Some statistical characteristics of monthly average wind speed at various heights

The article, which is a segment of a complex wind energy examination, uses statistical methods to analyze the time series of monthly average wind speed in the period between 1991 and 2000 measured on seven Hungarian meteorological stations. Empirical distribution of measured monthly average wind speeds is approximated by theoretical distributions to claim that certain distributions are universal, i.e. independent of orography. We used one of them, the Weibull distribution, to generate the distribution of monthly average wind speeds on levels different from anemometer altitude as well, then we calculate the averages for the entire period and we fit a power function on them. Thus we can demonstrate a correlation between Hellmann's wind profile law and the Weibull distribution.     

A methodology for modelling synthetic daily sequences of hourly power demand for villages and small towns, based on stochastic processes

A model to generate daily sequences of hourly power demand values is described. Inputs are the daily values of energy consumption and load-factors (the ratio between mean and peak load). The whole model covers three independent first-order autoregressive models to generate data sequences of, respectively, daily energy consumption, daily load-factor and hourly power demand. The analysis of a power demand data set reveals that energy consumption and load-factor are independent variables; two independent time series of daily values of energy consumption and load-factor are built; their statistical and sequential properties can be described with first-order autoregressive models. Assuming a villlage’s consumption-structure as characterized by load curves with a peak load at night, the load-factor is taken as a shape-factor for these curves. A frequency distribution is built on daily load factors. The data sequence is, then, sorted into groups of daily curves, each one characterized by a load-factor-class. A daily average load curve is estimated for each class, along with its daily standard deviation curve. An analysis of each group of daily curves shows that the statistical and sequential properties of each one can be also described with first-order autoregressive models. For modelling purposes, the autocorrelation coefficient is determined for each load-factor class. Thus, energy and power relate to each other under different load-factors. Application examples are offered, for design purposes.     

A wind energy analysis of Grenada: an estimation using the ‘Weibull’ density function

The Weibull density function has been used to estimate the wind energy potential in Grenada, West Indies. Based on historic recordings of mean hourly wind velocity this analysis shows the importance to incorporate the variation in wind energy potential during diurnal cycles. Wind energy assessments that are based on Weibull distribution using average daily/seasonal wind speeds fail to acknowledge that wind speed probabilities can vary significantly during day and night. In particular where wind energy estimation is linked to electricity loads neglecting diurnal wind patterns can result in significant under/overestimation of wind power potential.     

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.     

Climatic conditions for operation of wind turbines in Hungary

According to wind-climatic requirement of wind farms wind speed should exceed the so called cut-in speed. If this inequality is realized then regarding the wind-climatic features of Hungary the following conditions may occur: the wind turbine is operating with high probability, energy is generated; it is working in a regulated mode with low probability; it is not working with very low probability. Therefore in terms of continuous energy production by wind one question arises: are there any temporal and/or orographic shifts in different heights compared to the wind-climatic condition mentioned above. In this paper this question is analyzed on the basis of seven Hungarian meteorological stations that have hourly measured wind speed data considering the period between 1991 and 2000. The probability of wind speeds exceeding 3 m/s, statistics of wind speed intervals higher and lower than 3 m/s and statistics of average hourly wind speed intervals higher than 3 m/s were analyzed at the heights of 10, 30 and 60 m. A statistical parameter that is proportional to the average specific wind power of a day in a time period was defined and, its connection to the average length of those intervals that have higher or equal hourly average wind speeds more than 3 m/s in a given month was investigated. With the help of such parameters the value of monthly average specific wind power can be estimated.     

A statistical model for estimating electricity produced by wind energy

Potential wind power for a given period (e.g. a day) can be determined from wind speed data measured in certain hours of a period. Obviously, the sum of the cubes of wind speeds measured depends on the number of measurements. This dependence can be reduced in two ways: determining the average and the relative wind energy for a given time within a given period. The method of sliding averages uses both. Applying this method a given hourly average wind speed cube of a day is estimated on the basis of wind speeds measured in that hour of the day. Cubes of the wind speeds are in proportion with the total daily potential and produced wind energy. This model requires long-time series of wind speed data that are available only for weather stations in Hungary, where hourly average winds speeds are registered.For this reason, statistics required for the model were calculated from different subsets of ten-year-long hourly average wind speed time series of three Hungarian weather stations (Szombathely, Budapest-L?rinc and Debrecen). Using the statistics and hourly wind speed data measured in the vicinity of the wind turbines/on the wind turbines themselves, the model is suitable for giving estimations hourly of the potential wind energy for the whole day in a particular season or circulation type group. A software for the model is also presented here. Considering the results the sliding average model (SLIDAV) makes it possible to forecast average daily wind power 6–9 h before the end of the day with an error of 20%. The magnitude of the error of estimation depends on the given season and/or synoptic type group. These results may provide important information for wind turbine owners: daily amount of wind energy can be determined in this way. Thus the owner can decide whether to operate the turbine whole day, or to stop it periodically for maintenance for example.     

