J Electr Eng Technol.2016; 11(?): 0-000 http://dx.doi.org/10.5370/JEET.2016.11.3.0

0Copyright ⓒ The Korean Institute of Electrical Engineers

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Hourly Average Wind Speed Simulation and Forecast Based on ARMA Model in Jeju Island, Korea

Duy-Phuong N. Do*, Yeonchan Lee** and Jaeseok Choi†

Abstract – This paper presents an application of time series analysis in hourly wind speed simulation and forecast in Jeju Island, Korea. Autoregressive – moving average (ARMA) model, which is well in description of random data characteristics, is used to analyze historical wind speed data (from year of 2010 to 2012). The ARMA model requires stationary variables of data is satisfied by power law transformation and standardization. In this study, the autocorrelation analysis, Bayesian information criterion and general least squares algorithm is implemented to identify and estimate parameters of wind speed model. The ARMA (2,1) models, fitted to the wind speed data, simulate reference year and forecast hourly wind speed in Jeju Island.

Keywords: Autoregressive moving average processes, Autoregressive processes, Autocorrelation function, Time series model, Wind energy, Wind speed forecast, Wind speed simulation

1. Introduction

Nowadays, the penetration of wind power continues to increase in power system, especially in Korea. Wind is considered as an energy credit but it is also fluctuation. It needs to access economic and technological factors. The study of wind power forecast, comprehensive reliability and cost evaluation of the system is the answer. An essential step in the study is to model the wind speed of specific site. The wind speed model is used to reproduce accurately actual wind speed. The analysis of historical wind speed data is to determine the necessary parameters for the model.

Data of hourly average wind speed (HAWS) in a specific location is time series, which has the following basic characteristics. Firstly, it is numeric statistics whose characteristics are illustrated by specific parameters such as probability distribution, mean value, standard deviation. Secondly, the values of time series have a correlation that means the relation of the present time value to past time values. This correlation is reflected by auto-correlation functions (ACF) and partial auto-correlation functions (PACF). Ones of the favorite methods in modeling correlation characteristics of time series is Box-Jenkins methodology or Autoregressive moving average (ARMA) process. The ARMA models can use 3 years of historical HAWS data in Jeju Island and result in accurate short-term forecast of HAWS [11]. There are three classes of ARMA processes. Autoregressive AR(p) process has characteristics that the present time data value is defined by p previous time values and white noise. Moving average

MA(q) process has the present time data value which is defined by a weighted moving average of the noise pulse. And autoregressive moving average ARMA(p, q) process is mixed of the autoregressive and moving average characteristics [2].

Many previous studies had fitted ARMA process to wind speed data. These papers proposed the general approach for modeling wind speed [1] and case study of wind speed statistical models in specific site or multiple sites [3, 4, 6, 10-12]. The wind speed data were almost transformed from Weibull distribution to normal distribution by Dubey method which the shape parameters of data is transformed to 3.6 and the power m for the transformation was specified by measure of distribution symmetry [1], Skewness method [3, 4, 6, 10] or by Box-Cox method which the power λ for the transformation is specified by minimizing the Skewness of the data [8]. However, the transformed data was not checked the strongly stationary [1, 10] or instead of checking the strongly stationary of transformed data, normal distribution is only considered by comparing with corresponding normal probability density [3, 4, 8] or testing non-stationary of transformed data by Duckey-fuller test [9]. These papers assumed that transformed data fitted to a pth order autoregressive process AR(p) [1] or the transformed data fitted to a pth order autoregressive process AR(p) by autocorrelation, partial autocorrelation analysis in identification process but there was no using Bayesian information criterion (BIC) to select an accurate class of ARMA(p,q) [3] or ACF, PACF and BIC were analyzed but the AR(p) was selected too soon after ACF and PACF analysis [8], instead of analyzing ACF, PACF and BIC together or using only AIC [9, 10].

