice distribution provides a better fit of extreme wind speed data. Beyond these good results, our approach allows one to interpret the observed values of Weibull parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Anticipatory Control of Wind Turbines With Data-Driven Predictive Models

The concept of anticipatory control applied to wind turbines is presented. Anticipatory control is based on the model predictive control (MPC) approach. Unlike the MPC method, noncontrollable variables (such as wind speed) are directly considered in the dynamic equations presented in the paper to predict response variables, e.g., rotor speed and turbine power output. To determine future states of the power drive with the dynamic equations, a time series model was built for wind speed. The time series model was fused with the dynamic equations to predict the response variables over a certain prediction horizon. Based on these predictions, an optimization model was solved to find the optimal control settings to improve the power output without incurring large rotor speed changes. As both the dynamic equations and time series model were built by data mining algorithms, no gradient information is available. A modified evolutionary strategy algorithm was used to solve a nonlinear constrained optimization problem. The proposed approach has been tested on the data collected from a 1.5 MW wind turbine.      

Correlated synthetic time series generation for energy system simulations using Fourier and ARMA signal processing

As the contribution of renewable energy grows in electricity markets, the complexity of the energy mix required to meet demand grows, likewise the need for robust simulation techniques. While decades of wind, solar, and demand profiles can sometimes be obtained, this is too few samples to provide a statistically meaningful analysis of a system with baseload, peaker, and renewable generation. To demonstrate the viability of an energy mix, many thousands of samples are needed. Synthetic time series generation presents itself as a suitable methodology to meet this need. For a synthetic time series to be statistically viable, several conditions must be met. The series generator must produce independent, identically distributed samples, each having the same fundamental properties as the original signal without duplicating it exactly. One approach for such a generator is training a surrogate model using Fourier series decomposition for seasonal patterns and autoregressive moving average (ARMA) models to describe time-correlated statistical noise about the seasonal patterns. When combined, the Fourier plus ARMA (FARMA) model has been shown to provide an infinite set of independent, identically distributed sample time series with the same statistical properties as the original data [1]. When considering an energy mix with renewable electricity production, several time series of energy, grid, and weather measurements are needed for each synthetic year modeled to statistically comprehend the efficiency of any given energy mix. This includes measurements of solar exposure, air temperature, wind velocity, and electricity demand. These cannot be considered independent series in a given synthetic year; for example, in summer months demand may be higher when solar exposure and air temperature are high and wind velocity is low. To capture and reproduce the correlations that might exist in the measured histories, the ARMA can further be extended as a Vector ARMA (VARMA). In the VARMA algorithm, covariance in statistical noise is captured both within a history as part of the autoregressive moving average and with respect to the other variables in the time series. In this work, the implementation of the Fourier VARMA in the RAVEN uncertainty quantification and risk analysis software framework [2] is presented, along with examples of correlated synthetic history generation. Finally, methods to extend synthetic signals to multiyear samples are presented and discussed.     

Assessment of wind energy in Iran: A review

In this study, a ten minute period measuring wind speed data for year 2007 at 10 m, 30 m and 40 m heights for different places in Iran, has been statistically analyzed to determine the potential of wind power generation. Sixty eight sites have been studied. The objective is to evaluate the most important characteristics of wind energy in the studied sites. The statistical attitudes permit us to estimate the mean wind speed, the wind speed distribution function, the mean wind power density and the wind rose in the site at three different heights. Some local phenomena are also considered in the characterization of the site.     

Wind speed forecasting in three different regions of Mexico,using a hybrid ARIMA–ANN model

In this paper the wind speed forecasting in the Isla de Cedros in Baja California, in the Cerro de la Virgen in Zacatecas and in Holbox in Quintana Roo is presented. The time series utilized are average hourly wind speed data obtained directly from the measurements realized in the different sites during about one month. In order to do wind speed forecasting Hybrid models consisting of Autoregressive Integrated Moving Average (ARIMA) models and Artificial Neural Network (ANN) models were developed. The ARIMA models were first used to do the wind speed forecasting of the time series and then with the obtained errors ANN were built taking into account the nonlinear tendencies that the ARIMA technique could not identify, reducing with this the final errors. Once the Hybrid models were developed 48 data out of sample for each one of the sites were used to do the wind speed forecasting and the results were compared with the ARIMA and the ANN models working separately. Statistical error measures such as the mean error (ME), the mean square error (MSE) and the mean absolute error (MAE) were calculated to compare the three methods. The results showed that the Hybrid models predict the wind velocities with a higher accuracy than the ARIMA and ANN models in the three examined sites.     

Short-Term Prediction of Wind Farm Power: A Data Mining Approach

This paper examines time series models for predicting the power of a wind farm at different time scales, i.e., 10-min and hour-long intervals. The time series models are built with data mining algorithms. Five different data mining algorithms have been tested on various wind farm datasets. Two of the five algorithms performed particularly well. The support vector machine regression algorithm provides accurate predictions of wind power and wind speed at 10-min intervals up to 1 h into the future, while the multilayer perceptron algorithm is accurate in predicting power over hour-long intervals up to 4 h ahead. Wind speed can be predicted fairly accurately based on its historical values; however, the power cannot be accurately determined given a power curve model and the predicted wind speed. Test computational results of all time series models and data mining algorithms are discussed. The tests were performed on data generated at a wind farm of 100 turbines. Suggestions for future research are provided.      

