Renewable Energy 35 (2010) 925–930

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Renewable Energy

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Analysis and forecasting of wind velocity in chetumal, , using the single exponential smoothing method

E. Cadenas a, O.A. Jaramillo b,W.Riverab,* a Facultad de Ingenierı´a Meca´nica, Universidad Michoacana de San Nicola´s de , Santiago Tapia No. 403, Centro, Me´xico b Centro de Ivestigacio´n en Energı´a, Universidad Nacional Auto´noma de Me´xico, Apartado Postal 34, Temixco 62580, , Me´xico article info abstract

Article history: In this paper the analysis and forecasting of wind velocities in Chetumal, Quintana Roo, is pre- Received 15 July 2008 sented. Measurements were made by the Instituto de Investigaciones Ele´ctricas (IIE) during two years, Accepted 30 October 2009 from 2004 to 2005. This location exemplifies the wind energy generation potential in the coast Available online 14 November 2009 of Mexico that could be employed in the hotel industry in the next decade. The wind speed and wind direction were measured at 10 m above ground level. Sensors with high accuracy and a low starting Keywords: threshold were used. The wind velocity was recorded using a data acquisition system supplied by a 10 W Wind speed forecasting photovoltaic panel. The wind speed values were measured with a frequency of 1 Hz and the average Exponential smoothing method ANN wind speed was recorded considering regular intervals of 10 min. First a statistical analysis of the time ARMA series was made in the first part of the paper through conventional and robust measures. Also the ARIMA forecasting of the last day of measurements was made utilizing the single exponential smoothing Hybrid systems method (SES). The results showed a very good accuracy of the data with this technique for an a value of 0.9. Finally the SES method was compared with the artificial neural network (ANN) method showing the former better results. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction forecasts are required to best integrate wind electric potential into scheduling and dispatch decisions made by an energy provider. According to the World Wind Energy Association, by the end of Accurate wind forecasts will also help to remove barriers related June of 2008 the cumulative installed capacity was close to with the wind intermittence and unpredictability that make some 95,600 MW. The currently installed wind power capacity generates energy providers reluctant to pursue wind as an energy resource. 200 TWh per year, equaling 1.3% of the global electricity Wind is considered as one of the most difficult meteorological consumption. Wind power is now established as an energy source parameter to forecast. Wind is the result of the complex interac- in over 50 countries around the world, it is important to indicate tions such as pressure and temperature differences of the global that in some countries and regions, wind energy already contrib- environment, the rotation of the earth, and local characteristics of utes 40% and more. Europe has the lead in wind energy develop- the surface. The forecasting technique employed depends on the ment; however wind energy markets in the United States, China, available information and the time scale in question, and thus its and India are growing very fast. application. Some different techniques are applied to forecast Since January 2007, with the operation of the wind farm La periods in the range of a few hours or days. The approaches that are Venta II with an installed capacity of 83.3 MW, Mexico joins the list found in the literature include Numerical Weather Prediction and of countries that produce electricity from wind on a commercial Mesoscale models, Generalized Equivalent Markov models and scale. Mexico is ranked in second place in Latin America after Brazil time series approaches. The latter incorporates various techniques that presents 247 MW wind power installed. such as ARMA models, bilinear and smooth threshold autore- As wind energy can be considered as a significant contribution gressive models. Recently, artificial intelligence techniques have to the electric generation in various places around the world, the been proposed. They include the use of Multi-Layered Perceptrons, need for accurate predictions of available wind electric potential for Radial Basis Functions and Recurrent Neural Networks as well as a variety of time scales is increasing in importance. Accurate wind Fuzzy Logic and the combination of a Fuzzy Classifier with a Temporal Neural Network [1].

* Corresponding author. Tel.: þ52 777 362 0090 Ext. 29740. In 1996 Kariniotakis et al. [2] reported a model based on neural E-mail address: [email protected] (W. Rivera). networks for the prediction of power output profile of a wind park.

0960-1481/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2009.10.037 926 E. Cadenas et al. / Renewable Energy 35 (2010) 925–930

Table 1 Table 2 Specification of the measurement sensors. Statistics parameters of the data measurements (m/sec), in Chetumal, Quintana Roo.

