An Initial Review: Stochastic Application in Wind Speed Forecasting
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1 An Initial Review: Stochastic Application in Wind Speed Forecasting NORTAZI SANUSI 1,2, AZAMI ZAHARIM 1, KAMARUZZAMAN SOPIAN 1 1 Solar Energy Research Institute UniversitiKebangsaan Malaysia Bangi, Selangor MALAYSIA 2 Department of Structure and Materials, Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal, Melaka MALAYSIA nortazi@utem.edu.my,azami@eng.ukm.my, ksopian@vlsi.eng.ukm.my Abstract:- Wind energy is a commonly investigated renewable energy which is clean and easy to generate using unlimited sources. There are several parameters related to wind energy but wind speed is the most frequently researched parameter.this paper is concerned with the various stochastic approaches in forecasting real wind speed and generating synthetic data on wind speed. Several models have been reviewed and the significance of each is considered in this paper. The idea of this paper is limited to wind speed application and does not discuss wind direction and energy output. The discussion in this paper is based on one study in Malaysia and another 12 from abroad. Key-Words:Wind speed, stochastic process, stochastic model 1 Introduction Issues on natural energy sources have been debated not only in Malaysia but throughout the world. The high demand with decreasing and limited energy sources make this issues worst from year to year. Renewable energy sources such as solar, wind, thermal and wave are promising cleaner, safer output and the most important is there are unlimited sources. Wind energy is a kinetic energy produced by air movement. Itis an indirect form of solar energy and meteorologists estimate that about 1% of the incident solar radiation is converted into wind energy which is a very competitive source of energy for many applicationsin many locations [1]. With the use of air turbine, this kinetic energy will transform to mechanical and electrical energy. There are tremendous studies of wind and its potential in generating energy. Most of them are focusing on deterministic point of view compared to stochastic. This paper reviews the prior researches that have been applied stochastic as their tools. The findings for this paper will be beneficial in order to implement the stochastic application in the case of Malaysia wind studies. 2 Stochastic Processes Stochastic process has been important component in the world of energy system especially in forecasting and generating synthetic data. Other than it application in wind energy, stochastic process has also being applied in other environmental data. E.Silverman et al.[2] has used stochastic process which is Monte Carlo for modelling the dynamics of waterfowl aggregation. While N.Sharma [3]discussed the used of stochastic techniques for optimization in solar system. The significance of using stochastic process is driven by the random or the chance processes that involve in environmental data. Some of common process that involve with stochastic are Poisson, Markov process, Renewal process and Stationary process. This section will discussedthe theoretical part of Markov process as it ISBN:
2 is the most chosen by researchers in the field of wind energy. 2.1 Markov Chain Markov Chain is a stochastic process of which that (1) for all states and all. The value represents the probability that the process will, when in state i, next make a transition into state j. The probability is then can be represented in a transition probability matrix P; where,, P= Actually the above explanation is on Discrete- Time Markov Chains that usually being applied in a random walk model, gambling model and forecasting the weather. Another type Markov Chains is Continuous-Time Markov Chains. The process { is a continuous-time Markov chain if for all and nonnegative integers observation of the time series can be represented as a linear function (3) Define a backward shift operator B as follows: (4) Extending this operation, it can be written as (5) Using the operator B, (3) can be written as (6) An important special case of the general model is the autoregressive (AR) model. Let be represented as follows, based on the previous p observations and a random component: (7) Equation (7) is an AR model of order p [AR(p)]. Iterating successively of this equation, for can derive the infinite series in, k= -1,0,1,2,,n as (8) showing that the AR model is in fact a special case of the general model (6). Another important special case of general linear filter model (6) is the moving average (MA) process. Consider the representation (9) (2) Continuous-Time Markov Chains has wider variety of applications in the real world compare to the discrete type as for example is Birth and Death Process [4]. 2.2 Stochastic Model The stochastic models that being used in wind energy application are always considered as the stochastic models for time series. Suppose the This is a moving process of order q [MA(q)]. If an MA operator is defined this model can be put in the compact form (10) (11) Combining the AR(p) and MA(q) processes, one gets mixed autoregressive-moving average [ARMA(p,q)] models. Thus combining (8) and (11), we write ISBN:
