10 Module Deployment and Energy Rating
253
solar noon, when (in our example, at the Equator during the Equinox) θ = 0
◦ and
cosθ (t) = 1.
More or less the same profile is expected at any given latitude when modules are
installed at a tilt β, which is equal to the geographical latitude, as shown for example
in Fig. 10.2 for the upper module installed with a β = 66
◦ tilt at the Arctic Circle
(latitude: approximately 66
◦ ). In general the value of the maximum in-plane global
irradiance varies with the seasons between a maximum and a minimum.
4
So far we have implicitly considered PV modules installed at 0
◦ azimuth (i.e.
facing South in the Northern hemisphere or facing North in the Southern hemisphere).
The correlation between the orientation and Sun height is more complicated if we
consider installations with azimuth other than 0
◦ : this is usually the case in residential
installations, where modules are installed on the roof (typically laying parallel to the
roof slope) and, thus, have both tilt and azimuth that depend on the roof orientation.
But in general, the modules in real conditions see always varying global irradiance
from 0 to about 1000 W/m
2 . It is therefore important to know the performance of
the module not only at 1000 W/m
2 (STC), but also at lower irradiances. In fact, no
PV module is perfectly linear with irradiance: it has already been shown in previous
chapters that PV modules of different technologies have different efficiencies at
different irradiance levels.
Once the in-plane global irradiance as a function of time G(t) (depending on the
orientation as discussed above) and the module efficiency as a function of irradiance
η(G) are known, the power P of the module at time t could in principle be calculated
as
P(t) = η(G)G(t)A
(10.2)
where A is the module area. Then the total energy generated would be
E =
t
P(t)t
(10.3)
where the sum is performed over time (typically over 1 year) and t is a reasonably
short amount of time during which P(t) can be assumed to be constant. But in the
real practice (10.2) and (10.3) are correct only if the following assumptions hold:
• the efficiency of the module η(G) does not vary with temperature;
• the efficiency of the module η(G) does not vary with the angle of incidence θ(t);
• the diffuse component D(t) and the albedo R(t) are negligible;
• the efficiency of the module η(G) does not vary with the spectrum of in-plane
global irradiance (the so-called spectral in-plane global irradiance).
4 Although the reader may have already argued that the optimum tilt is equal to the geographical
latitude, this argument works only at the equinoxes: during the other seasons the optimal tilt is
different and the general practice is to install modules at a tilt that is 70–90% of the latitude value.
253
solar noon, when (in our example, at the Equator during the Equinox) θ = 0
◦ and
cosθ (t) = 1.
More or less the same profile is expected at any given latitude when modules are
installed at a tilt β, which is equal to the geographical latitude, as shown for example
in Fig. 10.2 for the upper module installed with a β = 66
◦ tilt at the Arctic Circle
(latitude: approximately 66
◦ ). In general the value of the maximum in-plane global
irradiance varies with the seasons between a maximum and a minimum.
4
So far we have implicitly considered PV modules installed at 0
◦ azimuth (i.e.
facing South in the Northern hemisphere or facing North in the Southern hemisphere).
The correlation between the orientation and Sun height is more complicated if we
consider installations with azimuth other than 0
◦ : this is usually the case in residential
installations, where modules are installed on the roof (typically laying parallel to the
roof slope) and, thus, have both tilt and azimuth that depend on the roof orientation.
But in general, the modules in real conditions see always varying global irradiance
from 0 to about 1000 W/m
2 . It is therefore important to know the performance of
the module not only at 1000 W/m
2 (STC), but also at lower irradiances. In fact, no
PV module is perfectly linear with irradiance: it has already been shown in previous
chapters that PV modules of different technologies have different efficiencies at
different irradiance levels.
Once the in-plane global irradiance as a function of time G(t) (depending on the
orientation as discussed above) and the module efficiency as a function of irradiance
η(G) are known, the power P of the module at time t could in principle be calculated
as
P(t) = η(G)G(t)A
(10.2)
where A is the module area. Then the total energy generated would be
E =
t
P(t)t
(10.3)
where the sum is performed over time (typically over 1 year) and t is a reasonably
short amount of time during which P(t) can be assumed to be constant. But in the
real practice (10.2) and (10.3) are correct only if the following assumptions hold:
• the efficiency of the module η(G) does not vary with temperature;
• the efficiency of the module η(G) does not vary with the angle of incidence θ(t);
• the diffuse component D(t) and the albedo R(t) are negligible;
• the efficiency of the module η(G) does not vary with the spectrum of in-plane
global irradiance (the so-called spectral in-plane global irradiance).
4 Although the reader may have already argued that the optimum tilt is equal to the geographical
latitude, this argument works only at the equinoxes: during the other seasons the optimal tilt is
different and the general practice is to install modules at a tilt that is 70–90% of the latitude value.