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#!/usr/bin/python
# -*- coding: utf-8 -*-
"""
Synthetic Solar Radiation Module
Copyright (C) 2014 Julius Susanto
Last edited: August 2014
Main Functions
--------------
- Aguiar_hourly_G0: generate annual sequence of hourly irradiances on a horizontal plane (W/m2)
- Aguiar_hourly_kt: generate sequence of hourly clearness indices for a single solar day
- Aguiar_daily_Kt: generate sequence of daily clearness indices given mean monthly Kt
- trend_sequence: generate annual sequence of hourly trend irradiances (no randomness)
Utility Functions
-----------------
- declination: calculate solar declination
- sunrise: calculate sunrise / sunset angle (in radians)
- eccentricity: calculate earth eccentricity correction factor
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 numpy as np
from math import floor
# np.seterr(all='raise')
def declination(n):
"""
Returns the solar declination (in radians) on the n-th day of the year using the accurate
approximation:
delta = -arcsin (0.39779 cos [0.98565(n+10) + 1.914 sin (0.98565 (n-2))])
(note that the quantities inside the cosine and sine are in degrees)
Inputs: n is the day of the year (where n=1 is midnight on January 1)
"""
delta = -np.arcsin(0.39779 * np.cos(np.radians(0.98565 * (n + 10) + 1.914 * np.sin(np.radians(0.98565 * (n - 2))))))
return delta
def sunrise(delta, lat):
"""
Returns the sunrise / sunset angle (in radians)
Inputs: delta is the solar declination angle (in radians)
lat is the latitude of the location (in radians)
"""
omega = np.arccos(-np.tan(delta) * np.tan(lat))
return omega
def eccentricity(n):
"""
Returns the earth's eccentricity correction factor according to Spencer's formula in the paper:
J. W. Spencer, “Fourier series representation of the position of the Sun”, Search, Vol. 2, 1972
Inputs: n is the day of the year (where n=1 is midnight on January 1)
"""
day_ang = 2 * np.pi * (n - 1) / 365
epsilon = 1.00011 + 0.034221 * np.cos(day_ang) + 0.00128 * np.sin(day_ang) + 0.000719 * np.cos(
2 * day_ang) + 0.000077 * np.sin(2 * day_ang)
return epsilon
def Aguiar_daily_Kt(Ktm, Kt0, nd):
"""
Generates a sequence of synthetic daily clearness indices (Kt) using the mean monthly clearness
index as the input. The algorithm is based on the method by Aguiar et al in the paper:
R. Aguiar and M. Collares-Pereira, "A simple procedure for the generation of sequences of
daily radiation values using Markov transition matrices", Solar Energy, vol. 40, 269-279, 1988
Inputs: Ktm is the mean clearness index for the month
Kt0 is initial clearness index (on the first day of the month)
nd is the number of daily clearness indices to generate
"""
# Markov Transition Matrices
MTM_lib = {}
MTM_states = [0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70]
