2018 International Conference on Frontiers of Information Technology (FIT)

Support Vector Machine and Gaussian Process

Regression based Modeling for Photovoltaic Power
Prediction
Sidra Kanwal Bilal Khan Sahibzada Muhammad Ali
Electrical Engineering Electrical Engineering Electrical Engineering
COMSATS University Islamabad, COMSATS University Islamabad, COMSATS University Islamabad,
Abbottabad Campus, Pakistan Abbottabad Campus, Pakistan Abbottabad Campus, Pakistan
sidrakanwal@ciit.net.pk bilalkhan@ciit.net.pk hallianali@ciit.net.pk

Chaudhry Arshad Mehmood Muhammad Qasim Rauf

Electrical Engineering Electrical Engineering
COMSATS University Islamabad, Capital University of Science &
Abbottabad Campus, Pakistan Technology, Islamabad, Pakistan
chaudhry@ciit.net.pk muhammadqasimrauf@gmail.com

Abstract— Grid integration of Solar energy positively affects forecasting is of great concern for grid interfaced PVGs [3].
energy market due to inexhaustible fuel supply and virtually The significance of power forecast is driven by
zero emissions. However, inexhaustible renewable fuel supply is overwhelming grid requirements, ranging from startup time
punctuated by the problem of intermittency. Intermittency of a conventional power plant to the energy market
exacerbates the problem of grid operators to bridge the supply
perspective [4]. The PVG output power depends on solar
and demand gap. Thus, precise output power forecast of grid
interfaced Photovoltaic (PV) systems is required for economic irradiance that in turns varies with cloud motion and
dispatch, market regulation, and stable grid operation. This movement of the earth. The grid instability takes place by the
study compares the statistical models of Gaussian Process abrupt variations of input supply from solar plant to grid.
Regression (GPR) and Support Vector Machine (SVM) for solar Thus, precise forecast is of key importance. The grid operator
power prediction. The models are trained to predict PV system notices the difference between predicted and generated power
output power against the backdrop of data recorded for to timely run the backup generators using an accurate
Abbottabad City, Pakistan. Both the models have been trained, forecast. Consequently, the low operation cost along with
validated, and compared with each other for varying irradiance grid reliability is ensured [5], [6]. Numerous techniques are
and temperature settings. The results depicted that SVM based
proposed in the literature to predict PVG power. Few models
modeling excel in solar power prediction with Root Mean
Square Error (RMSE) lower than GPR based modeling used exogenous data based on satellite images, sky imager
technique. Performance evaluation of models is conducted with information, and nearby installed PV models, while some
error metrics of RMSE, Mean Absolute Error (MAE), and other models used nonexogenous information of location [5].
Mean Square Error (MSE). Moreover, prediction quality is Forecasting span varies from instants to days. Conversely,
qualified based on residual analysis benchmarked by load line spatial prediction perspectives are from individual location to
analysis of PV system in Simulink. a district. Prediction span is categorized as short, medium,
and long duration forecast [7]. An Artificial Neural Network
Keywords – Gaussian process; Microgrid; Machine learning; (ANN) model based 48 hours ahead PVG output power
Photovoltaic system; Support Vector Machine; Solar Power
Prediction
forecasting technique for Italy was recommended in [8]. They
observed that suggested model forecasts PVG power for
I. INTRODUCTION sunny, partial shading and cloudy day having Root Mean
The power output of Photovoltaic Generators (PVGs) is Square Error (RMSE) of 12.5, 24, and 36.9 respectively.
intermittent unlike the conventional fossil fuel based power Autoregressive Moving Average with exogenous inputs
plants [1]. The key phenomena influencing PV systems (ARMAX) for PV power prediction was employed in [9].
performance are earth movements and cloud shading. Earth They established that suggested model improves output
movements are deterministic and hence the PVG output precision. A Numerical Weather Prediction (NWP) technique
power is calculated precisely during clear sky over various based PVG output power prediction was implemented in
time scales. However, cloud shading is random process. The [10]. Multivariate Adaptive Regression Splines (MARS) for
sudden irradiance variations due to partial shading induce power prediction of PV system was described in [11]. They
PVG output power variations. The grid operators are compared results with additional techniques as well. They
concerned for these variations because the abrupt changes in observed that suggested technique achieved better results
grid interfaced PVG power output will result into grid than other methods for testing and training [11].
perturbations [2]. The extensive literature exists about comparison of
The recent smart grid management requires real time statistical and deterministic techniques for modeling PV
energy production, incorporating demand variations and systems. Nonlinear behavior of PVG cannot be accurately
PVG input variations effectively and efficiently. Thus, modeled by using deterministic method. Five parameter
forecasting the energy produced by PVGs helps in the deterministic model is compared with Gaussian Process
effective and secure grid operation. 72 hours ahead Regression (GPR) based technique and superiority of GPR

