Empirical method to estimate solar radiation using Grasshopper

RENEWABLE ENERGY TECHNOLOGY II Assignment Part 1

𝐻 𝐻 𝑅 GSC ⍵ ⍵ 𝜑 𝛿 𝛽 𝛾 𝜃 𝑛 𝑁 𝐻 H 𝐻

𝐾 𝑎, 𝑏 𝜌 𝑀𝐵𝐸 𝑙𝑎𝑡 𝑙𝑜𝑛

𝐾

=𝑎+𝑏 𝐻 =

∗

∗

𝛿 = 23.45 sin 360

1 + 0.033 𝑐𝑜𝑠

[𝑐𝑜𝑠𝜑 𝑐𝑜𝑠𝛿 𝑠𝑖𝑛𝜔 + 𝜔 𝑠𝑖𝑛𝜑 𝑠𝑖𝑛𝛿 ] 𝜔 = 𝑐𝑜𝑠

(−𝑡𝑎𝑛𝜑 𝑡𝑎𝑛𝛿)

𝜃 = (𝑠𝑖𝑛𝛿𝑠𝑖𝑛𝜑𝑐𝑜𝑠𝛽) − (𝑠𝑖𝑛𝛿𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝛾) + (𝑐𝑜𝑠𝛿𝑐𝑜𝑠𝜑𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝜔) + (𝑐𝑜𝑠𝛿𝑠𝑖𝑛𝜑𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝛾𝑐𝑜𝑤𝜔) + (𝑐𝑜𝑠𝛿𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝜔)

𝜔 ≤ 81.4°

0.3 ≤ 𝐾

≤ 0.8

= 1.391 − 3.560𝐾 + 4.189𝐾 − 2.137𝐾

𝜔 > 81.4°

0.3 ≤ 𝐾

≤ 0.8

= 1.311 − 3.022𝐾 + 3.427𝐾 − 1.821𝐾

𝑅 =

𝑎 = (𝑠𝑖𝑛𝛿 𝑠𝑖𝑛𝜑 𝑐𝑜𝑠𝛽 − 𝑠𝑖𝑛𝛿 𝑐𝑜𝑠𝜑 𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛾 ) ∗ (𝜔 − 𝜔 ) + (𝑐𝑜𝑠𝛿 𝑐𝑜𝑠𝜑 𝑐𝑜𝑠𝛽 + 𝑐𝑜𝑠𝛿 𝑠𝑖𝑛𝜑 𝑠𝑖𝑛𝛽 cos 𝛾 ) ∗ (𝑠𝑖𝑛𝜔 − 𝑠𝑖𝑛𝜔 ) − (cos 𝛿 𝑠𝑖𝑛𝛽 𝑠𝑖𝑛𝛾) ∗ (𝑐𝑜𝑠𝜔 − 𝑐𝑜𝑠𝜔 ) 𝑏 = (𝑐𝑜𝑠𝜑𝑐𝑜𝑠𝛿 ) ∗ (𝑠𝑖𝑛𝜔 − 𝑠𝑖𝑛𝜔 ) + (𝑠𝑖𝑛𝜑 𝑠𝑖𝑛𝛿 ) ∗ (𝜔 − 𝜔 ) 𝐵𝑒𝑎𝑚 = 𝐻 𝑅 𝐷𝑖𝑓𝑓𝑢𝑠𝑒 = 𝐻 𝑔𝑟𝑜𝑢𝑛𝑑 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑠 = 𝐻𝜌 𝐻 = 𝐻 𝑅 +𝐻

+ 𝐻𝜌

𝜃,

𝐻

𝐻 𝐻

𝐻=𝐻 + 𝐻

𝐻 𝑅 𝐻

𝑅

𝜌

𝐻 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

𝐻

𝐻 𝛽

𝐻

𝑀𝐵𝐸 = 1 𝑘 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑

𝑅

𝜃

𝜃 𝛽 𝛾

𝛿

𝐾

𝛿

𝜑

𝜔

𝐻 𝜑 𝛽 𝛾 𝐾 𝜌 𝑅

𝐻



𝐻 =

∗

∗

1+ ∗

0.033 𝑐𝑜𝑠

∗

𝑐𝑜𝑠26 𝑐𝑜𝑠23.08 𝑠𝑖𝑛102.13 + .

𝑠𝑖𝑛26 𝑠𝑖𝑛23.08

  

𝐻=𝐻 𝐾 𝜔 ≤ 81.4°

 

𝐻

𝐾 = 0.61

𝐻 = 24.79(1.391 − 3.560 ∗ 0.61 + 4.189 ∗ 0.61 − 2.137 ∗ 0.61³)

𝑅 

𝜔 = −𝜔 = −(102.13) 𝑎 = (𝑠𝑖𝑛23.08 𝑠𝑖𝑛26 𝑐𝑜𝑠11 − 𝑠𝑖𝑛23.08 𝑐𝑜𝑠26 𝑠𝑖𝑛11 𝑐𝑜𝑠0) ∗

(

.

.

)

+

(𝑐𝑜𝑠23.08 𝑐𝑜𝑠26 𝑐𝑜𝑠11 + 𝑐𝑜𝑠23.08 𝑠𝑖𝑛26 𝑠𝑖𝑛11 cos 0) ∗ (𝑠𝑖𝑛102.13 − sin(−102.13)) − (cos 23.08 𝑠𝑖𝑛11 𝑠𝑖𝑛0) ∗ (𝑐𝑜𝑠102.13 − cos(−102.13)) = 2.103



𝑏 = (𝑐𝑜𝑠26𝑐𝑜𝑠23.08) ∗ (sin(−102.13) − 𝑠𝑖𝑛102.13) + (𝑠𝑖𝑛26 𝑠𝑖𝑛23.08) ∗ (



.

.

)

 

𝑅



𝐷𝑖𝑓𝑓𝑢𝑠𝑒 = 𝐻



𝑔𝑟𝑜𝑢𝑛𝑑 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑠 = 𝐻𝜌

𝐵𝑒𝑎𝑚 = 𝐻 𝑅 = 16.62 ∗ 0.942 = 15.67

24.79 ∗ 0.25(  𝛽

𝛾



𝛿 = 23.45 sin 360

 

𝜔 = 𝑐𝑜𝑠

𝜌

(−𝑡𝑎𝑛26 𝑡𝑎𝑛23.08)

𝜃 = (𝑠𝑖𝑛23.08𝑠𝑖𝑛26𝑐𝑜𝑠11) − (𝑠𝑖𝑛23.08𝑐𝑜𝑠26𝑠𝑖𝑛11𝑐𝑜𝑠0) + (𝑐𝑜𝑠23.08𝑐𝑜𝑠26𝑐𝑜𝑠11𝑐𝑜𝑠0) + (𝑐𝑜𝑠23.08𝑠𝑖𝑛26𝑠𝑖𝑛11𝑐𝑜𝑠0𝑐𝑜𝑤0) + (𝑐𝑜𝑠23.08𝑠𝑖𝑛11𝑠𝑖𝑛0𝑠𝑖𝑛0)

= 2.231



= 8.17(

) =

) = 0.06

𝐻 = 𝑏𝑒𝑎𝑚 + 𝑑𝑖𝑓𝑓𝑢𝑠𝑒 + 𝑔𝑟𝑜𝑢𝑛𝑑𝑅𝑒𝑓𝑙 = 15.67 + 16.19 + 0.06 = 23.82

𝜃