From above analyses, this paper presents ARMA model application to wind speed simulation and forecast in

† Corresponding Author: Dept. of Electrical Engineering, Gyeongsang National University, Korea. (jschoi@gnu.ac.kr)

* Dept. of Electrical Engineering, Gyeongsang National University,Korea. ({dndphuong, kkng1914}@gnu.ac.kr)

Received: June 25, 2015; Accepted: July 28, 2016

ISSN(Print) 1975-0102ISSN(Online) 2093-7423

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Duy-Phuong N. Do, Yeonchan Lee and Jaeseok Choi

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In consideration of checking the validity of the ARMA (2,1) models, the comparison of wind speed simulation and HAWS observation is occurred by autocorrelation functions, frequency distribution and error percentages. Although autocorrelation coefficients of the simulation are slight underestimation but they are no statistical significance for all months (Fig. 6). It is proved that the fitted models generated approximate HAWS observations. Using the fitted ARMA(2,1) model to produce a series of 24 hours x 31 days=744 values of reference month of January. The histogram reveals main characteristics of wind speed simulations and observations in Fig. 7. The frequency distribution of 24 hours x 31 days x 3 years = 2232 observed and 744 simulated values of January is also congruent that means the fit of the ARMA(2,1) model to actual wind speed data is very prospects. By the same way for each month, the fluctuation of average wind speed simulation in given months is presented in Fig. 8. The main characteristics of 3 years of HAWS observation is also reproduced by ARMA(2,1).

Fig. 8. Hourly average wind speed simulation in given

month

The comparison of hourly average wind speed simulations and observations of 24 hours periods of all day in given month and their standard deviations are as in Fig. 9. The simulated wind speed approximately revealed the daily variation characteristic and standard deviation of observed wind speed. It is also considered error of hourly average wind speed of 24 hours periods between the observation and simulation values in given month

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Proofreading

Hourly Average Wind Speed Simulation and Forecast Based on ARMA Model in Jeju Island, Korea

6 │ J Electr Eng Technol.2016; 11(?): 00-00

synthetic sequences are presented in Table 3. From the above analysis and results of Table 2 shows that observation (obs) and simulation (sim) of hourly wind speed are satisfactory. The simulations of generating all months represent the approximate real statistical characteristics of 3 years of HAWS data in Jeju Island, Korea.

5. Ahead of a Day Wind Speed Forecast The simulated ARMA(2,1) model is also used to forecast

hourly average wind speed in Jeju Island by the weighted sum of previous wind speed values [2]. The predicted wind speed is expressed as

π π ⋯ π 22

where π weights are obtained by inverted form of the ARMA(2,1) model

π π 1,2, … , 23

Because the π weights series is declined sharply, the

accuracy of predicted values is sufficient in moderate n previous values. The predicted wind speed with 24 lead time hours 24 is showed in Fig. 10, as example for March 7th, 2015. The wind speed forecast decays exponentially to mean value in long lead time. The error of wind speed forecast 24 is randomly fluctuation in acceptable range, exception of too low and suddenly varied values. Almost actual wind speed is on 95% probability limits of , which is variance of the wind speed forecast errors.

However, the uncorrelated wind speed forecast errors are decayed at longer lead times l. It is need to use ψ weights series for updating the old predicted values at origin time t and lead time l+k by new ones at origin time t+k and lead time l [2]

Fig. 10. The wind speed forecast in March 7th, 2015

ψ k 24

where ψ ψ ψ 1,2, … , and ψ = 1, ψ = 0 for l < 0 and = 0 for l > 1.

In this case, the predicted wind speed is updated in every hour 1 . The updated wind speed forecast sticks to the actual wind speed well (Fig. 10).

6. Conclusion The HAWS data, which is transformed to stationary

variable, is analyzed by Box – Jenkins methodology to build up wind speed models. Many subclass of ARMA(p,q) model is considered by autocorrelation, partial auto-correlation function and BIC criterion analysis to select the fitted models. Finally, in parameters estimating and diagnostic checking stage, ARMA(2,1) models are proposed for all months. The comparison between the observations and the simulations of autocorrelation function, frequency distribution and main statistical characteristics of demonstrates the models are fitted. These ARMA(2,1) models are used to generate reference monthly data which close to the actual statistical characteristics of the 3 year (from 2010 to 2012) time series of wind speed data in Jeju Island. These models are also developed to build up forecast model of wind speed in Jeju Island. In short-term, the wind speed forecast values are acceptable and keep on main characteristics of the models. It is useful tool for studying more in reliability analysis of power system including wind power in Jeju Island, Korea.

