Smart Grid and Renewable Energy, 2013, 4, 32-38
http://dx.doi.org/10.4236/sgre.2013.46A004 Published Online September 2013 (http://www.scirp.org/journal/sgre)
Decision Technique of Solar Radiation Prediction Applying
Recurrent Neural Network for Short-Term Ahea d Power
Output of Photovoltaic System
Atsushi Yona1, Tomonobu Senjyu1, Toshihisa Funabashi2, Paras Mandal3, Chul-Hwan Kim4
1University of the Ryukyus, Okinawa, Japan; 2Meidensha Corporation, Tokyo, Japan; 3University of Texas at El Paso, El Paso, USA;
4Sungkyunkwan University, Suwon City, South Korea.
Received May 8th, 2013; revised June 8th, 2013; accepted June 15th, 2013
Copyright © 2013 Atsushi Yona et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In recent years, introduction of a re newab l e en ergy source such as solar en ergy is exp ected. However, solar radiation is
not constant and power ou tput of photovoltaic (PV) system is influenced by weather conditions. It is difficult for getting
to know ac curate power ou tput of PV system. In or der to forecast the p ow e r output of PV system as accurate as possible,
this paper proposes a decision technique of forecasting model for short-term-ahead po wer output of PV system ba sed on
solar radiation p redictio n. Ap p lication of Recurrent Neural Network (RNN) is shown for solar r adiation prediction in
this paper. The proposed method in this paper does not require complicated calculation, but mathematical model with
only useful weather data. The validity of the proposed RNN is confirmed by comparing simulation results of solar ra-
diation forecasting with that obtained from other method
Keywords: Neural Network; Short-Term-Ahead Forecasting; Power Output for PV System; Solar Ra diation
Forecasting
1. Introduction
Solar energy is well-known as clean energ y because of
no carbon dioxide emission. Ther efore, photo-vo ltaic
(PV) systems are rapidly gaining acceptance as one of
the best solutions for the alternative energy source. How-
ever, solar radiation is not constant and the output of PV
system is influenced by solar radiation and weather con-
ditions. At the point of view to improve the control per-
formance of power systems, the r e should be an estima-
tion of output of PV system as accurate as possible. In
electric companies, solar radiation forecasting is an im-
portant tool for utilizing the hybrid power systems with
the storage b atter y, solar cells, wind generators, etc. For
example, amount of storage battery energy is decided by
forecasting data easily. These decisions are benef i t s for
effective running of hybrid power systems and conse-
quently their profitability depends on the forecast tech-
nique. Therefore, a good solar radi ation forecas ting
method is required. Although the technique to forecast
the generating p o wer of PV system based on solar radia-
tion forecasting is regarded as an effective method in
practical applications, it requires solving differential
equations by using large meteorological and topographic
data. In add ition, although Meteorological Agency or
weather service will pr ovide forecasting data free of
charge, the implementation of above-mentioned techni-
ques results in higher cost. Because, these data are fore-
casting data of a wide area mostly, and are difficult for
getting to know the exact value of the place in which the
PV system is installed. To overcome these problems,
forecasting technique should be inexpensive and easy-
to-use. Application of Neural Network (NN) is known as
a convenient technique for forecasting. It is possible to
forecast solar radiation with only meteorological data.
Most of the papers have reported application of feed-
forward neural network (FNN) for solar radiation fore-
casting [1-6]. However, what seems to be lacking is per-
formance comparison for solar radiation forecasting of
FNN and other NN. Because the forecast result of using
NN is usually case-by-case with stochastic appearance of
solar radiation. This paper proposes the power output
forecasting of PV system based on solar radiation fore-

Decision Technique of Solar Radiation Prediction Applying Recurrent Neural
Network for Short-Term Ahead Power Output of Photovoltaic System
33
casting at several-hour-ahead by using Recurrent Neural
Network (RNN). S ince RNN is known as a good tool for
time-series data forecasting [2-6], the authors propose the
application of RNN for solar r ad iation forecasting. In this
paper, the proposed technique for application of RNN is
trained by only historical data of solar rad iatio n and
tested for the target term. Additionally, these d ata are
observed only one site, and the type of RNN us ed is El-
man network [7-9]. Then, the power output of PV system
is calculated by the forecasted solar radiation data. The
validity of the proposed RNN is confirmed by comparing
the forecasting abilities of FNN and RNN on the com-
puter simulations at sev eral-hour -ahead.
