Pergamon
PII:
Solar Energy Vol. 70, No. 4, pp. 339–348, 2001
 2000 Elsevier Science Ltd
S 0 0 3 8 – 0 9 2 X ( 0 0 ) 0 0 1 5 1 – 1 All rights reserved. Printed in Great Britain
0038-092X / 01 / $ - see front matter
www.elsevier.com / locate / solener
A NEW METHOD FOR TYPICAL WEATHER DATA SELECTION TO
EVALUATE LONG-TERM PERFORMANCE OF SOLAR ENERGY SYSTEMS
M. GAZELA†,1 and E. MATHIOULAKIS 1
Solar and Other Energy Systems Laboratory, NCSR ‘DEMOKRITOS’, Patriarhou Gregoriou and
Neapoleos, GR-153 10 Aghia Paraskevi, Attiki, Greece
Received 18 October 1999; revised version accepted 9 September 2000
Communicated by DOUG HITTLE
Abstract—A new method is proposed for determining typical 1-year weather data from a multi-year record for
evaluation of solar energy systems. The procedure is very straightforward and can be utilised with ease when
determining the long-term performance of a solar hot water system (SHWS). It is made up of a concatenation
of 12 months individually selected from a multi-year database. The criterion for the selection is the
minimisation of error in the monthly solar gain prediction of the system. Considering this criterion, the
‘typicality’ of the weather pattern is taken into account, in addition to its influence on the behaviour of the
solar system. A comparison is made between the new method and others frequently referred to in the literature.
Based on simulation results for yearly, monthly and daily power delivered, six indicators have been calculated.
These indicators quantify the different behaviours of the system when ‘historical’ and typical weather data are
applied. The all inclusive comparison shows that the new method for deriving typical weather data leads to an
accurate evaluation of the long-term performance of a SHWS.  2001 Elsevier Science Ltd. All rights
reserved.
1. INTRODUCTION
Predicting the performance of a solar system by
using simulation methods requires weather data
input from the location where the system is being
installed. These sets of data should depict the
weather pattern of the location, examples of
which are widely known as Typical Meteorological Year (TMY), Weather Year for Energy Calculations (WYEC) and Test Reference Year (TRY).
The typical weather data (TWD) consists of 8760
values of various selected meteorological parameters such as ambient temperature, solar radiation,
relative humidity and wind velocity and are
originally derived from long-term data.
Several methods for TWD generation have
been reported in the literature. Procedures have
been proposed by Klein et al. (1976), Schweitzer
(1978), Hall et al. (1978), Crow (1981), ASHRAE Fundamentals (1997), Bahadori and
Chamberlain (1985), Pissimanis et al. (1988),
Festa and Ratto (1993), Marion and Urban
(1995). The primary objective of these methods is
to select single years or single months from a
multi-year database, preserving a statistical corre-
†
Author to whom correspondence should be addressed. Tel.:
130-1-650-3817;
fax:
130-1-654-4592;
e-mail:
[email protected]
1
ISES member.
spondence. This means that the occurrence and
the persistence of the weather should be as similar
as possible in the TWD to all available years. Yet,
the aforementioned methods often seem rather
convoluted and complex when put into use.
Moreover, as will be demonstrated below, the
various procedures significantly change the final
selected ‘typical’ months or years in the same
way as the results of the long-term prediction of
system performance. This could lead to dubious
results for the behaviour of the system and may
give rise to confusion, especially when the system
is being tested.
As a rule, it is important to maintain correspondence with weather sequences occurring in
the typical set and those occurring in the multiyear database. However, an issue arises, as occasionally it is not worthwhile to maintain this
correspondence. The adequacy of using typical
meteorological data with a simulation model to
provide an estimate of long-term system performance depends on the sensitivity of system
behaviour to hourly weather sequences (Klein et
al., 1974). None of the aforementioned procedures for deriving TWD take the sensitivity of the
system into account.
Another drawback of these procedures is that
all require meteorological parameters on an hourly or daily basis and these are not accessible in
many locations.
339
340
M. Gazela and E. Mathioulakis
The accuracy of using reduced or synthesised
sets of meteorological data has already been
investigated by Gansler et al. (1994). Their main
objective is to examine whether or not synthesised
meteorological data (produced by hourly weather
generator or compressed) can reliably be used in
the simulations of some solar energy systems.
