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WIND SPEED PREDICTION Sagar Gadsing, Electrical and Computer Engineering, Portland State University E-mail:sagar@pdx.edu ECE 557: Engineering Data Analysis and Modeling, Fall 2004 Instructor: James McNames Abstract – Wind speed is one of the most A. Data Collection important criteria for windsurfing. This paper predicts the wind speed, using the regression The data was collected from internet (NDBC model. Four factors affecting the wind speed have government link). The parameters considered for been taken into consideration. Various results predicting the wind speed are: average wind direction have been explained using graphs and tables. The measured in degrees clockwise from true North; wind speed prediction made for next 24 hours was direction in degrees clockwise from true North of the satisfactory. GSP; maximum 5-second peak gust during the measurement hour; the minute of the hour that the Index Terms – GSP occurred; the predicted wind speed for previous day. GSP: Maximum 5-second peak gust during the measurement hour. B. Statistics Summary I Introduction I had a very large data set. There were many reading Wind surfing is a very popular sport, especially along of wind speed along with the corresponding the coastal areas. Unfortunately, the adventure largely parameters, out of which I found that most of data was depends on the natural conditions, such as wind corrupted and was with repetitive values. There were speed. In this paper I have tried to predict the wind abrupt and periodic changes in the input values, which speed, which will be of help for the surfers. If the wind made me, feel that the data is corrupted. Every 3rd speed is predicted and put up on a popular website, reading was same and uniform through out the wind surfers can refer to the data and make their plans collected data. All the entries in these rows were 999’s. accordingly. If this kind of information is not made Hence much of the data was discarded. available, wind surfers may be disappointed after C. Prediction of Wind Speed reaching the coast only to find that it is either too windy or there is not wind at all. For predicting the wind speed a relationship between past parameters and present wind speed was There are many factors that affect the wind speed. I established. The following model was used for have made my best effort to use as many parameters achieving the goal. The model is given by as possible. I was not able to use the parameters I wanted, only because data for those parameters was ^ n not available. Y = wo + Σ ( wi * xi ) --- (1) i=1 An effort was made to predict the wind speed using fuzzy logic, though it was directed towards predicting Here ‘w’, represents the weights and Yhat is the the wind conditions for wind turbines [1]. There have expected value of the output. Xi, represents the input been hardly any efforts done for predicting wind speed parameter. The weights were calculated from the true for windsurfing. values and the pseudo inverse of data matrix. II. Methodology The data matrix ‘A’ is given by This section describes the methodology used to predict A = [ 1, x1, x2, …] ---(2) the wind speed at a given time. and the weight, w, is given by, w = A’ * Yt ---(3) Fig I shows the predicted values of wind speed against the true values. The inverse of matrix A cannot be calculated, since it is not a square matrix. Hence I calculated the pseudo The plot in fig I shows the variation of true and inverse of matrix A, using the MATLAB. predicted values of the wind speed. The values are very closely matched, which indicates that the model I started with a large data set, applied the test to it, but has performed well. at the end the value of performance coefficient (R2) turned out to be very insignificant (merely 11%). Then I analyzed the data, and found that there was a lot of inconsistency in it. There were many repetitive values, wind speed for 18th which were unexpected. Deleting much of the corrupted data, improved my value of R2, and I ended up with R2 = 0.9. 14 12 To measure performance of the model I calculated the performance coefficient (R2). The value of R2 indicates w i n d s p e e d (m / s ) 10 how well the data fits. 8 yt for 18/10 The performance coefficient is given by yh for 18/10 6 R2 = (1-SSE/SSTO) ---( 4 ) 4 The value of SSTO is calculated by 2 0 SSTO = Σ (yi – ymean)2 ---( 5 ) 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 and the value of SSE is calculated by time ^ SSE= Σ ( yi – y )2 ---( 6 ) th Fig II shows the predicted values for wind speed on 18 against the Code has been written in Matlab to calculate the true values. values of R2. The above graph shows the predicted wind speed on I have applied the above model for predicting the wind the 18th and the true wind speed plotted against the speed 24 hours in advance. For accomplishing this, I time. have established a relationship between the present inputs and present estimated value with wind speed after 24 hours. For example, suppose I want to predict the wind speed on the 22nd of Nov at 11am, the input wind speed for 19th parameters used are recorded at 11 am on 21st Nov. Also, I have predicted the wind speed for the 21st of 16 Nov on the 20th of Nov. This estimated wind speed has also been taken into account to predict the wind speed 14 on the 22nd. Thus the model essentially predicts wind 12 w i n d s p e e d (m / s ) speed for next 24 hours. 10 yt for 19/10 III. Results 8 yh for 19/10 wind speed measurement for 17th 6 4 18 16 2 14 0 wind speed (m/s) 12 10 yt for 17/10 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 8 yh for 17/10 time 6 4 2 th 0 Fig III shows the predicted values for wind speed on 19 plotted 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 against the true values. time The fig III shows the predicted wind speed for 19th The above scatter plot shows the relation among all plotted against the true values of the wind speed. It can the input and the output (predicted value of only 17th). be observed that the difference in the predicted values The X-axis starts with x1 all the extreme left and ends and the true values goes on increasing. with y output on the extreme right. Similarly on the Y- axis, the first value is y which goes up to output x1. In all of the above graphs the X-axis reads “time”, The scatter plot clearly shows that most of the inputs which is nothing but the every half hour of the day, i.e. are not correlated. However there is some correlation 1 corresponds to 12:00 O’clock, 2 corresponds to between the input variables x4 and the output y. Also a 11:30 and so on. significant correlation can be seen between the input variables x1 and x2. plot for r^2 IV Discussion 1.2 This paper predicts the wind speed 24 hours in 1 advance. If this model is used to estimate wind speed 0.8 48 hours in advance, using the estimated value after 24 hours, the error goes on accumulating. 0.6 r^2 Several different models can be built, each one 0.4 specifically designed to predict a value after a specified 0.2 duration. Also efforts can be made to increase the values of R2, which implies a more reliable model for 0 predicting the future values. Using a good set of data 17th 18th 19th will definitely help to build a better model. If there date would have been no corrupted data, the results would have been essentially unbiased. 2 Fig IV shows the values of R for different days. More accurate and better results would have been The above information depicts that, the farther the predicted, provided we get some more related value of wind speed I try to predict, the more parameters, such as temperature and altitude. inaccurate result I get. This is because; the error in the prediction goes on increasing. More number of samples per hour would have helped to predict the wind speed after a short duration, which Also I have used the current estimated values for is also useful for windsurfing. predicting the future values. The prediction error goes on adding up and the result becomes unreliable. V. Conclusion 400 200 x1 The wind speed can be predicted satisfactorily in 0 400 advance. The estimated values become more and 200 more unreliable as we try to predict the farther outputs. x2 Thus this paper shows how present input values and 0 10 the present predicted value can be used to predict a 5 future value. x3 0 VI. References 4000 2000 [1] “A New Approach for Wind Speed Prediction” by x4 0 Y.D.Song, Department of Electrical Engineering, North 20 Carolina. 10 y 0 [2] “Real time continuous wind data” from National 0 200 400 0 200 400 0 5 10 0 2000 4000 0 10 20 Data Buoy Center. x1 x2 x3 x4 y Fig V shows a scatter plot, which includes all the inputs and the output.