MTM_min = [0.031, 0.058, 0.051, 0.052, 0.028, 0.053, 0.044, 0.085, 0.010, 0.319]
MTM_max = [0.705, 0.694, 0.753, 0.753, 0.807, 0.856, 0.818, 0.846, 0.842, 0.865]
# Kt <= 0.30
MTM_lib[0] = np.matrix([[0.229, 0.333, 0.208, 0.042, 0.083, 0.042, 0.042, 0.021, 0.000, 0.000],
[0.167, 0.319, 0.194, 0.139, 0.097, 0.028, 0.042, 0.000, 0.014, 0.000],
[0.250, 0.250, 0.091, 0.136, 0.091, 0.046, 0.046, 0.023, 0.068, 0.000],
[0.158, 0.237, 0.158, 0.263, 0.026, 0.053, 0.079, 0.026, 0.000, 0.000],
[0.211, 0.053, 0.211, 0.158, 0.053, 0.053, 0.158, 0.105, 0.000, 0.000],
[0.125, 0.125, 0.250, 0.188, 0.063, 0.125, 0.000, 0.125, 0.000, 0.000],
[0.040, 0.240, 0.080, 0.120, 0.080, 0.080, 0.120, 0.120, 0.080, 0.040],
[0.000, 0.250, 0.000, 0.125, 0.000, 0.125, 0.125, 0.250, 0.063, 0.063],
[0.000, 0.250, 0.000, 0.125, 0.250, 0.000, 0.250, 0.000, 0.000, 0.125],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.500, 0.250, 0.000, 0.250]])
# 0.30 < Kt <= 0.35
MTM_lib[1] = np.matrix([[0.000, 0.000, 0.091, 0.000, 0.364, 0.091, 0.182, 0.000, 0.273, 0.000],
[0.118, 0.118, 0.176, 0.118, 0.059, 0.118, 0.176, 0.059, 0.059, 0.000],
[0.067, 0.267, 0.067, 0.200, 0.067, 0.000, 0.133, 0.133, 0.000, 0.067],
[0.118, 0.235, 0.000, 0.235, 0.059, 0.176, 0.118, 0.000, 0.059, 0.000],
[0.077, 0.154, 0.308, 0.077, 0.154, 0.077, 0.000, 0.077, 0.077, 0.000],
[0.083, 0.000, 0.167, 0.250, 0.083, 0.167, 0.000, 0.083, 0.167, 0.000],
[0.222, 0.222, 0.000, 0.111, 0.111, 0.000, 0.111, 0.222, 0.000, 0.000],
[0.091, 0.182, 0.273, 0.000, 0.091, 0.273, 0.000, 0.091, 0.000, 0.000],
[0.111, 0.111, 0.111, 0.222, 0.000, 0.000, 0.000, 0.222, 0.111, 0.111],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.500, 0.000, 0.000, 0.500]])
# 0.35 < Kt <= 0.40
MTM_lib[2] = np.matrix([[0.206, 0.088, 0.176, 0.176, 0.088, 0.029, 0.176, 0.029, 0.029, 0.000],
[0.120, 0.100, 0.140, 0.160, 0.120, 0.220, 0.100, 0.000, 0.020, 0.020],
[0.077, 0.123, 0.185, 0.123, 0.077, 0.139, 0.092, 0.123, 0.061, 0.000],
[0.048, 0.111, 0.095, 0.206, 0.206, 0.190, 0.095, 0.048, 0.000, 0.000],
[0.059, 0.137, 0.118, 0.137, 0.098, 0.118, 0.118, 0.157, 0.059, 0.000],
[0.014, 0.097, 0.139, 0.153, 0.125, 0.139, 0.208, 0.056, 0.042, 0.028],
[0.073, 0.101, 0.116, 0.145, 0.087, 0.159, 0.203, 0.087, 0.029, 0.000],
[0.019, 0.037, 0.111, 0.056, 0.074, 0.111, 0.185, 0.296, 0.074, 0.037],
[0.035, 0.069, 0.035, 0.000, 0.035, 0.103, 0.172, 0.138, 0.379, 0.035],
[0.000, 0.167, 0.167, 0.000, 0.167, 0.000, 0.000, 0.333, 0.000, 0.167]])
# 0.40 < Kt <= 0.45
MTM_lib[3] = np.matrix([[0.167, 0.167, 0.167, 0.000, 0.083, 0.125, 0.000, 0.167, 0.125, 0.000],
[0.117, 0.117, 0.150, 0.117, 0.083, 0.117, 0.200, 0.067, 0.017, 0.017],
[0.049, 0.085, 0.134, 0.158, 0.098, 0.110, 0.134, 0.134, 0.061, 0.037],
[0.039, 0.090, 0.141, 0.141, 0.167, 0.141, 0.090, 0.141, 0.039, 0.013],