Furthermore, five different methods for generating
TWD and some variations of them have been
implemented for typical energy systems by Argiriou et al. (1999). In every case, a performance
indicator of each system has been calculated to
evaluate the TWD with the ‘best’ performance.
This article proposes a new procedure (Weather
Year for Solar Systems, WYSS) for determining a
set of typical weather data in order to evaluate the
long-term performance of a SHWS. This set
consists of 8760 hourly values of the three
meteorological parameters: global horizontal
radiation, ambient temperature and wind velocity.
In cases in which hourly meteorological values
are not obtainable, WYSS can be also applied
with daily or mean daily values. The new selection process is quite straightforward, easily applicable and can be reliably applied in predicting the
long-term performance of a SHWS, minimising
the error in the estimation. The optimum selection
of each individual month, considering this error,
relies on the observation that the solar sensitivity
of the solar system to weather pattern affects the
accuracy of the prediction. Thus the primary
difference of the new procedure from the existing
ones is that it is system oriented. On the one hand
this resolves the problems which derive from the
subjectivity of the criteria for generating TWD
and on the other hand makes the new procedure
suitable for testing SHWS.
Five different techniques for generating TWD
were chosen to be applied to the 21-year database
in order to compare and evaluate WYSS. These
are: the Sandia National Laboratory method and
its modification by Pissimanis et al., the Festa and
Ratto method, the US National Oceanic and
Atmospheric Administration method approved by
ASHRAE and Weather Year for Energy Calculations. No method for comparing generated weather data (Knight et al., 1991) or compressed data
sets (Feuermann et al., 1985) has been examined
because it is beyond the main focus of this article.
2. INITIAL PROCESSING OF THE
METEOROLOGICAL DATA
These data have been collected and published by
the National Observatory of Athens (NOA). The
meteorological parameters used are: ambient temperature, relative humidity, global radiation on
horizontal surface and wind velocity. In cases in
which isolated values were missing, linear interpolation of the previous day and next day values
for the same hour were applied. Especially for
horizontal global radiation, weighted linear interpolation was used, considering solar altitude sinus
or daily sunshine duration as weighting factors
(Argiriou et al., 1999; Duffie and Beckman,
1991).
3. DESCRIPTION OF METHODOLOGIES FOR
TWD GENERATION
In this study five procedures were applied for
deriving TWD, based on 8760 values of each
available meteorological parameter. The criteria
for having chosen these particular methods were
the following:
• they are frequently used in practice;
• they employ quite different approaches to
generating TWD.
The lack of some meteorological parameters such
as atmospheric pressure, sunshine duration, diffuse solar radiation etc., made the application of
important methods for TWD generation such as
the Danish method (Lund and Eidorff, 1980) or
the National Solar Radiation Data Base method
(Marion and Urban, 1995) unfeasible.
3.1. The Sandia National Laboratory method
( Sandia method)
This method was initially developed by Hall et
al. (1978). The TWD is created by concatenating
twelve Typical Meteorological Months (TMM) to
form a complete year. The selection of the TMM
is made in two stages based on nine indices
consisting of: daily global radiation, daily maximum, mean and minimum for dry bulb and dew
point temperature, and daily maximum and mean
wind velocity. In the first stage, five candidate
months are chosen, having cumulative distribution
functions (CDF) ‘close’ to the respective longterm distributions. To measure the variation between short and long-term data, the Finkelstein
and Schafer (FS) statistic is calculated (Finkelstein and Schafer, 1971) for each index and month.
Additionally, a weighted sum (WS) according to:
O w FS
9
For generating TWD, a 21-year time series
(1977–1997) of hourly values has been used.
WS 5
j 51
j
j
(1)
A new method for typical weather data selection to evaluate long-term performance of solar energy systems
is calculated. Table 1 contains the values of the
weights for each index.
In the second stage the final selection of TMM
is obtained by examining 5 candidate months with
the lowest WS. The evidences taken into account
are defined statistics and the persistence structure
of daily mean dry bulb temperature and daily
global radiation. The statistics examined are the
FS and the deviations for the monthly mean and
median from the long-term mean and the median.
Persistence is characterised by frequency and run
length above and below fixed long-term percentiles. The final selected typical month must comprise a small FS statistic, a small deviation of
monthly mean and median from long-term mean
and median and a typical persistence structure.
Because adjacent months in the TWD may be
selected from different years, discontinuities at the
interfaces of the months are smoothed for 6 h on
each side, using the cubic spline technique.
