10 Module Deployment and Energy Rating
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Fig. 10.3 An example of efficiency versus irradiance and temperature at the AM1.5 spectrum for
a c-Si PV module; the dots indicate actual measurement points. Source [2]
angle of incidence, the following angular transmittance τ (θ ) can be introduced
τ (θ ) =
I sc (θ )
I sc (0)
1
cosθ
(10.5)
where I sc (θ ) and I sc (0) are the measured short-circuit currents, at the angle of incidence θ and at normal incidence, respectively. An example of τ (θ ) for c-Si is shown
in Fig. 10.4.
The curve τ (θ ) is mathematically equivalent to the following Equation, proposed
by Martin and Ruiz (see [3, 4]),
τ (θ ) =
1 − exp
−cosθ
a r
1 − exp
−1
a r
.
(10.6)
where a r is a dimensionless fitting parameter. The correction to the direct component
of irradiance B(t) is
B corr,AOI (t) = B(t)τ [θ (t)].
(10.7)
The contribution of τ (θ ) to the diffuse component is less straightforward; it obviously depends on the module orientation (via the tilt β) and has been calculated by
Martin and Ruiz assuming an isotropic distribution of the diffuse irradiance. The
related Equation can be found in the specialized literature (see [3, 4]).