# Examples of Radiation Calculations with the Three-Component Method

 Example 1 PV system in Bremen with a single-row solar generator with b — 30°, g — 0°. Mean ground reflection factor p: December, 0.3; January, 0.4; February, 0.35; rest of the year, 0.2. Calculation task: (a) Monthly and annual mean of total daily irradiation, as well as annual total HG incident on a solar generator that is out in the open. (b) Monthly and annual mean of total daily irradiation, as well as total annual HG incident on the same solar generator, if the latter is mounted on a dark-coloured southern facade of a very tall building (see Figure 2.38). Solution: (a) a1 — 0°, a2 — 0°. HG calculation using Table 2.8:

 Total annual HG: HGa — 365 d/a ■ 2.84 kWh/m2/d — 1037 kWh/m2/a. (b) a1 — 0°, a2 — 60°. HG calculation using Table 2.8:

 Total annual HG: HGa — 365 d/a ■ 2.45 kWh/m2/d — 894 kWh/m2/a.

Example 2

PV system with a horizontally mounted solar generator field (see Figure 2.37) located on Mont

Soleil (1270m) in Switzerland, with b — 45°, g — — 30°. The horizon elevation in the direction of

the solar generator azimuth is a1 — 12°. The reduced ground reflection radiation resulting from the

horizontal arrangement is taken into account via the somewhat reduced reflection factor p — 0.2

(May-October), p — 0.3 (November and April) and p — 0.4 (December-March).

(a) Monthly and annual mean of total daily irradiation and annual HG total on the upper edge of the topmost solar module (HG_top) of an array.

(b) Monthly and annual mean of total daily irradiation and annual HG total on the lower edge of the bottom solar module (HG-bottom) of an array.

(c) Irradiance GG-top at the upper edge of the topmost PV module and GG-bottom at the lower edge of the bottom PV module of an array, where G — GD — 200 W/m2 and p — 0.2.

Solution

(a) Hg – top. a1 — 0°, a2 — 0° ■ HG calculation using Table 2.8 (the front module does not shade the upper module edges, thus kB — 1 all year round).

Total annual HG. HGa — 365 d/a ■ 3.63 kWh/m2/d — 1325kWh/m2/a.

(b) HG. bottom: a1 — 12°, a2 — 0° ■ HG calculation using Table 2.8. First determine the shading correction factor kB using Figures 2.32 and 2.33. To do this, make a copy, cut it out, place it below the shading diagram and read off the shading point weightings (Figure 2.41).

Calculation of the shading correction factor kB as in Section 2.5.4.

SGPS — 19 ■ 3% + 12 ■ 2% + 6 ■ 1% — 87%

SGPB — 3.5 ■ 3% — 10.5% ) кв — 1 — SGPB/SGPS — 0.88 SGPS — 19 ■ 3% + 12 ■ 2% + 6 ■ 1% — 87%

SGPB — 2 ■ 3% — 6% ) kB — 1 — SGPB/SGPS — 0.93

SGPS — 19 ■ 3% + 12 ■ 2% + 6 ■ 1% — 87%

SGPB — 1.5 ■ 3% — 4.5% ) кв — 1 — SGPB/SGPS — 0.95 SGPS — 20 ■ 3% + 11 ■ 2% + 8 ■ 1% — 90%

SGPB — 1 ■ 3% — 3% ) kB — 1 — SGPB/SGPS — 0.97

Shadowing Diagram for PV Plant Mt. Soleil (47.2°N)

70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

-120 -105 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 105 120

Solar azimuth yS in degrees

Figure 2.41 Shading diagram for the Mont Soleil installation as in Example 2, with the solar generator azimuth entered and the horizon seen from the lowest module edge

Now determine HG using Table 2.8:

Energy yield calculation for grid connected PV plants (with three-component model!

