/
vf.py
2476 lines (1928 loc) · 114 KB
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vf.py
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# -*- coding: utf-8 -*-
"""
ViewFactor module - VF calculation helper files for bifacial-viewfactor
@author Bill Marion
@translated to python by sayala 06/09/17
"""
# ensure python3 compatible division and printing
from __future__ import division, print_function, absolute_import
import math
import numpy as np
from bifacialvf.sun import solarPos, sunIncident, perezComp, aOIcorrection
import logging
# TODO: set level or add formatters if more advanced logging required
LOGGER = logging.getLogger(__name__) # only used to raise errors
DTOR = math.pi / 180.0 # Factor for converting from degrees to radians
def getBackSurfaceIrradiances(rowType, maxShadow, PVbackSurface, beta, sazm,
dni, dhi, C, D, albedo, zen, azm, cellRows,
pvBackSH, rearGroundGHI, frontGroundGHI,
frontReflected, offset=0):
"""
This method calculates the AOI corrected irradiance on the back of the PV
module/panel. 11/19/2015
Added rowType and other changes to distinguish between types of rows.
4/19/2016
Added input of offset of reference cell from PV module back (in PV panel
slope lengths) for modeling Sara's reference cell measurements, should be
set to zero for PV module cell irradiances.
Added while loop so projected Xs aren't too negative causing array index
problems (<0) 12/13/2016::
while (projectedX1 < -100.0 || projectedX2 < -100.0):
# Offset so array indexes are >= -100.0 12/13/2016
projectedX1 += 100.0;
projectedX2 += 100.0;
Parameters
----------
rowType : str
Type of row: "first", "interior", "last", or "single"
maxShadow
Maximum shadow length projected to the front(-) or rear (+) from the
front of the module
PVbackSurface
PV module back surface material type, either "glass" or "ARglass"
beta
Tilt from horizontal of the PV modules/panels (deg) (for front surface)
sazm
Surface azimuth of PV panels (deg) (for front surface)
dni
Direct normal irradiance (W/m2)
dhi
Diffuse horizontal irradiance (W/m2)
C
Ground clearance of PV panel (in PV panel slope lengths)
D
Horizontal distance between rows of PV panels (in PV panel slope
lengths)
albedo
Ground albedo
zen
Sun zenith (in radians)
azm
Sun azimuth (in radians)
pvBackSH
Decimal fraction of the back surface of the PV panel that is shaded,
0.0 to 1.0
rearGroundGHI : array of size [100]
Global horizontal irradiance for each of 100 ground segments (W/m2)
frontGroundGHI : array of size [100]
Global horizontal irradiance for each of 100 ground segments (W/m2)
frontReflected : array of size [cellRows]
Irradiance reflected from the front of the PV module/panel (W/m2) in
the row behind the one of interest
offset
Offset of reference cell from PV module back (in PV panel slope
lengths), set to zero for PV module cell irradiances
Returns
-------
backGTI : array of size [cellRows]
AOI corrected irradiance on back side of PV module/panel, one for each
cell row (W/m2)
aveGroundGHI : numeric
Average GHI on ground under PV array
Notes
-----
1-degree hemispherical segment AOI correction factor for glass (index=0)
and ARglass (index=1)
"""
backGTI = []
SegAOIcor = [
[0.057563, 0.128570, 0.199651, 0.265024, 0.324661, 0.378968, 0.428391, 0.473670, 0.514788, 0.552454,
0.586857, 0.618484, 0.647076, 0.673762, 0.698029, 0.720118, 0.740726, 0.759671, 0.776946, 0.792833,
0.807374, 0.821010, 0.833534, 0.845241, 0.855524, 0.865562, 0.874567, 0.882831, 0.890769, 0.897939,
0.904373, 0.910646, 0.916297, 0.921589, 0.926512, 0.930906, 0.935179, 0.939074, 0.942627, 0.946009,
0.949096, 0.952030, 0.954555, 0.957157, 0.959669, 0.961500, 0.963481, 0.965353, 0.967387, 0.968580,
0.970311, 0.971567, 0.972948, 0.974114, 0.975264, 0.976287, 0.977213, 0.978142, 0.979057, 0.979662,
0.980460, 0.981100, 0.981771, 0.982459, 0.982837, 0.983199, 0.983956, 0.984156, 0.984682, 0.985026,
0.985364, 0.985645, 0.985954, 0.986241, 0.986484, 0.986686, 0.986895, 0.987043, 0.987287, 0.987388,
0.987541, 0.987669, 0.987755, 0.987877, 0.987903, 0.987996, 0.988022, 0.988091, 0.988104, 0.988114,
0.988114, 0.988104, 0.988091, 0.988022, 0.987996, 0.987903, 0.987877, 0.987755, 0.987669, 0.987541,
0.987388, 0.987287, 0.987043, 0.986895, 0.986686, 0.986484, 0.986240, 0.985954, 0.985645, 0.985364,
0.985020, 0.984676, 0.984156, 0.983956, 0.983199, 0.982837, 0.982459, 0.981771, 0.981100, 0.980460,
0.979662, 0.979057, 0.978142, 0.977213, 0.976287, 0.975264, 0.974114, 0.972947, 0.971567, 0.970311,
0.968580, 0.967387, 0.965353, 0.963481, 0.961501, 0.959671, 0.957157, 0.954555, 0.952030, 0.949096,
0.946009, 0.942627, 0.939074, 0.935179, 0.930906, 0.926512, 0.921589, 0.916297, 0.910646, 0.904373,
0.897939, 0.890769, 0.882831, 0.874567, 0.865562, 0.855524, 0.845241, 0.833534, 0.821010, 0.807374,
0.792833, 0.776946, 0.759671, 0.740726, 0.720118, 0.698029, 0.673762, 0.647076, 0.618484, 0.586857,
0.552454, 0.514788, 0.473670, 0.428391, 0.378968, 0.324661, 0.265024, 0.199651, 0.128570, 0.057563],
[0.062742, 0.139913, 0.216842, 0.287226, 0.351055, 0.408796, 0.460966, 0.508397, 0.551116, 0.589915,
0.625035, 0.657029, 0.685667, 0.712150, 0.735991, 0.757467, 0.777313, 0.795374, 0.811669, 0.826496,
0.839932, 0.852416, 0.863766, 0.874277, 0.883399, 0.892242, 0.900084, 0.907216, 0.914023, 0.920103,
0.925504, 0.930744, 0.935424, 0.939752, 0.943788, 0.947313, 0.950768, 0.953860, 0.956675, 0.959339,
0.961755, 0.964039, 0.965984, 0.967994, 0.969968, 0.971283, 0.972800, 0.974223, 0.975784, 0.976647,
0.977953, 0.978887, 0.979922, 0.980773, 0.981637, 0.982386, 0.983068, 0.983759, 0.984436, 0.984855,