2. Neural Network
Figure 1 shows the flow chart for the learning algorithm
of NN, which is adopted in this paper. NN is stratified as
shown in the block chart at the left of Figure 1. For the
purpose to compare the forecasting results of applying
FNN and RNN, input data is based on same meteoro-
logical data. The information of meteorological da ta
transmits to one direction between each layer in FNN.
On the other hand, RNN has feedback structure that in-
formation transmits from hidden-layer to input-layer in
the learning algorithm. That is the big difference between
FNN and RNN . NN is trained by iterating thes e informa-
tion transmissions. In so l ar radiation forecasting, the me-
teorological dat a u sed for training the NN are only the
historical data of actual sola r radiation (for the p eriod
of16 day). Solar radiation forecasting is obtained by us-
ing FNN and RNN with the abov e-mentioned learning
algorithm and forecasting technique. More detail struc-
ture and techniques for application of FNN and RNN are
mentioned in Sections 2.1 and 2.2.
2.1. Feed-Forward Neural Network
Figure 2 shows the FNN having n and m numbers of
input-layer neurons and hidden-layer neurons, and 1
output-layer neuron. These neurons are connected line-
arly by each other, and x1 ∼ xn are input data to NN.
There are con nection weights between each neur on.
Output of hidden-layer neurons are transformed nonline-
arly by the sigmoid function [1]. The sigmoid function is
pre s ented by (1), and the input-and-ou tput characteristic
is shown in Figure 3.
( )( )
21
1 exp2
fx x = −
+−
(1)
where, x is the input data.
In order to learn NN, input data x is standardized and
inputted so that each unit output mayexist in the activi-
Figure 1. Learning algorithm of NN.
Figure 2. Feed-forward neural network.
Figure 3. Hyperbolic tangent sigmoid function.
tion area shown in Figure 3. In this paper, input data was
standardized to between 1.0 and 1.0. Back Propaga-
tion(BP) method is adopted for learning the NN. Gener-
ally, BP is explained as follows. To begin with, output of
hidden units is transmitted to output units. Then, the out-
put of output units is compared with teaching signal T as
shown in Figure 2. Finally, to minimize the mean square

Decision Technique of Solar Radiation Prediction Applying Recurrent Neural
Network for Short-Term Ahead Power Output of Photovoltaic System
34
error margin, each connection weights and the value of
each unit are changed in direction of straight line from
output layer to input layer. In this paper, Levenberg-
Marquardt algorithm was adopted for updating each
connection weight of unit [10]. The inertia and learning
coefficient are the parameters of NN. The inertia pro-
motes learning speed acts rapidly by changing each con-
nection weights of neurons. The learning coefficient is
explained, this parameter is preferred to large. At this
time, it is necessary to stable the least square error mar-
gin of NN model. The authors decide these parameters
by trial-and-error method [5,6]. The effective learning
has been improved by multiplying the learning coeffi-
cient by the learning increase rate and the learning de-
crease rate, and then variable of least square error margin
is adjusted. Moreover, optimum number of hidden-layer
neurons is decided to minimize the output error of NN by
simulation result with using the training data [9].