The Sandia method for generating TWD is
widely applied although the final selection of a
TMM is to some extent subjective. In addition,
hourly weather data for the location of interest
should be available and this is not always possible. Another drawback of this method is its
complexity which mainly derives from the number of the criteria posed. Additionally, some
meteorological parameters taken into account
during the procedure, for instance maximum,
minimum and mean dew point temperatures, have
trivial influence on solar system performance.
A modification on the previous method was
performed in view of abridging the number of
statistical parameters in the final TMM selection
by Pissimanis et al. (1988) (Pissimanis method).
The first stage of the procedure is exactly the
same as in the Sandia method. But the deviations
of short term mean daily values of global radiation from respective long-term values are found
by estimating the Root Mean Square Difference
(RMSD) according to:
O (G
k
] 2
h, y 2Gh )
h51
RMSD 5 ]]]]]
k
3
TMM is the value of RMSD. If the candidate
months remain greater than one, the secondary
selection criteria are FS statistics of global radiation and air temperature. A cubic spline smoothing technique is implemented for the elimination
of discontinuities at the interfaces of the months
over the first and last 6 h of each month.
The modification made by Pissimanis et al.
significantly reduces the number of statistical
parameters examined, thus simplifying the procedure. Also the selection of the final typical
month is fairly objective. However, the weather
sequences occurring in the TWD and those occurring in the long-term data were neglected. Additionally in any stage of the selection process, wind
velocity, which affects solar system performance,
was disregarded.
3.2. The Festa–Ratto method
The method was proposed by Festa and Ratto
(1993). Typical months are selected according to
the deviations of short term values from long-term
values of some chosen meteorological parameters,
named x, which are considered to influence
simulated system performance. These deviations
are estimated by three standardised magnitudes X,
z and Z. In this study the meteorological data used
for X, z and Z determination are: maximum, mean
and minimum ambient temperature and relative
humidity, maximum and mean wind velocity, and
daily global radiation on horizontal surface. For
the estimation of X, the average daily value and
the respective standard deviation of the long-term
data are being determined for each day, month
and meteorological parameter. By smoothing
these values, mx (m, d) and sx (m, d) are derived.
The applied technique for the latter (Oppenheim
and Willsky, 1997) was altered by that proposed
by Festa et al. (1988) because by implementing
this smoothing technique the meteorological parameters were shifted. The Xs are calculated
according to:
x( y, m, d) 2 mx (m, d)
X( y, m, d) 5 ]]]]]].
sx (m, d)
1/2
4
(2)
The primary criterion for the final selection of
341
(3)
The magnitude z is the product of X in d day
multiplied by X for the next day (d 1 1) according
to:
Table 1. Weight factors used in Sandia National Laboratory method
Dry bulb temperature
Dew point temperature
Wind velocity
Daily global
Max
Min
Mean
Max
Min
Mean
Max
Mean
radiation
1 / 24
1 / 24
2 / 24
1 / 24
1 / 24
2 / 24
2 / 24
2 / 24
12 / 24
342
M. Gazela and E. Mathioulakis
z( y, m, d) 5 X( y, m, d) ? X( y, m, d 1 1).
(4)
The values of Z are derived by using the same
procedure through which X is determined, replacing x by z. The equation used is:
z( y, m, d) 2 mz (m, d)
Z( y, m, d) 5 ]]]]]].
sz (m, d)
(5)
Additionally mean monthly values of the standardised parameters X and Z are evaluated, as
well as the respective standard deviations and the
cumulative distribution functions for each year
and for the multi-year database. For the selection
of the typical months, the magnitudes listed below
are calculated:
d av ( y, m) 5 u }X ( y, m) 2 } } X (m)u,
d sd ( y, m) 5 u 6X ( y, m) 2 6 } X (m)u
d ks ( y, m) 5max u ^ y,m (X0 ) 2 ^m (X0 )u
X0
(6)
where }X ( y, m) and } } X (m) are the mean
monthly values of X of year y and long-term data,
respectively, 6X ( y, m) and 6 } X (m) are the standard deviations on monthly basis of X of year y
and long-term data, respectively, and finally
^X ( y, m) and ^ } X (m) the cumulative distribution
functions of m month of y year and long-term
data, respectively. These distances describe the
monthly deviation between the values of y year
from long-term data for the same month m. A
composite distance is also determined according
to:
d( y, m) 5 0.98 ? d ks ( y, m) 1 0.1 ? d av ( y, m)
1 0.1 ? d sd ( y, m)
(7)
for each meteorological parameter.
