2021 IEEE International Conference in Power Engineering Application (ICPEA), 8-9 March 2021

Solar irradiance prediction for voltage variance

analysis in the GCPV system using LSSVM.

Fahteem Hamamy Anuwar Ahmad Farid Abidin Ahmad Maliki Omar

Electrical Engineering Technology Faculty of Electrical Engineering Faculty of Electrical Engineering
Section) Universiti Teknology Mara Universiti Teknologi Mara
University Kuala Lumpur (British Shah Alam, Selangor, Malaysia Shah Alam, Selamgor, Malaysia
Malaysian Institute) ahmad924@uitm.edu.my maliki_salam@uitm.edu.my
Gombak, Selangor, Malaysia
fahteem@unikl.edu.my

Abstract—The large-scale deployment of green energy [13]. It is well known that the support vector machine (SVM)
technology has led to the explosive development of photovoltaic created by Vapnik [14] is a powerful method for exploring
2021 IEEE International Conference in Power Engineering Application (ICPEA) | 978-1-7281-8546-0/21/$31.00 ©2021 IEEE | DOI: 10.1109/ICPEA51500.2021.9417851

power generation. Prediction of accurate solar irradiance is suitable SVM regressors to construct an efficient prediction
essential to ensure system efficiency and performance. The model. The main aim of SVM regressors is to build the
Least Square Support Vector Machine (LSSVM) model is optimal prediction model that efficiently increases prediction
proposed for predicting solar irradiance of grid-connected accuracy. It is a regularization network which has an
photovoltaic (GCPV) output power. The impact of the increase advantage over the ANN model. To minimize high calculation
in photovoltaic power on the power flow of the grid voltage costs, Lest Square Support Vector Machine (LSSVM) use a
fluctuation is simulated and analyzed using MATPOWER. The
system of least- square parameters through a set of linear
result shows that LSSVM produces promising results for the
short-term prediction of solar irradiance and photovoltaic
equations based on structural risk minimization, thus
output. preventing excess training data and without iterative tuning of
model parameters [15] – [17]. To estimate monthly average
Keywords—LSSVM, solar irradiance, prediction, grid- daily solar radiation using low, medium, and maximum air
connected photovoltaic (GCPV), power flow. temperature measured at 24 sites in China, Wu and Liu have
studied an SVM model [18]. Seven SVMs and five numerical,
I. INTRODUCTION sunshine-based models were developed to predict global daily
Renewable electricity generation has gained momentum in solar radiation at three sites in Liaoning, China. The results
recent decades due to the availability and efficiency of wind showed that all SVMs gave higher performance than empirical
and solar resources. There have been a large number of wind models [19]. In the past year, LSSVM's smart model for
turbines and solar PV installations in recent decades [1] - [2] estimating the regular solar insolation in Turkey was proposed
When it comes to solar energy, various factors, including solar [20], and their applicability has extended in a broad array of
elevation haze and cloud cover, may induce variability in research fields [21] – [24].
energy production [3]. An erratic and non-variable MATPOWER is known to be an open-source power
performance may result in severe negative impacts on the system programming method to solve the problem of power
power grid, thereby restraining widespread green energy flow and optimum power flow. MATPOWER software has
adoption. In order to facilitate generation and transmission of been developed at CORNEL University [25] and uses
wind and solar power, forecasting of the output from power MATLAB as its common platform to provide the facility to
plants has gained importance. change the codes. This software aims to provide facilities for
Artificial neural network (ANN) technique has been research scholars, education professionals and industry related
known as a proven tool for producing accurate radiation issues [26].
prediction results [4] – [8]. The main advantage of ANNs is This research is intended to build a LSSVM basis model
that they do not require as many adjustable parameters as other for the prediction of solar irradiance for photovoltaic (GCPV)
traditional methods and have a better forecasting precision. grid-connected power prediction, which can provide the
Researcher in[9] proposed an ANN model based on a predictive accuracy required. MATPOWER was used to
multicollinear regression (MNLE) algorithm to approximate conduct the IEEE 9-bus system voltage analysis integrated
Turkey's monthly average cumulative global solar radiation. with 30MW GCPV Newton Raphson was selected to solve the
Multilayer perceptron and radial base function (RBF) power flow analysis in this study. The Newton-Raphson
strategies with comprehensive training structures and different method has been researched in [27] – [28], which is the most
combinations of inputs to forecast global horizontal irradiance accurate since it converges easily and is more precise.
in three major cities in the United Arab Emirates [10]. Two
ANNs [11] is used to measure worldwide day-to-day radiation II. BACKGROUND
and hourly direct natural irradiance for the University of
Salerno. ANNs have their drawback because the A. Least Square Support Vector Machine (LSSVM)
backpropagation neural network (BPNN) has difficulties LSSVM has a technical benefit over SVM by transforming
training input data due to iterative alignment of the parameters the quadratic optimization problem into a linear equation
required for secret neurons. After all, it does not always have system. Using time series historical values as data, and the
a uniquely global solution for various models; in addition, single output as a goal, the LSSVM model is developed. The
BPNN has a sluggish response due to its gradient-based principle of optimization has been designed to return the least
learning algorithm and requires a longer training time [12] – complex mathematical equation:

