# Total Energy Incident on Inclined Surfaces (Generic Case)

Adding together direct beam irradiated energy, diffuse radiation and ground reflection radiation results in the following general equation for total energy incident on an inclined surface:

where:

H — global irradiation incident on the horizontal plane HD — diffuse irradiation incident on the horizontal plane

kB — shading correction factor as described in Section 2.5.4 (non-shaded: kB — 1)

RB — direct beam irradiation factor as in Table 2.7 or the tables in Section A4 Rd — corrected diffuse radiation factor, RD — 1/2cos a2 + 1/2cos(a1 + b)

Rr — effective portion of reflective radiation, Rr — 1/2 — 1/2 cos b a1 — horizon elevation in the g direction

a2 — facade/roof edge elevation relative to the solar generator plane

b — inclination angle of the inclined surface relative to the horizontal plane

p — reflection factor (albedo) of the ground in front of the solar generator as in Table 2.6

Calculation of HG values using the three-component model is best done using a table in which the monthly H and HD values have been entered, as well as any other values needed for calculations entailing various monthly values. Then, after determining the monthly values HGB, HGD and HGR, add these values together to obtain HG. Table 2.8 or Table A1.2 can be used as a template for the aforementioned table.

 Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Year H Hd Rb кв HGB=kBRB(H-HD) Weo = Rd ‘Hd P k? GR = Rr ■ p • H HG = HGB + HGD + HGR
 Table 2.8 Tabular template for determining HG using the three-component model

Before filling the table, the diffuse radiation factor RD and the effective portion of reflected radiation Rr (these values are the same for all months) should be determined.

To determine the exact mean annual value HGa of total daily irradiation values HG, proceed as follows:

(a) determine the monthly total by multiplying the mean monthly total by the number of days nd in each month (28, 29, 30 or 31); and then (b) using the result of (a), determine the annual total. Determine total daily irradiation HG by dividing the annual total by the number of days in the year (365 or 366). As noted in Section 2.4, HGa is also obtainable as the mean of the monthly mean of total daily irradiation, albeit in most cases with a negligible error. To differentiate between the monthly or annual mean of total daily irradiation and monthly or annual total irradiation, it is best to use a clear unit of time as the denominator, where kWh/m2/d is the mean of total daily irradiance, kWh/m2/mt is a monthly total and kWh/m2/a is an annual total. The values obtained from this calculation all represent the same parameter – namely, the yield during the period entered.

Although the calculations in Table 2.8 can be readily carried out using a calculator, they are much quicker when performed on a computer using a spreadsheet program such as Excel.

Meteonorm4,5 or 6.1 [2.4,2.5,2.12], which can be run on Windows computers and sells for a few €100, are programs that readily allow for the calculation of irradiation on both the horizontal plane and an inclined surface for many locations in Europe and worldwide. These programs use a somewhat optimized model (the Perez model) for radiation calculations. For further information concerning this model, see [2.2], [Eic01] or [Qua03]. In this model, energy H incident on the horizontal plane is referred to as H_Gh, while the energy HG incident on the solar generator plane is referred to as H_Gk. The model also allows the effect of horizon shading to be taken into account. The program is worth purchasing for individuals who often need to perform these kinds of calculations. Some radiation calculation freeware is also available online (see Section 8.4).

Updated: August 3, 2015 — 3:14 am