[0.009, 0.139, 0.074, 0.093, 0.194, 0.139, 0.167, 0.093, 0.074, 0.019],
[0.036, 0.018, 0.117, 0.099, 0.144, 0.180, 0.180, 0.117, 0.072, 0.036],
[0.000, 0.046, 0.061, 0.061, 0.136, 0.159, 0.273, 0.167, 0.098, 0.000],
[0.016, 0.056, 0.080, 0.128, 0.104, 0.080, 0.160, 0.208, 0.136, 0.032],
[0.011, 0.053, 0.021, 0.043, 0.128, 0.096, 0.074, 0.223, 0.277, 0.074],
[0.000, 0.074, 0.037, 0.000, 0.074, 0.074, 0.074, 0.074, 0.333, 0.259]])
# 0.45 < Kt <= 0.50
MTM_lib[4] = np.matrix([[0.120, 0.200, 0.160, 0.120, 0.120, 0.120, 0.080, 0.000, 0.040, 0.040],
[0.100, 0.080, 0.120, 0.140, 0.140, 0.200, 0.180, 0.040, 0.530, 0.000],
[0.046, 0.114, 0.068, 0.171, 0.125, 0.171, 0.080, 0.159, 0.057, 0.011],
[0.015, 0.061, 0.084, 0.099, 0.191, 0.153, 0.153, 0.115, 0.115, 0.015],
[0.024, 0.030, 0.098, 0.098, 0.165, 0.195, 0.195, 0.140, 0.043, 0.012],
[0.015, 0.026, 0.062, 0.124, 0.144, 0.170, 0.170, 0.222, 0.062, 0.005],
[0.000, 0.013, 0.045, 0.108, 0.112, 0.175, 0.188, 0.224, 0.117, 0.018],
[0.008, 0.023, 0.054, 0.066, 0.093, 0.125, 0.191, 0.253, 0.183, 0.004],
[0.006, 0.022, 0.061, 0.033, 0.067, 0.083, 0.139, 0.222, 0.322, 0.044],
[0.000, 0.046, 0.091, 0.091, 0.046, 0.046, 0.136, 0.091, 0.273, 0.182]])
# 0.50 < Kt <= 0.55
MTM_lib[5] = np.matrix([[0.250, 0.179, 0.107, 0.107, 0.143, 0.071, 0.107, 0.036, 0.000, 0.000],
[0.133, 0.022, 0.089, 0.111, 0.156, 0.178, 0.111, 0.133, 0.067, 0.000],
[0.064, 0.048, 0.143, 0.048, 0.175, 0.143, 0.206, 0.095, 0.079, 0.000],
[0.000, 0.022, 0.078, 0.111, 0.156, 0.156, 0.244, 0.167, 0.044, 0.022],
[0.016, 0.027, 0.037, 0.069, 0.160, 0.219, 0.230, 0.160, 0.075, 0.005],
[0.013, 0.025, 0.030, 0.093, 0.144, 0.202, 0.215, 0.219, 0.055, 0.004],
[0.006, 0.041, 0.035, 0.064, 0.090, 0.180, 0.337, 0.192, 0.049, 0.006],
[0.012, 0.021, 0.029, 0.035, 0.132, 0.123, 0.184, 0.371, 0.082, 0.012],
[0.008, 0.016, 0.016, 0.024, 0.071, 0.103, 0.159, 0.270, 0.309, 0.024],
[0.000, 0.000, 0.000, 0.000, 0.059, 0.000, 0.059, 0.294, 0.412, 0.176]])
# 0.55 < Kt <= 0.60
MTM_lib[6] = np.matrix([[0.217, 0.087, 0.000, 0.174, 0.130, 0.087, 0.087, 0.130, 0.087, 0.000],
[0.026, 0.079, 0.132, 0.079, 0.026, 0.158, 0.158, 0.132, 0.158, 0.053],
[0.020, 0.020, 0.020, 0.040, 0.160, 0.180, 0.160, 0.200, 0.100, 0.100],
[0.025, 0.013, 0.038, 0.076, 0.076, 0.139, 0.139, 0.266, 0.215, 0.013],
[0.030, 0.030, 0.050, 0.020, 0.091, 0.131, 0.162, 0.283, 0.131, 0.071],
[0.006, 0.006, 0.013, 0.057, 0.057, 0.121, 0.204, 0.287, 0.185, 0.064],
[0.004, 0.026, 0.037, 0.030, 0.093, 0.107, 0.193, 0.307, 0.167, 0.037],
[0.011, 0.009, 0.014, 0.042, 0.041, 0.071, 0.152, 0.418, 0.203, 0.041],
[0.012, 0.022, 0.022, 0.038, 0.019, 0.050, 0.113, 0.281, 0.360, 0.084],
[0.008, 0.024, 0.039, 0.039, 0.063, 0.039, 0.118, 0.118, 0.284, 0.268]])