Acknowledgements This work was supported by the Korean National Re-

search Foundation (No. #2012R1A2A2A01012803)

References

[1] B. Brown, R. Katz. and A. Murphy, “Times Series Models to Simulate and Forecast Wind Speed and

0%

30%

60%

90%

120%

150%

02468

10

1 3 5 7 9 11 13 15 17 19 21 23

Err

or (%

)

Lead time (h)Vpredicted(24) Vupdated(1) VactualV(+) 95% limit V(-) 95% limit Verror(24)

Table 3. Statistics for Observed (Obs) and Simulated (Sim) HAWS in Jeju Island

Month Mean (m/s) Variance (m/s)2 Sim Obs Error% Sim Obs Error%

Jan 3.44 3.16 8.7% 2.19 2.17 1.1% Feb 2.86 3.09 7.2% 1.99 2.36 15.4%Mar 3.74 3.65 2.6% 2.72 3.06 10.8%Apr 3.70 3.38 9.3% 3.65 3.71 1.7% May 3.10 2.99 3.4% 3.11 3.11 0.2% Jun 2.72 2.72 0.2% 3.03 3.10 2.2% Jul 2.49 2.82 11.8% 2.92 3.15 7.2%

Aug 3.77 3.49 7.9% 5.01 6.59 24.0%Sep 3.34 3.18 5.2% 3.14 3.27 3.8% Oct 3.43 3.14 9.3% 1.77 2.04 13.5%Nov 2.65 3.02 12.2% 1.92 2.35 18.3%Dec 2.96 3.13 5.5% 2.03 2.61 22.2%

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Duy-Phuong N. Do, Yeonchan Lee and Jaeseok Choi

http://www.jeet.or.kr │ 7

Wind Power”, Climate and applied meteorology, vol. 23, 1984

[2] Box P. and Jenkins M., Times Series Analysis, Forecasting and Control, Holden-Day, San Franc, 1976

[3] H. Nfaoui, and M. Sayigh, “Stochastic Simulation of Hourly Wind Speed Sequences in Tangiers”, Solar Energy, vol. 56, no. 3, pp. 301-314, 1996

[4] K. Philippopoulos and D. Deligiorgi, “Statistical Simulation of Wind Speed in Athens, Greece Based on Weibull and ARMA Models” International Journal of Energy and Environment, issue.4, vol. 3, 2009

[5] P. Box, G. Cox, “An Analysis of Transformations”, Jour. Royal Sta. Sco., B26, 211, 1964

[6] R. Karki, P. Hu and R. Billinton, “A simplified wind power generation model for reliability evaluation” IEEE Trans. Energy Conversion, vol. 21, no. 2, 2006.

[7] D. R. Chandra, M. S. Kumari, M. Sydulu, F. Grimaccia and M. Mussetta, “Adaptive wavelet neural network based wind speed forecasting studies” JEET, vol. 9, no. 6, pp. 1812-1821, 2014

[8] Dániel Divényi, János Divényi, “Wind Speed Simul-ator Base on Wind Generation Using Autoregressive Statistical Model”, Electrotehnică, Electronică, Automatică, nr.2, 2012

[9] A. Kamjoo, A. Maheri, and G. Putrus, “Wind speed and solar irradiance variation simulation using ARMA models in design of hydrid wind-PV-battery system”, Journal of clean energy technologies, vol. 1, no. 1, 2013

[10] Lisa M. Bramer, Thesis: Method for modeling and forecasting wind characteristics, Iowa University, 2013

[11] M. Lei, L. Shiyuan, J. Chuanwen, L. Hongling, Z. Yan, “A Review on the Forecasting of Wind Speed And Generated Power”, Renewable and Sustainable Energy Reviews, 2009

Duy-Phuong N.Do He was born in Can Tho city, VietNam in 1982. He received B.S and M.Sc degree in electrical engineering from CanTho University and HoChiMinh University of Technology, respectively. His re-search interest is stability evaluation of power system. Now, he is studying as

Ph.D student in Gyeongsang National University.

Yeonchan Lee He was born in Gosung, Korea in 1987. His research interest includes Transmission Expansion Plan-ning using Reliability Evaluation of Power Systems. He received the B.Sc. degree from Gyeongsang National University in 2013.

Jaeseok Choi He was born in Kyeongju, Korea, in 1958. He received the B.Sc., M.Sc., and Ph.D. degrees from Korea University, Seoul. Since 1991, he has been on the faculty of Gyeongsang National University, Jinju, Korea, where he is a professor. He was a visiting professor at Cornell

University, Ithaca, NY, USA, in 2004. He is also adjunct professor at IIT, IL, USA since 2007. His research interests include fuzzy applications, probabilistic production cost simulation, reliability evaluation, and outage cost assess-ment of power systems.

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