This document describes a methodology for generating combined solar power forecasts using an ensemble of support vector regression models. The methodology includes: 1. Developing 24 individual SVR forecasting models from two different solar power datasets. 2. Using random forest regression to combine the forecasts from the 24 SVR models. 3. Evaluating the combined forecasts against individual model forecasts and a simple average combination, finding the ensemble approach improved accuracy in most months.

1. Random Forest Ensemble of
Support Vector Regression Models
for Solar Power Forecasting
1
Mohamed Abuella
Prof. Badrul Chowdhury
Energy Production and Infrastructure Center
Department of Electrical and Computer Engineering
University of North Carolina at Charlotte
Charlotte, USA
April 24, 2017

2. 2
Presentation
Outline
Solar Power
Forecasting
Combining Solar
Power Forecasts
Results and
Evaluation

3. Renewables Generations
(Wind and Solar) are Too
Variable
High Efficiency and
Large Energy Storage
Still not Exist
Reducing
Cost
and Pollution
Why
Forecast?
Variable Generations (V.G.) Forecasting

4. Variable Generations (V.G.) Forecasting
The usage of VG forecasting in US. electric
utilities and ISOs such as CAISO, MISO,
NYISO,…etc.
Botterud, J. Wang, V. Miranda, and R. J. Bessa, “Wind power forecasting in US electricity markets,” The Electricity
Journal, vol. 23, no. 3, pp. 71–82, 2010.
Elke Lorenz, “Solar Resource Forecasting” International Solar Energy Society (ISES) Webinar, 2016.
4
Forecast Horizons
Where
Forecast?
Post operating reserve
requirements
Clear DA market
using SCUC/SCED
Rebidding
for RAC Post-DA RAC
using SCUC
Prepare and
submit DA bids
Clear RT market using
SCED (every 5min)
Intraday RAC
using SCUC
Prepare and
submit RT bids Post results (RT
energy and
reserves)
Post results (DA
energy and
reserves)
Day Ahead:
Operating Day:
11:00 16:00 17:00
-30min
Operating hour
DA: Day Ahead.
RT: Real Time.
SCUC: Security Constrained Unit
Commitment.
SCED: Security Constrained
Economic Dispatch.
RAC: Reliability Assessment
Commitment.
Wind / Solar
Power
Forecasting

5. 5
Flowchart of the Combined Approach (Physical and
Statistical) of the Solar Power Forecasting
How
Forecast?
;
Solar Plant and
Terrain
Characteristics
Numerical Weather Prediction
(NWP)
Atmospheric variables
SCADA Data
Spatial Refinement
Local Roughness, topology.
Atmospheric Stability
Solar Power Plant
Modeling
Solar Power Conversion Equation/s
Model Output Statistics (MOS)
Systematic Error Correction
Solar Generation Forecast
Conversion to Power
Downscaling
Regression
Extrapolation
Solar Power Forecasting

6. 6
Normalizing the data is of paramount importance since the scale used for the values for each
variable might be different. The best practice is to normalize the data and transform all the
values to a common scale:
Xstandardized =
x − mean X
std(𝑋
XScaled = a +
x − min X
max X − min X
∗ b − a
where x is a sample from data variable X, {a, b} is the desired range of the normalized data,
such as {0, 1}, and X (min, max)=the minimum and maximum values of the observed data.
DATA NORMALIZINFG
These two techniques of data normalizing are used also to build different forecasting models
There is also a standardization technique, especially when the variance of the data is high,
which is making the data to have a zero mean and a unit standard deviation, as follows:

7. 7
The Model: The Support Vector Regression (SVR) is a Machine Learning tool that is deployed
here for short-term solar power forecasting.
Flowchart of Machine Learning (Black Box)
New Input X
Predicted Output Y
SVR is robust and reliable, to that it was chosen to carry out some different investigations
that need reliable results.
FORECASTING MODEL

8. 8
From Sklearn library, shows the effects of the optimal Hyperparameter of SVR model
The best parameters
are {C=1,
gamma=0.10}
Leads to 97% of
classification
accuracy
γ (Gamma)
C 1
100
0. 1 10
0.01
1
The Complexity of
the SVR model
changes by
changing its
parameters
(C, gamma)
Support Vector Regression (SVR) and its Hyperparameters (C and γ Gamma)
FORECASTING MODEL

9. 9
Grid Search of SVR’s Hyperparameters
Contour Plot of Grid Search of SVR’s Hyperparameters, C and Gamma
RMSE (as a Score of SVR)
C
γ (Gamma)
FORECASTING MODEL

10. 10
Construction of 12 SVR models from a dataset.
Another 12 SVRs from the other dataset. The total number of SVR models is 24
VARIOUS FORECASTING MODELS
The available data is divided into two sets: One dataset is consisting of all 26 months and
another dataset is consisting of the most recent 12 months only.

11. General diagram of combining different models
Model B
Model A
Model C
Model N
Method of
Combining The
Models
Combined Forecasts
Individual
forecasting
models
11
Combining Various Models
Methods of
Combining The
Models The random forest is chosen to be the learning ensemble
method for combining the various models’ outcomes.
ENSEMBLE LEARNING
The simple average of the various models’ outcomes.
Fcomb=WA*MA+ WB*MB + WC*MC ….+ WN*MN
WN is a weight is assigned to the outcome of a model MN