# 0.60 < Kt <= 0.65
MTM_lib[7] = np.matrix([[0.067, 0.133, 0.133, 0.067, 0.067, 0.200, 0.133, 0.133, 0.067, 0.000],
[0.118, 0.059, 0.059, 0.059, 0.059, 0.118, 0.118, 0.235, 0.118, 0.059],
[0.000, 0.024, 0.024, 0.049, 0.146, 0.073, 0.195, 0.244, 0.195, 0.049],
[0.026, 0.000, 0.026, 0.026, 0.053, 0.184, 0.263, 0.184, 0.237, 0.000],
[0.014, 0.000, 0.042, 0.056, 0.069, 0.097, 0.139, 0.306, 0.278, 0.000],
[0.009, 0.009, 0.052, 0.069, 0.052, 0.112, 0.215, 0.285, 0.138, 0.060],
[0.009, 0.009, 0.026, 0.017, 0.094, 0.099, 0.232, 0.283, 0.210, 0.021],
[0.010, 0.014, 0.016, 0.019, 0.027, 0.062, 0.163, 0.467, 0.202, 0.019],
[0.004, 0.007, 0.031, 0.017, 0.033, 0.050, 0.086, 0.252, 0.469, 0.050],
[0.000, 0.000, 0.015, 0.046, 0.031, 0.046, 0.077, 0.123, 0.446, 0.215]])
# 0.65 < Kt <= 0.70
MTM_lib[8] = np.matrix([[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 1.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 1.000, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.250, 0.250, 0.500, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.250, 0.000, 0.000, 0.375, 0.250, 0.125],
[0.000, 0.000, 0.000, 0.083, 0.000, 0.167, 0.167, 0.250, 0.333, 0.000],
[0.000, 0.000, 0.042, 0.042, 0.042, 0.083, 0.083, 0.292, 0.292, 0.125],
[0.000, 0.000, 0.032, 0.000, 0.000, 0.032, 0.129, 0.387, 0.355, 0.065],
[0.000, 0.000, 0.000, 0.038, 0.038, 0.075, 0.047, 0.340, 0.415, 0.047],
[0.004, 0.004, 0.007, 0.007, 0.011, 0.030, 0.052, 0.141, 0.654, 0.089],
[0.000, 0.000, 0.000, 0.000, 0.061, 0.061, 0.030, 0.030, 0.349, 0.470]])
# Kt > 0.70
MTM_lib[9] = np.matrix([[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 1.000, 0.000],
[0.100, 0.100, 0.100, 0.100, 0.100, 0.100, 0.100, 0.100, 0.100, 0.100],
[0.000, 0.000, 0.000, 0.250, 0.000, 0.000, 0.000, 0.500, 0.250, 0.000],
[0.000, 0.000, 0.143, 0.143, 0.000, 0.143, 0.143, 0.429, 0.000, 0.000],
[0.000, 0.000, 0.000, 0.200, 0.000, 0.000, 0.200, 0.400, 0.200, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.222, 0.444, 0.333, 0.000],
[0.000, 0.000, 0.000, 0.000, 0.080, 0.080, 0.080, 0.480, 0.240, 0.040],
[0.000, 0.000, 0.027, 0.009, 0.027, 0.018, 0.135, 0.523, 0.252, 0.009],
[0.000, 0.000, 0.000, 0.022, 0.000, 0.043, 0.043, 0.326, 0.511, 0.054],
[0.000, 0.000, 0.000, 0.143, 0.000, 0.000, 0.000, 0.143, 0.714, 0.000]])
# Determine the appropriate MTM based on the mean monthly Kt
MTM_index = np.digitize([Ktm], MTM_states)[0]
MTM = MTM_lib[MTM_index]
# Calculate states and step sizes
min_state = MTM_min[MTM_index]
max_state = MTM_max[MTM_index]
step_size = (max_state - min_state) / 10
states = np.arange(min_state, max_state, step_size)
# Generate daily clearness indices for nd days
Kti = Kt0
Kt = [Kti]
for i in range(nd - 1):
MTM_row = np.digitize([Kti], states)[0]
MTM_cum = np.ravel(np.cumsum(MTM[MTM_row - 1, :]))
R = np.random.rand()
