LS-SVM Based Wind Speed Forecasting

LS-SVM Based Wind Speed Forecasting

Manoj Kumar1 , Dr. M. K. Bhaskar2 , Bhawana Maurya3 , Prashant Baghmar4 , Dharmendra Jain5

1PG Scholar, Department of EE, MBM Engineering College, Jodhpur-Rajasthan-India

2Associate Professor, Department of EE, MBM Engineering College, Jodhpur-Rajasthan-India 3Assistant Professor, Department of IT, Govt. Women Engineering College, Ajmer-Rajasthan-India 4Lecturer, Department of ECE, Govt. Polytechnic College, Jodhpur-Rajasthan-India

5PG Scholar, Department of EE, MBM Engineering College, Jodhpur-Rajasthan-India

Abstract Wind energy is one of the most promising electricity sources of the 21st century, because it is clean, inexhaustible and free resource. Wind turbines convert the kinetic energy in moving air into rotational energy, which in turn is converted to electricity. Since wind speeds vary from month to month and second to second, the amount of electricity wind can make varies constantly, accurate forecasting of wind speed is necessary. This paper presents Least Square Support Vector Machine (LSSVM) based approach for wind speed forecasting. Actual wind speed data of one of the stations in Mumbai is used in the present work to validate the results of the algorithm.

Keywords Wind Speed, Wind speed forecasting, SVM, LSSVM

from non-renewable resources. With the recent and continued increase in penetration of wind power, the energy industry will need to adjust its thinking on how to integrate this intermittent power source into the electricity grid. Various forecasting techniques, associated with wind power and speed, based on numeric weather prediction (NWP), statistical approaches, artificial neural network (ANN) and hybrid techniques over different time-scales are reported in literature [2-7].

This paper is organized as follows. Section 2 describes brief theory of LSSVM. The detailed algorithm is given in section 3. Section 4 deals with the implementation of the algorithm using LSSVM and results obtained.

1. INTRODUCTION

   The Indian economy has experienced unprecedented economic growth over the last decade. Today, India is the ninth largest economy in the world, driven by a real GDP growth of 8.7% in the last 5 years (7.5% over the last 10 years). In 2010 itself, the real GDP growth of India was the 5th highest in the world [1]. This high order of sustained economic growth is placing enormous demand on its energy resources. The demand and supply imbalance in energy is pervasive across all sources requiring serious efforts by Government of India to augment energy supplies as India faces possible severe energy supply constraints.

   The original impetus to develop wind energy in India

2. LEAST SQUARE SUPPORT VECTOR MACHINE Least Square Support Vector Machine classifier was

   proposed by Suykens and Vandewalle [8]. LS-SVM is a class

   of kernel based learning methods. By LS-SVM one can find the solution by solving a set of linear equations instead of a convex quadratic programming for classical SVM. LS-SVM tries to minimize primal cost function subject to equality constraints instead of inequality ones. Therefore LS-SVM solves a set of linear equations instead of computational cost quadratic programming problem.

   The classification and regression problem is quite similar; therefore the two versions are described side by side as follows.

   came in early 1980s from the Government, when the Commission for Additional Sources of Energy (CASE) had

   The goal is to approximate a

   y gx

   function, based

   been set up in 1981 and upgraded to the Department of Non-

   x ,y N

   x N

   Conventional Energy Sources, DNES in 1982. This was followed in 1992 by the establishment of a full-fledged

   on a training data set i i i1 , where i

   a Ndimensional input vector and

   yi

   represents

   is the

   Ministry of Non-Conventional Energy Sources, MNES, renamed as Ministry of New and Renewable Energy Sources,

   corresponding scalar target output for regression, while in case

   MNRE in 2006. The Indian Renewable Energy Development Agency, IREDA was established in 1987 as a financial arm of the ministry to promote renewable energy technology in the

   of classification

   construct an

   yi {1,1} is a class label. Our goal is to

   y f x approximating function, which

   country. It provides finances to the manufacturers, consultancy services to the entrepreneurs, and also assists in the development and up gradation of technologies.

   Traditionally, electricity utilities and system operators are accustomed to understanding the supply side of load balancing with regards to the source of the energy, dispatchability and reserves, as well as the relative cost of producing electricity

   represents the dependence of the d training outputs on the x

   inputs. Lets define the form of this function as:

   Classification

   h

   L 0

   w

   N

   w k

   yk (xk )

   y(x) signw j j (x) b

   L N

   k 1

   j1

   b 0

   k yk 0

   sign wT (x) b

   Regression

   h

   y(x) w j j (x) b

   j1

   wT (x) b

   ..(1)

   L 0

   ek

   L 0

   k

   k 1

   k C ek

   k

   k

   y wT x

   k

   b1 e 0

   L 0

   w

   N

   w k (xk )

   N

   k 1

   where

   T

   L 0

   T b

   k 0

   w [w1 , w2 ,…, wh ] ,

   (x)h

   [1,2 ,…,h ] .

   L 0

   ek

   k 1

   k C ek

   .(4)

   The i

   i1

   is a set of given linearly independent

   L

   T

   basis functions, which maps the input data into an h dimensional feature space. The dimension of the feature space may be very large, even infinite.

