-
reviewed in [1,2]. These estimates are necessary in order
to:
Renewable Energy 31 (2006) 781790
www.elsevier.com/locate/reneneE-mail address:
[email protected]. Kaplanis*
Head of Renewable Energy Laboratory, TEI of Patra, Meg.
Alexandrou 1, Patra 26334, Greece
Received 30 November 2004; accepted 8 April 2005
Available online 9 June 2005
Abstract
This paper describes two new friendly and reliable approaches to
estimate hourly global solar
radiation on a horizontal surface even with a pocket
calculator.
Such fast and reliable predictions for the hourly solar
radiation are necessary for the real-time
management of both the solar energy sources, like a PV generator
output in the one hand and the
power loads, on the other.
The predicted global solar hourly radiation values are compared
with estimates from two existing
packages and the recorded solar radiation for the two biggest
cities of Greece.
The two methodologies presented in this paper can be applied to
any other site.
q 2005 Elsevier Ltd. All rights reserved.
Keywords: Hourly solar global radiation; Energy and load
management; Prediction
1. Introduction
Methodologies for the estimation of the hourly global solar
radiation in a day nj, on the
horizontal, I(h;nj), have been elaborated and proposed by many
researchers, as they areNew methodologies to estimate the
hourly
global solar radiation; Comparisons
with existing models0960-1481/$ - see front matter q 2005
Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2005.04.011
4366.* Address: Megalou Alexandrou 1, Koukouli, 26334 Patra,
Greece. Tel.: C30 261 036 9015; fax: C30 261 031
-
S.N. Kaplanis / Renewable Energy 31 (2006) 781790782thisand;nj)
for the representative day of the months January and July.
Third, a new approach to Jains model, as it was modified by Baig
[19,20], was tried in
paper and the new estimates for both cities in the same days, as
above, were obtainedI(ha. Size properly solar thermal or solar
power systems, i.e. PV-generators [3] and predict
their daily or their long term expected performance.
b. Manage simultaneously both the solar energy source, e.g. the
output of a PV system and
the power loads.
The target is to determine via the estimated global solar hourly
radiation the power
output to meet the loads, according to the priorities set in a
micro-processor control
system.
The aforementioned methodologies are based either on the
analysis of recorded
data [410] or on modeling techniques based on the analysis of
meteorological data,
like humidity, ambient temperature, wind speed, etc. in order to
predict I(h;nj) [11,12]
where h is the solar hour and nj is the number of the day
measured from the 1st of
January.
From the ASHRAE model of the clear sky [13], various
methodologies were elaborated
which resulted to sophisticated packages such as the METEONORM,
which is both a data
bank in meteo solar data and a software package [14], using
auto-regression techniques to
simulate expected stochastic variations in I(h;n).
The solar radiation data used for the prediction of I(h;n) in
the methodologies
proposed in this study, are usually available on an hourly or
monthly basis for Greece
[15,16]. Therefore 12 monthly values which give the solar
radiation on the horizontal are
provided.
From the 12 monthly figures of solar radiation one might use a
top down approach
to determine I(h;nj) from the determination of the clearness
index kt(h;nj) as described in
[17,18].
In general, although sophisticated packages try to simulate
stochastically and generate
I(h;nj) estimates with a good record, it is on the other hand,
very useful to build and have in
hand reliable and easy to use models to estimate mean I(h;nj)
values.
A model which was considered for comparison reasons to the model
proposed and
examined in this work is the one proposed by Jain [19] and its
modified version by Baig
et al. [20].
The solar insolation data for two cities in Greece, Athens and
Thessaloniki, available on
an hourly basis [15], were used to provide an estimate of the
basic parameters for both of
the above models [19,20]. Those recorded data served as the
basis for comparison with the
predicted I(h;nj) estimates.
Hence, a comparison of the predicted I(h;nj) values based on
[19,20] and the mean
hourly values derived from records over the past 10 years [15]
for the above cities, is
presented. The comparison has been extended to many cities
covering the
geographical latitude of Greece and for each mean monthly day
with very good
results. Here in this paper the comparison is shown for two big
cities and for 2
months, January and July.
Second, the METEONORM package was run to estimate the mean solar
radiationcompared with the results of the above methodologies.