All the calculated d for the same month m and
year y and X, Z values are sorted in ascending
order. Then the maximum d(m, y), called d max (m,
y) is selected so as to include the worst case —
meaning the greatest aberration. For choosing 12
representative months the minimum d min max (m, y)
of d max is selected according to:
d min max (m, 1) 5 minhd max i ( y, m),
1 # y # 21, 1 # i # 9j.
(8)
Finally, discontinuities at the interfaces of the
months are eliminated, applied for 6 h on each
side cubic spline technique.
Although the Festa–Ratto method for TWD
generation is in most cases very accurate, it still
seems rather complicated in practice.
3.3. The US National Oceanic and Atmospheric
Administration method ( NOAA method)
This method is proposed by the US National
Oceanic and Atmospheric Administration and was
approved by ASHRAE (ASHRAE Fundamentals,
1997). An entire ‘historical’ year is selected rather
than individual months. The criterion for the
selection is monthly mean temperatures. First the
extreme months are arranged in order of importance for energy comparisons. Hot Julys and cold
Januarys are assumed to be the most important.
All months are ranked by alternating between the
warm half (May to October) and the cold half
(November to April) of the year with priority
given to the months closest to late July or late
January. Then a marking of all 24 of the above
extreme months is done. For years remaining
without any marked month, marking continues
until only 1 year is left.
Although the above procedure is simple and
can be practised even when monthly mean values
of ambient temperature are obtainable, it results in
a serious drawback since neither global radiation
nor wind velocity are taken into account.
3.4. Weather Year for Energy Calculations
This method was initially proposed by Crow
(1981) and was called Weather Year for Energy
Calculations (WYEC). Although 12 representative months are selected to form a complete year
like the Sandia or the Festa–Ratto method, there
is a major difference. After the initial selection,
individual days or hours are adjusted. Replacing
some hourly or daily values leads the monthly
mean values to come closer to the respective
long-term values.
It should be noted that the monthly mean
temperatures of the 21 years are obtained by
averaging 21 maximum and 21 minimum measurements.
The initial selection of the months based on dry
bulb temperature values is focused on the 1 or 2
‘historical’ months with the closest proximity to
those of the 21-year period. The difference between the final adjusted months and multi-year
normal temperature ranges between 60.38C (Augustyn, 1998). Going on, an adjustment in solar
radiation values becomes necessary. Original
A new method for typical weather data selection to evaluate long-term performance of solar energy systems
hourly solar radiation data for each selected
month is modified until the monthly mean values
come within one-tenth of the monthly standard
deviation as developed from long-term data
(Crow, 1984).
The hourly sequences at the edges of the
substitute days require some additional adjustment
to avoid abrupt changes. A cubic spline smoothing technique is applied to normalise these irregularities and discontinuities at the interfaces of
the months.
This process for deriving Weather Year for
Energy Calculations is fairly manageable and
undemanding, though its original objective was
for building energy analysis. By adjusting certain
values for two meteorological variables — mean
monthly temperature and global radiation — these
then become almost identical to those of the
long-term data. Yet, this takes place at the expense
of the ‘historical’ data because chronological
series are modified. Moreover wind velocity is
neglected at any stage of the selection process.
4. THE NEW METHOD FOR SELECTING
TYPICAL WEATHER CONDITIONS
All the aforementioned methods for TWD
generation aim to represent the weather pattern at
a particular location. Special care is given to
choosing months (or year in NOAA method)
where weather sequences and persistence maintain correspondence to long-term data. However,
throughout the literature review, typicality appears
subjective. This is due to the fact that the selection criteria for typical months or year is based
mostly on mathematical and statistical methods
rather than the natural operation of the system.
The primary reason for having conducted this
research is that any kind of standardisation for
TWD generation is still missing. This is probably
due to the fact that some of the procedures,
343
though accurate, are hard to implement, while
others are easy but inaccurate (Petrie and McClintock, 1978). Additionally some procedures require
meteorological parameters which are not available
for many locations or for many years. Another
reason for having conducted this investigation is
that a remarkable fluctuation is noted among the
typical months, selected according to the procedure. Moreover the final results such as monthly
delivered power of the system when long-term
performance is estimated, are significantly different (Argiriou et al., 1999). This could be a serious
problem, especially when a solar system is tested
and the final conclusions for the system should be
reliable and accurate.
