Hourly solar irradiance forecasting based on machine learning
models (IEEE ICMLA 2016)
Young Statisticians Meeting 2017
F-N. Melzi, T. Touati, A. Samé and L. Oukhellou
[email protected]
French institute of sciences and technology for transport, development and networks
(IFSTTAR)
Taieb Touati (IFSTTAR,UPMC)
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Summary
Summary
1
Introduction
2
Dataset Description
3
Forecast models
Time series models
Machine learning models
4
Results and Discussion
5
Conclusion and Current Work
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Introduction
Global context
Augmentation of population in cities, Increasing of energy consumption
Scale up of infrastructures in terms of transport, telecommunications and public
equipment
In France 2015 : Nuclear 76.4 %, Hydro 10.8 % Other Renewable Energy 6.6 %
Challenge : increase the part of renewable energy production
Emergence of smart cities (Technologies)
Better monitoring of the renewable energy (photovoltaic, eolian,...)
Improve the quality of life, Respect of environment
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Introduction
Context and Motivation
Large amount of data collected from smart devices, smart meters and sensors
(Meteorological Sensors)
Development of technologies in terms of data storage
Need of Data analytics in the energy domain
Smart City Energy analytics (SCE) project launch, both academic and industrial
partners (GE, ENGIE, Alstom Transport, IFSTTAR and others)
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Introduction
Goals
Build decision tools based on Advanced Data Analytics in the Energy domain
Case study : Photovoltaic energy (One of the most used renewable energy
worldwide), dependence on the solar irradiance and weather condition
Focus
Forecast the hourly solar irradiance using only irradiance data
Machine learning techniques and Times series models.
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Dataset Description
Data set
Hourly solar irradiance of the Paris suburb of Alfortville provided by Reuniwatt
company
The irradiance is collected for a duration of 144 months (from 1st January 2004 to
31st December 2015)
Each curve consists of a daily solar irradiance
Figure – Solar irradiance curves during the year 2015
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Dataset Description
Figure – Evolution of the number of hours of sunshine over 12 years
The progression of the number of hours of sunshine is the same for one leap year to
another and even for the non-leap years
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Dataset Description
(a)
(b)
Figure – (a) Distribution of the number of hours of sunshine during a leap year (2012) ; (b) non
leap year (2015)
The year is divided into 9 groups of days
The number of hours of sunshine varies between 9 and 17 hours
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Forecast models
Figure – Hourly solar irradiance forcasting models
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Forecast models
Time series models
Time series models
Naive model
The predicted value is equal to the last observed
ch = irh−1
ir
Autoregressive Moving Average (ARMA)
Stochastic process describing each time series Xt∈N by the folowing : .
φ(L)Xt = Θ(L)t
such that φ and Θ are polynomials of degree p and q respectively, L is the
lag-operator, and t∈N is white noise independent from Xt∈N
The solar irradiance time series is not stationary (ADF-test)
Calculation of the clear sky index k (Lauret et al 2015) a :
k = X /Xclear
The clear sky index time series is fitted by an ARMA
The solar irradiance is given by :
h
ch = kbh × Xclear
ir
a. http ://www.soda-is.com/eng/index.html
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Forecast models
Machine learning models
Machine learning models
Figure – Methodology
Learning on the days having the same number of hours as the predicted day
Taking into account the previous hours of the forecasted day
Notation
{xih , yih }ni=1 → training data set
(x∗h , y∗h ) → test data
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Forecast models
Machine learning models
Support Vector Machine Regression (SVR)
Maximizing the margin between the hyperplane and the data
Minimizing the empirical risk
ch =
ir
n
X
αi K (x∗h , xih ) + b
i=1
Neural Network (NN)
Non linear parameterized mapping from an input xi to an output yi
The model is designed by h − 1 inputs, m hidden neurons and one single output
(hour to forecast)
h−1
m
X
X
ch =
ir
wj f (
wji x∗h + b1 ) + b2 ,
j=1
i=1
Similarity
Distance between the actual observation and the past observations in the history
n
X
ch =
ir
wih yih
i=1
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Results and Discussion
Evaluation of the models
Leave-one-out
Two years (2014 and 2015) are considered to train and evaluate the models
The training is performed on the n − 1 past observations
The test is carried out on the nth observation
The operation is repeated n times from 1st January 2015 to 31st December 2015
Normalized Root Mean Square Error (NRMSE)
→ Evaluation of the accuracy of each model
v
u
H
u 1 X
ch − irh )2
RMSE = t
(ir
H −1
h=2
NRMSE =
Taieb Touati (IFSTTAR,UPMC)
RMSE
¯
ir
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Results and Discussion
Error indicator
NRMSE
Naive
0.545
ARMA
0.208
Models
SIM
0.252
SVR
0.203
NN
0.16
Table – Normalized Root Mean Square Error for the hourly forecasting models
Better performance of ARMA, SIM, SVR and NN comparing to Naive
NRMSE of ARMA is comparable to that of Machine Learning methods.
NN is the best forecasting model
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Measured
Naive
ARMA
SIM
SVM
NN
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200
Irradiance (W/m2)
800
Results and Discussion
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Time (hour)
400
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Measured
Naive
ARMA
SIM
SVM
NN
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Irradiance (W/m2)
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Time (hour)
(b)
Figure – (a) Measured and forecasted values for a sunny day ; (b) cloudy day
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Results and Discussion
(a)
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(d)
Figure – (a) Evolution of the NRMSE according to the year 2015 for ARMA ; (b) SIM ; (c) SVR ;
(d) NN
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Conclusion and Current Work
Conclusion
An hourly solar irradiance forecasting is carried out
Three machine learning techniques are used (SIM, SVR and NN)
Comparison with time series methods (ARMA), Non stationarity of raw data.
Satisfactory results during the sunny days for machine learning methods and lesser
accuracy when dealing with cloudy days
Further Work
Test Hybrid models with meteorological variables
Perform daily forecasting
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Conclusion and Current Work
Thank you for your attention !
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