Statistical analysis of wind power in the region of Veracruz (Mexico)

The capacity of the Mexican electricity sector faces the challenge of satisfying the demand of the 80 GW forecast by 2016. This value supposes a steady yearly average increase of some 4.9%. The electricity sector increases for the next eight years will be mainly made up of combined cycle power plants which could be a threat to the energy supply of the country due to the fact that the country is not self-sufficient in natural gas.As an alternative wind energy resource could be a more suitable option compared with combined cycle power plants. This option is backed by market trends indicating that wind technology costs will continue to decrease in the near future as has happened in recent years.Evaluation of the eolic potential in different areas of the country must be carried out in order to achieve the best use possible of this option. This paper gives a statistical analysis of the wind characteristics in the region of Veracruz. The daily, monthly and annual wind speed values have been studied together with their prevailing direction. The data analyzed correspond to five meteorological stations and two anemometric stations located in the aforementioned area.     

Wind power energy potential at the northeastern region of Saudi Arabia

In the present study the energy potential of wind for the Eastern Province of Saudi Arabia is investigated. A suitable Weibull distribution is generated based on the data obtained for a duration of one complete year at a costal location in northeastern Saudi Arabia. Comparison of this model is made with the Rayleigh distribution of wind power densities. Two horizontal-axis type of wind energy conversion systems which operate at fixed rpm are considered and a model of quadratic power output function is used. It is found that the error in using the Rayleigh approximation will be less than 10% of the full rated power density level.     

基于KL散度的储能电站分布鲁棒规划方法

电化学储能的循环寿命受到充放电次数和放电深度的影响,为了更加准确地在新能源电力系统中规划储能电站,提出基于Kullback-Leibler(KL)散度的储能电站分布鲁棒规划方法.根据电化学储能循环寿命的幂函数,建立基于等效全循环次数的储能电站寿命模型,考虑储能电站寿命模型约束和系统运行约束,以储能电站的全寿命周期成本和...     

Energy and reliability benefits of wind energy conversion systems

The electrical energy production and reliability benefits of a wind energy conversion system (WECS) at a specific site depend on many factors, including the statistical characteristics of the site wind speed and the design characteristics of the wind turbine generator (WTG) itself, particularly the cut-in, rated and cut-out wind speed parameters. In general, the higher the degree of the wind site matching with a WECS is, the more are the energy and reliability benefits. An electrical energy production and reliability benefit index designated as the Equivalent Capacity Ratio (ECR) is introduced in this paper. This index can be used to indicate the electrical energy production, the annual equivalent utilization time and the credit of a WECS, and quantify the degree of wind site matching with a WECS. The equivalent capacity of a WECS is modeled as the expected value of the power output random variable with the probability density function of the site wind speed. The analytical formulation of the ECR is based on a mathematical derivation with high accuracy. Twelve WTG types and two test systems are used to demonstrate the effectiveness of the proposed model. The results show that the ECR provides a useful index for a WTG to evaluate the energy production and the relative reliability performance in a power system, and can be used to assist in the determination of the optimal WTG type for a specific wind site.     

Designing an index for assessing wind energy potential

To meet the increasing global demand for renewable energy, such as wind energy, an increasing number of wind parks are being constructed worldwide. Finding a suitable location requires a detailed and often costly analysis of local wind conditions. Plain average wind speed maps cannot provide a precise forecast of wind power because of the non-linear relationship between wind speed and production. We suggest a new approach to assess the local wind energy potential. First, meteorological reanalysis data are applied to obtain long-term low-scale wind speed data at specific turbine locations and hub heights. Second, the relation between wind data and energy production is determined via a five parameter logistic function using actual high-frequency energy production data. The resulting wind energy index allows for a turbine-specific estimation of the expected wind power at an unobserved location. A map of the wind power potential for Germany exemplifies our approach.     

An analysis of wind power potential in Greece

In this paper an analysis of the available wind data for the Aegean Sea region of Greece is carried out to ascertain its potential for wind energy development. The effect of the limited number of daily observations available on the accuracy of the mean wind speed and annual wind energy estimates is ascertained. The applicability of the Weibull distribution is then examined and plots of the Weibull parameters are given. The annual average wind energy flux is calculated and found to be quite high (in excess of 600 W/m² per yr at 10 m) which makes the Aegean Islands likely candidates for wind power utilization.     

Wind energy from turbulence: Constant tip speed ratio operation

The ability of a wind machine, operating at constant tip speed ratio, to extract power from the turbulent eddy fluctuations in the wind is examined. A model is constructed relating the inertia of the machine to its ability to follow the fluctuations. The model includes a transfer function from which a cutoff frequency can be predicted. A field test on the University of Massachusetts experimental wind turbine yielded a cutoff frequency close to that of the model. The fraction of the additional energy available in the turbulent fluctuations to be extracted by the machine may be between 3% and 37% more than would be predicted from hourly average wind speeds. A responsive wind machine operating at constant tip speed ratio could extract approximately 70% of the additional energy. Further, machines that do not operate at constant tip speed ratio may produce less power in turbulent winds than would be predicted from an hourly average.     

