Empirical method to estimate solar radiation using Grasshopper

Page 1

RENEWABLE ENERGY TECHNOLOGY II Assignment Part 1

𝐻 𝐻 𝑅 GSC ⍡ ⍡ πœ‘ 𝛿 𝛽 𝛾 πœƒ 𝑛 𝑁 𝐻 H 𝐻

𝐾 π‘Ž, 𝑏 𝜌 𝑀𝐡𝐸 π‘™π‘Žπ‘‘ π‘™π‘œπ‘›

𝐾

=π‘Ž+𝑏 𝐻 =

βˆ—

βˆ—

𝛿 = 23.45 sin 360

1 + 0.033 π‘π‘œπ‘ 

[π‘π‘œπ‘ πœ‘ π‘π‘œπ‘ π›Ώ π‘ π‘–π‘›πœ” + πœ” π‘ π‘–π‘›πœ‘ 𝑠𝑖𝑛𝛿 ] πœ” = π‘π‘œπ‘ 

(βˆ’π‘‘π‘Žπ‘›πœ‘ π‘‘π‘Žπ‘›π›Ώ)

πœƒ = (π‘ π‘–π‘›π›Ώπ‘ π‘–π‘›πœ‘π‘π‘œπ‘ π›½) βˆ’ (π‘ π‘–π‘›π›Ώπ‘π‘œπ‘ πœ‘π‘ π‘–π‘›π›½π‘π‘œπ‘ π›Ύ) + (π‘π‘œπ‘ π›Ώπ‘π‘œπ‘ πœ‘π‘π‘œπ‘ π›½π‘π‘œπ‘ πœ”) + (π‘π‘œπ‘ π›Ώπ‘ π‘–π‘›πœ‘π‘ π‘–π‘›π›½π‘π‘œπ‘ π›Ύπ‘π‘œπ‘€πœ”) + (π‘π‘œπ‘ π›Ώπ‘ π‘–π‘›π›½π‘ π‘–π‘›π›Ύπ‘ π‘–π‘›πœ”)

πœ” ≀ 81.4Β°

0.3 ≀ 𝐾

≀ 0.8

= 1.391 βˆ’ 3.560𝐾 + 4.189𝐾 βˆ’ 2.137𝐾

πœ” > 81.4Β°

0.3 ≀ 𝐾

≀ 0.8

= 1.311 βˆ’ 3.022𝐾 + 3.427𝐾 βˆ’ 1.821𝐾

𝑅 =

π‘Ž = (𝑠𝑖𝑛𝛿 π‘ π‘–π‘›πœ‘ π‘π‘œπ‘ π›½ βˆ’ 𝑠𝑖𝑛𝛿 π‘π‘œπ‘ πœ‘ 𝑠𝑖𝑛𝛽 π‘π‘œπ‘ π›Ύ ) βˆ— (πœ” βˆ’ πœ” ) + (π‘π‘œπ‘ π›Ώ π‘π‘œπ‘ πœ‘ π‘π‘œπ‘ π›½ + π‘π‘œπ‘ π›Ώ π‘ π‘–π‘›πœ‘ 𝑠𝑖𝑛𝛽 cos 𝛾 ) βˆ— (π‘ π‘–π‘›πœ” βˆ’ π‘ π‘–π‘›πœ” ) βˆ’ (cos 𝛿 𝑠𝑖𝑛𝛽 𝑠𝑖𝑛𝛾) βˆ— (π‘π‘œπ‘ πœ” βˆ’ π‘π‘œπ‘ πœ” ) 𝑏 = (π‘π‘œπ‘ πœ‘π‘π‘œπ‘ π›Ώ ) βˆ— (π‘ π‘–π‘›πœ” βˆ’ π‘ π‘–π‘›πœ” ) + (π‘ π‘–π‘›πœ‘ 𝑠𝑖𝑛𝛿 ) βˆ— (πœ” βˆ’ πœ” ) π΅π‘’π‘Žπ‘š = 𝐻 𝑅 𝐷𝑖𝑓𝑓𝑒𝑠𝑒 = 𝐻 π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘ π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘›π‘  = 𝐻𝜌 𝐻 = 𝐻 𝑅 +𝐻