new_state = np.digitize([R], MTM_cum)[0] + 1
if new_state > 10:
new_state = 10
# Calculate interpolation factor
if new_state == 1:
k_interp = R / MTM_cum[new_state - 1]
else:
if MTM_cum[new_state - 1] != MTM_cum[new_state - 2]:
k_interp = (R - MTM_cum[new_state - 2]) \
/ (MTM_cum[new_state - 1] - MTM_cum[new_state - 2])
else:
k_interp = max_state
Kti = k_interp * np.mean(np.cumsum(MTM[:, 0:new_state], axis=1)[:, new_state - 1])
Kt.append(Kti)
return Kt
def Aguiar_hourly_kt(Kt, n, lat, max_iter):
"""
Generates a sequence of synthetic hourly clearness indices (kt) using the mean daily clearness
index (Kt) as the input. The algorithm is based on the method by Aguiar et al in the paper:
R. Aguiar and M. Collares-Pereira, "TAG: A time-dependent, autoregressive Gaussian model
for generating synthetic hourly radiation", Solar Energy, vol. 49, 167-174, 1992
Inputs: Kt is the mean clearness index for the day
n is the day of the year (n=1 is midnight on January 1)
lat is the latitude of the location (degrees)
max_iter is the maximum number of iterations for each new kt
"""
# Solar declination in radians
delta = declination(n)
# Sunrise angle in radians
omega = sunrise(delta, np.radians(lat))
# Autocorrelation coefficient
phi = 0.38 + 0.06 * np.cos(7.4 * Kt - 2.5)
# Calculate algorithm constants
lmbda = -0.19 + 1.12 * Kt + 0.24 * np.exp(-8 * Kt)
eta = 0.32 - 1.6 * (Kt - 0.5) ** 2
kappa = 0.19 + 2.27 * Kt ** 2 - 2.51 * Kt ** 3
A = 0.14 * np.exp(-20 * (Kt - 0.35) ** 2)
B = 3 * (Kt - 0.45) ** 2 + 16 * Kt ** 5
# Generate kt for each solar hour
kt = []
y = []
for h in range(1, 25):
angle_start = (h - 13) * np.pi / 12 # Start of hour
angle_end = (h - 12) * np.pi / 12 # End of hour
if (angle_start > -omega) and (angle_end < omega):
# Clear sky clearness index
kcs = 0.88 * np.cos(np.pi * (h - 12.5) / 30)
# Angle at centre of hour
h_ang = (h - 12.5) * np.pi / 12
# Solar elevation/ altitude angle
hs = np.arcsin(
np.cos(h_ang) * np.cos(delta) * np.cos(np.radians(lat)) + np.sin(delta) * np.sin(np.radians(lat)))
# Average clearness index
ktm = lmbda + eta * np.exp(-kappa / np.sin(hs))
# Standard deviation
sigma = A * np.exp(B * (1 - np.sin(hs)))
# Generate new kt only if greater than 0 and less than clear sky kt
kti = -1
iter = 0
while (kti < 0) or (kti > kcs):
z = np.random.rand()
r = sigma * (z ** 0.135 - (1 - z) ** 0.135) / 0.1975
yi = phi * y[h - 2] + r
kti = ktm + sigma * yi
# Iteration control
iter = iter + 1
if iter > max_iter:
if kti < 0:
kti = 0
if kti > kcs:
kti = kcs
kt.append(kti)
y.append(yi)
else:
# For non-sunlight hours, set kt to zero
kt.append(0)
y.append(0)
return kt
def trend_sequence(lat):
"""
Generates an annual sequence of clear sky (extraterrestrial) hourly irradiance values
(on a horizontal plane) based on the annual trend for a given latitude. Estimation of the
