|
20.8 SOME CALCULATION TOOLS
20.8.1 Generation of Daily Radiation Sequences
Long series (many years) of daily irradiation data are sometimes required for particular
purposes, for example, when studying the long-term reliability of stand-alone photovoltaic
systems. However, long series of historical data are scarce and hard to obtain. This leads
to the need for methods that are able to generate a series starting from widely available
information, such as the 12 long-term average monthly mean values of the daily irradia-
tion,
G
dm
(0). The idea is that the generated series must keep some statistical properties
believed to be universal, as they are also found in historical data, when available. In
particular, the persistence of solar radiation, that is, the dependence of today’s irradiation
on the irradiation of the precedent days, is adequately described by a first-order auto-
regressive process [35]. Moreover, the probability function of the daily clearness index
for any given period has a form associated with only its average value for the period.
Several methods for the generation of daily irradiation sequences are available in the
literature [36]. The method proposed by Aguiar [37] is the most widely used today.
20.8.2 The Reference Year
As already mentioned, the most widely available information related to the solar radiation
resource at a given location is the set of 12 monthly mean values of global horizontal daily
irradiation,
G
dm
(0). The methods presented above allow estimation of all the radiation
components incident on any surface of arbitrary orientation and at any moment of the
average year, and even at any moment of a long sequence of years. This can be applied
to all the problems related to the design of photovoltaic systems: sizing, prediction of
energy yields, impact of shadowing, optimisation of tilt angles and so on.
Nevertheless, the solar radiation is still the object of systematic recording, and
more and more irradiance and irradiation data are being accumulated and put at public
disposal. Such data whether in the form of crude recorded data or in the form of elaborate
mathematical tools, attempt to properly represent the climate of the concerned location.
The most widely used is the so-called Reference Year, also called the Typical Meteoro-
logical Year [18],
TMY
, or the Standard Year. The
TMY
for a location is a hypothetical
938
ENERGY COLLECTED AND DELIVERED BY PV MODULES
year in which months are real months, but are chosen from different years from the whole
period for which data are available. In practice [38], the months are chosen such that the
monthly mean of the daily global irradiation on the horizontal represents an average value
for all values contained in the database. For example, January of 1986 was chosen for
the
TMY
of Madrid, because it had a value of
G
dm
(
0
)
=
1
.
98 kWh/m
2
, the closest to the
average value of
G
dm
(
0
)
=
1
.
99 kWh/m
2
for all the months of January on record [16].
The most widely used
TMY
for photovoltaic applications is set in a one-hour
time scale. Hence, it contains 4380
1
values of global horizontal irradiation. Ambient
temperature values are also specified for each hour. This huge number of initial data
can lead to the impression that the corresponding results should be much more accurate
than those obtained when simply using the 12
G
dm
(0) values as input. However, this
impression is largely wrong. On the one hand, because the representativeness of any
data – it should be again remembered – is limited by the random nature of the solar
radiation, small differences in the results are scarcely meaningful. On the other hand,
because the results obtained from the 12
G
dm
(0) values and from the
TMY
are very
similar, provided the initial data are coherent (i.e. the monthly means in the
TMY
coincides
with the 12
G
dm
(0) values) and that the selected correlations and diffuse radiation models
to transpose from horizontal to inclined surfaces are the same. The physical reasons for
this lie in the quasi-linear power-irradiance relationship in most PV devices, and in the
fact, initially shown by Liu and Jordan [19], that the solar climate of a particular location
can be well characterised by only the monthly mean daily clearness index. As already
mentioned, they have demonstrated that, irrespective of latitude, the fractional time during
which daily global radiation is equal to or less than a certain value depends only on this
parameter. Surely, to go into this question in-depth would increase the reader’s boredom
which is probably already large enough; hence, we will restrict ourselves to describing a
representative case from our own experience:
In 1992, the Solar Energy Institute in the University of Madrid, IES-UPM, was
involved in the design of the 1 MW PV plant in Toledo, Spain. It was the biggest
European PV project at that time, so very careful studies were required at the initial
project stage. Fortunately, a large historical database, containing 20 years of hourly
irradiation data, was available from a nearby meteorological station, and was directly
used to calculate the expected energy yields. Both static and sun-tracked photovoltaic
arrays were analysed while taking into account detailed features such as shadowing
from adjacent rows, back-tracking features and so on. Moreover, the same calcu-
lation was also performed using as input the
TMY
, previously derived from the
historical radiation sequence, and also using as the only input the 12
G
dm
(0) values
and computing for just the mean day of each month. The results from the three calcu-
lation procedures never differed more than 2%! As a matter of fact, the results were
much more sensitive to the considerations of the solar angle of incidence effects [39]
described below.
A clever friend, not involved in this project but being aware of this anecdote, posed
the questions: Then why go into such exhaustive detail when they give similar results?
1
There are 8760 hours per year, and the sun shines exactly half of the year in any location, hence there are
4380 hours of sunshine per year.
SOME CALCULATION TOOLS
939
80
60
40
20
0
−
120
−
90
−
60
−
30
0
30
60
90
120
Elevation angle
[
g
S
(
°
)]
Azimuth angle
[
Ψ
S
(
°
)]
Do'stlaringiz bilan baham: |
