EFFECTS OF THE ANGLE OF INCIDENCE AND OF DIRT

The reflectance and transmittance of optical materials depends on the angle of incidence. The glass covers of solar collectors are no exception, and therefore the optical input of photovoltaic modules is affected by their orientation with respect to the sun, due to the angular variation of the glass reflection. Theoretical models, based on the well-known Fresnel formulae, have been developed for clean surfaces. The most popular formulation is from ASHRAE [30]. For a given incidence angle, 9s, it can be described by the simple expression

FTB(9s) = 1 – b0 (- l) (22.45)

cos 9s )

where FTb(9s ) is the relative transmittance, normalised by the total transmittance for normal incidence, and b0 is an adjustable parameter that can be empirically determined for each type of photovoltaic module. If this value is unknown, a general value b0 = 0.07 may be used. The effect of the angle of incidence on the successfully collected solar radiation can be calculated by applying Equation (22.45) to the direct and circumsolar irradiances, and by considering an approximate value FT = 0.9 for the isotropic diffuse and reflected radiation terms. Figure 22.16 shows a plot of FTb(9s) versus 9s. It presents a pronounced knee close to 60°. In practical terms, that means the effects of the angle of incidence are negligible for all the 9s well below this value. For example, FTb(40°) = 0.98.

The ASHRAE model is simple to use, but has noticeable disadvantages. It cannot be used for 9s > 80°, and, still worse, it cannot take into consideration the effects of dust. Dust is always present

EFFECTS OF THE ANGLE OF INCIDENCE AND OF DIRT

in real situations, and not only reduces the transmittance at normal incidence, but also influences the shape of FTb(0s). Figure 22.16 shows that the relative transmittance decreases because of dust at angles from about 40 to 80°. Real FTb(0s) are best described [31] by

where ar is an adjustable parameter mainly associated with the degree of dirtiness, as shown in Table 22.3. Note that the degree of dirtiness is characterised by the corresponding relative normal transmittance, Tdirt(0yTclean(0). Equation (22.46) applies for direct and circumsolar radiation components. Consistent equations for the angular losses for isotropic diffuse and albedo radiation components are given in reference [31]

It must be noted that FTb(0) = 1. That means, this function does not include the effect of dirt on the relative normal transmittance, but only the angular losses relative to normal incidence. In other words, the ‘effective’ direct irradiance reaching the solar cells of a PV module, should be computed as

Tdirt (0)

SeffOS, a) = B(fi, a) x x FTB(9S) (22.47)

T clean (0)

Following the example of 15 April in Portoalegre, Brazil, we can now calculate the effective irradiances over a surface tilted to the latitude, neglecting the albedo, supposing a medium dirtiness degree and by applying FTb(0s) not only to the direct radiation, but also to the circumsolar component of the diffuse radiation.

The last column of this table describes the losses due to both dirt and angular effects. Taking into consideration that dirt reduces normal transmittance by a factor of 3% (Tdirt(0yTclean(0) = 0.97), it can be noted that pure angular losses dominate for « > 30°.

Finally, it should be stressed that angular-dependent reflection is often neglected in PV simulations. However, they become significant in many practical situations, for example, where vertical (facade-integrated PV generators) or horizontal (N-S horizontal trackers) surfaces are concerned. Furthermore, they help to explain the observed low irradiance effects in PV module performance. This is because low irradiance just happens when the incidence angle is large or when solar radiation is mainly diffuse. In both cases, angular losses are particularly important. As a matter of fact, the failure to consider angular losses has been signalled as the main cause of error in some energy models [32].