978-1-5386-9355-1/18/$31.00 ©2018 IEEE 117

DOI 10.1109/FIT.2018.00028
over deterministic modeling is established for internal reserve from GP and basis functions, ℎ [14].The covariance
estimation of PVG in [12]. The highlight of this work is to function assures smooth response. The conversion of (1) is
train Support Vector Machine (SVM) and GPR for PV illustrated in (2).
system power prediction. Both the techniques are then
compared with each other for accuracy. The technique with = ℎ( ) + ( ),
(2)
low estimated forecasting error is declared as appropriate for ( )~ (0, ( , )),
output power prediction.
where ( , ) depicts covariance function. At any time,
The main contributions of this paper are: y is illustrated as (3).
x GPR based statistical modeling of PV system is
developed by considering weather conditions of , ~ ℎ + , ,
(3)
Abbottabad, Pakistan. System is designed for output
power prediction of PVG and Maximum Power Point ( | , )~ ( | + , ),
(MPP) estimation in ambient weather. The remaining model parameters are initial coefficients
x SVM technique for power prediction of PVG is also ( = 1.0855 + 5 ), and variance ( = 72.97 + 3 ).
developed for varying temperature and irradiance Matern 5/2 is chosen as the kernel or covariance function ( ),
settings. The model is also formulated for MPP in as illustrated in (4).
ambient weather settings.
x Both the statistical models are compared with each other
, = 1+
√
+ exp −
√
. (4)
for accurate solar power prediction. Moreover,
performance evaluation of models is conducted with
error metrics. where = − − is the Euclidean
The work is structured as: Section II demonstrates distance between and [14].
statistical techniques of GPR and SVM for output power
prediction of PV system. The generally used performance B. Support Vector Machine
evaluation indicators are also described. Section III presents SVM is a kernel function based nonparametric technique.
microgrid architecture, training data description, and The technique is created on Structural Risk Minimization
comparative analysis of GPR and SVM. Finally, conclusion (SRM). The SRM based learning algorithms involve control
and future directions are illustrated in Section IV. of two factors namely empirical risk and confidence interval
value. First term in inequality of (5) is empirical risk and
II. MATERIALS AND METHODS
other is confidence interval.
Artificial intelligence teaches computer to learn a specific
task independently using data without relying on ≤ + Φ . (5)
mathematical analysis. Machine learning demonstrates ℎ
computers to acquire from experience. The algorithms where /ℎ denotes relation between training samples and
adaptively learn accurately by increasing training data Vapnik-Chervonenkis (VC) dimension of machine’s
samples. The image and speech recognition, electricity load functions. SVM keeps empirical risk value fixed or zero and
forecasting, and data mining are numerous applications of minimize value of confidence interval. Thus, the task is to
machine learning, categorize as supervised and unsupervised search for function that results in minimized error for training
learning. Supervised learning predicts future response by data samples. SVM implement sets of functions, as depicted
training input samples. Regression learning estimates in (6).
continuous response, while Classification learning estimates
categorical output [13]. GPR and SVM techniques of
supervised learning is used in this paper for PVG output ( , , )= ( , )− . (6)
power prediction.
A. Gaussian Process Regression where is an integer, scalars in are = 1, … . . , ,
In this section, GPR method is summarized for predicting while vectors in are = 1, … . . , . ( , ) is kernel
dynamic system of PVG. The regression framework takes symmetric function [15]. Continuous function of accurate
degree can be approximated by using neural network,
training sets = , = 1, … . . } as input, where , x,
polynomial or radial basis function kernel type. The kernels
and y presents observations, covariates, and response generating polynomials, radial basis function, and neural
respectively. Trained GPR forecasts for an input . networks to obtain approximating functions are illustrated in
The model is represented in (1). (7), (8), and (9) respectively. Thus, learning machine is
(1) categorized by only varying kernel ( , ) in SVM. The
= + , ~ (0, ), best possible results are achieved, if vectors in (6) overlap
with majority vectors of training datasets.
where denotes error variance and are coefficients
calculated from input data. ( , ) = [( ∗ ∗)
+ 1] . (7)
Gaussian Process (GP) is definite random variables count
having collective Gaussian distribution. GPR model converts ( , )= (| − |). (8)
(1) by incorporating latent variables , = 1,2, … ,515,