daily irradiation and hourly irradiance on a horizontal plane is based on the method outlined
in Chapter 20 of:
A. Luque, S. Hegedus, “Handbook of Photovoltaic Science and Engineering”, Wiley, 2003
Inputs: lat is the latitude of the location (in decimals)
"""
n = np.arange(1, 366)
lat_rad = np.radians(lat)
epsilon = eccentricity(n)
delta = declination(n)
omega = sunrise(delta, lat_rad)
# Daily extraterrestrial irradiation (on a horizontal plane) Wh/m2/day
# (Refer to Section 20.4 of Luque and Hegedus)
B0d = 24 / np.pi * 1367 * epsilon * (
omega * np.sin(delta) * np.sin(lat_rad) - np.cos(delta) * np.cos(lat_rad) * np.sin(-omega))
# Set up hour angles
h = np.arange(1, 25)
h_start = (h - 13) * np.pi / 12 # Start of hour
h_end = (h - 12) * np.pi / 12 # End of hour
h_ang = (h - 12.5) * np.pi / 12 # Centre of hour
# Hourly clear sky irradiance (on a horizontal plane) W/m2
G0c = []
for d in range(1, 366):
omega_s = -omega[d - 1] # Sunrise angle for the day
a = 0.409 - 0.5016 * np.sin(omega_s + 60 * np.pi / 180)
b = 0.6609 + 0.4767 * np.sin(omega_s + 60 * np.pi / 180)
# Hourly irradiance on a horizontal plane
# (Refer to Section 20.5.2 of Luque and Hegedus)
G0ci = np.pi / 24 * (np.cos(h_ang) - np.cos(omega_s)) / (omega_s * np.cos(omega_s) - np.sin(omega_s)) * (
a + b * np.cos(h_ang)) * B0d[d - 1]
h_sunrise = np.digitize([omega_s], h_start)[0]
h_sunset = np.digitize([-omega_s], h_end)[0]
G0ci[0:h_sunrise] = 0
G0ci[h_sunset:24] = 0
G0c.extend(G0ci)
return G0c
def Aguiar_hourly_G0(Ktm, lat):
"""
Generates an annual sequence of synthetic hourly irradiance values G0 (on a horizontal plane)
based on monthly mean clearness indices. The methods proposed by Aguiar et al for the generation
of synthetic daily and hourly irradiance values is used to create the sequence.
Inputs: Ktm is an array of monthly mean clearness indices
lat is the latitude of the location (in decimals)
"""
days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
# Generate daily clearness indices for each day in the year
Kt = []
Kt0 = Ktm[11]
for i in range(12):
Kti = Aguiar_daily_Kt(Ktm[i], Kt0, days[i])
Kt.extend(Kti)
Kt0 = Ktm[i]
# Generate hourly clearness indices for each hour in the year
kt = []
for d in range(365):
kti = Aguiar_hourly_kt(Kt[d], d, lat, 20)
kt.extend(kti)
# Generate trend irradiances for each hour in the year
G0c = trend_sequence(lat)
# Calculate synthetic irradiance for each hour of the year
G0 = G0c * np.array(kt)
return G0, G0c, np.array(kt)
def Aguiar_hourly_Kt_list(Ktm, lat):
"""
Generates an annual sequence of synthetic hourly irradiance values G0 (on a horizontal plane)
based on monthly mean clearness indices. The methods proposed by Aguiar et al for the generation
of synthetic daily and hourly irradiance values is used to create the sequence.