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 ∙ 1 III. DATASET DESCRIPTION
This section explains the location of the site where the data
is measured. It will demonstrate how the information was
In function estimation, the optimization problem is collected and then processed to fit the proposed model.
formulated by minimizing the regular function as:
1 1
A. GCPV System
∙ 2
2 2
Data used in this study have been obtained from the GCPV
system installed at the Green Energy Research Center
(GERC), Universiti Teknologi MARA (UiTM) Shah Alam,
Selangor. Five kWp system using a polycrystalline module
Subject to equality constrains: and retrofitted to a metal deck is used. Data used as input to
∙ 1,2, … 3 the model have been recorded over three years (1 January
2015 to 31 December 2017). The data was sampled every five
minutes using a dedicated data logger. Historical statistics for
To solve this optimization problem, the Lagrange function is the same month shall be drawn from all three years for training
constructed as: and testing.

1
, , : ‖ ‖ !
The irradiance dispersion in January 2015 and January
2
2016 can be seen in Fig.1. At 1.30 p.m., the peak irradiance
value can be observed. It was clear that the trend rose from 10
a.m. and peaked at noon before declining. Three inputs and
one output variables go through the analysis of this prediction
" ! # 4 model. LSSVM model uses two input variables: the number
of days in the month and the cell temperature. Meanwhile,
solar irradiance is the output of the predictor model.
where αi is a Lagrange multiplier. The solution of the B. Data Preparation
equation (4) can be obtained by the partially differentiating A major factor in generating an effective prediction model
concerning w, b, αi, ei and accordingly.
%
is the selection of input variables. Informative inputs causes
0→ 5
the model to map the output effectively and prevent failure.
%& There were 133 samples every day used for the research
sampled every 5 minutes, from 8.00 a.m to 7.00 p.m. Training
%
0→ 0 6
was carried out using the number of days in each month,
%
ambient temperature, cell temperatures and solar irradiance
historical data from January 2015 and January 2016. For each

%
input in January for the two years, cumulative samples of 8246
0→ 7
data are used for network training to obtain model parameters.
% Table I indicates the association of all variables with the
power produced by the PV system. Irradiances indicate a
%
0→ ! 0 8
higher value of the correlation coefficient, suggesting a deeper
%
relationship. A fully clear change follows the change in this
variable in power produced by the PV system. Module cell
temperature and ambient temperature are also important
After the elimination of e and w, the solution is given by the factors that influence the efficiency of the PV system. The
following set of linear equations: effective forecasting of solar irradiance is therefore critical for

0 1 0
the operation and maintenance of solar power plants.
- 3- 3 - 3 9
1 . /0 1
2

where y = [y1, … … yn] and α = [α1, … … αn] This finally

leads to the following LSSVM model for function estimation:

5 , 10

where αi and b are the solutions to the linear system. Several

kernel functions used in LSSVM such as linear, polynomial,
radial basis function (RBF), sigmoid etc. LSSVM is a
technique for regression and provides a computational
Fig. 1. Solar irradiance in January 2015 and 2016.
advantage over SVM. The methods use equality constraints
and adopt the least-square linear system as its function loss
which gave good convergence and high precision.