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 Fig. 1. Schematic of Machine Learning based grid interfaced PV system.

( , )= ( ( ∗ ) + ). (9)
1 (12)
= .
SVM has low complexity and good data fitting feature.
SVM performs multiple linear regression employing
transformed predictors. The objective is to observe and fine III. RESULTS AND DISCUSSION
tune three major parameters: precision (H), cost (C) to handle The comparison of SVM and GPR based PVG modeling
tradeoff concerning model complexity and accuracy, and
is presented here. The model with an appropriate output
kernel regulator (J). The underlying ability of SVM to
power prediction is qualified as better technique for opted
generalize solutions for non-linear problems is remarkable
[15]. climate conditions. RMSE, MBE, and MSE serve as
prediction quality parameters. Moreover, model reliability is
C. Evaluation of Model Parameters established through visual analysis of residual plots of
Few standard statistical error metrics are employed in this respective modeling technique.
work. The purpose is to evaluate and compare two techniques
of GPR and SVM for accurate output power prediction [13]. A. Microgrid Architecture
Mean Absolute Error (MAE) and Mean Biased Error (MBE) The system under observation is a microgrid model
are presented in (10) and (11). consisted upon 100kW PVG and 50kW backup diesel
generator connected to a utility grid, as depicted in Fig. 1. The
1 (10)
= ( , − , ). diesel generator serves as a peaker plant to balance supply
demand variance, after the PVG’s internal power reserve is
exhausted. Unbalance of supply and demand is reflected by
1 (11) the grid frequency deviation. The power demand greater than
= , − , .
supply results in grid frequency rise from nominal 60Hz, and
vice versa. Microgrid Control System (MCS) is a centralized
where , denotes measured power, , represents
microgrid control architecture, that supplies PWM for
forecast of prediction method, and N is data samples. suboptimal MPP operation[12]. The suboptimal MPP is
suggested by either the SVM or GPR model, and is fine-tuned
MBE is not a consistent parameter, because data
based on the unbalance grid frequency. MCS also generates
residuals constantly compensate one another. However, MBE
presents model’s capability for estimation. RMSE is depicted inverter control signals to produce three phase grid interfaced
in (12). Meteorology, Economics, and Regression analysis 240V (RMS) voltages. During utility grid faults, MCS
are few fields using RMSE as performance evaluation isolates the microgrid by connecting microgrid islanding
indicator [13]. relay. Finally, in the event of the PVG saturation at 95% of
MPP operation, MCS activates secondary frequency
protection layer by triggering the peaker plant.

