Using the sun as a renewable energy source isn't really a new invention. Plants have been relying on it for millions of years and our - mostly - green friends seem to handle it pretty well on an instinctive method of operation.

Let's have a simplified look on how much we already depend on solar energy:

• Global freshwater distribution (oceans→clouds→rain)
• Global atmospheric conditions/weather/temperature (direct) → flora/fauna
• Global flora → atmospheric conditions/weather/temperature (indirect)

and which parts we use technically:

• Agriculture (photosynthesis) → Food
• Solar energy conversion to heat (mirror/focus)
• Direct solid-state photon→electron conversion for electrical power

Global solar radiation (Rs) is of funfamental importance for human life on earth. We're depending very much on knowing how much solar energy can be harvested on a certain point on the planet's surface, yet we still commonly refer to 1000W/m2 on any point on Earth as a clear-sky reference. The following model is an open-resource based starting point for a new common model to predict the convertible solar output on a clear-sky day and incorporate any given conversion technique (currently only PV).

• being able to have a more accurate prediction of maximum PV output for a given site/configuration
• keep PV panel at optimum elevation without a separate optical solar tracker

The system can be easily extended to estimate the optimum parabolic oven-reflector size, to satisfy the energy needs for a given community and their specific position on the planet.

Possibility to calibrate a pyranometer in the field, without another calibrated reference, on a clear-sky day.

Usable as basis for agricultural applications (growth/photosynthetic calculations)

This model is based on algorithms developed by the Environmental and Water Resources Institute of the American Society of Civil Engineers and a few common NOAA/NASA calculations. Apollo-NG's energy management, prediction and logging system fuses this rational prediction model with real time sensor data in order to predict the nominal output power of a PV system and compares the actual output to it.

By now it has become a very advanced clear-sky prediction model, incorporating the following factors:

• Position on Earth
• Day of Year
• Distance Sun-Earth
• Angle through atmosphere
• Water in atmosphere
• Atmospheric turbidity (smog, dust etc.)
• Direct/diffuse beam radiation
• PV-Module surface/type/temperature/age

#!/usr/bin/env python
# -*- coding: UTF-8 -*-
#
########################################################################
#
#   This program is free software: you can redistribute it and/or modify
#   it under the terms of the GNU General Public License as published by
#   the Free Software Foundation, either version 3 of the License, or
#   (at your option) any later version.
#
#   This program is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU General Public License for more details.
#
#   You should have received a copy of the GNU General Public License
#   along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
########################################################################

import math, calendar
from math import pi

# Solar constant for the mean distance between the Earth and sun #######

sol_const		=				1367.8

########################################################################
# GEO Parameters (to be fed from GPS)

lat				=				23
lon				=				11
alt				=				0

########################################################################
# Time and Offsets (to be fed from GPS)

day				=				22
month			=				06
year			=				2011
ToD				=				12
tz_off_deg		=				0+lon
dst_off			=				0

########################################################################
# Atmospheric Parameters (to be fed from Argus current sensor data)

# air temperature

atm_temp		=				25.0	

# relative humidity

atm_hum			=				20.0	

# turbidity coefficient - 0 < tc < 1.0 - where tc = 1.0 for clean air
# and tc < 0.5 for extremely turbid, dusty or polluted air

atm_tc			=				0.8

########################################################################
# PV System Parameters (actual PV data of Odysseys modules)

# Solar Panel Surface in m²

pv_a			=				1.67

# Module Efficiency %

pv_eff			=				20

# Mod. neg. Temp. Coeff (0.35=mono)

pv_tk			=				0.35

# Mod. Temperature in °C - should be measured on the back of module

pv_temp			=				30

# Mod. Age related Coeff (95% after 1-2y)

pv_ak			=				0.98



########################################################################
##  MAIN
########################################################################

# get Julian Day (Day of Year)

if 								calendar.isleap(year):

	# Leap year, 366 days
	lMonth 		= 		[0,31,60,91,121,152,182,213,244,274,305,335,366]

else:

