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Multi-objective Optimization of Solar Irradiance and Variance at Pertinent Inclination Angles

  • Dhanesh JainEmail author
  • Mahendra Lalwani
Original Contribution
  • 40 Downloads

Abstract

The performance of photovoltaic panel gets highly affected bychange in atmospheric conditions and angle of inclination. This article evaluates the optimum tilt angle and orientation angle (surface azimuth angle) for solar photovoltaic array in order to get maximum solar irradiance and to reduce variance of radiation at different sets or subsets of time periods. Non-linear regression and adaptive neural fuzzy interference system (ANFIS) methods are used for predicting the solar radiation. The results of ANFIS are more accurate in comparison to non-linear regression. These results are further used for evaluating the correlation and applied for estimating the optimum combination of tilt angle and orientation angle with the help of general algebraic modelling system and multi-objective genetic algorithm. The hourly average solar irradiation is calculated at different combinations of tilt angle and orientation angle with the help of horizontal surface radiation data of Jodhpur (Rajasthan, India). The hourly average solar irradiance is calculated for three cases: zero variance, with actual variance and with double variance at different time scenarios. It is concluded that monthly collected solar radiation produces better result as compared to bimonthly, seasonally, half-yearly and yearly collected solar radiation. The profit obtained for monthly varying angle has 4.6% more with zero variance and 3.8% more with actual variance, than the annually fixed angle.

Keywords

Solar energy Tilt angle and orientation angle ANFIS Genetic algorithm Renewable energy Solar radiation GAMS software 

Notations

I

Global solar irradiance on horizontal surface

Iavg

Mean solar irradiances

Iavg,1

Mean solar irradiances for January

Iavg,10

Mean solar irradiances for October

Iavg,11

Mean solar irradiances for November

Iavg,11–12

Mean solar irradiances for Nov–Dec

Iavg,12

Mean solar irradiances for December

Iavg,1–2

Mean solar irradiances for Jan–Feb

Iavg,12–2

Mean solar irradiances for Dec–Feb

Iavg,2

Mean solar irradiances for February

Iavg,3

Mean solar irradiances for March

Iavg,3–4

Mean solar irradiances for March–April

Iavg,3–5

Mean solar irradiances for March–May

Iavg,4

Mean solar irradiances for April

Iavg,5

Mean solar irradiances for May

Iavg,5–6

Mean solar irradiances for May–June

Iavg,6

Mean solar irradiances for June

Iavg,6–8

Mean solar irradiances for June–August

Iavg,7

Mean solar irradiances for July

Iavg,7–8

Mean solar irradiances for July–August

Iavg,8

Mean solar irradiances for August

Iavg,9

Mean solar irradiances for September

Iavg,9–11

Mean solar irradiances for Sept–Nov

Iavg,c

Mean solar irradiances for cold period

Iavg,h

Mean solar irradiances for hot period

Iavg,y

Mean solar irradiances for a year

Iavg9–10

Mean solar irradiances for Sept–Oct

Ib

Beam solar irradiance on horizontal surface

Id

Diffuse solar irradiance on horizontal surface

Itb

Beam solar irradiance on tilted surface

Itb,i

Beam solar irradiance on tilted surface for ith hour

Itd

Diffuse solar irradiance on tilted surface

Itd,i

Diffusion solar irradiance on tilted surface for ith hour

Itg

Total solar irradiance on tilted surface

Itg,i

Global solar irradiance on tilted surface for ith hour

Itr

Reflected solar irradiance on tilted surface

Itr,i

Reflected solar irradiance on tilted surface for ith hour

Lst

Standard longitude

Lloc

Location longitude

n

Day of the year, starting from 1st January

R2

Coefficient of determination

RSS

Residual sum of squares

STD

Standard deviation

TS

Solar time,

Tstd

Standard time

Varavg

Mean variance

Varavg,1

Mean variance for January

Varavg,10

Mean variance for October

Varavg,11

Mean variance for November

Varavg,11–12

Mean variance for Nov–Dec

Varavg,12

Mean variance for December

Varavg,1–2

Mean variance for Jan–Feb

Varavg,12–2

Mean variance for Dec–Feb

Varavg,2

Mean variance for February

Varavg,3

Mean variance for March

Varavg,3–4

Mean variance for March–April

Varavg,3–5

Mean variance for March–May

Varavg,4

Mean variance for April

Varavg,5

Mean variance for May

Varavg,5–6

Mean variance for May–June

Varavg,6

Mean variance for June

Varavg,6–8

Mean variance for June–August

Varavg,7

Mean variance for July

Varavg,7–8

Mean variance for July–August

Varavg,8

Mean variance for August

Varavg,9

Mean variance for September

Varavg,9–10

Mean variance for Sept–Oct

Varavg,9–11

Mean variance for Sept–Nov

Varavg,c

Mean variance for cold period

Varavg,h

Mean variance for hot period

Varavg,y

Mean variance for a year

β

Tilt angle,

β1

Tilt angle for January

β10

Tilt angle for October

β11

Tilt angle for November

β11–12

Tilt angle for November–December

β12

Tilt angle for December

β1–2

Tilt angle for January–February

β12–2

Tilt angle for December–February

β2

Tilt angle for February

β3

Tilt angle for March

β3–4

Tilt angle for March–April

β3–5

Tilt angle for March–May

β4

Tilt angle for April

β5

Tilt angle for May

β5–6

Tilt angle for May–June

β6

Tilt angle for June

β6–8

Tilt angle for June–August

β7

Tilt angle for July

β7–8

Tilt angle for July–August

β8

Tilt angle for August

β9

Tilt angle for September

β9–10

Tilt angle for September–October

β9–11

Tilt angle for September–November

βc

Tilt angle for cold period

βh

Tilt angle for hot period

βy

Tilt angle for year

γ

Orientation angle

δ

Declination angle

ω

Hour angle

θz

Zenith angle

θi

Incident angle

φ

Location latitude, here, all irradiance are in kW/m2 and angles are in degree

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Copyright information

© The Institution of Engineers (India) 2018

Authors and Affiliations

  1. 1.Department of Renewable EnergyRajasthan Technical UniversityKotaIndia
  2. 2.Department of Electrical EngineeringRajasthan Technical UniversityKotaIndia

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