Specification Anemometer Wind Vane Data Min. Max. Mean Median St. Dev Q1 Q3 Measuring rank 0.78–45 m/s 0–360 4464 0.00 6.10 2.25 2.25 1.20 1.40 3.00 Exactness 5% 5% Resolution 0.78 m/s 1 m/s

In 2008 Costa et al. [7] made a review of history of wind power In the model are employed simple methods like persistence, as well short-term prediction. In their work included the first ideas and as classical methods and it was implemented into a real control sketches of the theme to actual state of the art on models and tools. system of an autonomous wind-diesel power system. The techniques for wind speed forecasting suppose that the In 1998 Alexiadis et al. [3] studied the operation of power systems time series conformed for the measurements are a sum of different with integrated wind parks. They proposed artificial neural networks patterns and a random error. The objective of the most of the models for forecasting average values of 10 min or 1 h. The methods techniques used in forecasting is the patterns separation (hori- were tested using data collected over seven years at six different sites zontal, seasonal, cyclical and trend) that conform the series. on islands of the South and Central Aegean Sea in Greece. Recently diverse statistical techniques and artificial intelligence At the end of 1999, Sfetsos [1] reported a comparison of various have been used for the time series forecasting [8–11], even more, forecasting approaches, using time series analysis, on mean hourly some of this techniques have been combined with the purpose of wind speed data. In his work includes the traditional linear (ARMA) reducing the forecasting errors generating more accuracy predic- models and the commonly used feed forward and recurrent neural tions [12–14]. networks, other approaches are also examined including the There are other statistical techniques denominated exponential Adaptive Neuro-Fuzzy Inference Systems (ANFIS) and Neural Logic smoothing that besides to forecast, smooth the analyzed function, Networks. allowing a more convenient presentation of the data and elimi- In 2006, Chan et al. [4] discussed the problem of ‘‘over-fitting’’ nating until certain degree, the random errors that appear. These and some common generalization learning techniques in the ANN techniques are based on the intuitive application of movable literature, as well as introducing a new Genetic Algorithm-based averages, in where the tool to smooth the function is the mean of regularization method called ‘‘GARNET’’ for short-term load the last observations. forecasting. Their work included four generalization learning The exponential smoothing methods have been used in diverse techniques, namely: Early-Stopping, Bayesian Regularization, fields [15,16], however, they practically have not been used in wind Adaptive-Regularization and GARNET. Those techniques are speed forecasting [17], in spite of the potential that they have in the applied to train Multi-Layer Perceptrons networks (MLP) for day- forecasting where the last observations have more weight in the ahead load forecasting on limited amount of hourly data from a US forecasting of the present ones, as the case of wind speed short utility. They showed that forecasters trained by these four methods term measurements [18]. consistently produce lower prediction error than those trained by The main advantage of the exponential smoothing methods is the standard error minimization method. their robustness [19], that allows a fast and efficient implementa- In 2007 Bilgili et al. [5] studied ANN to predict the mean tion of the technique together with the descriptive and the infer- monthly wind speed of any target station using the mean monthly ential statistic. wind speeds of neighboring stations which are indicated as refer- The Instituto de Investigaciones Ele´ ctricas, IIE [20] has carried ence stations. They reported that resilient propagation (RP) out studies of the wind potential assessment of Me´xico. These learning algorithm was applied in their simulation. studies have been developed through measurement programs in Mabel and Ferna´ndez [6] reported in 2008 a case study of wind various locations throughout the country. Some important power generation based on ANN. The model reported was devel- locations are: La Ventosa in [21], Negro in Baja oped with the help of neural network methodology. It involves California Sur (BCS) [22], Cerro La Virgen in , Laguna three input variablesdwind speed, relative humidity and genera- Verde in , La Rivera Maya in Quintana Roo, and in the tion hours and one output variable-energy output of wind farms. village of Chetumal in the same state of Quinta Roo. Considering

6 180

160 5 140

4 120

100 3 80 Frecuency 2

Wind speed (m/sec) 60

1 40

20 0 0 00 1160 2320 3480 0.0 0.9 1.8 2.7 3.6 4.5 5.4 Time (min) Wind speed (m/sec)

