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This is an old revision of the document!

Solar-Output prediction model

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

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 solar output on a clear-sky day and incorporate any given conversion technique (currently only PV).

Use-Cases

Photo-Voltaic Systems

  • 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

Solar-Ovens

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.

Pyranometer Reference Model

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

Agricultural

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

Development

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

Code

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#!/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

Download:
Source Code

Please feel free to contribute by verifying these calculations or extend them to an even more accurate/versatile model for all of us. 

# 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

Sources

clear-sky-solar-radiation.pdf

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Trace: solar-prediction-model

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