0.985453, 0.985916, 0.986417, 0.986934, 0.987182, 0.987435, 0.988022, 0.988146, 0.988537, 0.988792,
0.989043, 0.989235, 0.989470, 0.989681, 0.989857, 0.990006, 0.990159, 0.990263, 0.990455, 0.990515,
0.990636, 0.990731, 0.990787, 0.990884, 0.990900, 0.990971, 0.990986, 0.991042, 0.991048, 0.991057,
0.991057, 0.991048, 0.991042, 0.990986, 0.990971, 0.990900, 0.990884, 0.990787, 0.990731, 0.990636,
0.990515, 0.990455, 0.990263, 0.990159, 0.990006, 0.989857, 0.989681, 0.989470, 0.989235, 0.989043,
0.988787, 0.988532, 0.988146, 0.988022, 0.987435, 0.987182, 0.986934, 0.986417, 0.985916, 0.985453,
0.984855, 0.984436, 0.983759, 0.983068, 0.982386, 0.981637, 0.980773, 0.979920, 0.978887, 0.977953,
0.976647, 0.975784, 0.974223, 0.972800, 0.971284, 0.969970, 0.967994, 0.965984, 0.964039, 0.961755,
0.959339, 0.956675, 0.953860, 0.950768, 0.947313, 0.943788, 0.939752, 0.935424, 0.930744, 0.925504,
0.920103, 0.914023, 0.907216, 0.900084, 0.892242, 0.883399, 0.874277, 0.863766, 0.852416, 0.839932,
0.826496, 0.811669, 0.795374, 0.777313, 0.757467, 0.735991, 0.712150, 0.685667, 0.657029, 0.625035,
0.589915, 0.551116, 0.508397, 0.460966, 0.408796, 0.351055, 0.287226, 0.216842, 0.139913, 0.062742]]
# Tilt from horizontal of the PV modules/panels, in radians
beta = beta * DTOR
sazm = sazm * DTOR # Surface azimuth of PV module/panels, in radians
# 1. Calculate and assign various paramters to be used for modeling
# irradiances
# For calling PerezComp to break diffuse into components for zero tilt
# (horizontal)
iso_dif = 0.0; circ_dif = 0.0; horiz_dif = 0.0; grd_dif = 0.0; beam = 0.0
# Call to get iso_dif for horizontal surface
ghi, iso_dif, circ_dif, horiz_dif, grd_dif, beam = perezComp(
dni, dhi, albedo, zen, 0.0, zen)
# Isotropic irradiance from sky on horizontal surface, used later for
# determining isotropic sky component
iso_sky_dif = iso_dif
# For calling PerezComp to break diffuse into components for 90 degree tilt
# (vertical)
inc, tiltr, sazmr = sunIncident(0, 90.0, 180.0, 45.0, zen, azm)
# Call to get horiz_dif for vertical surface
vti, iso_dif, circ_dif, horiz_dif, grd_dif, beam = perezComp(
dni, dhi, albedo, inc, tiltr, zen)
# Horizon diffuse irradiance on a vertical surface, used later for
# determining horizon brightening irradiance component
F2DHI = horiz_dif
index = -99
n2 = -99.9
if (PVbackSurface == "glass"):
# Index to use with 1-degree hemispherical segment AOI correction
# factor array
index = 0
n2 = 1.526 # Index of refraction for glass
elif (PVbackSurface == "ARglass"):
# Index to use with 1-degree hemispherical segment AOI correction
# factor array
index = 1
n2 = 1.300 # Index of refraction for ARglass
else:
raise Exception(
"Incorrect text input for PVbackSurface."
" Must be glass or ARglass.")
# Reflectance at normal incidence, Duffie and Beckman p217
Ro = math.pow((n2 - 1.0) / (n2 + 1.0), 2.0)
# Average GHI on ground under PV array for cases when x projection exceed
# 2*rtr
aveGroundGHI = 0.0
for i in range(0,100):
aveGroundGHI += rearGroundGHI[i] / 100.0
# Calculate x,y coordinates of bottom and top edges of PV row in back of desired PV row so that portions of sky and ground viewed by the
# PV cell may be determined. Origin of x-y axis is the ground pobelow the lower front edge of the desired PV row. The row in back of
# the desired row is in the positive x direction.
h = math.sin(beta); # Vertical height of sloped PV panel (in PV panel slope lengths)
x1 = math.cos(beta); # Horizontal distance from front of panel to rear of panel (in PV panel slope lengths)
rtr = D + x1; # Row-to-row distance (in PV panel slope lengths)
PbotX = rtr; # x value for poon bottom egde of PV module/panel of row in back of (in PV panel slope lengths)
PbotY = C; # y value for poon bottom egde of PV module/panel of row in back of (in PV panel slope lengths)
PtopX = rtr + x1; # x value for poon top egde of PV module/panel of row in back of (in PV panel slope lengths)
PtopY = h + C; # y value for poon top egde of PV module/panel of row in back of (in PV panel slope lengths)
# 2. Calculate diffuse and direct component irradiances for each cell row
for i in range (0, cellRows):
# Calculate diffuse irradiances and reflected amounts for each cell row over it's field of view of 180 degrees,
# beginning with the angle providing the upper most view of the sky (j=0)
#PcellX = x1 * (i + 0.5) / ((double)cellRows); # x value for location of PV cell
#PcellY = C + h * (i + 0.5) / ((double)cellRows); # y value for location of PV cell
PcellX = x1 * (i + 0.5) / (cellRows) + offset * math.sin(beta); # x value for location of PV cell with OFFSET FOR SARA REFERENCE CELLS 4/26/2016
PcellY = C + h * (i + 0.5) / (cellRows) - offset * math.cos(beta); # y value for location of PV cell with OFFSET FOR SARA REFERENCE CELLS 4/26/2016
elvUP = math.atan((PtopY - PcellY) / (PtopX - PcellX)); # Elevation angle up from PV cell to top of PV module/panel, radians
elvDOWN = math.atan((PcellY - PbotY) / (PbotX - PcellX)); # Elevation angle down from PV cell to bottom of PV module/panel, radians
if (rowType == "last" or rowType == "single"): # 4/19/16 No array to the rear for these cases
elvUP = 0.0;
elvDOWN = 0.0;
#Console.WriteLine("ElvUp = 0", elvUP / DTOR);
#if (i == 0)
# Console.WriteLine("ElvDown = 0", elvDOWN / DTOR);
#123
#iStopIso = Convert.ToInt32((beta - elvUP) / DTOR); # Last whole degree in arc range that sees sky, first is 0
#Console.WriteLine("iStopIso = 0", iStopIso);
#iHorBright = Convert.ToInt32(max(0.0, 6.0 - elvUP / DTOR)); # Number of whole degrees for which horizon brightening occurs
#iStartGrd = Convert.ToInt32((beta + elvDOWN) / DTOR); # First whole degree in arc range that sees ground, last is 180