Since typicality inevitably remains subjective,
the most important criterion for selecting typical
months is the use to which the TWD is being put.
The new method (WYSS) is directed towards the
prediction of long-term behaviour of a SHWS. In
this case, the performance indicator is characterised by the delivered power of the system.
Therefore the selection is based on monthly solar
gain. In this way, the term TMY receives a
specified orientation, a bit different from the one
it already has. This is due to the combination of
climatological conditions, weather sequences and
system characteristics which affect its behaviour.
The WYSS for the selection of the typical
meteorological values consists of three stages
(Fig. 1). In the first stage the monthly solar gain
of the SHWS is calculated by simulation methods
for all the 21 years (i.e. SGy m for m51, 2, . . . , 12
and y51, 2 . . . , 21). In the second stage the
typical months are selected for the WYSS according to the following procedure.
• Calculation of the mean value of the solar
gains of all the 21 years
SO SG
21
y
D
m
y 51
]
SGm 5 ]]]].
21
Fig. 1. The three stages for selecting typical months according to WYSS.
(9)
344
M. Gazela and E. Mathioulakis
Table 2. Characteristic parameters of four SHWS used by
DST long-term
Ac
Vs
A *c
U *c
Us
Cs
faux
Sc
DL
System A
System B
System C
System D
5
300
3.261
5.887
2.665
1.240
0.498
0.035
0.024
4
240
2.612
5.787
2.479
0.991
0.498
0.035
0.024
3
180
1.957
5.687
2.147
0.744
0.498
0.035
0.024
2
120
1.306
5.587
1.753
0.496
0.498
0.035
0.024
• Calculation of the 21 values
]
ty m 5fSGy m 2SGmg 2 .
(10)
• Designation of the month m of year y in which
ty m is minimum. This month m is considered
typical and is selected for the WYSS.
In the third and final stage, cubic spline is applied
for elimination of abrupt changes at the interfaces
of the months.
5. RESULTS
In the evaluation and comparison of all the
aforementioned methods, a SHWS is considered
(system A). This system is considered in the ISO
9459-5 standard (ISO, 1997) as a benchmarking
system.
The program used to simulate solar system
performance is Dynamic System Testing (DST)
(Spirkl, 1997) which is also included in the
previously mentioned standard. The characteristic
parameters of the system are shown in the first
column, Table 2. To estimate the performance of
the system, three draw-offs have been conducted
during the day, equal to double the volume of the
storage tank.
The particular solar system as well as the
simulation program are chosen because this study
is mainly interested in testing procedures. How-
ever, TRNSYS (Solar Energy Laboratory, 1994)
was also implemented, producing the same results.
The typical months or years that emerge,
following the already described methods are
shown in Table 3. From the latter table it can be
easily seen that, according to the applied procedure, selected typical months vary significantly.
Even between the Sandia method and its modification by Pissimanis et al. (1988), only 7
months are characterised as typical for both
procedures. For instance, between the Festa–Ratto
method and that of WYEC, only 2 months are the
same, between the Sandia and the Festa–Ratto
method or the Sandia method and the WYEC,
only 1 month is the same.
Furthermore Fig. 2 illustrates the average of the
21-year monthly solar gains, from May to August
and the respective monthly solar gains for typical
months as calculated by simulating system A. It
seems from Fig. 2 that the monthly solar gains of
the system depend on the procedure through
which the TWD has been derived. Actually, the
relative difference between monthly delivered
power according to the applied procedure could
be more than 30% in February. Notice that the
]
averaged solar gain SGm almost coincides with the
one calculated by implementing WYSS. Solar
gains estimated by applying the Festa–Ratto
method and the NOAA method differ significantly
for May and June. However, the Sandia and the
Pissimanis method as well as WYEC offer fairly
]
accurate results with respect to SGm .
Additionally, in order to investigate the sensitivity of the WYSS many SHWS were simulated. The results demonstrate — as was originally expected — that the proportion of storage tank
volume to the total surface of the collector (Vs /A c )
defines the ‘typicality’ of the month. So WYSS
was also applied to estimate the long-term data of
three other systems (systems B, C, D) where this
Table 3. The years in which the selected typical months belong to, according to the applied method, for system A
Months
Sandia
method
Pissimanis
method
Festa–Ratto
method
NOAA
method
WYEC
WYSS
1
2
3
4
5
6
7
8
9
10
11
12
1977
1991
1986
1992
1982
1990
1989
1996
1993
1990
1979
1997
1977
1994
1986
1992
1982
1990
1989
1981
1993
1983
1991
1980
1992
1987
1991
1988
1989
1991
1978
1977
1993
1990
1992
1994
1982
1982
1982
1982
1982
1982
1982
1982
1982
1982
1982
1982
1979
1988
1988
1988
1979
1987
1986
1980
1985
1990
1989
1983
1979
1994
1989
1996
1985
1979
1985
1993
1993
1992
1994
1982
A new method for typical weather data selection to evaluate long-term performance of solar energy systems
345
Fig. 2. Monthly solar gains from May to August for all the applied procedures for system A.