-
kt(h;nj): the hourly clearness index
kt,m(h;nj): the hourly clearness index of the average daily
profile
S.N. Kaplanis / Renewable Energy 31 (2006) 781790 783y(h): an
auto-regression function of first order
h: hour.
As hourly variations are simulated in METEONORM, while in this
work mean
hourly values I(h;nj) are sought, METEONORM package was run for
a group of 5
days, that is 2 days before the representative day of the month
January and 2 days
after it, i.e. the I(h;nj) values for the 16th of January was
obtained by grouping the
values of 2 days before and 2 days after the selected day. The
same methodology was
followed for July.
Hence, I(h;nj) values were obtained by running METEONORM for the
14th, 15th, 16th,
17th, 18th for January and July. Those values were averaged for
each hour.
The results for the cities Athens and Thessaloniki for the 16th
of January and July arewhere1. the first, calculates the average
energy daily profile, and
2. the second, simulates the intermittent hourly variations by
superimposing an auto-
regressive procedure based upon:
kth; nj Z kt;mh; njCyh (2)parshots.Au2. Models to estimate
I(h;nj)
2.1. The METEONORM package
The I(h;nj) values are generated from the Aguiar and
Collares-Perreira Time dependent,
to-regressive, Gaussian model [6], as described briefly in [14],
which consists of twown in Fprocessor for the management of the
solar energy and the loads, too.proposed reliable and friendly
models, easily programmable in the frame of a micro-Finally, an
estimation of I(h;nj) is attempted with a new model proposed in
this work
based on the formula:
Ih; nj Z a Cb cos2ph=24 (1)a and b depend on f and nj, i.e
latitude and day, respectively.
Instead of developing sophisticated and complex functions to
determine them, a
methodology is developed, which uses two conditions easily built
along with this proposed
model.
The target of this paper is to assess whole I(h;nj) estimates
derived from the twoigs. 14.
-
Athens 16/1
0
50
100
150
200
250
300
350
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
MeasuredJain's modelNew approachMETEONORM Proposed by author
Fig. 1. A comparison between mean recorded I(h,nj) values for
the 16th of January for Athens and estimated
values from the METEONORM package, the Baig et al. model, and
the two proposed methodologies.
S.N. Kaplanis / Renewable Energy 31 (2006) 7817907842.2. The
Baig et al. model [21]
It is based on Jains model [20] which tries to fit solar
insolation to a Gaussian type
function,
rh Z1
s2p
p exp K h K122
2s2
(3)Athens 16/7
0
100
200
300
400
500
600
700
800
900
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
MeasuredJain's modelNew approachMETEONORM Proposed by author
Fig. 2. A comparison between mean recorded I(h,nj) values for
the 16th of July for Athens and estimated values
from the METEONORM package, the Baig et al. model, and the two
proposed methodologies.
-
Thessaloniki 16/1
0
50
100
150
200
250
300
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
MeasuredJain's modelNew approachMETEONORM Proposed by author
S.N. Kaplanis / Renewable Energy 31 (2006) 781790 785whi
Fig.
valurh12 Z Ih Z 12 Z 1p (4)is the standard deviation of the
Gaussian curve. s is obtained from (3), when h is set
equal to 12, i.e. solar noon. Then, the value of rh at hZ12 is
equal to:rh: is the ratio of I(h;nj) over the daily solar
insolation H(nj)
h: solar time
s:
Fig. 3. A comparison between mean recorded I(h,nj) values for
the 16th of January for Thessaloniki and estimated
values from the METEONORM package, the Baig et al. model, and
the two proposed methodologies.Hnj s 2pch provides a formula to
derive s.
Thessaloniki 16/7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
240
100
200
300
400
500
600
700
800
900
MeasuredJain's modelNew approachMETEONORM Proposed by author
4. A comparison between mean recorded I(h,nj) values for the
16th of July for Thessaloniki and estimated
es from the METEONORM package, the Baig et al. model, and the
two proposed methodologies.
-
The I(h;nj) estimated values are shown in Figs. 14, for the 16th
of January and 16th of
S.N. Kaplanis / Renewable Energy 31 (2006) 781790786July for
Athens and Thessaloniki, Greece.