iStopIso = int(round((beta - elvUP) / DTOR)); # Last whole degree in arc range that sees sky, first is 0
#Console.WriteLine("iStopIso = 0", iStopIso);
iHorBright = int(round(max(0.0, 6.0 - elvUP / DTOR))); # Number of whole degrees for which horizon brightening occurs
iStartGrd = int(round((beta + elvDOWN) / DTOR)); # First whole degree in arc range that sees ground, last is 180
backGTI.append(0.0) # Initialtize front GTI
for j in range (0, iStopIso): # Add sky diffuse component and horizon brightening if present
backGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * iso_sky_dif; # Sky radiation
# backGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * iso_sky_dif; # Sky radiation
if ((iStopIso - j) <= iHorBright): # Add horizon brightening term if seen
backGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * F2DHI / 0.052264; # 0.052246 = 0.5 * [cos(84) - cos(90)]
#backGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * F2DHI / 0.052264; # 0.052246 = 0.5 * [cos(84) - cos(90)]
if (rowType == "interior" or rowType == "first"): # 4/19/16 Only add reflections from PV modules for these cases
for j in range (iStopIso, iStartGrd): #j = iStopIso; j < iStartGrd; j++) # Add relections from PV module front surfaces
L = (PbotX - PcellX) / math.cos(elvDOWN); # Diagonal distance from cell to bottom of module in row behind
startAlpha = -(j - iStopIso) * DTOR + elvUP + elvDOWN;
stopAlpha = -(j + 1 - iStopIso) * DTOR + elvUP + elvDOWN;
m = L * math.sin(startAlpha);
theta = math.pi - elvDOWN - (math.pi / 2.0 - startAlpha) - beta;
projectedX2 = m / math.cos(theta); # Projected distance on sloped PV module
m = L * math.sin(stopAlpha);
theta = math.pi - elvDOWN - (math.pi / 2.0 - stopAlpha) - beta;
projectedX1 = m / math.cos(theta); # Projected distance on sloped PV module
projectedX1 = max(0.0, projectedX1);
#Console.WriteLine("j= 0 projected X1 = 1,6:0.000 projected X2 = 2,6:0.000", j, projectedX1, projectedX2);
PVreflectedIrr = 0.0; # Irradiance from PV module front cover reflections
deltaCell = 1.0 / cellRows; # Length of cell in sloped direction in module/panel units (dimensionless)
for k in range (0, cellRows): # Determine which cells in behind row are seen, and their reflected irradiance
cellBot = k * deltaCell; # Position of bottom of cell along PV module/panel
cellTop = (k + 1) * deltaCell; # Position of top of cell along PV module/panel
cellLengthSeen = 0.0; # Length of cell seen for this row, start with zero
if (cellBot >= projectedX1 and cellTop <= projectedX2):
cellLengthSeen = cellTop - cellBot; # Sees the whole cell
elif (cellBot <= projectedX1 and cellTop >= projectedX2):
cellLengthSeen = projectedX2 - projectedX1; # Sees portion in the middle of cell
elif (cellBot >= projectedX1 and projectedX2 > cellBot and cellTop >= projectedX2):
cellLengthSeen = projectedX2 - cellBot; # Sees bottom of cell
elif (cellBot <= projectedX1 and projectedX1 < cellTop and cellTop <= projectedX2):
cellLengthSeen = cellTop - projectedX1; # Sees top of cell
#Console.WriteLine("cell= 0 cellBot = 1,5:0.00 cellTop = 2,5:0.00 Cell length seen = 3,5:0.00", k, cellBot, cellTop, cellLengthSeen);
PVreflectedIrr += cellLengthSeen * frontReflected[k]; # Add reflected radiation for this PV cell, if seen, weight by cell length seen
PVreflectedIrr /= projectedX2 - projectedX1; # Reflected irradiance from PV modules (W/m2)
backGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * PVreflectedIrr; # Radiation reflected from PV module surfaces onto back surface of module
# End of adding reflections from PV module surfaces
#Console.WriteLine("");
#if (i == 0)
#Console.WriteLine("iStartGrd = 0", iStartGrd);
for j in range (iStartGrd, 180): # Add ground reflected component
startElvDown = (j - iStartGrd) * DTOR + elvDOWN; # Start and ending down elevations for this j loop
stopElvDown = (j + 1 - iStartGrd) * DTOR + elvDOWN;
projectedX2 = PcellX + np.float64(PcellY) / math.tan(startElvDown); # Projection of ElvDown to ground in +x direction (X1 and X2 opposite nomenclature for front irradiance method)
projectedX1 = PcellX + PcellY / math.tan(stopElvDown);
actualGroundGHI = 0.0; # Actuall ground GHI from summing array values
#if (i == 0)
# Console.WriteLine("j= 0 projected X1 = 1,6:0.0", j, 100 * projectedX1 / rtr);
if (abs(projectedX1 - projectedX2) > 0.99 * rtr):
if (rowType == "last" or rowType == "single"): # 4/19/16 No array to rear for these cases
actualGroundGHI = ghi; # Use total value if projection approximates the rtr
else:
actualGroundGHI = aveGroundGHI; # Use average value if projection approximates the rtr
else:
projectedX1 = 100.0 * projectedX1 / rtr; # Normalize projections and multiply by 100
projectedX2 = 100.0 * projectedX2 / rtr;
#Console.WriteLine("projectedX1 = 0 projectedX2 = 1", projectedX1, projectedX2);
if ((rowType == "last" or rowType == "single") and (abs(projectedX1) > 99.0 or abs(projectedX2) > 99.0)): #4/19/2016
actualGroundGHI = ghi; # Use total value if projection > rtr for "last" or "single"
else:
while (projectedX1 >= 100.0 or projectedX2 >= 100.0): # Offset so array indexes are less than 100
projectedX1 -= 100.0;
projectedX2 -= 100.0;
while (projectedX1 < -100.0 or projectedX2 < -100.0): # Offset so array indexes are >= -100.0 12/13/2016
projectedX1 += 100.0;
projectedX2 += 100.0;
#Console.WriteLine("projectedX1 = 0 projectedX2 = 1", projectedX1, projectedX2);
index1 = (int)(projectedX1 + 100.0) - 100; # Determine indexes for use with rearGroundGHI array and frontGroundGHI array(truncates values)