Table 4. The years in which the typical months belong to,
following WYSS for B, C and D systems
Months
System B
System C
System D
1
2
3
4
5
6
7
8
9
10
11
12
1979
1994
1989
1996
1985
1979
1985
1993
1993
1992
1994
1992
1979
1994
1989
1996
1985
1979
1985
1993
1993
1992
1994
1992
1979
1994
1989
1996
1985
1979
1977
1993
1993
1997
1994
1992
proportion remains constant, equal to 60 l / m 2 .
The characteristic parameters of those systems are
presented in Table 2 and the resulting typical
months in Table 4.
Comparing the last column of Table 3 and the
typical months of Table 4, it was found that
differentiations in the month selection for each of
the above analysed systems show little aberration
— at the most 3 months. Furthermore, for system
A where the selected December is of the year
1982, December of 1992 is the second candidate
month very close to the former one. Exactly the
same happens with the typical July (1977) and
typical October (1997) of system D.
Evaluation of procedures for TWD generation
was conducted by comparing the solar gains of
each year — historical data — on a yearly,
monthly and daily basis, to the equivalent values
of ‘typical’ data. The calculated aberrations were
found on all four systems mentioned above. Yet, it
was demonstrated that the results were identical,
henceforth all the following illustrated calculations refer to system A.
In Fig. 3 the flow-chart of the work done is
given in order to determine the optimum procedure for creating a ‘typical’ yearly set of data
with respect to the error introduced in the prediction of long-term system performance.
Fig. 3. Flow-chart for evaluating the accuracy of each applied procedure.
346
M. Gazela and E. Mathioulakis
As mentioned above, the comparison was made
with yearly, monthly and daily solar gains, by
calculating six selected indicators. The point was
to ascertain the behaviour of the system itself
when the real data of the 21-year period are
applied and also to check its behaviour when
typical years are in use. The indicator F1 is the
root mean square difference of the yearly solar
gains of system A. It quantifies the deviation
between the yearly delivered power for each of
the 21 years and the typical year. The indicators
F2 and F5 are the total standard error of estimates
of monthly and daily solar gains, respectively.
They represent the error between solar gains,
when historical data and TWD were applied. The
indicator F3 is the chi square ( x 2 ) parameter on
monthly solar gains. This indicator is of particular
interest because the sample means deviation
(s]
SG m ) operates as a weighting factor when the
accuracy of the method is assessed. Actually the
x 2 function provides evidence about the relation
between the deviation of the TWD from historical
data and the consistency (dispersion) of these
data. Finally, the indicators F4 and F6 are the root
mean squares of the 21-year mean solar gain
minus the solar gains of the TWD on a monthly
and daily basis. Analytically, the equations used
to estimate these indicators are:
• yearly solar gain:
]]]]]
21
œ
O (SG 2 SG )
y
2
t
y51
F1 5 ]]]]]
21
(11)
• monthly solar gain:
O
1 12
F2 5 ]
SEEm
12 m51
5O 3O
21
1
5]
12
1/2
2
(SGy m 2 SGt m )
y 51
]]]]]]
20
12
m51
46
(12)
F3 5 x 5
]
SGm 2 SGt m
]]]]
s]
SG m
OS
12
2
m 51
D
2
(13)
S O
D
1 12 ]
F4 5 ] ?
(SGm 2 SGt m )2
12 m51
1/2
(14)
• daily solar gain:
O SEE
365
d
d 51
F5 5 ]]]
365
O (SG
21
1
5]
365
5O 3
365
d51
1/2
2
y d 2 SGt d )
y 51
]]]]]
20
46
(15)
S O
1 365 ]
F6 5 ] ? sSGd 2 SGt dd 2
365 d51
D
1/2
(16)
The values of the six indicators as calculated for
system A are presented in Table 5.
