Ultra short‐term probability prediction of wind power based on LSTM network and condition normal distribution

Considering the inevitable prediction errors in the traditional point predictions of wind power, in this paper, a new ultra short‐term probability prediction method for wind power is proposed, in which the long short‐term memory (LSTM) network, wavelet decomposition (WT), and principal component analysis (PCA) are combined together for ultra short‐term probability prediction of wind power, a conditional normal distribution model that is developed to describe the uncertainty of prediction errors. First, WT and PCA are jointly used to smooth the original time series, then the point prediction model for subsequence data based on LSTM network is proposed. It is worth pointing out that the input matrix of the model includes many features, such as wind power and wind speed, which will be helpful for improving prediction performance. After optimizing the index of the ultra short‐term probability prediction interval (PI) of wind power by particle swarm optimization (PSO), the conditional normal distribution model of prediction errors is developed. Thus, the ultra short‐term PIs for wind power are obtained. Finally, based on the data of two wind farms in China, simulation results are provided to illustrate the usefulness of the proposed prediction model. It follows from those results that the proposed method can improve the accuracy of prediction, and the reliability of probability prediction for wind power is also improved.     

Windstorm risk assessment for offshore wind farms in the North Sea

The North Sea is becoming increasingly attractive to wind energy developers and investors, with 38 wind farms belonging to five different countries and representing over€35 billion of assets. Concerns about offshore wind turbines being damaged by extreme windstorms pose a challenge to insurers, investors and regulators. Catastrophe modeling can adequately quantify the risk. In this study, a Monte Carlo simulation approach is used to assess the number of turbines that buckle using maximum wind speeds reaching each wind farm. Damage assessment is undertaken for each wind farm using a log‐logistic damage function and a left‐truncated Weibull distribution. The risk to offshore wind power in the North Sea is calculated using an exceedance probability (EP) curve for the portfolio of wind farms. The European Union Solvency II directive requires insurance companies to hold sufficient capital to guard against insolvency. The solvency capital requirement (SCR) is based on a value‐at‐risk measure calibrated to a 99.5% confidence level over a 1‐year time horizon. The SCR is estimated at €0.049 billion in the case of yawing turbines. Simulations are repeated for different climate change scenarios. If wind speeds grow by 5% and the frequency of storms increases by 40%, the SCR is seen to rise substantially to €0.264 billion. Relative to the total value of assets, the SCR is 0.14% compared with 0.08% for European property, confirming that these wind farm assets represent a relatively high risk. Furthermore, climate change could increase the relative SCR to levels as high as 0.75%.     

Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties

Increasing penetration of wind power in power systems causes difficulties in system planning due to the uncertainty and non dispatchability of the wind power. The important issue, in addition to uncertain nature of the wind speed, is that the wind speeds in neighbor locations are not independent and are in contrast, highly correlated. For accurate planning, it is necessary to consider this correlation in optimization planning of the power system. With respect to this point, this paper presents a probabilistic multi-objective optimal power flow (MO-OPF) considering the correlation in wind speed and the load. This paper utilizes a point estimate method (PEM) which uses Nataf transformation. In reality, the joint probability density function (PDF) of wind speed related to different places is not available but marginal PDF and the correlation matrix is available in most cases, which satisfy the service condition of Nataf transformation. In this paper biogeography based optimization (BBO) algorithm, which is a powerful optimization algorithm in solving problems including both continuous and discrete variables, is utilized in order to solve probabilistic MO-OPF problem. In order to demonstrate performance of the method, IEEE 30-bus standard test case with integration of two wind farms is examined. Then the obtained results are compared with the Monte Carlo simulation (MCS) results. The comparison indicates high accuracy of the proposed method.     

Comparative analysis of methods for modelling the short‐term probability distribution of extreme wind turbine loads

We have tested the performance of statistical extrapolation methods in predicting the extreme response of a multi‐megawatt wind turbine generator. We have applied the peaks‐over‐threshold, block maxima and average conditional exceedance rates (ACER) methods for peaks extraction, combined with four extrapolation techniques: the Weibull, Gumbel and Pareto distributions and a double‐exponential asymptotic extreme value function based on the ACER method. For the successful implementation of a fully automated extrapolation process, we have developed a procedure for automatic identification of tail threshold levels, based on the assumption that the response tail is asymptotically Gumbel distributed. Example analyses were carried out, aimed at comparing the different methods, analysing the statistical uncertainties and identifying the factors, which are critical to the accuracy and reliability of the extrapolation. The present paper describes the modelling procedures and makes a comparison of extrapolation methods based on the results from the example calculations. Copyright © 2015 John Wiley & Sons, Ltd.     