index2 = (int)(projectedX2 + 100.0) - 100; # (int)(1.9) = 1 and (int)(-1.9) = -1; (int)(1.9+100) - 100 = 1 and (int)(-1.9+100) - 100 = -2
#Console.WriteLine("index1=0 index2=1", index1, index2);
if (index1 == index2):
if (index1 < 0):
actualGroundGHI = frontGroundGHI[index1 + 100];
#actualGroundGHI = 0.0;
else:
actualGroundGHI = rearGroundGHI[index1]; # x projections in same groundGHI element THIS SEEMS TO ADD HICCUP 4/26/2016 ***************************
#actualGroundGHI = 0.0;
else:
for k in range (index1, index2+1): #for (k = index1; k <= index2; k++) # Sum the irradiances on the ground if projections are in different groundGHI elements
if (k == index1):
if (k < 0):
actualGroundGHI += frontGroundGHI[k + 100] * (k + 1.0 - projectedX1);
else:
actualGroundGHI += rearGroundGHI[k] * (k + 1.0 - projectedX1);
elif (k == index2):
if (k < 0):
actualGroundGHI += frontGroundGHI[k + 100] * (projectedX2 - k);
else:
actualGroundGHI += rearGroundGHI[k] * (projectedX2 - k);
else:
if (k < 0):
actualGroundGHI += frontGroundGHI[k + 100];
else:
actualGroundGHI += rearGroundGHI[k];
actualGroundGHI /= projectedX2 - projectedX1; # Irradiance on ground in the 1 degree field of view
#if (i == 0)
# Console.WriteLine("j=0 index1=1 index2=2 projectX1=3,5:0.0 projectX2=4,5:0.0 actualGrdGHI=5,6:0.0", j, index1, index2, projectedX1, projectedX2, actualGroundGHI);
# End of if looping to determine actualGroundGHI
backGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * actualGroundGHI * albedo; # Add ground reflected component
#Console.WriteLine("actualGroundGHI = 0,6:0.0 inputGHI = 1,6:0.0 aveArrayGroundGHI = 2,6:0.0", actualGroundGHI, dhi + dni * math.cos(zen), aveGroundGHI);
# End of j loop for adding ground reflected componenet
# Calculate and add direct and circumsolar irradiance components
inc, tiltr, sazmr = sunIncident(0, 180-beta / DTOR, sazm / DTOR - 180, 45.0, zen, azm) # For calling PerezComp to break diffuse into components for downward facing tilt
gtiAllpc, iso_dif, circ_dif, horiz_dif, grd_dif, beam = perezComp(dni, dhi, albedo, inc, tiltr, zen) # Call to get components for the tilt
cellShade = pvBackSH * cellRows - i;
if (cellShade > 1.0): # Fully shaded if > 1, no shade if < 0, otherwise fractionally shaded
cellShade = 1.0;
elif (cellShade < 0.0):
cellShade = 0.0;
if (cellShade < 1.0 and inc < math.pi / 2.0): # Cell not shaded entirely and inc < 90 deg
cor = aOIcorrection(n2, inc); # Get AOI correction for beam and circumsolar
backGTI[i] += (1.0 - cellShade) * (beam + circ_dif) * cor; # Add beam and circumsolar radiation
# End of for i = 0; i < cellRows loop
return backGTI, aveGroundGHI;
# End of GetBackSurfaceIrradiances
def divideAndAlignAlbedos(albedo, n_divisions, isOneAxisTracking,
horizontalLength, rowToRow, surface_rotation):
'''
#(const std::vector<double>& albedo /*-*/, size_t n_divisions /*-*/,
# bool isOneAxisTracking /*-*/,
#double horizontalLength /*m*/, double rowToRow /*m*/, double
# surface_rotation /*rad*/)
# Sil Note: size_t = 100 divisions..
Subdivide spatial albedos and if 1-axis tracking change reference from the
row midline to the front
'''
if (n_divisions % len(albedo)) == 0:
print("Functionality only works for even divisions, exiting.")
return
# Upsample vector to n_divisions
# Sil Note: THIS IS WRONG.
albedo_aligned = []
# C++: for (size_t i = 0; i < albedo.size(); i++) {
# for (size_t j = 0; j < n_divisions / albedo.size(); j++) {
# albedo_aligned.push_back(albedo.at(i));
for i in range(0, len(albedo)):
for j in range(0, n_divisions / len(albedo)):
albedo_aligned.append(albedo[i])
if isOneAxisTracking:
# Flip the albedo array if tracking after solar noon (because the
# tilt range = [0, 90] degrees, therefore the tilt convention flips
# at solar noon)
if surface_rotation > 0:
np.reverse(albedo_aligned.begin(), albedo_aligned.end())
#C++: reverse(albedo_aligned.begin(), albedo_aligned.end());
# Rotate the albedo vector so the first index is at (or overlapping) the front of the row instead of at center
L_division = rowToRow / n_divisions # length of a single albedo division
n = 0.5 * horizontalLength / L_division # fractional number of albedo
# segments between front of row and center of row
size_t leading_segments = n_divisions - np.ceil(n) # whole albedo
# segments between center of row and front of row behind
rotate(albedo_aligned.begin(), albedo_aligned.begin() +
leading_segments, albedo_aligned.end()) # move the leading
# segments to the back of the vector
// 'Shift' the actual ground albedo locations to front of row by weighting-averaging adjacent divisions
double frac_div_extending = std::ceil(n) - n; // fraction of now first albedo division extending beyond front of row
double albedo_front_orig = albedo_aligned.front();
for (size_t i = 0; i < n_divisions - 1; i++) { // do last segment separately
albedo_aligned.at(i) = albedo_aligned.at(i) * (1 - frac_div_extending) + albedo_aligned.at(i + 1) * frac_div_extending;
}
albedo_aligned.back() = albedo_aligned.back() * (1 - frac_div_extending) + albedo_front_orig * frac_div_extending;
}
return albedo_aligned;
}
def condenseAndAlignGroundIrrad(ground_irr, size_t, n_divisions, isOneAxisTraking, horizontalLength, rowToRow, surface_rotation)
#std::vector<double> condenseAndAlignGroundIrrad(const std::vector<double>& ground_irr /*W/m2*/, size_t n_divisions /*-*/, bool isOneAxisTracking /*-*/,
# double horizontalLength /*m*/, double rowToRow /*m*/, double surface_rotation /*rad*/) {
'''
Condense spatial ground irradiances and if 1-axis tracking change reference from the row front to the midline
'''
if (len(ground_irr) % n_divisions) == 0:
print("Functionality only works for even divisions, exiting.")
