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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

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2018 Impact Factor: 1.701

Front. Energy    2020, Vol. 14 Issue (2) : 347-358    https://doi.org/10.1007/s11708-018-0553-3
RESEARCH ARTICLE
Comparison of modeling methods for wind power prediction: a critical study
Rashmi P. SHETTY1(), A. SATHYABHAMA1, P. Srinivasa PAI2
1. Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal 575025, India
2. Department of Mechanical Engineering, NMAMIT, Nitte, KarkalaTaluk 574110, India
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Abstract

Prediction of power generation of a wind turbine is crucial, which calls for accurate and reliable models. In this work, six different models have been developed based on wind power equation, concept of power curve, response surface methodology (RSM) and artificial neural network (ANN), and the results have been compared. To develop the models based on the concept of power curve, the manufacturer’s power curve, and to develop RSM as well as ANN models, the data collected from supervisory control and data acquisition (SCADA) of a 1.5 MW turbine have been used. In addition to wind speed, the air density, blade pitch angle, rotor speed and wind direction have been considered as input variables for RSM and ANN models. Proper selection of input variables and capability of ANN to map input-output relationships have resulted in an accurate model for wind power prediction in comparison to other methods.

Keywords power curve      method of least squares      cubic spline interpolation      response surface methodology      artificial neural network (ANN)     
Corresponding Author(s): Rashmi P. SHETTY   
Just Accepted Date: 12 February 2018   Online First Date: 12 April 2018    Issue Date: 22 June 2020
 Cite this article:   
Rashmi P. SHETTY,A. SATHYABHAMA,P. Srinivasa PAI. Comparison of modeling methods for wind power prediction: a critical study[J]. Front. Energy, 2020, 14(2): 347-358.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-018-0553-3
https://academic.hep.com.cn/fie/EN/Y2020/V14/I2/347
Fig.1  Methodology adopted in this paper
Sl. No Wind speed/(m•s–1) Power/kW
1 5 250
2 6 250
3 7 480
4 8 730
5 9 980
6 10 1200
7 11 1400
8 12 1450
9 13 1500
10 14 1500
11 15 1500
12 16 1500
Tab.1  Power values for various wind speeds from manufacturer’s power curve
Fig.2  Manufacturer’s power curve of the turbine considered for this paper
Local time Outdoor temp/ºC Wind direction degree Wind speed/(m•s–1) Nacelle temp/ºC Blade pitchangle/(°) Rotor speed/(r•m–1) Active power/kW
8/1/2013 0:10 22 -0.1 11.8 26 4.9 16.3 1347.7
8/1/2013 0:20 22 -0.8 13 26 9.7 16.5 1491.1
8/1/2013 0:30 22 -0.5 12.8 26 7.7 16.4 1448.7
8/1/2013 0:40 22 -0.4 12.4 26.1 7.2 16.4 1482.4
8/1/2013 0:50 22 -0.5 12.5 26 8 16.5 1481.3
Tab.2  Sample data set collected from the SCADA
Model Description
Model-1 Model based on wind power equation
Model-2 Model based on presumed shape of power curve
Model-3 Model based on method of least squares
Model-4 Model based on cubic spline interpolation
Model-5 Model based on response surface methodology
Model-6 Model based on ANN
Tab.3  Details of the models developed
Sl. No Wind speed/(m•s–1) Actual power/kW
1 5.667 250.85
2 6.017 289.383
3 7 447.433
4 8.033 637.133
5 9 820.9
6 10 981.15
7 11.017 1201.067
8 12 1392.217
9 13 1473.733
10 14 1500.183
11 15.233 1487.85
12 16.117 1475.533
Tab.4  Data selected for comparison of performances of the models
Sl. No Wind speed/(m•s–1) Actual power/kW Model-2 Model-3 Model-4 Model-5 Model-6
Power/kW RMSE Power/kW RMSE Power/kW Power/kW Power/kW RMSE Power/kW RMSE
1 5.667 250.85 250.05 0.565 200.61 35.52 200.73 35.43 222.28 20.19 269.01 12.84
2 6.017 289.38 302.55 9.31 263.24 18.48 253.24 25.55 280.07 6.57 282.42 4.92
3 7 447.43 450 1.81 485 26.56 480 23.02 425.91 15.21 432.50 10.55
4 8.033 637.13 604.95 22.75 730.06 65.71 716.20 55.91 625.30 8.36 635.84 0.91
5 9 820.9 750 50.13 996 123.81 992 120.98 786.48 24.33 793.43 19.42
6 10 981.15 900 57.38 1212 163.23 1278 209.90 960.39 14.67 963.64 12.37
7 11.017 1201.06 1052.55 105.01 1370.13 119.54 1401.78 141.92 1171.69 20.76 1182.68 12.99
8 12 1392.21 1200 135.91 1464 50.75 1450 40.85 1346.63 32.23 1359.93 22.82
9 13 1473.73 1350 87.49 1500 18.57 1500 18.57 1437.08 25.91 1440.81 23.27
10 14 1500.18 1500 0.129 1500 0.12 1500 0.129 1476.85 16.49 1491.60 6.06
11 15.233 1487.85 1500 8.59 1500 8.59 1500 8.59 1478.45 6.64 1487.69 0.11
12 16.117 1475.53 1500 17.30 1500 17.30 1500 17.30 1468.35 5.07 1470.87 3.29
Tab.5  Comparison of power predicted by different modeling methods
Fig.3  Surface plot for power by varying two variables: wind speed and pitch angle
Fig.4  Surface plot for power by varying two variables: wind speed and wind direction
Fig.5  Surface plot for power by varying two variables: wind speed and density
Fig.6  Surface plot for power by varying two variables: wind speed and rotor speed
Fig.7  Variation of MSE with number of neurons in the hidden layer for MLP model
Fig.8  Comparison of RMSE of different modeling methods
P Power output of a wind turbine/kW
r Air density/(kg·m–3)
R Radius of the rotor/m
Cp Power coefficient
b Blade pitch angle/(° )
l Tip speed ratio
v Wind speed/(m·s–1)
Wr Rotor speed/(rad·s–1)
ve Effective wind speed perpendicular to the rotor plane/(m·s–1)
Pe Estimated power/kW
vc Cut-in wind speed/(m•s–1)
vr Rated wind speed/(m•s–1)
vf Cut-out wind speed/(m·s–1)
a Momentum parameter
η Learning rate
Tab.6  
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