Fig. 1. Time Series of the wind speed of Chetumal, Quintana Roo. Fig. 2. Wind speed frequency and Normal distribution curve. E. Cadenas et al. / Renewable Energy 35 (2010) 925–930 927

6 6 * outliers

5 5 Highest value within upper limit

4 Third quatile (Q3) 4

3 3

Median Wind speed (m/sec) 2 Wind speed (m/sec) 2

1 First quartile (Q1) Lowest value within lower limit 1 0 00 06 12 18 24 30 36 42 48 Centered Moving Average (CMA)

Fig. 3. Data spread in a box diagram. Fig. 5. Moving average centered in 1000 data. the wind potential assessments, the most important regions in Me´xico are La Ventosa in Oaxaca, the North-Pacific Region concept of ecotourism which use solar or wind energy to meet the (including and ), the State of electricity demand. It is possible to consider the use of small wind Veracruz and the State of Quintana Roo. turbines (20 kW or less) to generate electricity required for the Chetumal is the capital city of the Mexican State of Quintana hotels. The analysis and forecasting of wind speed in Chetumal is Roo. This city is situated at the eastern coast of the Yucata´n very important to predict the wind power variations and perfor- Peninsula (Coordinates: 18300N, 88200W) just north of ; it mance of the individual wind turbines. lies only 10 m above sea level. The warm waters of the Caribbean In our research, the wind speed and wind direction were Sea contribute to the climate, which is generally warm and humid. measured at 10 m above ground level where the wind speed values The average temperature range is 25.5–26.5 C, with maximum were measured with a frequency of 0.5 Hz and the average wind high temperatures between 36 C and 38 C and low temperatures speed was recorded considering regular intervals of 10 min. ranging from 12 Cto14C. The highest monthly average rainfall Sensors with high accuracy and a low starting threshold were used. occurs in September. Anemometers with three cone-shaped cups were used to measure In the south of Chetumal and the in Me´xico, about wind speed. This type of anemometer was selected because its 36 ecotourism developments represent the main attraction of this design has been shown to exert a more uniform torque throughout area, leaving an important economy. The objective of these projects a revolution. Conventional wind vanes were used to measure the is to diversify the tourism in the southern state and in parallel to wind direction or the azimuth angle of the wind. The starting encourage productive projects in communities. Investment funds threshold was 0.5 m/s for the anemometer and the wind vane. The for ecotourism projects, is the result of agreements with the three wind velocity was recorded using a data acquisition system levels of government and coordinated by various state institutions supplied by a 10 W photovoltaic panel. It is worth mentioning that such as the Ministry of Planning and Development (Seplader), the average values were calculated for all parameters on a ten- Ministry of Tourism (Sedetur) and the Ministry of Development minute basis, which is now the international standard period for Agricultural, Rural and Indigenous (Sedari). wind measurement. Except for wind direction, the average is Currently, the association called ‘‘The Island of Chetumal’’, defined as the mean of all samples. For wind direction, the average which brings together local and international investment, is should be a unit vector (resultant) value. Average data are used in developing various ecotourism projects on the shores of Lake reporting wind speed variability, as well as wind speed and direc- and Rio Hondo. The hotels are been developed under the tion frequency distributions.

6 5.5

5 5.0 D 4.5 4 4.0 3 C 3.5 Vel_Viento 2 B 3.0 Wind Speed (m/sec) 1 2.5 A 2.0 0 1.5 1000 2000 3000 4000 963 181512 272421 30 T(min) Centered Moving Average (CMA)

Fig. 4. Data division proposed. Fig. 6. Moving average centered in 1500 data. 928 E. Cadenas et al. / Renewable Energy 35 (2010) 925–930

5.5 8

5.0 7

4.5 6 5 4.0 4 3.5 3 3.0 Wind speed (m/sec) Wind speed (m/sec) 2 2.5 1 2.0 0

2018161412108642 483624121 60 120108968472 Centered Moving Average (CMA) Time (10 min)

Fig. 7. Moving average centered in 2500 data. Fig. 9. Time series of the last day.