return
ground_aligned = ground_irr
if (isOneAxisTracking)
#// Rotate the ground irradiance vector so the first index is at (or overlapping) the center of the row instead of at the midline
double L_division = rowToRow / ground_aligned.size(); # // length of a single ground division
double n = 0.5 * horizontalLength / L_division; # // fractional number of ground segments between front of row and center of row
size_t leading_segments = std::floor(n); # // whole ground segments between front of row and center of row
rotate(ground_aligned.begin(), ground_aligned.begin() + leading_segments, ground_aligned.end())# // move the leading segments to the back of the vector
// 'Shift' the actual ground irradiance locations to center of row by weighting-averaging adjacent divisions
double frac_div_extending = n - std::floor(n); // fraction of now first ground division extending beyond center of row
double ground_front_orig = ground_aligned.front();
for (size_t i = 0; i < ground_aligned.size() - 1; i++) { // do last segment separately
ground_aligned.at(i) = ground_aligned.at(i) * (1 - frac_div_extending) + ground_aligned.at(i + 1) * frac_div_extending;
}
ground_aligned.back() = ground_aligned.back() * (1 - frac_div_extending) + ground_front_orig * frac_div_extending;
// Flip the ground irradiance if tracking after solar noon (because the tilt range = [0, 90] degrees, therefore the tilt convention flips at solar noon)
if (surface_rotation > 0.) {
std::reverse(ground_aligned.begin(), ground_aligned.end());
}
}
// Downsample vector to n_divisions
std::vector<double> ground_condensed;
size_t num_to_avg = ground_aligned.size() / n_divisions;
size_t i = 0;
double sum = 0.;
while (i < ground_aligned.size()) {
sum += ground_aligned.at(i);
if ((i + 1) % num_to_avg == 0) {
ground_condensed.push_back(sum / num_to_avg); // add average to output
sum = 0.;
}
i++;
}
return ground_condensed
def getFrontSurfaceIrradiances(rowType, maxShadow, PVfrontSurface, beta, sazm,
dni, dhi, C, D, albedo, zen, azm, cellRows,
pvFrontSH, frontGroundGHI):
"""
This method calculates the AOI corrected irradiance on the front of the PV
module/panel and the irradiance reflected from the the front of the PV
module/panel. 11/12/2015
Added row type and MaxShadow and changed code to accommodate 4/19/2015
Parameters
----------
rowType : str
Type of row: "first", "interior", "last", or "single"
maxShadow
Maximum shadow length projected to the front (-) or rear (+) from the
front of the module row (in PV panel slope lengths), only used for
`rowTypes` other than "interior"
PVfrontSurface
PV module front surface material type, either "glass" or "ARglass"
beta
Tilt from horizontal of the PV modules/panels (deg)
sazm
Surface azimuth of PV panels (deg)
dni
Direct normal irradiance (W/m2)
dhi
Diffuse horizontal irradiance (W/m2)
C
Ground clearance of PV panel (in PV panel slope lengths)
D
Horizontal distance between rows of PV panels (in PV panel slope
lengths)
albedo
Ground albedo
zen
Sun zenith (in radians)
azm
Sun azimuth (in radians)
pvFrontSH
Decimal fraction of the front surface of the PV panel that is shaded,
0.0 to 1.0
froutGroundGHI : array of size [100]
Global horizontal irradiance for each of 100 ground segments in front
of the module row
Returns
-------
frontGTI : array of size [cellRows]
AOI corrected irradiance on front side of PV module/panel, one for each
cell row (W/m2)
frontReflected : array of size [cellRows]
Irradiance reflected from the front of the PV module/panel (W/m2)
aveGroundGHI : numeric
Average GHI on the ground (includes effects of shading by array) from
the array frontGroundGHI[100]
Notes
-----
1-degree hemispherical segment AOI correction factor for glass (index=0)
and ARglass (index=1). Creates a list containing 5 lists, each of 8 items,
all set to 0
"""
frontGTI = []
frontReflected = []
#w, h = 2, 180;
#SegAOIcor = [[0 for x in range(w)] for y in range(h)]
SegAOIcor = ([[0.057563, 0.128570, 0.199651, 0.265024, 0.324661, 0.378968, 0.428391, 0.473670, 0.514788, 0.552454,
0.586857, 0.618484, 0.647076, 0.673762, 0.698029, 0.720118, 0.740726, 0.759671, 0.776946, 0.792833,
0.807374, 0.821010, 0.833534, 0.845241, 0.855524, 0.865562, 0.874567, 0.882831, 0.890769, 0.897939,
0.904373, 0.910646, 0.916297, 0.921589, 0.926512, 0.930906, 0.935179, 0.939074, 0.942627, 0.946009,
0.949096, 0.952030, 0.954555, 0.957157, 0.959669, 0.961500, 0.963481, 0.965353, 0.967387, 0.968580,
0.970311, 0.971567, 0.972948, 0.974114, 0.975264, 0.976287, 0.977213, 0.978142, 0.979057, 0.979662,
0.980460, 0.981100, 0.981771, 0.982459, 0.982837, 0.983199, 0.983956, 0.984156, 0.984682, 0.985026,
0.985364, 0.985645, 0.985954, 0.986241, 0.986484, 0.986686, 0.986895, 0.987043, 0.987287, 0.987388,
0.987541, 0.987669, 0.987755, 0.987877, 0.987903, 0.987996, 0.988022, 0.988091, 0.988104, 0.988114,
0.988114, 0.988104, 0.988091, 0.988022, 0.987996, 0.987903, 0.987877, 0.987755, 0.987669, 0.987541,
0.987388, 0.987287, 0.987043, 0.986895, 0.986686, 0.986484, 0.986240, 0.985954, 0.985645, 0.985364,