2.3. A new approach to Jains and Baigs models
This work proceeded to a different approach to determine s
without using the values
of I(hZ12). Two versions of this approach are presented as it
concerns the determinationof s.
1st version. So, the day length of the day nj, as determined
from (6), is set equal to the
time distance between the points, where the tangents at the two
turning points of the
hypothetical Gaussian, which fits the hourly I(h;nj) data,
intersect the h axis. These two
points are at G2s distance from the axis origin [21]. Then, s is
interrelated directly withSo, as SoZ4s.
2nd version. If one draws the tangent at the two points which
correspond to the full
width at half-maximum, FWHM, of a Gaussian curve it can be
easily determined that the
tangent of each one point intersects the horizontal axis, i.e.
the hour, h, axis at points G2.027s, instead of G2s as in first
version.
Hence; in this case : So Z 4:054s; or s Z 0:246So (9)
This s value has to be compared with the one given by a related
formula; see Eq. (7).
In this new approach, the determination of s, by either version
does not require any
recorded data like, I(hZ12), as the Baig et al. model
does.Estimates of I(h;nj) under this new approach, compared with
the previous models, areBaig et al. modified the above model to
better fit the recorded data during the start and
the end periods of a day.
In this model, rh is estimated by:
rh Z1
2s2p
p exp K h K122
2s2
Ccos 180
h K12So K1
(5)
So is the day length of the day nj, at a site with latitude
f:
So Z2
15cosK1Ktan 4 tan d (6)
where d is the suns declination.
So is further investigated for a possible correlation with s.
So, is proposed in [21] to
satisfy the expression below:
s Z ASo CB; where A Z 0:21G0:02 and B Z 0:26G0:18 (7)
From the hourly data [16], taking I(hZ12) and H(nj), one may
determine s from (4)and/or (7). Then, from (5), rh values are
obtained to provide:
Ih; nj Z rh !Hnj (8)plotted in Figs. 14.
-
estimates of the previous models for Athens and
Thessaloniki.
S.N. Kaplanis / Renewable Energy 31 (2006) 781790 7873.
Conclusions
The estimation of I(h;nj) was tried for a large number of Greek
cities applying the four
methodologies as outlined above. In this paper, the results are
given only for two big cities,
Athens and Thessaloniki. It is clear that the two models, the
new approach to Jains model
and the proposed by S. Kaplanis, are very simple, fast,
effective and reliable. Estimations
can be derived even by a pocket calculator.
The estimates obtained by both of them are very close to the
recorded mean I(h;nj)
values as provided by the two data banks [16,17].
A comparison of the results of Jains model and the new approach
to Jains model
shows that they lie, also, very close as it regards the recorded
solar hourly radiation. Their
differences are less than 2% with the new approach model giving
better estimates.
Also, the proposed data by the author model estimates I(h;nj)
are quite close to the
recorded solar radiation data during the day length.
During solar noon for both cities investigated, model no. 4
gives an underestimation of
about 23%, for the worst case, which is January at solar noon,
while for the rest of the day
I(h;nj) estimates are very close to recorded values, even better
than that achieved by other
models 2 and 3. It is remarkable to underline that the
statistical standard variation of the
recorded I(h;nj) values is G10% for January.As it concerns s and
its relationship with So, the empirical formula sZASoCB by [21]2.4.
The proposed model by S. Kaplanis
In this model a and b are parameters which have to be determined
for any site and for
any day, nj. Their determination is quite simple and is as
follows:
Let; Ih; nj Z anjCbnjcos2ph=24 (10)Integrating (10) over h, from
sunrise, tsr, to sunset, tss, one obtains:tss
tsr
Ih; njdt Z Hnj Z 2a!nj !tsr K12C 24bp
sin2ptss24
(11)
H(nj) values are taken from recorded data see databank [15] or
by fitting the function
Hnj Z A CB sin2pnj=365 CC (12)over the 12 monthly values, E(mo),
of the solar radiation [15,16].
A second boundary condition provides a relationship between a
and b. That is at hZtss,I(tss;nj)Z0. Hence, from (10) one gets:
anjCbnjcos2ptss=24 Z 0 (13)Relationships (11) and (13) provide
the value of a(nj) and b(nj).