For any wind development project, there is a need for informa- Considering that F is the forecast at some point of the time tion on the 10-minute average wind speed for the development site t series and Y is the available observation, thus the forecast errors is to determine suitability for wind turbine technologies in accordance t found to be: with loading guidelines, such as those of the International Electro- technical Commission (IEC 61400-1 and IEC 61400-2). Short-term et ¼ Yt Ft (1) wind speed variations of interest include turbulence and gusts. Short-term variations usually mean variations over time intervals of The method of single exponential smoothing method (SES) 10 min or less. Ten-minute averages are typically determined using takes the forecast for the previous period and adjusts it using the a sampling rate of about 1 s. It is generally accepted that variations in forecast error. Therefore, the forecast for the next period is: wind speed with periods from less than a second to 10 min and that have a stochastic character are considered to represent turbulence. Ftþ1 ¼ Ft þ aðYt FtÞ (2) For wind energy applications, turbulent fluctuations in the flow where a is a constant between 0 and 1. need to be quantified for the turbine design considerations based on Of this way, it can be seen that the new forecast is simply the old maximum load and fatigue prediction, structural excitations, forecast plus an adjustment for the error that occurred in the last control, system operation, and power quality. forecast. When a has a value close to 1 means that the new forecast will include a substantial adjustment for the error in the previous forecast. Conversely, if a is close to 0 means that the new forecast 2. Single exponential smoothing method will include very little adjustment.

In conventional moving average forecast, the mean of the past n observations is used as a forecast. This implies equal weights (equal 3. Statistics measures to determine the accuracy to 1/n) for all n data points. However, with forecasting, the most of the forecast recent observations will usually provide the best guide to predict the future. Furthermore a weighting scheme that has decreasing In order to determine quantitatively the best model, five fore- weights as the observations get older can give better results. cast error measures were employed for model evaluation and If the weights decrease exponentially when the observations get older the exponential smoothing methods can be very useful for forecasting. 8

7 Var Real 4.5 alfa(0.1) 6 alfa(0.5) alfa(0.9) 4.0 5

4 3.5 3 3.0 Wind speed (m/sec) 2 Wind speed (m/sec)

2.5 1

0 2.0 FebEne AbrMar May JulJun DicNovOctSepAgo 96847260483624121 120108 Month Time (10 min)

Fig. 8. Monthly average wind velocities. Fig. 10. Short time forecasting of wind velocities in Chetumal. E. Cadenas et al. / Renewable Energy 35 (2010) 925–930 929

Table 3 Table 4 Statistical error measurements for the SES method for different a values. Comparison of the statistical error measurements for the SES and ANN methods.