0.985020, 0.984676, 0.984156, 0.983956, 0.983199, 0.982837, 0.982459, 0.981771, 0.981100, 0.980460,
0.979662, 0.979057, 0.978142, 0.977213, 0.976287, 0.975264, 0.974114, 0.972947, 0.971567, 0.970311,
0.968580, 0.967387, 0.965353, 0.963481, 0.961501, 0.959671, 0.957157, 0.954555, 0.952030, 0.949096,
0.946009, 0.942627, 0.939074, 0.935179, 0.930906, 0.926512, 0.921589, 0.916297, 0.910646, 0.904373,
0.897939, 0.890769, 0.882831, 0.874567, 0.865562, 0.855524, 0.845241, 0.833534, 0.821010, 0.807374,
0.792833, 0.776946, 0.759671, 0.740726, 0.720118, 0.698029, 0.673762, 0.647076, 0.618484, 0.586857,
0.552454, 0.514788, 0.473670, 0.428391, 0.378968, 0.324661, 0.265024, 0.199651, 0.128570, 0.057563],
[0.062742, 0.139913, 0.216842, 0.287226, 0.351055, 0.408796, 0.460966, 0.508397, 0.551116, 0.589915,
0.625035, 0.657029, 0.685667, 0.712150, 0.735991, 0.757467, 0.777313, 0.795374, 0.811669, 0.826496,
0.839932, 0.852416, 0.863766, 0.874277, 0.883399, 0.892242, 0.900084, 0.907216, 0.914023, 0.920103,
0.925504, 0.930744, 0.935424, 0.939752, 0.943788, 0.947313, 0.950768, 0.953860, 0.956675, 0.959339,
0.961755, 0.964039, 0.965984, 0.967994, 0.969968, 0.971283, 0.972800, 0.974223, 0.975784, 0.976647,
0.977953, 0.978887, 0.979922, 0.980773, 0.981637, 0.982386, 0.983068, 0.983759, 0.984436, 0.984855,
0.985453, 0.985916, 0.986417, 0.986934, 0.987182, 0.987435, 0.988022, 0.988146, 0.988537, 0.988792,
0.989043, 0.989235, 0.989470, 0.989681, 0.989857, 0.990006, 0.990159, 0.990263, 0.990455, 0.990515,
0.990636, 0.990731, 0.990787, 0.990884, 0.990900, 0.990971, 0.990986, 0.991042, 0.991048, 0.991057,
0.991057, 0.991048, 0.991042, 0.990986, 0.990971, 0.990900, 0.990884, 0.990787, 0.990731, 0.990636,
0.990515, 0.990455, 0.990263, 0.990159, 0.990006, 0.989857, 0.989681, 0.989470, 0.989235, 0.989043,
0.988787, 0.988532, 0.988146, 0.988022, 0.987435, 0.987182, 0.986934, 0.986417, 0.985916, 0.985453,
0.984855, 0.984436, 0.983759, 0.983068, 0.982386, 0.981637, 0.980773, 0.979920, 0.978887, 0.977953,
0.976647, 0.975784, 0.974223, 0.972800, 0.971284, 0.969970, 0.967994, 0.965984, 0.964039, 0.961755,
0.959339, 0.956675, 0.953860, 0.950768, 0.947313, 0.943788, 0.939752, 0.935424, 0.930744, 0.925504,
0.920103, 0.914023, 0.907216, 0.900084, 0.892242, 0.883399, 0.874277, 0.863766, 0.852416, 0.839932,
0.826496, 0.811669, 0.795374, 0.777313, 0.757467, 0.735991, 0.712150, 0.685667, 0.657029, 0.625035,
0.589915, 0.551116, 0.508397, 0.460966, 0.408796, 0.351055, 0.287226, 0.216842, 0.139913, 0.062742]]);
beta = beta * DTOR # Tilt from horizontal of the PV modules/panels, in radians
sazm = sazm * DTOR # Surface azimuth of PV module/panels, in radians
# 1. Calculate and assign various paramters to be used for modeling irradiances
iso_dif = 0.0; circ_dif = 0.0; horiz_dif = 0.0; grd_dif = 0.0; beam = 0.0; # For calling PerezComp to break diffuse into components for zero tilt (horizontal)
ghi, iso_dif, circ_dif, horiz_dif, grd_dif, beam = perezComp(dni, dhi, albedo, zen, 0.0, zen) # Call to get iso_dif for horizontal surface
# print "PEREZCOMP1 = "
# print "ghi = ", ghi
# print "iso_dif = ", iso_dif
# print "circ_dif = ", circ_dif
# print "horiz_dif = ", horiz_dif
# print "grd_dif = ", grd_dif
# print "beam = ", beam
iso_sky_dif = iso_dif; # Isotropic irradiance from sky on horizontal surface, used later for determining isotropic sky component
inc, tiltr, sazmr = sunIncident(0, 90.0, 180.0, 45.0, zen, azm) # For calling PerezComp to break diffuse into components for 90 degree tilt (vertical)
# print "sunIncident 1."
# print "inc = ", inc
# print "tiltr = ", tiltr
# print "sazmr = ", sazmr
vti, iso_dif, circ_dif, horiz_dif, grd_dif, beam = perezComp(dni, dhi, albedo, inc, tiltr, zen) # Call to get horiz_dif for vertical surface
# print "PEREZCOMP1 = "
# print "vti = ", vti
# print "iso_dif = ", iso_dif
# print "circ_dif = ", circ_dif
# print "horiz_dif = ", horiz_dif
# print "grd_dif = ", grd_dif
# print "beam = ", beam
F2DHI = horiz_dif; # Horizon diffuse irradiance on a vertical surface, used later for determining horizon brightening irradiance component
index = -99;
n2 = -99.9;
if (PVfrontSurface == "glass"):
index = 0; # Index to use with 1-degree hemispherical segment AOI correction factor array
n2 = 1.526; # Index of refraction for glass
elif (PVfrontSurface == "ARglass"):
index = 1; # Index to use with 1-degree hemispherical segment AOI correction factor array
n2 = 1.300; # Index of refraction for ARglass
else:
raise Exception("Incorrect text input for PVfrontSurface. Must be glass or ARglass.")
Ro = math.pow((n2 - 1.0) / (n2 + 1.0), 2.0); # Reflectance at normal incidence, Duffie and Beckman p217
aveGroundGHI = 0.0; # Average GHI on ground under PV array for cases when x projection exceed 2*rtr
for i in range (0,100):
aveGroundGHI += frontGroundGHI[i] / 100.0;
# Calculate x,y coordinates of bottom and top edges of PV row in front of desired PV row so that portions of sky and ground viewed by the
# PV cell may be determined. Origin of x-y axis is the ground pobelow the lower front edge of the desired PV row. The row in front of