3 or in detail, (12) In order to exhibit nonstationary properties in process, a generalized autoregressive operator which incorporates a stationary operator as well as a stationary operator in the form may be introduced. A model corresponding to (12) may now be written as where (13), d=0,1,2. (14) This model is known as the autoregressive integrated moving average process of order (p,d,q) [ARIMA(p,d,q)] [5]. 3 Stochastic in Wind SpeedForecasting Studies on wind energy parameters such as wind speed, wind direction and wind power has leads to the development of forecasting model of the energy output. Among all, wind speed becomes the most common parameter studied by researchers. F.Casteno et al.[6] used Markov Chain process in his study and came out with two models of 2 nd order Discrete Auto Regressive, DAR (2) and a model on Markov Chain. The first model was developed to describe intra-channel dynamics of wind direction while the second one was to describe intra-channel dynamics of wind speed. Another model that based on Markov Chain was used to determine interchannel transition. All the analysis was done by using a set of data consisted of 42 years (1951 to 1992) recorded at 10metre above ground level located near Brindisi Airport, Italy. H.NFaoui et al.[7]used 12 years data of wind speed, collected at Tangiers International Airport for the period of January 1978 to December 1989 in order to show the effect of the duration of data on the order of autoregressive AR (p) and moving average process ARMA (p,q) and its ability to simulate the hourly average wind speed, HAWS. As the direct application of stochastic model on HAWS is not possible due to non-gaussian distribution, the data is transformed to make it approximately Gaussian and then standardized to remove diurnal nonstationarity.it showed that AR (2) was capable to simulate HAWS and it could be used to generate reference monthly data. A. D. Sahin and Z. Sen[8] proposed the First Order Markov Chain model in their study for the synthetic wind speed generation. The generated wind speed data is then compared with the actual wind speed value in order to assess the suitability of the proposed model. The comparison are based on the corresponding measured and generated parameters values It shows that First Order Markov Chain model is sufficient to preserve most of the parameters values. However the Second Order Markov Chain model will improve the correspondence of the parameters better than the first order. Then H.NFaouiet al.[9] applied a Markovian process by using the same data set as the previous research which is HAWS. The Markovian model is expected to generate a synthetic wind speed time series, which can be used for numerical simulation of any wind system. The developed model is then undergoing a complete validation to make sure the acceptance of it. Seven parameters which allow a quantification between the simulated wind and the observed one that being investigate are mean, variance, transition probability matrix, probability density, energy spectral density, auto correlation function and persistence probability. It was found that a 12 x 12 transition probability matrix was necessary to generate an acceptable synthetic time series. By using this transition probability matrix developed from the observed wind data, the synthetic wind speed time series are generated. The literature is then followed by H.Kantz et al.[10]which introduced a method for stochastic modelling and prediction of arbitrary nonlinear nonstationary stochastic processes with finite memory. This proposed method used to predict the turbulent surface of wind velocity which mainly to solve problem in electricity power generation by wind energy turbines. The approximate stochastic dynamics by a continuous state of Markov Chain with order m is then being discussed and selected for representing the stochastic modelling of wind speed data. The danger of turbulent wind gusts is ISBN:
4 also discussed in this paper and predicting probabilities is identified to make a meaningful forecast of turbulent gusts. Ironically, H.Aksoy et al.[11] did not used stochastic method to model wind speed but used it to compare with his findings. A newly developed wavelet approach was introduced. There are many functions that can qualify as wavelet such as Morlet, Mexican Hat and Shannon and Meyer. In this study, Haar wavelet was used due to its simplicity. The findings from wavelet approach is then being compared with the traditional approach which are Normal and Weilbull Distribution, Autoregressive AR(1) and AR(2) and Markov Chain. It is found that wavelet method is proposed as the best substitute tool for the traditional scheme generation of hourly mean wind speed data. Shamsad A. et al.[12]used first and second order of transition probability matrix of Markov Chain for modelling and data simulation in their study. Then the synthetically generated wind speed data was compared with the observed data. Basically the comparison based on several statistical properties such as mean, standard deviation, median, percentiles, Weilbull distribution parameters and the autocorrelations. The study revealed that the second order of Markov Chain model has improved the autocorrelation AR of synthetic generated wind speed data, as expected. S.Bivona et al.