The expected yearly energy yields have been calculated using a specially developed software (Real Reporting Conditions Rating) [10]. In contrast to the power evaluation in standard test conditions (STC), it provides a rating of module performances under real conditions over an extended period of time. In addition to module parameters (see below), the software uses climate data bases to account for temperature and illumination conditions at the different geographical locations. The simulations have been realised for four different places (see table 2).

The input data for the modules were:

1) The efficiency in standard test conditions (STC)

2) The normalised spectral response

3) The variation of the short-circuit current as a function of the angle

4) The variation of the efficiency as a function the temperature

5) The variation of the efficiency as a function of the irradiance

6) The NOCT of the modules

For both the module with AR glass (Module AR) and for the module without AR (Module NG), the orientation was the same, chosen at values yielding the optimum energy output at each location. The data for the points 1)-3) have been directly taken from the results described in this paper. For point 4), a temperature dependence of the efficiency of —

0. 5%/°C has been assumed. For the point 5) we have first assumed that the short-circuit current Isc was proportional to the irradiance. For the module AR, Isc was set 2.65% higher than for the module Normal for perpendicular illumination. The efficiency as a function of the short-circuit current has then been calculated using the I-V characteristics obtained

from a two-diode model (see ref. [11], or [14] for a detailed application of the model), taking into account typical values for the series and parallel resistances of the solar cells. The efficiency as a function of Isc is then given by maximising the output power density VI. This procedure permits to reproduce accurately the fact that efficiencies at low irradiance in modules with crystalline Si solar cells are lower than at high irradiance for a given temperature. In particular, at low light level, this procedure leads to an additional efficiency gain for the module AR, because Voc and the fill factor FF are also improved when the current is higher. For the simulations, 3°C was added to the outdoor measured backskin temperature to account for temperature gradients through the module [12]. An NOCT of 45.2°C was hence taken for the modules Normal and of 46.4°C for the module AR. In summary, besides the higher short-circuit current and the better angular dependence, the module AR describes a realistic situation with one advantageous factor (increased efficiency because of the current increase) and a detrimental one (higher NOCT).

Table 2 gives the estimated module yearly energy outputs at 4 different locations: Wuerzburg, Freiburg and Essen in Germany and Miami in USA. Essen was taken as a prototype place with an important part in diffuse light and moderate temperature, whereas Freiburg is a slightly warmer and sunnier location. Miami represents a more equatorial position with a higher irradiation level. We have indicated for the module Normal the yearly efficiency n and the energy

yield per installed nominal Wp of power. The yearly efficiency is lower in Miami because of the higher operating temperature of the module. The most important results are given in the last two columns (energy output for the modules Normal and AR), and in Fig.4, where the relative improvement of the yearly energy yield in % is displayed for the module with the AR layers when compared to the performance of the module Normal. For the module AR, the gain in

Miami is 3.4% which is around 0.2% lower than the sum of the gain in perpendicular illumination (2.65%) plus the integral of the extra-gain in current integrated between -90° and +90°. The higher component of diffuse light and the lower temperature in Essen are favourable for an extra energy yield gain for the AR module. An energy yield gain give a gain of 3.54 to 3.67% for the three German locations. Although the result is slightly lower in Miami with 3.4%, the absolute gain in produced kWh remains however the highest.