2.2. Recurrent Neural Network
Figure 4 shows the RNN model of Elman type [8]. Neu-
ron characteristic of RNN is the same as that of FNN,
and it trained by BP. But, as shown in Figure 4, RNN
has context-layer. These layers are copy of one-step de-
layed hidden-layer, and added as feedback structure. The
context-layer reflects both input-layer and output-layer
information to the structure of RNN, by intervening the
feedback structure between output of input-layer and
hidden-layer. In consequence, the historical information
is maintained to RNN with the progress of learning. In
Figure 4, Yt is the output of the hidden-layer, and Ytn is
the output of the context-layer. Yt is represented by the
following equation:
21
12 3n tntttt n
YY rYrYrY
−
−− −−
=+ +++ (2)
where, r is called a residual ratio. The value of r is be-
tween 0 and 1. Resulting from training RNN, historical
information is reflected to RNN. In time-series data fo-
recasting, it is difficult to maintain the historical infor-
mation by using simply FNN. But, the composition of
RNN thath as the feedback structure is said to be effec-
tive [8].
2.3. Input Data
The meteorological data of last 16 days were used for
training the NN. NN was learned by every pattern data of
several-hour-ago and several-hour-ahead. Solar radiation
changes greatly with seasonal change. Thu s, it is difficult
to forecast solar radiation on the same study conditions.
Therefore, correlation with NN and solar radiation data
for forecasting was strengthened by using the data of the
amount of global horizontal solar radiation. The maxi
mum solar radiation n value is determined by “Top-
of-Atmosphere”, which is incoming to unit area on at-
mosphere outside, namely global horizontal solar radia-
tion [11]. As shown in Figure 5, global horizontal solar
radiation changes under a constant regularity in every
year. In solar radiation forecasting, it becomes effective
to make time progresses learn to NN together with global
horizontal solar radiation. Moreover, solar radiation is
strongly influenced by the monthly distribution of at-
mospheric pressure. Because the distribution of atmos-
pheric pressure changes with “migratory anti-cyclone in
4-day cycle” in Japan. Hence, learning data of NN are
needed sufficien tly. Therefo re, th e meteoro logical d ata of
last 16 days were used for training the NN. Moreover,
predicted temperature was used as learning data of NN.
Since temperature is strongly influenced by the solar
radiation change, solar radiation forecasting is improved
by correlation of NN with using predicted temperature.
Forecast area is Okinawa Prefecture, Naha City of Japan.
In this paper, learning data of NN is used for the ground
observation data that the “Japan Meteorological Business
Support Center” had issued [12]. In solar radiation fore-
Context-layer
tn
Y t
Y
H 1
H 2
x
2
x
3
x
1
x
l
.
.
.
.
.
.
H m
.
.
.
.
.
.
.
.
.
I 1
I 2
I
l
I 3
.
.
.
.
.
.
.
O 1
T 1
O 2
T 2
O n
y n
T n
..
.
.
.
.
y
y
1
2
Figure 4. Recurrent neural network (Elman type).
0
1.00
2.00
3.00
4.00
5.00
6.00
51015 20
21 Jun., 2000, at NAHA
Time t [hour]
Solar radiation I [MJ/m ]
2
Global horizontal solar radiation
Ground-based solar radiation
Figure 5. Global horizontal solar radiation for Top-of-At-
mosphere.

Decision Technique of Solar Radiation Prediction Applying Recurrent Neural
Network for Short-Term Ahead Power Output of Photovoltaic System
35
casting, input data x1 - x12 as shown in Figures 2 and 3,
x1 - x3 is (solar r adiatio n data of 3 hour before)-(1 hour
before), x4 - x6 is (atmospheric global solarradiation of 3
hour before)-(1 hour before), x7 - x9 is (atmospheric
pressure of 3 hour before) - (1hour bef ore), x10 - x12 is
(temperature of 3 hour before)-(1 hour before), and
teaching signal T1 - T3 is (solar radiation data of 3 hour
after)-(1 hour after). These data of NN are shown in Ta-
ble 1. At forecasting time, since the forecast results are
obtained by only x1 - x12 to NN as input data, teaching
signal T1 - T3 are not needed. But, predicted temperatures
x10 - x12 are needed for input of NN. Although predicted
temperature could predict by c hanging teaching signal
Tinto temperature, in this paper, predicted temperature
inputted actual data. Because of that is to compare the
forecasting results by us in g the historical da ta which
made x10 - x12 (temperature of 3 hour before) - (1 hour
before). Calculation results of the forecasted error from
solar radiation forecasting in each month are shown in
Section 4.