I(h;nj) estimates of this model are presented in Figs. 14 and
are compared with thegives for A a value of 0.21G0.01, while s as
determined in this work takes a value either
-
0.25, if the first version of model no. 3 is followed, or
sZ0.246, for the second version ofthat model.
One should remark that the new approach to Jains model and the
one proposed by S.
Kaplanis, as developed for our research in contrast to Jains
model, require only the
monthly values of the global solar radiation in a site.
Then, the daily solar radiation, H(nj), required for the new
approach to Jains model and
the one proposed by S. Kaplanis, is obtained from the 12 monthly
values when a function:
c1 Cc2 cos2pnj=365 Cc3 (14)similar to the one proposed in [4] is
fitted on them.
c1, c2, c3 are constants to be derived for any climatic zone in
Greece.
In the model proposed by S. Kaplanis constants a and b change
with site, f, and with
the day nj. Especially, a becomes zero at equinox, njZ81, as it
becomes obvious, since I(h;
S.N. Kaplanis / Renewable Energy 31 (2006) 781790788njZ81)
should provide symmetry for day and night time lengths over the 24
h.Constant a was determined for Athens and Thessaloniki and for all
mean monthly days,
see Tables 1 and 2. Its behavior is of the type of Eq. (14) with
a correction coefficient of
higher than 0.99.
I(h;nj) estimations all year round, with METEONORM package,
exhibits, even a
filtering procedure is followed, rather strong fluctuations,
which are obvious both for the
winter, and the summer months, too, see Figs. 14.
As it concerns the Jain model modified by Baig, the estimates of
I(h;nj) show the
symmetry close and around solar noon, as imposed by the fitting
functions. The fitting is
based on rh(12), obtained by the I(12;nj) recorded values. This
model seems to provide a
very reliable performance, close to solar noon, which is due to
the I(12;nj) recorded values
required by this model. For the rest of the day estimates of
I(h;nj) decline within the
standard deviation.
It is remarkable that the modified, by this work, Baig model,
does not require the I(12;nj)
value, as now s is determined directly by the boundary
conditions set, as in Eq. (9).
The target of a further work is to apply the proposed by S.
Kaplanis model to a large
geographical area and to provide formulae to estimate parameters
a and b which are
Table 1
Constants a and b values for the representative days of the
months for Athens
Month a (W/m2) b (W/m2)
January K128,26 K425,87
February K85,50 K457,07
March K18,41 K505,71April 72,05 K540,57
May 148,78 K558,29
June 188,70 K569,41
July 177,32 K597,82August 112,43 K625,32
September 10,15 K636,97
October K89,03 K610,96
November K149,24 K540,48December K157,04 K467,54
-
the basis of the I(h;nj) estimation without using the values
H(nj) or the I(hZ12), by the
Acknowledgements
S.N. Kaplanis / Renewable Energy 31 (2006) 781790 789The author
acknowledges his research student N. Papanastasiou from the
University of
Applied Science of Aachen, as well as Mrs L. Androutsopoulou and
V. Spartianou, for
calculations of I(h;nj) for various Greek cities.proposed by the
author model and Jains model, respectively.
To recreate a real case scenario, fluctuating I(h;nj) values may
be further predicted
through a Gaussian sampling procedure applied on the model
proposed here, as this will be
presented in a next paper.Table 2
Constants a and b values for the representative days of the
months for Thessaloniki
Month a (W/m2) b (W/m2)
January K116,32 K351,46
February K81,27 K396,40
March K17,63 K451,88April 71,42 K488,39
May 148,04 K503,34
June 187,36 K512,31
July 175,83 K538,62August 111,64 K564,49
September 10,64 K573,97
October K86,37 K544,18November K141,98 K467,56
December K143,31 K387,14References
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S.N. Kaplanis / Renewable Energy 31 (2006) 781790790
New methodologies to estimate the hourly global solar radiation;
Comparisons with existing modelsIntroductionModels to estimate
I(h;nj)The METEONORM packageThe Baig et al. model [21]A new
approach to Jains and Baigs modelsThe proposed model by S.
Kaplanis
ConclusionsAcknowledgementsReferences