In Table 5 it is noted that in yearly solar gains
WYSS introduces a slightly larger deviation than
that in the Festa–Ratto method and that of
NOAA, while in monthly and daily solar gains the
deviation of the WYSS is less than or equal to
that of the methods mentioned above. As seen in
Table 5, when the indicators are calculated on a
monthly basis (from F2 to F4 ), the WYSS results
in a notably lower error in the estimation of
long-term solar gain.
In Fig. 4 the standard error of estimates (SSEm
Eq. (12)) of monthly solar gain is shown, with
regard to the typical sets of data examined. When
WYSS is applied, the monthly standard error of
estimates is lower for all months. SEEm are
acquired greater values for all months, when the
NOAA method is implemented.
In Fig. 5 the values of x 2 are depicted. In order
to distinguish the lines, the values are depicted in
semi-log scale. The line which corresponds with
the NOAA method, acquires greater values especially in February and September. Lower values
of x 2 are observed when the Sandia and Pissimanis method as well as WYEC are implemented. The values of x 2 when WYSS is
applied, remains low during the 12 months.
Table 5. The values of the indicators, calculated for system A
Sandia method
Pissimanis method
Festa–Ratto method
NOAA method
WYEC
WYSS
F1
F2
F3
F4
F5
F6
17.57
17.38
17.15
17.17
17.45
17.19
437.87
431.36
452.60
497.01
427.15
419.69
23.93
8.62
41.51
115.63
9.45
0.73
10.79
6.64
10.93
23.29
7.08
1.95
113.19
112.27
113.39
124.94
117.63
112.34
82.41
81.61
85.12
104.41
90.85
80.33
A new method for typical weather data selection to evaluate long-term performance of solar energy systems
347
Fig. 4. Standard error of estimates in monthly basis (SEEm ) for each applied procedure.
6. CONCLUSIONS
Let us observe Table 5 and assess Figs. 4 and 5
described above. The findings show error minimisation when the weather year for solar systems is
utilised. Error minimisation refers to the accuracy
of the long-term prediction of SHWS performance, compared to the remaining procedures for
TWD generation.
Figs. 4 and 5 show that weather year for solar
systems gives sufficiently accurate results comparing with methods which are currently in extensive use such as Sandia and WYEC. Yet, the new
methodology seems simpler and more easily
applicable. It can be successfully applied even
when only daily or monthly values of ambient
temperature, global radiation and wind velocity
are available. Another advantage of weather year
for solar systems is that it could be applied even
when only short time period data are available,
still assuring the minimisation of error in estimating the long-term behaviour of a SHWS. This is
due to the fact that the new methodology is
system oriented.
As it has already been mentioned, the typical
months’ differentiation is negligible when the
weather year for solar systems is applied to
systems with similar characteristics. The long-
Fig. 5. The value of x 2 in monthly basis ( x 2m ) for each applied procedure.
348
M. Gazela and E. Mathioulakis
term solar gain predictability is only slightly
influenced. However, it should be noted that in
case of an extended application of the suggested
method the definition of a reference system seems
pertinent.
NOMENCLATURE
SGy
SGt
SGy m
SGt m
]
SGm
s]
SG m
SGy d
SGt d
]
SGd
]
Gh
^ y,m
^m
}X ( y, m)
} } X (m)
6 } X (m)
6X ( y, m)
Ac
A c*
Cs
DL
F
faux
FSj
Gh , y
k
Sc
SEEd
SEEm
U *c
Us
Vs
wj
yearly solar gain of y year (W)
yearly solar gain of a typical year t (W)
monthly solar gain of m month and y year (W)
monthly solar gain of m month of a typical year t
(W)
mean value of monthly solar gain of m month of
long-term data (W)
standard deviation of sample means of monthly
solar gain of m month (W)
daily solar gain of d day of y year (W)
daily solar gain of d day of typical year t (W)
mean value of daily solar gain of d day of longterm data (W)
mean hourly solar radiation of long-term data for
a specific month (W/ m 2 )
cumulative distribution function of m month and y
year (%)
cumulative distribution function of m month of
long-term data (%)
mean monthly value of X of y year
mean monthly value of X of long-term data
standard deviation on monthly basis of X value of
long-term data
standard deviation on monthly basis of X value
and y year
total collector area (m 2 )
effective collector area (m 2 )
thermal heat capacitance of the store (MJ K 21 )
mixing constant (–)
indicators
fraction of the store volume used for auxiliary
heating (–)
FS statistic of j parameter
hourly solar radiation for h hour of y year for a
specific month
number of hours where solar radiation is not zero
stratification parameter (–)
standard error of estimates on daily gain of d day
(W)
standard error of estimates on monthly gain of m
month
effective collector loss coefficient (W m 22 K 21 )
loss coefficient of the store (W K 21 )
storage volume (l)
weighting value of j parameter
REFERENCES
Argiriou A., Lykoudis S., Kontoyiannidis S., Balaras C. A.,
Asimakopoulos D., Petrakis M. and Kassomenos P. (1999)
Comparison of methodologies for TMY generation using 20
years data for Athens, Greece. Solar Energy 66(1), 33–45.