12. 12
Flowchart of an illustrative example of using the decision
trees for the solar power forecasting
The trees model is trained with
historical data to find the rules
that will be set and then used for
combining other models’
outcomes and obtain Combined
Forecasts.
Decision Trees for the Solar Forecasting
Flowchart of Machine Learning (Black Box)
Hypothesis could be
regression or
classification
ENSEMBLE LEARNING
New Input X
Predicted Output Y
Temp>75
Pred_value=AX1+BX2+..
Cloud Cover>0.5
Pred_value=AX1+BX2+..
Temp<75
Pred_value=AX1+BX2+..
Cloud Cover<0.5
Pred_value=AX1+BX2+..
Solar Irradiance>400
Pred_value=AX1+BX2+..
Solar Power<1500
Solar Irradiance<400
Pred_value=AX1+BX2+..
Root Node
Terminal Node
Terminal Node
Terminal Node
Terminal Node

13. METHODOLOGY SCHEMES
Day Month
1
:
June
: July
:
:
:
:
:
:
: April
30 May
31
00:00
:
23:00
Weather Data
:
:
:
:
: :
:
:
:
:
:
:
: :
: :
:
:
:
:
:
:
PV Power
:
:
(PastObservations)
:
:
:
:
:
:
Forecasts
(Model’s
Outcomes)
at 00:00
Day Month
1
:
June
: July
:
:
:
:
:
:
: April
30 May
31
00:00
:
23:00
Weather Data
:
:
:
:
: :
:
:
:
:
:
:
: :
: :
:
:
:
:
:
:
Models’ Outcomes
:
:
:
:
:
:
: : :
:
:
:
:
:
:
:
:
:
: : :
: : :
Forecasts
PV Power
:
:
(PastObservations)
:
:
:
:
:
:
Combined
Forecasts
(a) (b)
(a) Day-ahead forecasting by
Support Vector Regression models
13
(b) Combining by Random Forest
Day-ahead forecasts and combining them, for May 31st

14. Data Description:
14
The solar power system is in Australia The panel type is Solarfun SF160-24-1M195,
consisting of 8 panels, its nominal power of (1560W), and panel orientation 38° clockwise from
the north, with panel tilt (of 36°). The historical observed solar power data are normalized to
the rated capacity (i.e., 1560W).
https://crowdanalytix.com/contests/global-energy-forecasting-competition-2014-probabilistic-solar-power-forecasting
Benchmark
Data
Scatter & Box
plots the
Data
Cleansing the
Data
Correlation and
Sensitivity
Analysis
Select most
Effective
Variables
Flowchart of Data Preparation
CASE STUDY
Training
Testing

15. 15
Flowchart of Solar Power Combined Forecasts

16. 16
RESULTS and EVALUATION
Root Mean Squared Error
The lower RMSE, the
better forecasts
accuracy
The Performance evaluation are carried out by: Some statistical metrics, plots, and comparison.
Best Model (4) =All-months dataset + Normalize (A) + Parm10_08 + Orig12ins
The comparison is carried out over the entire year, between: The ensemble learning model vs.:
The Simple Average methodand
The higher
positive
improvement rate,
the better
ensemble forecasts
Improvement % = 1 −
RMSEEnsemble Model
RMSEOther Model
∗ 100
(also called Skill Score)

17. 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Days
RMSE
The RMSE of the Models
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
M21
M22
M23
M24
Combined Forecasts
Average Forecasts
Daily RMSEs of different models and Ensemble forecasts, October
RESULTS and EVALUATION

18. 18
Monthly RMSE of All Forecasts
RESULTS and EVALUATION
0.000
0.020
0.040
0.060
0.080
0.100
0.120
RMSE
Monthly RMSE
Simple Average Best Model Ensemble
Root Mean Squared Error
The lower RMSE, the
better forecasts
accuracy

19. 19
Improvement % = 1 −
RMSEEnsemble Model
RMSEOther Model
∗ 100
(also called Skill Score)
The higher
positive
improvement rate,
the better
ensemble forecasts
June July August September October November December January February March April May
Best. Model -4% 3% 3% 3% 18% 11% 14% 7% 5% -6% 1% 0%
Simple Average 3% 3% 5% 12% 28% 20% 19% 13% 10% -3% 2% 0%
-7%
-2%
3%
8%
13%
18%
23%
28%
33%
Improvement(%)
Improvement (Skill Score ) of Ensemble Forecasts over:
Best. Model Simple Average
RESULTS and EVALUATION

20. 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Importance of Features, October
Weather Features
ImportanceScore
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Importance of Features, March
Weather Features
ImportanceScore
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Importance of outcomes, October
Models’ Outocmes
ImportanceScore
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Importance of outcomes, March
Models’ Outocmes
ImportanceScore
The estimation of weather features importance by Random Forest
(a) October (b) March
The estimation of models’ outcomes importance by Random Forest
(a) October (b) March
RESULTS and EVALUATION

21. 21
The standard deviation and the correlation of different models
0.950
0.955
0.960
0.965
0.970
0.975
0.980
0.985
0.990
0.995
1.000
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
Correlation
Std.Dev.
Std. Dev. and Correlation of Models
Std.Dev.
Correlation
The performance of
the ensemble
forecasts is better
with models of
higher variance
(higher std. dev.) or
less correlated
models.
RESULTS and EVALUATION
-7%
-2%
3%
8%
13%
18%
23%
28%
33%
Improvement(%)
Improvement (Skill Score) of Ensemble Forecasts over:
Best. Model Simple Average

22. 22
CONCLUSION
• Combining the forecasts yields accurate forecasts and a stable performance;
• The ensemble learning is efficient for assigning the weights of combined forecasts;
• The combined forecasts by the simple average are not as accurate as by ensemble learning;
• The combined forecasts out of diverse models are more accurate;
• Adding the past generated forecasts increases the accuracy of the combined forecasts.

23. 23
Thanks for Listening
Any Question?
http://epic.uncc.edu/
Energy Production and Infrastructure Center
Department of Electrical and Computer Engineering
University of North Carolina at Charlotte
Mohamed Abuella
mabuella@uncc.edu