# the desired row is in the negative x direction.
h = math.sin(beta); # Vertical height of sloped PV panel (in PV panel slope lengths)
x1 = math.cos(beta); # Horizontal distance from front of panel to rear of panel (in PV panel slope lengths)
rtr = D + x1; # Row-to-row distance (in PV panel slope lengths)
PbotX = -rtr; # x value for poon bottom egde of PV module/panel of row in front of (in PV panel slope lengths)
PbotY = C; # y value for poon bottom egde of PV module/panel of row in front of (in PV panel slope lengths)
PtopX = -D; # x value for poon top egde of PV module/panel of row in front of (in PV panel slope lengths)
PtopY = h + C; # y value for poon top egde of PV module/panel of row in front of (in PV panel slope lengths)
# 2. Calculate diffuse and direct component irradiances for each cell row
for i in range (0, cellRows):
# Calculate diffuse irradiances and reflected amounts for each cell row over it's field of view of 180 degrees,
# beginning with the angle providing the upper most view of the sky (j=0)
PcellX = x1 * (i + 0.5) / (cellRows); # x value for location of PV cell
PcellY = C + h * (i + 0.5) / (cellRows); # y value for location of PV cell
elvUP = math.atan((PtopY - PcellY) / (PcellX - PtopX)); # Elevation angle up from PV cell to top of PV module/panel, radians
elvDOWN = math.atan((PcellY - PbotY) / (PcellX - PbotX)); # Elevation angle down from PV cell to bottom of PV module/panel, radians
if (rowType == "first" or rowType == "single"): # 4/19/16 No array in front for these cases
elvUP = 0.0;
elvDOWN = 0.0;
#Console.WriteLine("ElvUp = 0", elvUP / DTOR);
#if (i == 0)
# Console.WriteLine("ElvDown = 0", elvDOWN / DTOR);
if math.isnan(beta):
print( "Beta is Nan")
if math.isnan(elvUP):
print( "elvUP is Nan")
if math.isnan((math.pi - beta - elvUP) / DTOR):
print( "division is Nan")
iStopIso = int(round(np.float64((math.pi - beta - elvUP)) / DTOR)) # Last whole degree in arc range that sees sky, first is 0
#Console.WriteLine("iStopIso = 0", iStopIso);
iHorBright = int(round(max(0.0, 6.0 - elvUP / DTOR))); # Number of whole degrees for which horizon brightening occurs
iStartGrd = int(round((math.pi - beta + elvDOWN) / DTOR)); # First whole degree in arc range that sees ground, last is 180
# print "iStopIso = ", iStopIso
# print "iHorBright = ", iHorBright
# print "iStartGrd = ", iStartGrd
frontGTI.append(0.0) # Initialtize front GTI
frontReflected.append(0.0); # Initialize reflected amount from front
for j in range (0, iStopIso): # Add sky diffuse component and horizon brightening if present
#for (j = 0; j < iStopIso; j++)
frontGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * iso_sky_dif; # Sky radiation
frontReflected[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * iso_sky_dif * (1.0 - SegAOIcor[index][j] * (1.0 - Ro)); # Reflected radiation from module
if ((iStopIso - j) <= iHorBright): # Add horizon brightening term if seen
frontGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * F2DHI / 0.052264; # 0.052246 = 0.5 * [cos(84) - cos(90)]
frontReflected[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * (F2DHI / 0.052264) * (1.0 - SegAOIcor[index][j] * (1.0 - Ro)); # Reflected radiation from module
#if (i == 0)
# Console.WriteLine("iStartGrd = 0", iStartGrd);
for j in range (iStartGrd, 180): # Add ground reflected component
#(j = iStartGrd; j < 180; j++)
startElvDown = (j - iStartGrd) * DTOR + elvDOWN; # Start and ending down elevations for this j loop
stopElvDown = (j + 1 - iStartGrd) * DTOR + elvDOWN;
projectedX1 = PcellX - np.float64(PcellY) / math.tan(startElvDown); # Projection of ElvDown to ground in -x direction
projectedX2 = PcellX - PcellY / math.tan(stopElvDown);
actualGroundGHI = 0.0; # Actuall ground GHI from summing array values
#if (i == 0)
# Console.WriteLine("j= 0 projected X1 = 1,6:0.0", j, 100 * projectedX1 / rtr);
if (abs(projectedX1 - projectedX2) > 0.99 * rtr):
if (rowType == "first" or rowType == "single"): # 4/19/16 No array in front for these cases
actualGroundGHI = ghi; # Use total value if projection approximates the rtr
else:
actualGroundGHI = aveGroundGHI; # Use average value if projection approximates the rtr
else:
projectedX1 = 100.0 * projectedX1 / rtr; # Normalize projections and multiply by 100
projectedX2 = 100.0 * projectedX2 / rtr;
if ((rowType == "first" or rowType == "single") and (abs(projectedX1) > rtr or abs(projectedX2) > rtr)): #4/19/2016
actualGroundGHI = ghi; # Use total value if projection > rtr for "first" or "single"
else:
while (projectedX1 < 0.0 or projectedX2 < 0.0): # Offset so array indexes are positive
projectedX1 += 100.0;
projectedX2 += 100.0;
index1 = int(projectedX1); # Determine indexes for use with groundGHI array (truncates values)
index2 = int(projectedX2);
if (index1 == index2):
actualGroundGHI = frontGroundGHI[index1]; # x projections in same groundGHI element
else:
for k in range (index1, index2+1): # Sum the irradiances on the ground if projections are in different groundGHI elements
#for (k = index1; k <= index2; k++)
#Console.WriteLine("index1=0 index2=1", index1,index2);
if (k == index1):
actualGroundGHI += frontGroundGHI[k] * (k + 1.0 - projectedX1);
elif (k == index2):
if (k < 100):
actualGroundGHI += frontGroundGHI[k] * (projectedX2 - k);
else:
actualGroundGHI += frontGroundGHI[k - 100] * (projectedX2 - k);
else:
if (k < 100):
actualGroundGHI += frontGroundGHI[k];
else:
actualGroundGHI += frontGroundGHI[k - 100];
actualGroundGHI /= projectedX2 - projectedX1; # Irradiance on ground in the 1 degree field of view
#if (i == 0)
# Console.WriteLine("j=0 index1=1 index2=2 projectX1=3,5:0.0 projectX2=4,5:0.0 actualGrdGHI=5,6:0.0", j, index1, index2, projectedX1, projectedX2, actualGroundGHI);
frontGTI[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * SegAOIcor[index][j] * actualGroundGHI * albedo; # Add ground reflected component
frontReflected[i] += 0.5 * (math.cos(j * DTOR) - math.cos((j + 1) * DTOR)) * actualGroundGHI * albedo * (1.0 - SegAOIcor[index][j] * (1.0 - Ro)); # Reflected ground radiation from module
#Console.WriteLine("actualGroundGHI = 0,6:0.0 inputGHI = 1,6:0.0 aveArrayGroundGHI = 2,6:0.0", actualGroundGHI, dhi + dni * math.cos(zen), aveGroundGHI);
# End of j loop for adding ground reflected componenet
# Calculate and add direct and circumsolar irradiance components
inc, tiltr, sazmr = sunIncident(0, beta / DTOR, sazm / DTOR, 45.0, zen, azm) # For calling PerezComp to break diffuse into components for 90 degree tilt (vertical)