Assessment of wind energy potential for selected areas in Jordan

This paper presents a technical assessment of wind power potential for seven locations in Jordan using statistical analysis to determine the wind characteristic based on the measured wind data. Rayleigh distribution is used to model the monthly average data and used to estimate the wind power in the selected locations. Energy calculations, capacity factors and cost of wind energy production were determined for the selected locations with wind machines of different sizes ranging between 1.65 MW and 3 MW. The quantitative estimates of the technical and economic potential are presented graphically. Rayleigh parameter is adjusted to the hub height using one seventh power law to estimate the power output of the machine. The energy cost analyses show that all selected sites have high economic potential with unit cost less than $0.04/kWh of electricity. The lowest unit cost per kWh is obtained by using GE 2.5 MW at Tafila site. Finally, the results of this study reveal that Jordan has high potential wind energy and its environmental and energy policy targets can be met by exploitation wind energy.     

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.     

Hour-ahead wind power and speed forecasting using simultaneous perturbation stochastic approximation (SPSA) algorithm and neural network with fuzzy inputs

Wind energy is currently one of the types of renewable energy with a large generation capacity. However, since the operation of wind power generation is challenging due to its intermittent characteristics, forecasting wind power generation efficiently is essential for economic operation. This paper proposes a new method of wind power and speed forecasting using a multi-layer feed-forward neural network (MFNN) to develop forecasting in time-scales that can vary from a few minutes to an hour. Inputs for the MFNN are modeled by fuzzy numbers because the measurement facilities provide maximum, average and minimum values. Then simultaneous perturbation stochastic approximation (SPSA) algorithm is employed to train the MFNN. Real wind power generation and wind speed data measured at a wind farm are used for simulation. Comparative studies between the proposed method and traditional methods are shown.     

A new semi-empirical wind turbine capacity factor for maximizing annual electricity and hydrogen production

The capacity factor is an important wind turbine parameter which is ratio of average output electrical power to rated electrical power of the wind turbine. Another main factor, the AEP, the annual energy production, can be determined using wind characteristics and wind turbine performance. Lower rated power may lead to higher capacity factor but will reduce the AEP. Therefore, it is important to consider simultaneously both the capacity factor and the AEP in design or selecting a wind turbine. In this work, a new semi-empirical secondary capacity factor is introduced for determining a rated wind speed at which yearly energy and hydrogen production obtain a maximum value. This capacity factor is expressed as ratio of the AEP for wind turbine to yearly wind energy delivered by mean wind speed at the rotor swept area. The methodology is demonstrated using the empirical efficiency curve of Vestas-80 2 MW turbine and the Weibull probability density function. Simultaneous use of the primary and the secondary capacity factors are discussed for maximizing electrical energy and hence hydrogen production for different wind classes and economic feasibility are scrutinized in several wind stations in Kuwait.     

Spatial dependence in wind and optimal wind power allocation: A copula-based analysis

The investment decision on the placement of wind turbines is, neglecting legal formalities, mainly driven by the aim to maximize the expected annual energy production of single turbines. The result is a concentration of wind farms at locations with high average wind speed. While this strategy may be optimal for single investors maximizing their own return on investment, the resulting overall allocation of wind turbines may be unfavorable for energy suppliers and the economy because of large fluctuations in the overall wind power output. This paper investigates to what extent optimal allocation of wind farms in Germany can reduce these fluctuations. We analyze stochastic dependencies of wind speed for a large data set of German on- and offshore weather stations and find that these dependencies turn out to be highly nonlinear but constant over time. Using copula theory we determine the value at risk of energy production for given allocation sets of wind farms and derive optimal allocation plans. We find that the optimized allocation of wind farms may substantially stabilize the overall wind energy supply on daily as well as hourly frequency.     

Lowering post-construction yield assessment uncertainty through better wind plant power curves

Many operational analyses of wind power plants require a statistical relationship, which can be called the wind plant power curve, to be developed between wind plant energy production and concurrent atmospheric variables. Currently, a univariate linear regression at monthly resolution is the industry standard for post-construction yield assessments. Here, we evaluate the benefits in augmenting this conventional approach by testing alternative regressions performed with multiple inputs, at a finer time resolution, and using nonlinear machine-learning algorithms. We utilize the National Renewable Energy Laboratory's open-source software package OpenOA to assess wind plant power curves for 10 wind plants. When a univariate generalized additive model at daily or hourly resolution is used, regression uncertainty is reduced, in absolute terms, by up to 1.0% and 1.2% (corresponding to a ?59% and ?80% relative change), respectively, compared to a univariate linear regression at monthly resolution; also, a more accurate assessment of the mean long-term wind plant production is achieved. Additional input variables also reduce the regression uncertainty: when temperature is added as an input to the conventional monthly linear regression, the operational analysis uncertainty connected to regression is reduced, in absolute terms, by up to 0.5% (?43% relative change) for wind power plants with strong seasonal variability. Adding input variables to the machine-learning model at daily resolution can further reduce regression uncertainty, with up to a ?10% relative change. Based on these results, we conclude that a multivariate nonlinear regression at daily or hourly resolution should be recommended for assessing wind plant power curves.