Fundamentals, ASHRAE Handbook, ASHRAE, Atlanta,
26.1–26.4.
Augustyn J. R. (1998) WYEC2 User’s Manual and Software
Toolkit. ASHRAE Trans, 32–40.
Bahadori M. N. and Chamberlain M. J. (1985) A simplification of weather data to evaluate daily and monthly energy
needs of residential buildings. Solar Energy 36(6), 499–
507.
Crow L. (1981) Development of hourly data for weather year
for energy calculations (WYEC), including solar data, at 21
stations throughout the US. ASHRAE Trans., 896–905,
December.
Crow L. (1984) Weather year for energy calculations. ASHRAE J., 42–47, June.
Duffie J. A. and Beckman W. A. (1991). In 2nd edn, Solar
Engineering of Thermal Processes, pp. 13–20, Wiley Interscience, New York.
Festa R., Ratto C. F. and DeGol D. (1988) A procedure to
obtain average daily values of meteorological parameters
from monthly averages. Solar Energy 40(4), 309–313.
Festa R. and Ratto C. F. (1993) Proposal of a numerical
procedure to select reference years. Solar Energy 50(1),
9–17.
Feuermann D., Gordon J. M. and Zarmi Y. (1985) A typical
meteorological day (TMD) approach for predicting the
long-term performance of solar energy systems. Solar
Energy 35(1), 63–69.
Finkelstein J. and Schafer R. (1971) Improved goodness of fit
tests. Biometrica 58(3), 641–645.
Gansler R. A., Klein S. A. and Beckman W. A. (1994)
Assessment of the accuracy of generated meteorological
data for use in solar energy simulation studies. Solar Energy
53(3), 279–287.
Hall I. J., Prairie R. R., Anderson H. E. and Boes E. C. (1978)
Generation of a typical meteorological year. In Report
SAND-78 -1096 C, CONF-780639 -1, Sandia Laboratories,
Albuquerque, NM.
ISO 9459-5 (1997). System Performance Characterization by
Means of Whole System — System Tests and Computer
Simulation.
Klein S. A., Beckman W. A. and Duffie J. A. (1976) A design
procedure for solar heating systems. Solar Energy 18, 113–
127.
Klein S. A., Duffie J. A. and Beckman W. A. (1974) Transient
consideration of flat-plate solar collector. J. Eng. Power —
Trans. ASME, 109–113.
Knight K. M., Klein S. A. and Duffie J. A. (1991) A
methodology for the synthesis of hourly weather data. Solar
Energy 46(2), 109–120.
Lund H. and Eidorff S. (1980). Selection Methods Production
of Test Reference Years, Appendix D, Contact No. 284-77
ES DK, Final Report, EUR 7306 EN.
Marion W. and Urban K. (1995). User’ s Manual TMY2 s —
Typical Meteorological Year, National Renewable Energy
Laboratory, Golden, CO.
Oppenheim A. V. and Willsky A. S. (1997). In 2nd edn, Signal
and Systems, pp. 245–249, Prentice-Hall, London.
Petrie W. and McClintock M. (1978) Determining typical
weather for use in solar energy simulations. Solar Energy
21, 55–59.
Pissimanis D., Karras G., Notaridou V. and Gavra K. (1988)
The generation of a ‘typical meteorological year’ for the
city of Athens. Solar Energy 40(5), 405–411.
Schweitzer S. (1978) A possible ‘average’ on Israel’s coastal
plain for solar system simulations. Solar Energy 21, 511–
515.
Solar Energy Laboratory (1994). A Transient System Simulation Program ( TRNSYS), University of Wisconsin–
Madison, Reference Manual, Version 14.1.
Spirkl W. (1997). Dynamic System Testing, Program Manual,
Version 2.7.