Response load extrapolation for wind turbines during operation based on average conditional exceedance rates

The paper explores a recently developed method for statistical response load (load effect) extrapolation for application to extreme response of wind turbines during operation. The extrapolation method is based on average conditional exceedance rates and is in the present implementation restricted to cases where the Gumbel distribution is the appropriate asymptotic extreme value distribution. However, two extra parameters are introduced by which a more general and flexible class of extreme value distributions is obtained with the Gumbel distribution as a subclass. The general method is implemented within a hierarchical model where the variables that influence the loading are divided into ergodic variables and time‐invariant non‐ergodic variables. The presented method for statistical response load extrapolation was compared with the existing methods based on peak extrapolation for the blade out‐of‐plane bending moment and the tower mudline bending moment of a pitch‐controlled wind turbine. In general, the results show that the method based on average conditional exceedance rates predicts the extrapolated characteristic response loads at the individual mean wind speeds well and results in more consistent estimates than the methods based on peak extrapolation. Copyright © 2011 John Wiley & Sons, Ltd.     

A new probabilistic method to estimate the long-term wind speed characteristics at a potential wind energy conversion site

This paper proposes the use of a new Measure-Correlate-Predict (MCP) method to estimate the long-term wind speed characteristics at a potential wind energy conversion site. The proposed method uses the probability density function of the wind speed at a candidate site conditioned to the wind speed at a reference site. Contingency-type bivariate distributions with specified marginal distributions are used for this purpose. The proposed model was applied in this paper to wind speeds recorded at six weather stations located in the Canary Islands (Spain). The conclusion reached is that the method presented in this paper, in the majority of cases, provides better results than those obtained with other MCP methods used for purposes of comparison. The metrics employed in the analysis were the coefficient of determination (R²) and the root relative squared error (RRSE). The characteristics that were analysed were the capacity of the model to estimate the long-term wind speed probability distribution function, the long-term wind power density probability distribution function and the long-term wind turbine power output probability distribution function at the candidate site.     

High‐throughput computation and the applicability of Monte Carlo integration in fatigue load estimation of floating offshore wind turbines

Long‐term fatigue loads for floating offshore wind turbines are hard to estimate because they require the evaluation of the integral of a highly nonlinear function over a wide variety of wind and wave conditions. Current design standards involve scanning over a uniform rectangular grid of metocean inputs (e.g., wind speed and direction and wave height and period), which becomes intractable in high dimensions as the number of required evaluations grows exponentially with dimension. Monte Carlo integration offers a potentially efficient alternative because it has theoretical convergence proportional to the inverse of the square root of the number of samples, which is independent of dimension. In this paper, we first report on the integration of the aeroelastic code FAST into NREL's systems engineering tool, WISDEM, and the development of a high‐throughput pipeline capable of sampling from arbitrary distributions, running FAST on a large scale, and postprocessing the results into estimates of fatigue loads. Second, we use this tool to run a variety of studies aimed at comparing grid‐based and Monte Carlo‐based approaches with calculating long‐term fatigue loads. We observe that for more than a few dimensions, the Monte Carlo approach can represent a large improvement in computational efficiency, but that as nonlinearity increases, the effectiveness of Monte Carlo is correspondingly reduced. The present work sets the stage for future research focusing on using advanced statistical methods for analysis of wind turbine fatigue as well as extreme loads. Copyright © 2015 John Wiley & Sons, Ltd.     

Environmental contours for circular‐linear variables based on the direct sampling method

Environmental contours are often used in the design of engineering structures to identify extreme environmental conditions that may give rise to extreme loads and responses. The perhaps most common application of environmental contours is for wave climate variables such as significant wave height and wave period. However, for the design of wind energy installations, the joint distribution of wind speed and wind direction may be equally important. In this case, joint modelling of linear (wind speed) and circular (wind direction) variables are needed, and methods for establishing environmental contours for circular‐linear variables will be required. In this paper, different ways of establishing environmental contours for circular‐linear variables will be presented and applied to a joint distribution model for wind speed and wind direction. In particular, the direct sampling approach to environmental contours will be modified to the case where one of the variables is cyclic. In addition, contours based on exceedance planes in polar coordinates will be established, and circular‐linear contours will also be calculated based on the inverse FORM (I‐FORM) approach.     