Alfa ME MAE MSE MPE MAPE (%) Model ME MAE MSE MPE MAPE (%) 0.1 0.0804 0.8162 1.2206 89.27 110.41 SES L0.0109 0.5251 0.5303 L25.78 49.68 0.2 0.0485 0.7002 0.9831 70.39 90.88 ANN 0.3577 0.5617 0.6403 40.42 55.97 0.3 0.0327 0.6328 0.8365 58.01 78.66 0.4 0.0245 0.5930 0.7319 48.93 70.04 0.5 0.0196 0.5686 0.6567 42.04 63.70 0.6 0.0164 0.5521 0.6035 36.71 58.76 through a network of measurement stations located in the interest 0.7 0.0141 0.5413 0.5668 32.45 55.27 places. The sensors were located in the measurement towers at 0.8 0.0039 0.5403 0.5508 28.03 53.03 10 m above the ground level. Their characteristics are shown in 0.9 L0.0109 0.5251 0.5303 L25.78 49.68 Table 1. The information generated by the sensors is accumulated in the data acquisition systems through chips or memory cards that later model comparison, being these: the mean error (ME), the mean are unloaded in a computer for their processing. square error (MSE), the mean absolute error (MAE), the mean The data acquisition measures the wind velocity every 1 s and percentage error (MPE) and the mean absolute percentage error every 10 min the mean value was estimated. In total 52,560 wind (MAPE). velocity data were measurement through the period. The standard statistical error measures can be defined as: Because of the amount of data was too big, the sample was divided per month given a total of 4464 data. Fig. 1 shows the time 1 Xn MSE ¼ e2 (3) series of the wind speed for January which is taken as an example n t t ¼ 1 for the analysis. The mean absolute error as: 5. Data analysis 1 Xn MAE ¼ jetj (4) Table 2 shows the statistics parameters of the wind speed n t ¼ 1 measurements in Chetumal. From the central tendency parameters The mean percentage error as: it can be seen that the sample has a Normal behavior. The frequency distribution and Normal behavior curve of the 1 Xn data are shown in Fig. 2. It can be observed that the wind velocities MPE ¼ PE (5) n t varied in a range from 0 m/s to 6 m/s. The 75% of the wind velocities t ¼ 1 are over 1.3 m/s. And the mean absolute percentage error as: Fig. 3 shows the data spread by means of a box diagram. This figure shows the quartiles and it can be seen that the median is in 1 Xn the middle of the rectangle showing the symmetric of the data. Also MAPE ¼ jPE j (6) n t it can be observed a higher spread in the upper quartile. t 1 ¼ From the analysis of Fig. 3 it is clear that the time series should Where n is the number of periods of time. be divided into for sections as it is shown in Fig. 4 in order to develop separated models. To continue with the data analysis, the moving average centered 4. Data measurement technique was applied for smoothing the data to find and to identify tendency, trend-cycle or seasonal components. The Instituto de Investigaciones Ele´ctricas (IIE) made the Fig. 5 shows a plot of the moving average centered in one measurements of the wind speed for two years from 2004 to 2005, thousands data. It can be observed that the lower wind velocities

8 1.4 Variable 7 Real SES 1.2 6 ANN 1.0 5 0.8 4

0.6 3 Wind speed (m/sec) 2 Wind speed (m/sec) 0.4 Variable Real 1 0.2 ANN SES 0 0.0 12010896847260483624121 2018161412108642 Time (10 min) Time (10 min)

Fig. 11. Comparison of the SES and ANN methods against real data. Fig. 12. Comparison of the SES and ANN methods for the last 20 observations. 930 E. Cadenas et al. / Renewable Energy 35 (2010) 925–930 occur at the beginnings and end of year and the maximum veloc- through conventional and robust measures. Also the forecasting of ities in the middle of this one. the last day of measurements was made utilizing the exponential Figs. 6 and 7 show the moving average plots centered in one smoothing method. The results showed that the exponential thousands five hundred and two thousands five hundred respec- smoothing method is a good alternative for the wind forecasting for tively. In Fig. 6 it can be seen a negative tendency of the series and a values close to 1 for the analyzed data. For short term wind speed Fig. 7 a regular behavior of this one. forecasting this technique responds of a satisfactory way to the Finally, Fig. 8 shows the overall behavior of the series through necessities of precision and accuracy required to support the the monthly averages. It can be observed that January, November operators of the Electric Utility Control Centre. Because of its and December are the months with the lowest average wind simplicity and exactness, compared with another techniques such velocities. March, April, May, June and July with the higher average ANN, this technique showed to be very useful for wind speed velocities and in particular June with the highest average velocities. forecasting. As it was observed from the previous analysis, there exist in some cases a trend in downward direction of the data, for this Acknowledgments reason the mean method is not a precise method to be used for forecasting purposes, furthermore the exponential smoothing We thank technical support from Jose´ de Jesu´ s Quin˜ones Aguilar method was utilized. and Carlos Alberto Perez-Ra´bago. This work has been partially In order to do the forecasting, a data sample of wind velocities supported by DGAPA-UNAM through Grant PAPIIT IN-106207-3. every 10 min was taken from the last day of the time series. Fig. 9 shows the time series of the data selected. Fig. 10 shows the forecasting of the selected data generated by References Eq. (2) for a values of 0.1, 0.5 and 0.9 compared with the real series [1] Sfetsos A. A comparison of various forecasting techniques applied to mean of time. It can be observed that for the a value of 0.1 just a rough hourly wind speed time series. 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