3. Solar Radiation Forecasting Result by
Using FNN and RNN
Table 2 shows the parameters in learning of NN, each
parameter is fixed. The calculation time was 20 - 30
seconds. The learning of NN was simulated with
CPU-Intel(R)-Celeron(R)-2.7GHz computer. This Sec-
tion shows the simulation results of solar radiation fore-
casting and calcul a t ed Mean Absolute Percentage Er-
ror(MAPE) for the forecasted error by using FNN and
Table 1. Input data.
x1 - x3 Solar radiation at 2 hour ago-present time
x4 - x6 Atmospheric global solar radiationat 2 hour
ago-present time
x7 - x9 Atmospheric pressure at 2 hour ago-present time
x10 - x12 T emperature at 1 hour ahead-3 hour ahead
Teaching signal
T1 - T3 Solar radiation at 1 hour ahead-3 hour ahead
Table 2. Learning parameters of NN.
Number of input layer neuron 12
Number of hidden layer neuron 20
Number of output layer neuron 3
Learning coefficient 0.01
Inertia coefficient 0.25
Learning time 800
RNN in each month. MAPE is represen t e d by:
[ ]
1
100
%
ii
Nfa
i
ia
PP
MAPE NP
=
−
=∑
(3)
where, N is the number of data, Pf is the forecast value,
Pa is the actual value, and i is the number of forecasting
days. Figure 6(a) is the resul t of using only the historical
data in solar radiation forecasting. Figure 6(b) is there
sult of using predicted temperature. As shown in Figure
6, that a forecast error was decreased by using predicted
temperature. In this paper, to compare the forecast per-
formance of FNN and RNN by simulation, each parame-
ters of NN, e.g., number of neurons, learning coe fficient,
and input data are limited.
However, the number of hidden-layer neurons is de-
cided to minimize the output error of NN by simulation
result with using the training da ta. There are some meth-
ods for obtaining the number of hidden-layer neurons;
however, there is no general solution for this problem. In
this paper, a trial-and-error method has been used to de-
(a)
(b)
Figure 6. Forecast error to number of hidden-neurons. (a)
Using past data of temperature; (b) Using forecasted data of
temperature.

Decision Technique of Solar Radiation Prediction Applying Recurrent Neural
Network for Short-Term Ahead Power Output of Photovoltaic System
36
termine the appropriate number of hidden-layer neurons
[9]. It starts with 1 neuron and the n gradually incr eases
the number and calculates the learning error. Learning of
NN is carried out until it reaches the lowest tr ain ing error.
In Figure 6(b) for this study, th e op timized number of
hidden-layer neurons is 20. Thus, trial-and-error method
has been used to d etermine the number of input neurons,
too. Hence, appropriate parameters of NN are determined
in this paper.
Figure 7 shows the results of solar radiation forecast-
ing in June. These results show th e forecast errors are
(a)
(b)
(c)
Figure 7. Several hours ahead solar radiation forecasting
(Jun., 2000). (a) 1 hour ahead; (b) 2 hour ahead; (c) 3 hour
ahead.
minimize d by using RNN. The result of using RNN,
forecast error (MAPE) is 10.85% in 1-hourahead, 12.61%
in 2-hour ahead, and 12.97% in 3-hour ahead. The result
of using FNN, forecast error is 12.36% in 1-hour ahead,
12.81% in 2-hour ahead, and 1 3. 90% in 3-ho ur ahead. As
shown in Figu re 7, it is possible to o b tain go od forecast-
ing results by the progress of effective learning in the
solar radiation changing with regularity. Figure 8 shows
the results of solar radiation forecasting in July. The re-
sult of using RNN, forecast error (MAPE) is 15.86% in
1-hour ahe ad, 16.06% in 2-hour ahead, and 15.40% in
3-hour ahead.