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.     

An analysis of wind power density derived from several wind speed density functions: The regional assessment on wind power in Malaysia

In wind turbine design and site planning, the probability distribution of wind speed becomes critically important in estimating energy production. The utilization of accurate distribution will minimize the uncertainty in wind resource estimates, and consequently, it will improve the result in the site assessment phase of planning. In general, different region will have different wind regime. Hence, it is reasonable that different wind speed distribution will be found for different region. In this study, the features of wind power density based on the dependency of the suitable wind speed density have been obtained analytically using transformation technique. Since the wind power density has been obtained, the mean power density which is referred as an important indices related to the estimation of potential wind energy have been obtained by using the concept of raw moment and Monte Carlo approach. An analysis of semivariogram indicates the lack of spatial correlation of the wind power in Malaysia. The map of the mean power density over Malaysia indicates that several regions such as northeast, northwest and southeast region of Peninsular Malaysia and southern region of Sabah are found as the best region to be further investigated in the future for the wind energy development.     

Estimating future balancing power requirements in wind–PV power system

This paper presents a general model—based on the Monte Carlo simulation—for the estimation of power system uncertainties and associated reserve and balancing power requirements. The proposed model comprises wind, PV and load uncertainty, together with wind and PV production simulation. In the first stage of the model, wind speed and solar irradiation are simulated, based on the plant disposition and relevant data. The second stage of the model consists of wind speed, PV power and load forecast error simulation, based on the associated statistical parameters. Finally, both wind and PV forecast error are combined with the load forecast error, resulting in the net uncertainty. This net uncertainty, aggregated on a yearly level, presents a dominant component in balancing power requirements. Proposed model presents an efficient solution in planning phase when the actual data on wind and PV production is unavailable.     

Uncertainty of power curve measurement with a two‐beam nacelle‐mounted lidar

Nacelle lidars are attractive for offshore measurements since they can provide measurements of the free wind speed in front of the turbine rotor without erecting a met mast, which significantly reduces the cost of the measurements. Nacelle‐mounted pulsed lidars with two lines of sight (LOS) have already been demonstrated to be suitable for use in power performance measurements. To be considered as a professional tool, however, power curve measurements performed using these instruments require traceable calibrated measurements and the quantification of the wind speed measurement uncertainty. Here we present and demonstrate a procedure fulfilling these needs. A nacelle lidar went through a comprehensive calibration procedure. This calibration took place in two stages. First with the lidar on the ground, the tilt and roll readings of the inclinometers in the nacelle lidar were calibrated. Then the lidar was installed on a 9m high platform in order to calibrate the wind speed measurement. The lidar's radial wind speed measurement along each LOS was compared with the wind speed measured by a calibrated cup anemometer, projected along the LOS direction. The various sources of uncertainty in the lidar wind speed measurement have been thoroughly determined: uncertainty of the reference anemometer, the horizontal and vertical positioning of the beam, the lack of homogeneity of the flow within the probe volume, lidar measurement mean deviation and standard uncertainty. The resulting uncertainty lies between 1 and 2% for the wind speed range between cut‐in and rated wind speed. Finally, the lidar was mounted on the nacelle of a wind turbine in order to perform a power curve measurement. The wind speed was simultaneously measured with a mast‐top mounted cup anemometer placed two rotor diameters upwind of the turbine. The wind speed uncertainty related to the lidar tilting was calculated based on the tilt angle uncertainty derived from the inclinometer calibration and the deviation of the measurement height from hub height. The resulting combined uncertainty in the power curve using the nacelle lidar was less than 10% larger on average than that obtained with the mast mounted cup anemometer. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical wind direction modeling for the analysis of large scale wind power generation

Understanding the effects of large‐scale wind power generation on the electric power system is growing in importance as the amount of installed generation increases. In addition to wind speed, the direction of the wind is important when considering wind farms, as the aggregate generation of the farm depends on the direction of the wind. This paper introduces the wrapped Gaussian vector autoregressive process for the statistical modeling of wind directions in multiple locations. The model is estimated using measured wind direction data from Finland. The presented methodology can be used to model new locations without wind direction measurements. This capability is tested with two locations that were left out of the estimation procedure. Through long‐term Monte Carlo simulations, the methodology is used to analyze two large‐scale wind power scenarios with different geographical distributions of installed generation. Wind generation data are simulated for each wind farm using wind direction and wind speed simulations and technical wind farm information. It is shown that, compared with only using wind speed data in simulations, the inclusion of simulated wind directions enables a more detailed analysis of the aggregate wind generation probability distribution. Copyright © 2016 John Wiley & Sons, Ltd.     

