Statistical bivariate modelling of wind using first-order Markov chain and Weibull distribution

Ettoumi, Fatiha Youcef; Sauvageot, Henri; Adane, A.

doi:10.1016/s0960-1481(03)00019-3

Cited by 92 publications

(52 citation statements)

References 17 publications

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“…In [18], Youcef Ettoumi et al report various statistical features of the wind in Oran (Algeria). Three-hourly wind data were modeled using Markov chains; first-order nine-state Markov chains were found to adequately match the wind direction data, whereas first-order three-state Markov chains were found to adequately match the wind speed data.…”

Section: Wind Speed Probabilistic Modelmentioning

confidence: 99%

Probabilistic analysis of weather data for a hybrid solar/wind energy system

Tina

Gagliano

2011

Int. J. Energy Res.

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SUMMARYIn this paper, a procedure for the probabilistic treatment of solar irradiance and wind speed data is reported as a method of evaluating, at a given site, the electric energy generated by both a photovoltaic system and a wind system. The aim of the proposed approach is twofold: first, to check if the real probability distribution functions (PDFs) of both clearness index and wind speed overlap with Hollands and Huget and Weibull PDFs, respectively; and then to find the parameters of these two distributions that best fit the real data. Further, using goodness-of-fit tests, these PDFs are compared with another set of very common PDFs, namely the Gordon and Reddy and Lognormal functions, respectively.The results inform the design of a pre-processing stage for the input of an algorithm that probabilistically optimizes the design of hybrid solar wind power systems. In this paper, the validity of the proposed procedure was tested using long-term meteorological data from Acireale (Italy).

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Section: Wind Speed Probabilistic Modelmentioning

confidence: 99%

Probabilistic analysis of weather data for a hybrid solar/wind energy system

Tina

Gagliano

2011

Int. J. Energy Res.

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“…Evolutionary algorithms such as genetic algorithm and local search technique are also used in wind speed modelling [21] despite their time consuming procedure [4]. The Markov chain model, which retains chronology and consumes less time, could, therefore, be employed to synthesise wind speed time series for dynamic simulation and wind power forecasting [10,[22][23][24]. The accuracy of a Markov model increases…”

Section: Introductionmentioning

confidence: 99%

“…Much attention is curwith its order [22]. The first-order model is often adopted for its simplicity and economic computing time [24]. A modified Markov model may show better performances than the corresponding normal model in preserving the properties of wind speed series [25].…”

Section: Introductionmentioning

confidence: 99%

Characterisation of wind speed series and power in Durban

Legesse¹,

Saha²,

Carpanen³

2017

J. energy South. Afr.

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Both the planning and operating of a wind farm demand an appropriate wind speed model of its location. The model also helps predict the dynamic behaviour of wind turbines and wind power potential in the location. This study characterises the wind speed series and power in Durban (29.9560°S, 30.9730°E) IntroductionDepletion of fossil fuel reserves, global warming, security concerns, and rising commodity prices are pushing the world to go green. Much attention is currently given to the development of renewable energy, among which harnessing wind energy is the cheapest alternative [1][2][3]. Feasibility studies related to wind power require an appropriate wind speed model of a site [4,5]. These models are also important in planning and operating wind turbines. Hence, the wind speeds of a specified site should be appropriately characterised to determine wind energy potential and attain comprehensive results in the investigations of the dynamics of the wind turbines [4,6,7]. Moreover, a good characterisation of wind speed helps transmission system operators in scheduling their power dispatch [4]. Wind is a random stochastic process whose dynamic behaviour can be represented by a stochastic model [8]. Naturally, it depends on pressure gradient, waves, jet streams, and local weather conditions [9]. Its stochastic modelling is a complicated task because of its strong variability in time and land terrains. Over a year, wind speed is periodic, showing seasonal variations; however, hourly average wind speed is a stochastic process with a Weibull probability density function; whereas within minutes, it follows a Gaussian distribution [10].Different methods have been employed for time series characterisation of wind processes. Traditionally Weibull distribution is widely used to represent wind speed series at a given site [4,[11][12][13]. Normal, Gamma, Lognormal or combination of these distributions with Weibull distribution [4,7,[14][15][16], empirical wavelet [17] or Kernel density method [18] can also be used to model wind speed series. Shokrzadeh et al. [19] and Kazemi and Goudarzi [20] employed advanced parametric and nonparametric and least square approximation methods to forecast wind power. A typical distribution may not necessarily represent the cumulative wind behaviour of all locations in a region [7]. Thus, the wind speed for a particular location needs to be modelled. The above distributions cannot be used, however, when chronology is considered [4]. A rough observation on the raw wind speed data from Durban demonstrated that the current wind speed depended on the previous wind speed, indicating that chronology should be considered in modelling the wind speeds. Evolutionary algorithms such as genetic algorithm and local search technique are also used in wind speed modelling [21] despite their time consuming procedure [4]. The Markov chain model, which retains chronology and consumes less time, could, therefore, be employed to synthesise wind speed time series for dynamic simulation and wind power f...

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“…First-and second-order Markov chains have been used to model wind speed or the wind vector [27][28][29]. Birth and death Markov chain models have been tested [30].…”

Section: Introductionmentioning

confidence: 99%

“…Most models focus primarily on simulating wind speed or wind power for one temporal sampling frequency, with a few exceptions that model the wind vector [29,32,35]. Some more advanced approaches that use Markov-switching autoregressive [36] or vector autoregressive models have been proposed [20] with the underlying assumption that many locations tend to observe one of a few prevailing wind regimes, and characteristics within these regimes may differ dramatically [37,38].…”

Section: Introductionmentioning

confidence: 99%

A Markov-Switching Vector Autoregressive Stochastic Wind Generator for Multiple Spatial and Temporal Scales

2015

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Despite recent efforts to record wind at finer spatial and temporal scales, stochastic realizations of wind are still important for many purposes and particularly for wind energy grid integration and reliability studies. Most instances of wind generation in the literature focus on simulating only wind speed, or power, or only the wind vector at a particular location and sampling frequency. In this work, we introduce a Markov-switching vector autoregressive (MSVAR) model, and we demonstrate its flexibility in simulating wind vectors for 10-min, hourly and daily time series and for individual, locally-averaged and regionally-averaged time series. In addition, we demonstrate how the model can be used to simulate wind vectors at multiple locations simultaneously for an hourly time step. The parameter estimation and simulation algorithm are presented along with a validation of the important statistical properties of each simulation scenario. We find the MSVAR to be very flexible in characterizing a wide range of properties in the wind vector, and we conclude with a discussion of extensions of this model and modeling choices that may be investigated for further improvements.

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Statistical bivariate modelling of wind using first-order Markov chain and Weibull distribution

Cited by 92 publications

References 17 publications

Probabilistic analysis of weather data for a hybrid solar/wind energy system

Probabilistic analysis of weather data for a hybrid solar/wind energy system

Characterisation of wind speed series and power in Durban

A Markov-Switching Vector Autoregressive Stochastic Wind Generator for Multiple Spatial and Temporal Scales

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