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Vol.
6
(201
6
) No.
4
ISSN: 2088
-
5334
Future Solar Irradiance Prediction using Least Square Support
Vector Machine
Fahteem Hamamy Anuwar# and Ahmad Maliki Omar*
# Electrical Technology Section, UniKL BMI, Gombak, Selangor, Malaysia
E-mail: fahteem@unikl.edu.my
* Green Energy Research Centre, Uitm Shah Alam, Shah Alam, 40150, Selangor, Malaysia
E-mail: maliki_omar@salam.edu.my
Abstract— Support vector machine (SVM) based on statistical learning theory has shown its advantage in regression and prediction.
This paper presents the future prediction of the solar irradiance using least square support vector machine (LSSVM) which is a kind
of SVM with quadric loss function. SVM has greater generalization ability and guarantee global minima for given training data set
which will give good performance for solar irradiance with time series prediction. In order to improve the prediction performance of
the LSSVM, the experimental data have to be normalized and appropriate parameters are selected by generic algorithm. In this
research, solar irradiance data are collected daily at monitoring station located at Green Energy Research Centre (GERC) UiTM,
Shah Alam. This related information will be used in prediction of the future data which useful for designing new PV systems and
monitoring existing systems performance. The results show good agreement between the predicted against the actual values
measured. The proposed solar irradiance time series prediction method is considerable practical value which can be used in other
datasets.
Keywords— Solar irradiance; support vector machine; least square support vector machine; time series prediction
I. INTRODUCTION
Energy is important in all aspects of development to
support population growth, urbanization, industrialization as
well as tourism industry. Seventy five percent of total global
energy demand is supplied by the burning of fossil fuels
which contribute to air pollution, global warming concerns,
diminishing fossil fuels and increasing costs. Energy
consumption is also increasing and several alternative green
energy sources are seriously taken into consideration to
fulfill energy demand.
The possibility to obtain electrical energy from the sun
and to supply electrical energy has been realized due to
development of solar panel and power electronic converters.
Photovoltaic (PV) technology provides an attractive method
of power generation and meets the criteria of clean energy
and sustainability [1-3].
Photovoltaic systems are the most promising way to
produce clean electricity which directly converts sunlight
into electricity easily. Changes in the intensity of the solar
irradiance give a major impact to the performance of the PV
systems. Fluctuations of the solar irradiance cause troubles
between demand and supply and reduce the power quality.
Accurate solar irradiance data is required for modelling and
designing of solar energy systems such as photovoltaic, solar
thermal and any other applications.
Many research have been carried out related to the
estimation of solar energy potential in various locations
based on conventional physical models or some statistical
assumptions [4-13]. Advanced development in computer
technology especially in artificial intelligent techniques have
been used for prediction in many engineering areas. Several
methods for estimating solar irradiance with artificial
intelligent techniques have been done by previous
researchers [14-28].
In recent years, Support Vector Machine (SVM) theory
was developed by Vapnik [29-30]. There have been an
intensive studies on SVM for regression and prediction in
which SVM is quite satisfying in theoretical point of view,
which leads to a great potential and superior performance in
practical applications. The structural risk minimization
(SRM) in SVM has been proved superior to the empirical
risk minimization (ERM) principle as adopted in neural
network. SVM shows powerful generalization ability and
guarantee global minima. In addition, SVM is adaptive to
complex systems and robust in dealing with corrupted data.
Least Square Support Vector Machine (LSSVM) [31-32]
520
uses equality constraints instead of inequality constraints and
a least squares error term in order to obtain a linear set of
equations in the dual space. This unique feature make
LSSVM have the advantages of simple structure and high
speed. Many great research have been successfully adopted
SVM and LSSVM techniques such as fingerprint recognition
[33], document categorization [34], traffic pattern
recognition [35], forecasting of financial market [36],
forecasting of electricity price [37], estimation of power
consumption and time series prediction [38].
This research is carried out to investigate the capability of
least square support vector machine in forecasting solar
irradiance by using the actual measured data obtained from
measurement stations. LSSVM model for predicting one day
ahead of solar irradiance values by using the real climate
data obtained from the monitoring station located at Green
Energy Research Centre (GERC) UiTM, Shah Alam.
MATLAB was employed for LSSVM applications.
II. DESCRIPTION OF THE GCPV SYSTEM
The Grid Connected Photovoltaic (GCPV) power system
involved in this research situated in Green Energy Research
Center (GERC), University of Technology MARA (UiTM)
Shah Alam, Selangor. The system can be described as Table
1. The data of solar irradiance, module temperature, power,
voltage and current has been analysed from May 2012 which
are recorded every 5 minutes interval using dedicated in-
built data logger in the individual grid inverter.