Inputs: Ktm is an array of monthly mean clearness indices
lat is the latitude of the location (in decimals)
"""
days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
# Generate daily clearness indices for each day in the year
Kt = []
Kt0 = Ktm[11]
for i in range(12):
Kti = Aguiar_daily_Kt(Ktm[i], Kt0, days[i])
Kt.extend(Kti)
Kt0 = Ktm[i]
# Generate hourly clearness indices for each hour in the year
kt = []
for d in range(365):
kti = Aguiar_hourly_kt(Kt[d], d, lat, 10)
kt.extend(kti)
return kt
def Kt_single_day(Ktm, day):
"""
Generates a single day synthetic hourly irradiance values G0 (on a horizontal plane)
based on monthly mean clearness indices. The methods proposed by Aguiar et al for the generation
of synthetic daily and hourly irradiance values is used to create the sequence.
Inputs: Ktm is an array of monthly mean clearness indices
lat is the latitude of the location (in decimals)
"""
days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
# Generate daily clearness indices for each day in the year
Kt = []
Kt0 = Ktm[11]
for i in range(12):
Kti = Aguiar_daily_Kt(Ktm[i], Kt0, days[i])
Kt.extend(Kti)
Kt0 = Ktm[i]
return Kt[day]
def trend_single_day(lat, day):
"""
Generates a single day sequence of clear sky (extraterrestrial) hourly irradiance values
(on a horizontal plane) based on the annual trend for a given latitude. Estimation of the
daily irradiation and hourly irradiance on a horizontal plane is based on the method outlined
in Chapter 20 of:
A. Luque, S. Hegedus, “Handbook of Photovoltaic Science and Engineering”, Wiley, 2003
Inputs: lat is the latitude of the location (in decimals)
"""
n = np.arange(day - 1, day + 1)
lat_rad = np.radians(lat)
epsilon = eccentricity(n)
delta = declination(n)
omega = sunrise(delta, lat_rad)
# Daily extraterrestrial irradiation (on a horizontal plane) Wh/m2/day
# (Refer to Section 20.4 of Luque and Hegedus)
B0d = 24 / np.pi * 1367 * epsilon * (
omega * np.sin(delta) * np.sin(lat_rad) - np.cos(delta) * np.cos(lat_rad) * np.sin(-omega))
# Set up hour angles
h = np.arange(1, 25)
h_start = (h - 13) * np.pi / 12 # Start of hour
h_end = (h - 12) * np.pi / 12 # End of hour
h_ang = (h - 12.5) * np.pi / 12 # Centre of hour
# Hourly clear sky irradiance (on a horizontal plane) W/m2
G0c = []
for d in range(1):
omega_s = - omega[d - 1] # Sunrise angle for the day
a = 0.409 - 0.5016 * np.sin(omega_s + 60 * np.pi / 180)
b = 0.6609 + 0.4767 * np.sin(omega_s + 60 * np.pi / 180)
# Hourly irradiance on a horizontal plane
# (Refer to Section 20.5.2 of Luque and Hegedus)
G0ci = np.pi / 24 * (np.cos(h_ang) - np.cos(omega_s)) / \
(omega_s * np.cos(omega_s) - np.sin(omega_s)) * (a + b * np.cos(h_ang)) * B0d[d - 1]
h_sunrise = np.digitize([omega_s], h_start)[0]
h_sunset = np.digitize([-omega_s], h_end)[0]
G0ci[0:h_sunrise] = 0
G0ci[h_sunset:24] = 0
G0c.extend(G0ci)
return G0c[0:24]
globalavgkt = np.load('synthetic_solar/globalavgkt.npy')
def monthlyKt(lat, lon, data=globalavgkt):
'''
:param lat: degrees
latitude
:param lon: degrees
longitude
:return: numpy array
10 year monthly Kt at given lat, lon
'''
latindex = -floor(lat) + 90 - 1
lonindex = floor(lon) + 180
if latindex == 180:
latindex = 0
if lonindex == 360:
lonindex = 0
rawdata = data[latindex, lonindex, :]
rawdata[rawdata == -999] = 'nan'
return data[latindex, lonindex, :]