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B. Site Description and Data
The training data for both statistical models are yearly
irradiance and temperature recorded for Abbottabad,
Pakistan. During Autumn and Spring, temperature changes
from mild to warm. However, hot weather is experienced in
middle of year with cool to mild conditions in Winter time.
Heavy monsoon season in July through September is
followed by sparse snowfall in the months of December and
January [16]. Both GPR and SVM is trained for the climate
data of Abbottabad, Pakistan.
The irradiance data illustrated in Fig. 2 as scatter plot is
recorded annually in HOMER software. Hours, days, and
irradiance are depicted on the x, y, and z axis respectively.
Fig. 3 presents average temperature per month during 2009-
Fig. 4. Training data of Irradiance, Maximum power, and Temperature for
2017 [17]. Peak temperature is observed in the mid of every GPR and SVM based modeling.
year. The relation of maximum output power, temperature,
and irradiance is represented in Fig. 4. The collected data of C. Model Training
irradiance, temperature, and computed maximum power are SVM and GPR models are trained for data obtained from
used to train GPR Matern 5/2 and SVM technique. Maximum the load line analysis of a 100kW PVG. The climate
power output is predicted using trained model for ambient conditions of Abbottabad, Pakistan are tabulated as training
irradiance and temperature settings. inputs or predictors. The maximum power of PVG obtained
from load line study in Simulink is tabulated as training
output or response. The 515 predictor samples and respective
response observations are fed into Statistics and Machine
Learning Toolbox of MATLAB. Model for training are SVM
and GPR Matern 5/2 model. The models are anticipated to
forecast maximum power output as anticipated by the
respective irradiance and temperature, learnt from training.
Predicted versus Actual plot in Fig. 5. compares SVM and
GPR responses with true response. The technique of best
prediction quality is expected to lie flatly on the diagonal line,
represented by the true response. Fig. 5. depicts a close
matching of the two modeling techniques.

Fig. 2. Photovoltaic annual irradiance model of Abbottabad,

Pakistan.

Fig. 5. Response plot comparing SVM and GPR response with true
response.

Fig. 6. and Fig. 7. represent individual impact of input

predictors of irradiance and temperature on the predicted
response, that is PVG output power of two modeling
Fig. 3. Average temperature of Abbottabad, Pakistan observed per techniques. The individual predictor impact of the two
month in 2009-2017. techniques is also closely matched, as anticipated from the
Predicted versus Actual plot in Fig. 5.

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 The superiority of SVM is further cemented by comparing
performance indices of two techniques, as highlighted in
Table 1. The indicators opted for evaluation are MSE, RMSE,
and MAE. It is clear from Table I that SVM technique
estimates nonlinear behavior of PV system more
appropriately than GPR and thus accurately predicts output
power.
TABLE I. Performance indicators comparison of GPR and SVM.

Gaussian Process Support Vector

Performance Indicators
Regression Machine
Root Mean Square
102.32 22.31
Fig. 6. Irradiance impact on plot comparing SVM and GPR response with Error (RMSE)
true response. Mean Absolute Error
76.21 15.43
(MAE)
Mean Square Error
10468.72 497.93
(MSE)
Training Time (s) 19.97 16.87

IV. CONCLUSION AND FUTURE WORK

Numerous models for PV system output power prediction
are proposed and tested lately. In this work, GPR and SVM
based statistical model is trained for output power forecast of
PV system. The techniques have been trained, tested, and
validated for varying temperature and irradiance conditions
of Abbottabad, Pakistan. The performance of both statistical
techniques is evaluated using standard statistical error
Fig. 7. Temperature impact on plot comparing SVM and GPR response
with true response.
metrics. It is observed that RMSE for GPR is 102.32, while
that of SVM is 22.31. Thus, SVM based trained model is
Residual plot is another helpful tool to minutely compare better than GPR for proposed scenario of power prediction.
the prediction quality of any model. Residual plot displays In future, extended microgrid incorporating multiple
the error between the predicted and the true response. The sources will be simulated. Hardware validation of the
model with residuals concentrated symmetrically across the statistical techniques will be carried out for testing purpose.
x-axis is expected to perform better. The residuals of SVM
are more symmetrically concentrated along the x-axis, as
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