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 TABLE I. CORRELATION COEFFICIENT BETWEEN VARIABLES. kernel. As a result, the RBF kernel was used as a kernel
function for estimating irradiance in this study.
Power (MW)
Irradiance(W/m )2
0.9981 A. Prediction Results
Ambient Temperature(°C) 0.7477 The simulation was run to verify the developed prediction
Cell Temperature(°C) 0.8329
model by predicting solar irradiance values for 1st, 2nd, and
3rd January 2017. Both data from the experiments are run in
the same predictor model. Historical data on solar irradiance
The data collection containing monthly irradiance, from January 2015 and January 2016 were used for training.
ambient temperature and cell temperature statistics are Fig.2 is the product of the LSSVM training data model. The
provided in Tables II, III and IV. Monthly results observed optimum gamma and sigma values are 610.651 and 293.015,
revealed a similarly distorted distribution for each result. It has respectively. The correlation coefficient (R) of 0.9556 is
been well observed that the spectrum of training is much obtained during the training period, as seen in fig.3. It can be
higher as more data is used in the processing. noted that the projected training results are nearly identical to
the real results.
TABLE II. STATISTIC FOR IRRADIANCE DATA SET
The test of the model is conducted by using the given
Dataset Mean Standard Skewness ymin ymax gamma and sigma value. The efficiency of the proposed
(W/m2) Deviation (W/m2) (W/m2) (W/m2) model in terms of statistical measurement is shown in Table
Training 391.1663 313.8040 0.7053 0 1375 V. RMSE, MAPE and R2 are presented for each model.
Testing 437.2105 299.3364 0.6391 20 1171
Entire 389.9549 311.6866 0.7138 0 1375 The relation between the prediction and the calculated data
for 1-day forecasting is seen in Fig. 4(a) and (b) The accuracy
TABLE III. STATISTIC FOR AMBIENT TEMPERATURE DATA SET of the projection is 87.18% with RMSE 43.83% and MAPE
0.4293%
Dataset Mean (°C) Standard Skewness ymin ymax
Deviation(°C) (°C) (°C) (°C) The findings of the 2-day and 3-day prediction model are
Training 33.7972 5.3921 0.0775 22.7 47.1 seen in Fig. 5 and the fig.6, respectively. For the determination
Testing 35.5782 4.2082 -0.8407 24.6 43.2 of correlation R2, the model showed 88.49% and 88.43%
Entire 33.8246 5.3455 0.0623 22.7 47.1 accuracy for both prediction models. Generally, it can be
found in the test data set that the LSSVM model can produce
TABLE IV. STATISTIC FOR CELL TEMPERATURE DATA SET reasonable outcomes in terms of predicting various time
horizons. The results of the three models are shown in Table
Dataset Mean (°C) Standard Skewness ymin ymax
Deviation(°C) (°C) (°C) (°C)
V.
Training 43.7624 12.4484 0.2887 21.9 73.1
Testing 46.5985 10.1538 -0.2437 24.5 68.2
Entire 43.7746 12.3414 0.2844 21.9 73.1

C. Prediction Measurement
The performance analysis of the proposed model is
assessed with a variety of statistical methods. These are root
mean square error (RMSE), mean absolute percentage error
(MAPE) and coefficient of determination (R2). All the
performance is defined as follows respectively:
7 ! 78
R 1! - 3 1
7
Fig. 2. LSSVM training result