	# Normal year, 365 days
	lMonth 		= 		[0,31,59,90,120,151,181,212,243,273,304,334,365]

DoY 			= 				lMonth[month-1] + day

print "--------------------------------------------------------------"

print "%d.%d.%d | %d | %f | " % (day, month, year, DoY, ToD, )

print "--------------------------------------------------------------"

print "Solar Constant                               : %s" % sol_const
print "Atmospheric turbidity coefficient            : %s" % atm_tc

print "--------------------------------------------------------------"


# inverse relative distance factor for distance between Earth and Sun ##

sun_rel_dist_f 	= 1.0/(1.0-9.464e-4*math.sin(DoY)- 						\
				+ 0.01671*math.cos(DoY)- 								\
				+ 1.489e-4*math.cos(2.0*DoY)-2.917e-5*math.sin(3.0*DoY)-\
				+ 3.438e-4*math.cos(4.0*DoY))**2

print "Inverse relative distance factor             : %s" % sun_rel_dist_f


# solar declination ####################################################

sun_decl 		= (math.asin(0.39785*(math.sin(((278.97+(0.9856*DoY)) 	\
				+ (1.9165*(math.sin((356.6+(0.9856*DoY)) 				\
				* (math.pi/180)))))*(math.pi/180))))*180) 				\
				/ math.pi


print "Sun declination                              : %s°" % sun_decl


# equation of time #####################################################
# (More info on http://www.srrb.noaa.gov/highlights/sunrise/azel.html)

eqt				= (((5.0323-(430.847*math.cos((((2*math.pi)*DoY)/366)+4.8718)))\
				+ (12.5024*(math.cos(2*((((2*math.pi)*DoY)/366)+4.8718))))\
				+ (18.25*(math.cos(3*((((2*math.pi)*DoY)/366)+4.8718))))\
				- (100.976*(math.sin((((2*math.pi)*DoY)/366)+4.8718))))\
				+ (595.275*(math.sin(2*((((2*math.pi)*DoY)/366)+4.8718))))\
				+ (3.6858*(math.sin(3*((((2*math.pi)*DoY)/366)+4.871))))\
				- (12.47*(math.sin(4*((((2*math.pi)*DoY)/366)+4.8718)))))\
				/ 60

print "Equation of time                             : %s min" % eqt


# time of solar noon ###################################################

sol_noon		= ((12+dst_off)-(eqt/60))-((tz_off_deg-lon)/15)

print "Solar Noon                                   : %s " % sol_noon


# solar zenith angle in DEG ############################################

sol_zen			= math.acos(((math.sin(lat*(math.pi/180)))				\
				* (math.sin(sun_decl*(math.pi/180))))					\
				+ (((math.cos(lat*((math.pi/180))))						\
				* (math.cos(sun_decl*(math.pi/180))))					\
				* (math.cos((ToD-sol_noon)*(math.pi/12)))))				\
				* (180/math.pi)

# in extreme latitude, values over 90 may occurs.
#if sol_zen > 90:

print "Solar Zenith Angle                           : %s° " % sol_zen


# barometric pressure of the measurement site
# (this should be replaced by the real measured value) in kPa

atm_press		= 101.325												\
				* math.pow(((288-(0.0065*(alt-0)))/288)					\
				, (9.80665/(0.0065*287)))

atm_press=100.5

print "Estimated Barometric Pressure at site        : %s kPa" % atm_press


# Estimated air vapor pressure in kPa ###################################

atm_vapor_press	= (0.61121*math.exp((17.502*atm_temp)					\
				/ (240.97+atm_temp)))									\
				* (atm_hum/100)

print "Estimated Vapor Pressure at site             : %s kPa" % atm_vapor_press


# extraterrestrial radiation in W/m2 ###################################

extra_terr_rad	= (sol_const*sun_rel_dist_f)							\
				* (math.cos(sol_zen*(math.pi/180)))

print "Estimated Extraterrestrial radiation         : %s W/m²" % extra_terr_rad


# precipitable water in the atmosphere in mm ###########################

atm_prec_h2o	= ((0.14*atm_vapor_press)*atm_press)+2.1

print "Estimated precipitable water in Atmosphere   : %s mm" % atm_prec_h2o


# clearness index for direct beam radiation [unitless] #################

clr_idx_beam_rad= 0.98*(math.exp(((-0.00146*atm_press)					\
				/ (atm_tc*(math.sin((90-sol_zen)*(math.pi/180)))))		\
				- (0.075*(math.pow((atm_prec_h2o						\
				/ (math.sin((90-sol_zen)*(math.pi/180)))),0.4)))))