(a)
(b)
(c)
Figure 8. Several hours ahead solar radiation forecasting
(Jul., 2000). (a) 1 hour ahead; (b) 2 hour ahead; (c) 3 hour
ahead.

Decision Technique of Solar Radiation Prediction Applying Recurrent Neural
Network for Short-Term Ahead Power Output of Photovoltaic System
37
The result of using FNN, forecast error is 18.58% in
1-hour ahead, 20.10% in 2-hour ahead, and20.33% in
3-hour ahead. As shown in Figure 8, as forecast time
lengthens, forecast error increases. That appeared promi-
nently in resul t of Figu re 8( c). In th at case, mean
squa red error of NN model becomes unstable. Although
the time-series information is destroyed by the fluctua-
tion of solar radiation in Ju ly , forecast errors are mini-
mized by using RNN. Figure 8 demonstrated the re-
sultsthat time-series information is maintained to RNN
structure by the progress of effective learning. Figure 9
shows the calculated MAPE of solar rad iatio n for ecast in
(a)
(b)
(c)
Figure 9. Mean absolute percentage error in each month(1
Jan. 31 Dec., 2000, solar radiation). (a) 1 hour ahead; (b) 2
hour ahead; (c ) 3 hour ahead.
each month. Result of maximum forecast error is ap-
peared in July, and result of minimum error is appeared
in June, and there are 5% - 0% difference. That reason is
above-mentioned in Fig ure 8, and forecast erro rs are
minimize d by using RNN from 1-hour ahead to 3-hour
ahead forecasting. The validity of using RNN is con-
firmed from results of Figure 9.
4. Forecasting Result of Power Output for
PV System
In this Section, the method of calculating the power gen-
eration electric power of PV system from the solar radia-
tion forecasting value obtained by NN are shown. And,
the authors confirm the validity of the proposed method.
In the PV system [13], per unit area of power output Ps is
given as:
( )
( )
2
10.00525 kW/m
O
Ps SIt η

=−+

(4)
where, η is the conversion efficiency of solar cell array
(%), S is the array area (m2), I is thesolar radiation (kW
/m2), tO is the outside air temperature (˚C). If the above
equation of PV system is used, the power outpu t of PV
system can be forecasted by using only weather data. In
this paper, assume that sum total solar r adiation w ill be
falling on the solar cell array, and it does not consider the
incidence angle of solar radiation and solar cell array.
Moreover, assume that the conversion efficie ncy of solar
cell array η is 15.7%, array are a S is 1 m2. As shown in
(4), since conversion efficiency of solar cell η and array
area S are constant. There f ore, we can see the power out-
put Ps is the function of outsid e air temperature tO and
solar radiation I. In this paper, power output of PV sys-
tem is computed as temperature data x10 - x12 which used
in the solar radiation forecasting is temperature tO. The
forecast pow er output result of the PV system in July that
the solar radiation forecast error has been improved is
shown in Figur e 10. Thus, the p ower output of PV sys-
tem can be forecasted from the solar radiation forecast-
ing.
5. Conclusion
This paper proposed the power outpu t f orecastin g for PV
system ba sed on solar rad iat io n fo r ecas ti ng by using
RNN. The merit of the proposed method is that it does
not require complicated calculations but the mathemati-
cal model with only meteorological data. At that time of
solar radiation forecasting, it can be possible to shorten
the forecast time by using only historical data. Moreover,
RNN is a good tool for time-series data forecasting. RNN
is able to forecast solar radiation accuracy. In fact, it is
possible to forecast preferred results by using only his-
torical data in short time. The validity of the pro-

Decision Technique of Solar Radiation Prediction Applying Recurrent Neural
Network for Short-Term Ahead Power Output of Photovoltaic System
38
(a)
(b)
(c)
Figure 10. Forecast results of several hour ahead power
output for PV system (Jul., 2000). (a) 1 hour ahead; (b) 2
hour ahead; (c ) 3 hour ahead.
posed RNN is confirmed by comparing forecasting re-
sults with that obtained from FNN. It is found that fore-
cast errors are greatly minimized by RNN. Hence, the
proposed RNN shows a good performance to forecast
power output of PV system.