Influence of local wind speed and direction on wind power dynamics – Application to offshore very short-term forecasting

Wind power time series usually show complex dynamics mainly due to non-linearities related to the wind physics and the power transformation process in wind farms. This article provides an approach to the incorporation of observed local variables (wind speed and direction) to model some of these effects by means of statistical models. To this end, a benchmarking between two different families of varying-coefficient models (regime-switching and conditional parametric models) is carried out. The case of the offshore wind farm of Horns Rev in Denmark has been considered. The analysis is focused on one-step ahead forecasting and a time series resolution of 10 min. It has been found that the local wind direction contributes to model some features of the prevailing winds, such as the impact of the wind direction on the wind variability, whereas the non-linearities related to the power transformation process can be introduced by considering the local wind speed. In both cases, conditional parametric models showed a better performance than the one achieved by the regime-switching strategy. The results attained reinforce the idea that each explanatory variable allows the modelling of different underlying effects in the dynamics of wind power time series.     

Viability and economic analysis of wind energy resource for power generation in Johannesburg,South Africa

In this study, wind characteristics and wind power potential of Johannesburg are investigated using 5-min average time series wind speed collected between 2005 and 2009 at anemometer height of 10 m. The statistical distribution that best fits the empirical wind speed data at the site of study is first determined based on the coefficient of determination and root mean square error criteria. The statistical parameters and wind power density based on this model are estimated for different months of the year using standard deviation method. Economic analyses of some wind turbines are also carried out. Some of the key results show that the site is only suitable for small wind turbines in a standalone application. A 10 kW wind turbine with cut-in wind speed of 3.5 m/s, rated wind speed of 9 m/s, and cut-out wind speed of 25 m/s seems most appropriate in Johannesburg with the lowest cost that varies from 0.25 to 0.33 $/kWh.     

Analytical methods for wind persistence: Their application in assessing the best site for a wind farm in the State of Veracruz,Mexico

The properties of wind persistence are an essential parameter in carrying out a complete analysis of possible sites for a wind farm. This parameter can be defined as a measure of the mean duration of wind speed within a given interval of values for a concrete site. In this study the persistence properties are evaluated from the methods based on the autocorrelation function, conditional probability and the curves of speed duration, used satisfactorily by other authors. The statistical analysis of the series of useful persistence is also carried out to validate the results obtained. These methods have been applied to hourly data of wind speed corresponding to five Weather Stations (WS) in the State of Veracruz, Mexico in the period 1995–2006. The results obtained indicate that the coastal areas have the best properties of wind speed persistence and are, therefore, the most indicated for the generation of electricity from this renewable energy source.     

Assessment of the benefits of numerical weather predictions in wind power forecasting based on statistical methods

Several forecast systems based on Artificial Neural Networks have been developed to predict power production of a wind farm located in a complex terrain, where geographical effects make wind speed predictions difficult) in different time horizons: 1,3,6,12 and 24 h.In the first system, the neural network has been used only as a statistic model based on time series of wind power; later it has been integrated with numerical weather predictions, by which an interesting improvement of the performance has been reached, especially with the longer time horizons. In particular, a sensitivity analysis has been carried out in order to find those numerical weather parameters with the best impact on the forecast.Then, after the implementation of forecast systems based on a single ANN, the two best prediction systems individuated through the sensitivity analysis, have been employed in a hybrid approach, made up of three different ANNs.Besides, a prediction system based on the wavelet decomposition technique has been also carried out in order to evaluate its contribute on the forecast performance in two time horizons (1 and 24 h).The error of the different forecast systems is investigated and the statistical distributions of the error are calculated and presented.     

Wind resource assessment of an area using short term data correlated to a long term data set

A method of estimating the annual wind energy potential of a selected site using short term measurements related to one year’s recorded wind data at another reference site is presented. The proposed method utilizes the 1-year measured wind speed of one site to extrapolate the annual wind speed at a new site, using an artificial neural network (ANN). In this study, concurrent measurements from target and reference sites over periods of 1-month and 2-month were used to “train” the ANN. Topographical details or other meteorological data are not required for this approach. After derivation of the simulated wind speed time series for the target site, its mean value and its corresponding Weibull distribution parameters are calculated. The derived Weibull distribution of the simulated wind speed is used to make an assessment of the annual wind energy resource in the new area with respect to a particular wind turbine model. Three pairs of measuring stations in the southwest of Ireland were examined, where the wind potential is high and technically exploitable. Analysis of the measurements showed a reasonable cross-correlation coefficient of the wind speed between the sites. Results indicate that with this method, only a short time period of wind data acquisition in a new area might provide the information required for a satisfactory assessment of the annual wind energy resource. To evaluate the accuracy of the method, simulation results of the 1-month and 2-month training periods are compared to the corresponding actual values recorded at the sites. Also, a comparison with the results of a commercial wind energy assessment software package is presented showing similar results.