1 7 ! 78
9:;< = > ? 2
7

|78 ! 7 |
:@A< × 100% 3
|7 |
where qi is the measured value and qı̅ of the data, N is the
amount of data.
IV. RESULTS AND DISCUSSION
The simplex algorithm and cross-validation procedure
were considered to obtain the hyperparameters of the LSSVM
model. For each parameter pair, 10-fold cross-validation of
the training set was conducted to predict the error of
prediction. Earlier experiments in the LSSVM time series Fig. 3. Correlation coefficient of the training dataset.
prediction shows the beneficial performance of the RBF

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 (a) Measured and predicted result (a) Measured and predicted result

(b) Linear regression of the model (b) Linear regression of the model
Fig. 4. (a) and (b) show the result for 1-day forecasting. Fig. 6. (a) and (b) show the result for 3-day forecasting.

TABLE V. FORECASTING PERFORMANCE INDICES.

Forecasting
RMSE MAPE R2
Horizon
1 day 43.8246 0.4293 0.8718
2 days 56.5128 0.3473 0.8849
3 days 59.2018 0.3279 0.8883

B. GCPV System Performance

The IEEE 9 bus test system is used to test the solar GCPV
system with a generation profile derived from the radiation
forecast. The performance power of the PV system is
predicted using the predictive irradiance data. MATPOWER
software is used to do a load flow analysis. The primary
research focuses on the expected capacity of the PV system
and the voltage deviation in each bus when the solar PV is
(a) Measured and predicted result
attached to the grid. The research is conducted for the
introduction of the 30MW PV system on bus 4. Fig.7 displays
the IEEE 9 bus system used in this study.
Fig.8 shows the actual and predicted power generated by
the 30MW PV system. The curve in the generation profile
shows increasing generation between 8.00 a.m to 2.00 p.m.
Highest power generated was recorded at 12.35 p.m. with
21MW power.
From Fig. 9, it can be observed that the power output of
the PV system is proportional to the intensity of the solar
irradiance. The module can generate more power represented
by higher peaks on the curves. The highest power of 21MW
generated with an irradiance of 1092W/m2. Fig.10 illustrate
that as irradiance increases, the PV generates a higher voltage
(b) Linear regression of the model in the horizontal axis. Thus, the voltage and power
Fig. 5. (a) and (b) show the result for 2-day forecasting. relationship of a PV module vary at different irradiance levels

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 Fig. 10. Relationship between irradiance and voltage injected at bus 4.

Fig. 7. IEEE 9 bus system

Fig. 11. Bus voltage.

TABLE VI. VOLTA DEVIATION AT BUSES

BUS NO. PV = 0MW PV = 30MW Voltage Deviation
Fig. 8. Actual and predicted power generation.
1 1.0400 1.0400 0.000%
2 1.0250 1.0250 0.000%
3 1.0250 1.0250 0.000%
4 1.0258 1.0261 0.030%
5 1.0127 1.0129 0.023%
6 1.0324 1.0324 0.006%
7 1.0159 1.0159 0.007%
8 1.0258 1.0258 0.007%
9 0.9956 0.9959 0.023%

V. CONCLUSION
Fig. 9. Relationship between irradiance and power generated.
In this research, the LSSVM forecast technique for short-
The load flow analysis results display the percentage of term meteorological time series prediction is presented. This
change in the voltage differential during solar PV penetration. model is used to estimate potential value based on the value
The incorporation of solar PV into bus 4 results in various that has been observed in the past. The results demonstrated
voltage differences as can be seen in fig.11. As the PV is that the LSSVM model could provide a good modelling
attached to the IEEE 9 bus system on bus 4, it can be found approach for the forecasting of solar irradiance in various time
that there is a minor voltage fluctuation in the busses. The horizons.
fluctuation, however, is not too large and within limits. The The power prediction for the GCPV system is required for
results of the voltage deviation for each bus are shown in accurate power planning. The output power of the GVPV
Table VI. Bus 4 voltage rises the most because it is the point system has been estimated based on the LSSVM irradiance
of PV penetration. Other busses affected are busses 5 and 9. prediction model. The result shows that the proposed model is
very efficient and feasible to estimate the output power of the
GCPV system with a value of 0.9965 R2.

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