   The main difference from the standard SVM is in the

   0

   k

   w xk

   • b ek yk 0

   constraints. LS-SVM applies equality constraints, so the constrained optimization tasks will be ( k 1,…, N ):

   The corresponding linear equation sets (a KarushKuhn Tucker (KKT) system) are:

   1 1 N

   0 yT

   b

   0

   min J

   (w,e)

   wT w C

   e2

   k

   1

   ,

   w,b,e p 2

   2 k 1

   y C

   I

   1

   with constraints:

   i, j yi y j K(xi , x j )

   k

   k

   T

   k

   y wT x b 1 e

   0 1 b 0

   1 1 N

   1 ,

   min J

   w,b,e

   p (w,e)

   wT w C e2

   k

   2 2

   1 C

   I

   y

   ..(5)

   with constraints:

   k 1

   ..(2)

   i, j

   K(xi , x j )

   k

   k

   y wT x

   b ek

   where

   y [ y , y ,…, y ]T , [ , ,..,

   ]T ,

   T

   1 2 N 1 2 N

   The first term is responsible for finding a smooth solution,

   1 [1,…,1] , K(xi , x ) x x is a kernel

   T

   j

   i

   j

   while the second one minimizes the training errors (C is the tradeoff parameter between the terms).

   function, C

   is a positive constant, b is the bias and

   From this, the following Lagrangian can be formed:

   the response of the LS-SVM can be obtained in the form:

   L(w,b,e;) J p (w,e)

   y(x) signN y Kx, x b

   k 1

   k k k

   N

   k

   k d k 1

   wT x

   b1 e

   y(x) N

   k Kx, xk

   b

   ..(6)

   k

   k 1

   k

   k

   L(w,b,e;) J p (w,e)

   N

   k k 1

   wT x

   b ek

   • yk

   ..(3)

3. WIND SPEED FORECASTING ALGORITHM

   Step 1: Data Collection

   IMD data consists of synoptic observations from

   where the k parameters are the Lagrange multipliers. The conditions for optimality are the followings ( k 1,…, N ):

   over 400 stations. It consists of balloon observations at a height of 10 m. The data of 1998 to 2007 (10 years) at one of the stations in Mumbai is used in the present problem of wind speed forecasting.

   Step 2: Data Preprocessing

   IMD data consists of mean hourly wind speed in km/hr round the clock for all the days of the year 1998 to 2007. It is first converted into daily mean hourly wind speed in km/hr. For the best results all the data is normalized between 0 and 1.

   Step 3: Design of LS-SVM model for Wind Speed Forecasting

   The available wind speed data of 10 years is divided into two parts: training data and testing data. By conducting the series of experiments, different LS-SVM model is developed. Step 4: Calculate Mean Squared Error.

   Step 4: Calculate Mean Squared Error

   To evaluate the performance of the model mean squared error (MSE) is calculated. Let x1,, xl be the testing data and f(x1),, f(xl) be decision values (target values) predicted by SVM model. If the true labels (true target values) of testing data are known and denoted as y1,.., yl, then,

   develop model for wind speed forecasting. In the present work, data is divided into five subsets of equal size. Sequentially one subset is used for testing using the LSSVM model trained on the remaining subsets. Fig.1 displays the results of the algorithm. It is observed that the forecasted values of wind speed are nearly equal to the observed values. Mean squared error of 7.54 x 10-4 is obtained.

   V. CONCLUSION

   Forecasting wind speed is considered as one of the most important tasks for the large-scale integration of intermittent wind-powered generators into power systems. The LS-SVM regression models developed in this dissertation work serve as an introduction to wind speed forecasting mainly for wind power companies operating in electricity wholesale markets.

   REFERENCES

   1. Energy Statistics, Central Statistics Office, National Statistical Organisation, Ministry of Statistics and Programme Implementation,

      Government of India, Twentieth Issue, 2013, www.mospi.gov.in

   2. Hunt, K., and G.P. Nason: Wind speed modelling and short-term

      MSE

      1 ( f (xi) yi)2

      l

      l i1

      .(7)

      prediction using wavelets. Wind Engineering 25 (1), pp. 55-61

      (2001).

   3. Giebel, G., L. Landberg, C. Bjerge, M.H. Donovan, A. Juhl, K. Gram- Hansen, H.-P. Waldl, T. Pahlke, J. Giebhardt, M. Rebbeck, R. Ruffle,

      O. Brady: CleverFarm – First results from anintelligent wind farm. Paper presented at the European Wind Energy Conference and Exhibition,Madrid, Spain, 16-19 June 2003.

4. IMPLEMENTATION AND RESULTS

The proposed algorithm for wind speed forecasting using LS-SVM is implemented using LS-SVM Lab MATLAB toolbox [9]. The main objective of the present work is to

Fig. 1 : Wind Speed Forecasting Results

1. Anurag More and M. C. Deo, Forecasting wind with neural networks, Marine Structures, Volume 16, Issue 1, January-February 2003, pp. 35-49

2. Fonte, P.M.; Quadrado, J.C., ANN approach to WECS power forecast, 10th IEEE Conference on Emerging Technologies and Factory Automation, Volume 1, 19-22 Sept. 2005, pp.1069-1072.

3. Rohrig, K.; Lange, B., Application of wind power prediction tools for power system operations, IEEE Power Engineering Society GeneralMeeting, 18-22 June 2006

4. Alexiadis, M.C.; Dokopoulos, P.S.; Sahsamanoglou, H.S., Wind speed and power forecasting based on spatial correlation models, IEEE Transactions on Energy Conversion, 14, (3), Sept. 1999, pp:836 842.

5. J.A.K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least squares Support Vector Machines, World Scientic, 2005.

6. LS-SVM Lab home page, http://www.esat.kuleuven.ac.be/sista/lssvmlab/