 ft0- ‘■» COS ft, * Vi COS(rri 4 ft 0 772 n.. « s cos |9« 0 146 Jan Fat> Mar Apr May June July Aug Sent Осі Not Doc Уваг H 1.39 2.10 3 09 3.99 «М 4.99 6.57 4.79 3.93 242 1.44 114 3 25 MP 0.69 0.98 1.49 1.01 2.23 2.42 2.49 2.14 IM 1.14 0.71 0.96 !ЛЗ *’ 1,4. 1.42 1.13 0.90 0.09 0.92 1.00 1.99 глі 2.90 ft. 093 09; 1 1 1 1 t 1 1 0.99 0.88 No.= *,-»VtW .« 2.01 2.33 2.32 2.22 22b 2Л1 2.71 294 2.19 1.62 1.3Й 217 «ran* Яn’At 0.B0 ore 1 12 1.4Г yn %A1 1 90 1.69 1 28 099 0.99 0 42 1.19 P 0Л 0.4 0.4 0.3 ал ал 0.2 0.2 0.2 0.2 0.3 0.4 Mnm* R,’/l N 0M «.« 019 0.1? 0.13 a is 0 16 0.14 0.11 007 ОМ 0.0? 012 dq* МцН dnjl W|« 2.19 290 393 3.99 407 4 30 4.92 4.9? 3 93 3.10 2.14 167 347

Total annual HG: HGa — 365 d/a ■ 3.47 kWh/m2/d = 1267 kWh/m2/a.

(c) This scenario entails diffuse radiation only: G — GD — 200 W/m2, GB — 0 ) Gg – top — Rd — top ■ Gd + Rr ■ p ■ G — 177 W/m2.

^ GG — bottom — RD — bottom ■ GD + RR ■ p ■ G — 160 W/m.

In this scenario (presence of diffuse irradiance only), the radiation incident on the bottom edge of an array is only about 90% of that incident on the top edge. Although this effect is less pronounced

in the presence of direct beam irradiance (e. g. 600 W/m2 incident on the solar generator), there is still a 2% discrepancy between the two edges. This results in a radiation mismatch that is unavoidable for this particular installation.

Note: The actual Mont Soleil PV system has an inclination angle b — 50° and a mean solar generator orientation of about g — —26°. Inasmuch as a table showing the RB values for this parameter could not be included here for reasons of space, the next closest tabular values were used for the example. The resulting discrepancy is relatively minor.

Energy yield calculation for grid-connected PV plant* (with three-component model)

 R„ – *4 cos n, • 4 costa, * tt – 0.070 Ц coa |9- 0.020 Jan Mar Apr May June July Aug Sept Oct Nov Dec Year M 4.87 400 5 16 4.60 4.61 4.61 442 4.64 6.00 4.83 4.62 4.69 4.78 Hp 2.20 2.26 2.30 2.20 2.10 2.04 2.03 2.14 2.25 2^4 2.10 2.14 2.17 no 104 0.06 1.00 1.13 1.11 1.06 0.06 1 01 1.06 1.12 t 1 1 1 1 1 1 1 1 1 1 1 2.94 2.04 2.72 2.62 2.74 2.70 2.06 2.07 2.64 2.72 2.84 2.66 2.79 Rp-H. 2.12 2.10 2.22 2.12 2.04 1.06 1.07 2.06 2.16 2.17 2.12 2.08 2.11 P 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 H 0.02 0.03 002 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 003 Mu – Wu.» Moot 5.10 5.00 408 4.70 4.81 4.00 4.06 4.70 4.66 4.02 4.00 4.07 4.89

Red Sommer in northern hemisphere. Inclination toward* north

Example 4

PV system in Perth with a single-row solar generator with b — 35°, g — 0°. Mean year-round ground reflection factor: p — 0.3.

Calculation task: Monthly and annual mean of total daily irradiation, as well as annual total HG incident on a solar generator that is out in the open.

Updated: August 3, 2015 — 7:48 am