print "Clearness index for direct beam radiation    : %s" % clr_idx_beam_rad


# transmissivity index for diffuse radiation [unitless] ################

if 								(clr_idx_beam_rad > 0.15):
	trns_idx_diff_rad=			0.35-(0.36*clr_idx_beam_rad)
else:
	trns_idx_diff_rad=			0.18+(0.82*clr_idx_beam_rad)

print "Transmissivity index for diffuse radiation   : %s" % trns_idx_diff_rad


# Model Estimated Shortwave Radiation (W/m2) ###########################

est_sol_rad		= 				(clr_idx_beam_rad + trns_idx_diff_rad)	\
				* 				extra_terr_rad

print "--------------------------------------------------------------"
print "Model Estimated Shortwave Radiation (RSO)    : \033[1;33m%3.1f W/m²\033[0m" % est_sol_rad


# Estimate Output of Odyssey (solar panels at nominal Efficiency) ######

est_p_out		= 				(est_sol_rad*pv_a) / 100 * pv_eff

print "Model Estimated Max. PV-Power Output         : \033[1;31m%3.1f W\033[0m \033[1;37m@ %d%% Mod Eff\033[0m" % (est_p_out, pv_eff)


# Estimate conversion loss due to module temperature ###################

if 								( pv_temp > 25 ):
	
    pv_p_loss 	= 				(pv_temp-25 ) * pv_tk
	pv_p_loss_p = 				(est_p_out/100) * pv_p_loss

print "Model estimated PV-Module temp conv. loss       : \033[1;37m%2.1f W / %2.1f%%\033[0m" % (pv_p_loss_p, pv_p_loss)

# Estimate conversion loss due to module age

est_pv_age_loss	= 				est_p_out - (est_p_out*pv_ak)

print "Model estimated PV-Module aging loss            : \033[1;37m%03.1f W\033[0m" % est_pv_age_loss

# Optimal PV Module Angle to Sun

print "Model recommends PV-Module angle to Sun      : \033[1;37m%02.1f°\033[0m" % sol_zen

# Estime Power output of Odyssey (solar panels at corrected Efficiency)

est_real_p_out	= 				est_p_out - est_pv_age_loss-pv_p_loss_p

print "--------------------------------------------------------------"
print "Model Estimated Real PV-Power Output         : \033[1;31m%3.1f W\033[0m" % est_real_p_out

# python solar-prediction.py 
--------------------------------------------------------------
22.6.2011 | 173 | 12.000000 | 
--------------------------------------------------------------
Solar constant                               : 1367.8
Atmospheric turbidity coefficient            : 0.8
--------------------------------------------------------------
Inverse relative distance factor             : 0.968392237142
Sun declination                              : 23.4438070502°
Equation of time                             : -1.71440597602 min
Solar Noon                                   : 12.0285734329 
Solar zenith angle                           : 0.593383030197° 
Estimated barometric Pressure at site        : 100.5 kPa
Estimated vapor pressure at site             : 0.633406906142 kPa
Estimated extraterrestrial radiation         : 1324.49586817 W/m²
Estimated precipitable water in atmosphere   : 11.0120351694 mm
Clearness index for direct beam radiation    : 0.670704071246
Transmissivity index for diffuse radiation   : 0.108546534352
--------------------------------------------------------------
Model estimated shortwave radiation (RSO)    : 1032.1 W/m²
Model estimated max. PV-Power output         : 344.7 W @ 20% Mod Eff
Model estimated PV-Module temp conv. loss    : 6.0 W / 1.8%
Model estimated PV-Module aging loss         : 6.9 W
Model recommends PV-Module angle to Sun      : 0.6°
--------------------------------------------------------------
Model estimated real PV-Power output         : 331.8 W

clear-sky-solar-radiation.pdf