# print "sunIncident 2."
# print "inc = ", inc
# print "tiltr = ", tiltr
# print "sazmr = ", sazmr
# print " INCIDENT REALY NEEDED for AOI ", inc
gtiAllpc, iso_dif, circ_dif, horiz_dif, grd_dif, beam = perezComp(dni, dhi, albedo, inc, tiltr, zen) # Call to get components for the tilt
# print "PEREZCOMP 2 = "
# print "gtiAllpc = ", vti
# print "iso_dif = ", iso_dif
# print "circ_dif = ", circ_dif
# print "horiz_dif = ", horiz_dif
# print "grd_dif = ", grd_dif
# print "beam = ", beam
cellShade = pvFrontSH * cellRows - i;
if (cellShade > 1.0): # Fully shaded if > 1, no shade if < 0, otherwise fractionally shaded
cellShade = 1.0;
elif (cellShade < 0.0):
cellShade = 0.0;
if (cellShade < 1.0 and inc < math.pi / 2.0): # Cell not shaded entirely and inc < 90 deg
cor = aOIcorrection(n2, inc); # Get AOI correction for beam and circumsolar
frontGTI[i] += (1.0 - cellShade) * (beam + circ_dif) * cor; # Add beam and circumsolar radiation
#frontReflected[i] += (1.0 - cellShade) * (beam + circ_dif) * (1.0 - cor * (1.0 - Ro)); # Reflected beam and circumsolar radiation from module
# End of for i = 0; i < cellRows loop
return aveGroundGHI, frontGTI, frontReflected;
# End of GetFrontSurfaceIrradiances
def getGroundShadeFactors(rowType, beta, C, D, elv, azm, sazm):
"""
This method determines if the ground is shaded from direct beam radiation
for points on the ground from the leading edge of one row of PV panels to
the leading edge of the next row of PV panels behind it. This row-to-row
dimension is divided into 100 ground segments and a ground shade factor is
returned for each ground segment, with values of 1 for shaded segments and
values of 0 for non shaded segments. The fractional amounts of shading of
the front and back surfaces of the PV panel are also returned. 8/20/2015
4/18/2016 - Modified to account for different row types. Because the ground
factors may now be different depending on row, they are calculated for the
row-to-row dimension to the rear of the leading module edge and to the
front of the leading edge. Also returned is the maximum shadow length
projected to the front or rear from the front of the module row
Parameters
----------
rowType : str
"first", "interior", "last", or "single"
beta
Tilt from horizontal of the PV modules/panels (deg)
C
Ground clearance of PV panel (in PV panel slope lengths)
D
Horizontal distance between rows of PV panels (in PV panel slope
lengths)
elv
Sun elevation (in radians)
azm
Sun azimuth (in radians)
sazm
Surface azimuth of PV panels (deg)
Returns
-------
pvFrontSH : numeric
Decimal fraction of the front surface of the PV panel that is shaded,
0.0 to 1.0
pvBackSH : numeric
Decimal fraction of the back surface of the PV panel that is shaded,
0.0 to 1.0
rearGroundSH : array of size [100]
Ground shade factors for ground segments to the rear, 0 = not shaded,
1 = shaded
frontGroundSH : array of size [100]
Ground shade factors for ground segments to the front, 0 = not shaded,
1 = shaded
maxShadow : numeric
Maximum shadow length projected to the front(-) or rear (+) from the
front of the module row (in PV panel slope lengths), only used later
for rowTypes other than "interior"
"""
rearGroundSH = []
frontGroundSH = []
beta = beta * DTOR # Tilt from horizontal of the PV modules/panels, in radians
sazm = sazm * DTOR # Surface azimuth of PV module/pamels, in radians
h = math.sin(beta); # Vertical height of sloped PV panel (in PV panel slope lengths)
x1 = math.cos(beta); # Horizontal distance from front of panel to rear of panel (in PV panel slope lengths)
rtr = D + x1; # Row-to-row distance (in PV panel slope lengths)
# Divide the row-to-row spacing into 100 intervals for calculating ground shade factors
delta = rtr / 100.0;
x = -delta / 2.0; # Initialize horizontal dimension x to provide midpoof intervals
Lh = (h / math.tan(elv)) * math.cos(sazm - azm); # Horizontal length of shadow perpindicular to row from top of module to bottom of module
Lhc = ((h + C) / math.tan(elv)) * math.cos(sazm - azm); # Horizontal length of shadow perpindicular to row from top of module to ground level
Lc = (C / math.tan(elv)) * math.cos(sazm - azm); # Horizontal length of shadow perpindicular to row from bottom of module to ground level
ss1 = 0.0; se1 = 0.0; ss2 = 0.0; se2 = 0.0; # Initialize shading start (s) and end (e) to zeros for two potential shading segments
pvFrontSH = 0.0;
pvBackSH = 0.0;
if (rowType == "interior"):
if (Lh > D): # Front side of PV module partially shaded, back completely shaded, ground completely shaded
pvFrontSH = (Lh - D) / (Lh + x1);
pvBackSH = 1.0;
ss1 = 0.0; # Ground shaded from 0.0 to rtr
se1 = rtr;
elif (Lh < -(rtr + x1)): # Back side of PV module partially shaded, front completely shaded, ground completely shaded
pvFrontSH = 1.0;
pvBackSH = (Lh + rtr + x1) / (Lh + x1);
ss1 = 0.0; # Ground shaded from 0.0 to rtr
se1 = rtr;
else: # Ground is partially shaded (I assume)
if (Lhc >= 0.0): # Shadow to rear of row, module front unshaded, back shaded
pvFrontSH = 0.0;
pvBackSH = 1.0;
Ss = Lc; # Shadow starts at Lc
Se = Lhc + x1; # Shadow ends here
while (Ss > rtr):
Ss -= rtr; # Put shadow in correct rtr space if needed
Se -= rtr;
ss1 = Ss;
se1 = Se;
if (se1 > rtr): # then need to use two shade areas
se1 = rtr;
ss2 = 0.0;
se2 = Se - rtr;
if (se2 > ss1):
# This would mean ground completely shaded, does this occur?
ss1 = 0.0; # Ground shaded from 0.0 to rtr
se1 = rtr;
else: # Shadow to front of row, either front or back might be shaded, depending on tilt and other factors
Ss = 0.0; # Shadow starts at Lc, initialize
Se = 0.0; # Shadow ends here, initialize
if (Lc < Lhc + x1):
pvFrontSH = 0.0;
pvBackSH = 1.0;
Ss = Lc; # Shadow starts at Lc
Se = Lhc + x1; # Shadow ends here
else:
pvFrontSH = 1.0;
pvBackSH = 0.0;
Ss = Lhc + x1; # Shadow starts at Lhc + x1
Se = Lc; # Shadow ends here
while (Ss < 0.0):
Ss += rtr; # Put shadow in correct rtr space if needed
Se += rtr;
ss1 = Ss;
se1 = Se;
if (se1 > rtr): # then need to use two shade areas
se1 = rtr;
ss2 = 0.0;
se2 = Se - rtr;
if (se2 > ss1):