On the tails of the wind ramp distributions

We analyzed several multiyear wind speed datasets from 4 different geographical locations. The probability density functions of wind ramps from all these sites revealed remarkably similar shapes. The tails of the probability density functions are much heavier than a Gaussian distribution, and they also systematically depend on time increments. Quite interestingly, from a purely statistical standpoint, the characteristics of the extreme ramp‐up and ramp‐down events are found to be almost identical. With the aid of extreme value theory, we describe several other inherent features of extreme wind ramps in this paper.     

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.     

风电场50年一遇安全风速计算方法的对比分析

利用耿贝尔Ⅰ型极值概率法和MeteodynWT软件(CFD模型),结合气象站与风电场的风速关系,推算了不同复杂程度的风电场轮毂高度处50年一遇的安全风速,并将计算结果进行对比分析。分析结果显示:2种方法计算得到的风电场极大风速存在一定的差别;对于平坦地区,耿贝尔Ⅰ型极值概率法计算得到的极大风速与MeteodynWT推算结果相差较小,但对于一些复杂地区,2种方法计算得到的极大风速结果相差很大。     

Avoided demand charges and behind‐the‐meter wind: insights from an application at the University of Minnesota

One common ownership structure for community‐scale wind development in the USA is a behind‐the‐meter installation. In addition to allowing the displacement of retail energy, such installations may also affect peak demand, which is frequently an important component of electricity tariffs (via ‘capacity’ or ‘demand’ charges). This paper uses Monte Carlo simulation techniques on original wind and load data for the University of Minnesota at Morris in order to estimate the savings associated with lower peak demand, as a result of the installation of a 1.65‐MW turbine in 2005. Results represent the first (to our knowledge) quantitative effort to estimate this aspect of the economics of wind power projects, and they suggest these previously ignored savings comprise nearly 10% of this project's gross projected revenue stream, even though the local utility's demand charge in this case is only 63% of the industry average. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of impact of grid‐connected wind power on small signal stability

The power system small signal stability analysis considering wind generation intermittence is studied comprehensively in this paper. The modelling of doubly‐fed induction generator (DFIG) involving the converters with application of stator flux‐oriented vector control strategy is addressed briefly. In order to reveal how the intermittent nature of wind power affects the operating behaviour of an existing power system, a probabilistic small signal stability analysis method based on Monte Carlo simulation technique is proposed to explore and exploit the impact of intermittent grid‐connected wind power on small signal stability. The IEEE New England test system is applied as benchmark to verify the proposed model and approach. Total 3 scenarios are elaborately designed to figure out the potential relationship between the small signal stability indices and the wind generation intermittence. Finally, some preliminary conclusions and comments were drawn based on the numerical simulation results. Copyright © 2010 John Wiley & Sons, Ltd.     

考虑多参数影响的风电场多状态出力概率性评估

大规模风电并网会对电力系统的可靠性带来严峻挑战,其出力的随机性也会对电力系统可靠性评估带来难题。为了准确地对风电场出力进行评估,结合风速的随机性,考虑了风电机组的故障、降额和随机投产状态以及风速分布的威布尔参数对风电场出力的影响,建立了风电场多状态出力的可靠性模型;基于蒙特卡洛法对风电场的有功出力进行了概率性评估,并分析了不同状态数、不同降额概率、故障停运概率、随机投产率及不同的风速分布威布尔尺度参数和形状参数等对评估结果的影响。仿真结果表明,所建模型切实可行,能有效地对风电场出力进行评估。     

The analytical Monte Carlo method for approximating thedistribution of a plant's electrical generation

A method for approximating the distribution of a plant's generation (and, therefore, of its fuel burn) as a function of both uncertainty in load forecasts and the plant's performance. The method is applicable to all-thermal systems. The moments of the distribution of the plant's generation are estimated by combining the statistical method of the generation of system moments with probabilistic production costing in a way that analytically models a Monte Carlo process. The resulting algorithm, referred to as the analytical Monte Carlo method, is evaluated by comparing its estimates of the moments of each plant's generation with that obtained using a Monte Carlo model. Results indicate that the method yields practical estimates for evaluating uncertainty that can be used in long-term studies