[13]believed that stochastic model is the best model for time series in order to achieve optimal forecasting and control. But, it is difficult and challengingto choose a proper model. Several proposed stochastic models for wind speed time series have been discussed involving ARMA, ARFIMA, ARIMA and SARIMA. In this study, ARFIMA clash with their modelling performance. So, it can be concluded that the effectiveness of ARFIMA as forecasting tool can still be argued and questioned. In different study, S.Bivona et al.[14]proposed a SARIMA class of models with class s=24 hour for forecasting wind speed. In order to select the most appropriate model, a model selection criterion which is biased-corrected, Akaike s Information Criterion (AIC) is introduced. Then, the accuracy of selected model is assessed using Ljung-Box-Pierce (L-B-P) statistics by analysing and testing their residuals. The chosen model is compared with those provided by suitable artificial neural network (ANN). In order to assess the out of sample forecasting performance of the model, four different indicators of accuracy were used which are Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Scaled Error (MASE) and Mean Absolute Percentage Error (MAPE). PourmousaviKani and M. M. Ardehali[15] developed a new ANN-MC model involving artificial neural network (ANN) and Markov Chain (MC) approach for forecasting wind speed in very short time scale (about minutes or seconds). In this study, the very short term wind speed pattern is captured by ANN while for the short term is done by MC and four neighbourhood indices. For prediction of very short term wind speed in a few second in the future, data patterns for short term (about an hour) and very short term (about minutes or seconds) are recorded. Transition probability matrix (TPM) is calculated for Markov Chain while two ANNs has been analysed in order to develop the best model. The proposed model shows that it has reduce the uncertainty of prediction as well as the prediction errors MAPE, MAE and other. The common problem for ANN in prediction which is over training and extrapolation has also been avoided by this model. 4 Conclusion This paper compares the relevance studies on wind speed and also environmental data that implement stochastic process and model in their researches. Study on wind direction and the combination of both is still far behind. As for the stochastic process, most of researchers used Markov Chain as their choice except [15] that used the combination of Markov Chain and Artificial Neural Network. The comparison of various time series models on mean hourly wind speed data indicated that second order Markov Chain is better than the first order. While as for AR(p), ARMA (p,q) and ARIMA (p,d,q) explained the data well compared to others. The continuous studies on wind energy especially with combine wind speed and wind direction will gives a great innovation in the field of renewable energy and would be beneficial to the energy output forecasting. References: [1] A. Lashin and A. Shata, An analysis of wind power potential in Port Said, Egypt, Renewable and Sustainable Energy Reviews, Vol. 16, No. 9, Dec. 2012, pp [2] E. Silverman, M. Kot, and E. Thompson, Testing a simple stochastic model for the dynamics of waterfowl ISBN:
5 aggregations,oecologia, Vol. 128, No. 4, Aug. 2001, pp [3] N. Sharma, Stochastic techniques used for optimization in solar systems: A review,renewable and Sustainable Energy Reviews, Vol. 16, No. 3, Apr. 2012, pp [4] M. R. Sheldon, Introduction to Probability Models, 9th editio. Academic Press, 2007, pp [5] U. N. Bhat and G. K.Miller, Elements of Applied Stochastic Processes, Third edit. John Wiley & Sons,Inc, 2002, pp [6] F. Castino, R. Festa, and C. Ratto, Stochastic modelling of wind velocities time series,journal of Wind Engineering and Industrial Aerodynamics, Vol , Apr. 1998, pp [7] H. Nfaoui, J. Buret, and A. A. M. Sayigh, Stochastic Simulation of Hourly Average Wind Speed, Solar Energy, Vol. 56, No. 3, 1996, pp [8] A. D. Sahin and Z. Sen, First-order Markov chain approach to wind speed modelling,journal of Wind Engineering and Industrial Aerodynamics, Vol. 89, No. 3 4,Mar. 2001, pp [9] H. Nfaoui, H. Essiarab, and a. a. M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco,Renewable Energy, Vol. 29, No. 8, Jul. 2004, pp [10] H. Kantz, D. Holstein, M. Ragwitz, and N. K. Vitanov, Markov chain model for turbulent wind speed data, Physica A: Statistical Mechanics and its Applications, Vol. 342, No. 1 2, Oct. 2004, pp [11] H. Aksoy, Z. Fuat Toprak, A. Aytek, and N. Erdem Ünal, Stochastic generation of hourly mean wind speed data,renewable Energy, Vol. 29, No. 14, Nov. 2004, pp [12] A Shamshad, M. Bawadi, W. Wanhussin, T. Majid, and S. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy, Vol. 30, No. 5, Apr. 2005, pp [13] S. Bivona, G. Bonanno, R. Burlon, D. Gurrera, and C. Leone, Stochastic Models for Wind Speed Time Series: A Case Study, Vol. 41, No. 5, 2010, pp [14] S. Bivona, G. Bonanno, R. Burlon, D. Gurrera, and C. Leone, Stochastic models for wind speed forecasting,energy Conversion and Management, Vol. 52, No. 2, Feb. 2011, pp [15] S. A. Pourmousavi Kani and M. M. Ardehali, Very short-term wind speed prediction: A new artificial neural network Markov chain model,energy Conversion and Management, Vol. 52, No. 1,Jan. 2011, pp ISBN:
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