+ 𝐻𝜌

πœƒ,

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

𝑀𝐡𝐸 = 1 π‘˜ π‘šπ‘’π‘Žπ‘ π‘’π‘Ÿπ‘’π‘‘ βˆ’ π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘

𝑅

πœƒ

πœƒ 𝛽 𝛾

𝛿

𝐾

𝛿

πœ‘

πœ”

𝐻 πœ‘ 𝛽 𝛾 𝐾 𝜌 𝑅

𝐻

ο‚·

𝐻 =

βˆ—

βˆ—

1+ βˆ—

0.033 π‘π‘œπ‘ 

βˆ—

π‘π‘œπ‘ 26 π‘π‘œπ‘ 23.08 𝑠𝑖𝑛102.13 + .

𝑠𝑖𝑛26 𝑠𝑖𝑛23.08

ο‚· ο‚· ο‚·

𝐻=𝐻 𝐾 πœ” ≀ 81.4Β°

ο‚· ο‚·

𝐻

𝐾 = 0.61

𝐻 = 24.79(1.391 βˆ’ 3.560 βˆ— 0.61 + 4.189 βˆ— 0.61 βˆ’ 2.137 βˆ— 0.61Β³)

𝑅 ο‚·

πœ” = βˆ’πœ” = βˆ’(102.13) π‘Ž = (𝑠𝑖𝑛23.08 𝑠𝑖𝑛26 π‘π‘œπ‘ 11 βˆ’ 𝑠𝑖𝑛23.08 π‘π‘œπ‘ 26 𝑠𝑖𝑛11 π‘π‘œπ‘ 0) βˆ—

(

.

.

)

+

(π‘π‘œπ‘ 23.08 π‘π‘œπ‘ 26 π‘π‘œπ‘ 11 + π‘π‘œπ‘ 23.08 𝑠𝑖𝑛26 𝑠𝑖𝑛11 cos 0) βˆ— (𝑠𝑖𝑛102.13 βˆ’ sin(βˆ’102.13)) βˆ’ (cos 23.08 𝑠𝑖𝑛11 𝑠𝑖𝑛0) βˆ— (π‘π‘œπ‘ 102.13 βˆ’ cos(βˆ’102.13)) = 2.103

ο‚·

𝑏 = (π‘π‘œπ‘ 26π‘π‘œπ‘ 23.08) βˆ— (sin(βˆ’102.13) βˆ’ 𝑠𝑖𝑛102.13) + (𝑠𝑖𝑛26 𝑠𝑖𝑛23.08) βˆ— (

ο‚·

.

.

)

ο‚· ο‚·

𝑅

ο‚·

𝐷𝑖𝑓𝑓𝑒𝑠𝑒 = 𝐻

ο‚·

π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘ π‘Ÿπ‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘›π‘  = 𝐻𝜌

π΅π‘’π‘Žπ‘š = 𝐻 𝑅 = 16.62 βˆ— 0.942 = 15.67

24.79 βˆ— 0.25( ο‚· 𝛽

𝛾

ο‚·

𝛿 = 23.45 sin 360

ο‚· ο‚·

πœ” = π‘π‘œπ‘ 

𝜌

(βˆ’π‘‘π‘Žπ‘›26 π‘‘π‘Žπ‘›23.08)

πœƒ = (𝑠𝑖𝑛23.08𝑠𝑖𝑛26π‘π‘œπ‘ 11) βˆ’ (𝑠𝑖𝑛23.08π‘π‘œπ‘ 26𝑠𝑖𝑛11π‘π‘œπ‘ 0) + (π‘π‘œπ‘ 23.08π‘π‘œπ‘ 26π‘π‘œπ‘ 11π‘π‘œπ‘ 0) + (π‘π‘œπ‘ 23.08𝑠𝑖𝑛26𝑠𝑖𝑛11π‘π‘œπ‘ 0π‘π‘œπ‘€0) + (π‘π‘œπ‘ 23.08𝑠𝑖𝑛11𝑠𝑖𝑛0𝑠𝑖𝑛0)

= 2.231

ο‚·

= 8.17(

) =

) = 0.06

𝐻 = π‘π‘’π‘Žπ‘š + 𝑑𝑖𝑓𝑓𝑒𝑠𝑒 + π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘π‘…π‘’π‘“π‘™ = 15.67 + 16.19 + 0.06 = 23.82

πœƒ

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