REFERENCES
[1] P. D. Wasserman, “Neural Computing: Theory and Prac-
tice,” Van Nostrand Reinhold, New York, 1989.
doi:10.1016/0893-6080(90)90059-T
[2] T. Hiyama and K. Kitabayashi, “Neural Network Based
Estimation of Maximum Powergeneration from PV Mod-
ule Using Environmental Information,” IEEE Transaction
on Energy Conversion, Vol. 12, No. 3, 1997, pp.
241-247. doi:10.1109/60.629709
[3] A. Sozen, E. Arcakhoglu, M. Ozal p and N. Caglar, “Fore-
casting Based on Neural Network Approach of Solar Po-
tential in Turkey,” Renewable Energy, Vol . 30, No. 7,
2005, pp. 1075-1090. doi:10.1016/j.renene.2004.09.020
[4] H. K. Elminir, F. F. Areed and T. S. Elsayed, “Estimation
of Solar Radiation Components Incident on Helwansite
Using Neural Networks,” Solar Energy, Vol. 79, No. 3,
2005, pp. 270-279. doi:10.1016/j.solener.2004.11.006
[5] K. S. Reddy and M. Ranjan, “Solar Resource Estimation
Using Artificial Neural Networks and Comparison with
Other Correlation Models,” Energy Conversion and Man-
agement, Vol. 44, No. 15, 2003, pp. 2519-2530.
doi:10.1016/S0196-8904(03)00009-8
[6] M. Mohandes, A. Balghonaim, M. Kassas,S. Rehm an and
T. O. Halawani, “Use of Functions for Estimating Monthly
Solar Radiation,” Solar Energy, Vol. 68, No. 2, 2000, pp.
161-168. doi:10.1016/S0038-092X(99)00071-7
[7] Y. Kitamura and A. Matsuda, “Study on Raising Effi-
ciency of Heat Accumulating Air Conditioning System
Using Knowledge Precessing Techniques,” Journal of
Mitsubishi Research Institute, No. 36, 2000, pp. 31-51.
[8] J. F. Elman, “Finding Structure in Time,” Cognitive Sci-
ence, Vol. 14, No. 2, 1990, pp. 179-211.
doi:10.1016/0364-0213(90)90002-E
[9] B. Kermanshahi, “Recurrent Neural Network for Fore-
casting Next 10 Years Loads of Nine Japanese Utilities,”
Neurocomputing, Vol. 23, No. 1-3, 1998, pp. 125-133.
doi:10.1016/0364-0213(90)90002-E
[10] M. T. Hagan and M. B.Menhaj, “Training Feed-Forward
Networks with the Marquardt Algorithm,” IEEE Trans-
actions on Neural Networks, Vol. 5, No. 6, 1994, pp. 989-
993. doi:10.1109/72.329697
[11] M. Santamouris, G. Mihalakakou, B. Psiloglou, G. Eftax-
ias and D. N. Asimakopoulos, “Modeling the Global So-
lar Radiation on the Earth’s Surface Using Atmospheric
Deterministic and Intelligent Data-Driven Techniques,”
American Meteorological Society, Vol. 12, No. 10, 1999,
pp. 179-211.
[12] AmdView(C) Weather Toy, “Meteorological Data Base:
Ground Observation Ver. 1.00,” Japan Meteorological
Business Support Center, Tokyo, 2004.
[13] A. Iga and Y. Ishihara, “Character istics and Embodiment
of the Practical Use Method of ‘Monthly Temperature
Coefficient’ of the Photovoltaic Generat ion System,” IEEE
Japan Transactions on Power and Energy, Vol. 126, No.
8, 2006, pp. 767-775.