TABLE I
GCPV SYSTEM DESCRIPTION
Description System
Parameters
Pmp (W)
Vmp (V)
Imp (A)
fdirt
fcable_loss
fmm
faging (%)
Monocrystalline
250
30.5
8.2
-0.42
0.04
0.97
0.98
0.95
1
Array Configuration 2 parallel X 20 series
Total Capacity 10kWp
Type of Inverter/
Efficiency (%) Sunny Tripower STP8000TL
98.3
Type of Mounting
Structure Retrofitted on metal deck
III. LEAST SQUARE SUPPORT VECTOR MACHINES
LSSVM is an alteration of the standard SVM and was
improved by Suykens et al. [39]. LSSVM uses equality
constraints instead of inequality constraints and a least
squares error term instead of the standard error term.
Giving a training data set of N samples
{x_k,y_k }_(k=1)^Nwith input data x_k∈R^n and output
data y_k ∈R one considers the following optimization
problem in primal weight space:
(1)
Subject to
With a function which maps the input space into
a higher dimensional feature space, weight vector in
primal weight space, error variables and bias term b.
Note that the cost function J consists of a sum squared error
fitting error and a regularization term, which is also a
standard procedure for the training of multilayer
perceptrons’s and is related to ridge regression. The relative
importance of these terms is determined by the positive real
constant .
In primal weight space one has the model
(2)
The weight vector w can be infinite dimensional, which
makes a calculation of w from (2) impossible in general.
Therefore, one computes the model in the dual space instead
of the primal space. One defines the Lagrangian
(3)
With Lagrange multipliers called support values.
The conditions for optimality are given by
(4)
These conditions are similar to standard SVM optimally
conditions, expect for the condition . At this point
one loses the sparseness property in LSSVM.
After elimination of w, e one obtains the solution
(5)
with
521
and
According to Mercer’s condition, there exists a mapping
and an expansion
(6)
If and only if, for any such that is finite,
one has
(7)
As a result, one can choose a kernel such
that . The
resulting LSSVM model for function estimation becomes
(8)
Where a, b is the solution for (8). Chosen different kernel
function can build up different LSSVM.
A. LSSVM Model
The design process of LSSVM predictor, error parameter
called hypermeter and kernel function with its parameter
are assigned by user. Parameter determines the trade-off
between margin maximization and training error
minimization. Large give higher penalties to errors and
lower generalization. With different kernel function, the
predictor will perform differently. This research focused on
RBF kernel exp for solar irradiance
prediction.
The parameters included in RBF function
and error parameter in estimate
function.
IV. RESULTS AND DISCUSSION
This research focused on the one day ahead prediction of
solar irradiance. With the time series model and parameters
listed above, the solar irradiance predictors built up with
LSSVM. According to the theory of LSSVM, model should
be built under the training samples. Utilize the 864 groups
minutes solar irradiance (00.00 a.m. to 11.55p.m, Jun 1st-3th,
2014) as training set and the other 864 groups minutes solar
irradiance as testing set to predict solar irradiance values for
the next day (Jun 4th,2014). Prediction on the next day
followed the same steps with previous day solar irradiance
data’s. After grid search and cross validate, RBF kernel
function was selected as shown in Table 2. Fig 1- Fig.3
shows the final prediction results.
By using the assigned values, the testing of the model
is performed. Fig. 1 shows the prediction of solar irradiance
for the whole day. From the graph we can see changes in
three different periods of time including in the morning, in
the noon (maximum sun peak) and the evening. LSSVM
predictor can analyze the characteristic of the solar
irradiance and accurately forecast the solar irradiance for the
next day with 95.43% of accuracy.
TABLE II
PARAMETERS VALUES IN SOLAR IRRADIANCE PREDICTORS.
Parameters Jun 4th Jun 5th Jun 6th
21.9453 14.5980 16.4697
2.0029 1.1534 6.0540
Fig.1. Measured and predicted values (Jun 4th)
Fig. 2. Measured and predicted values (Jun 5th)
Fig. 3. Measured and predicted values (Jun 6th)
Fig. 2 describes the prediction for Jun 5th . We can see that
the trend of solar irradiance almost the same from the
previous day. LSSVM predictor accurately forecast the solar
irradiance with 96.87% accuracy. In Fig.3 we can see the
prediction for the next day based on the previous data.
LSSVM predictor successfully forecast the values and gave
97.75% accuracy. From the results obtained, The LSSVM
522
predictor gave the accuracies which can meet engineering
practice needs.
V. CONCLUSIONS
The performance of the grid connected PV system is
majorly influence by the solar irradiance and module
temperature. The one day ahead of solar irradiance has been
predicted by the LSSVM model. Based on the results, it
shows LSSVM accurately estimating solar irradiance values
by using the previous measured data as inputs. As solar
irradiance change continuously during the day, this
prediction will help preventing from the unbalanced
electricity production caused by uncertain irradiance
conditions.
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