引入

最近项目需要计算地外水平/斜面的太阳理论辐照度，为此搜集了资料，并在python中进行了实现，现将其分享于此。

水平理论辐照度

地球与太阳之间的相对运动，即地球自转与公转，会对理论辐照度产生影响。在忽略极移和地轴进动微小影响的条件下地球大气层上界单位面积、单位时间接收的太阳辐射与日地距离的平方成反比。地球自转对应太阳时角和太阳高度角的变化，公转对应太阳赤纬和日地距离的变化。

水平太阳辐照度的计算公式为：

在计算某地太阳福射时采用的是当地的真太阳时，所以需要根据当地的区时和经度来求取对应的真太阳时和太阳时角，此求取过程分步完成：①根据当地经度对已知的当地区时进行修正得到当地的地方时；②根据真太阳时和平太阳时之间的时差对该地方时进行修正得到当地的真太阳时；③根据当地的真太阳时计算得到当地区时对应的太阳时角。

按照上式，可计算得到指定地点、指定日期的水平地外辐照度理论值，并绘制对应的地外辐照度理论值曲线。

任意斜面的太阳辐照度

代码

python代码如下，略长，主要牵扯到真太阳时转换数组的赋值。
代码最后有运行示例。

import pandas as pd
import numpy as np
import math
from datetime import datetime, timedeltadef calculate_sun_time(time_str, latitude, longitude, tilt, azimuth, longitude_time):"""从datetime类型的时间计算日出日落及白天时间"""cur_time = datetime.strptime(time_str, '%Y-%m-%d %H:%M:%S')day_year = int(datetime.strftime(cur_time, '%j'))  # j是积日delta = 23.45 / 180 * math.pi * math.sin(2 * math.pi * (284 + day_year) / 365)  # 计算太阳赤纬(弧度)latitude = latitude / 180 * math.pi     # 纬度转换为弧度cos_omega = - math.sin(delta) * math.sin(latitude) / (math.cos(delta) * math.cos(latitude))omega = math.acos(cos_omega)            # 计算真太阳时时角true_time_down = (omega * 180 / math.pi / 15 + 12) * 60   # 计算基于真太阳时的日落时间true_time_up = 60 * 24 - true_time_downtime_sun = (true_time_down - 12 * 60) * 2# 计算偏差时间bias_time = dif_true_solar_time(day_year).split(':')if '-' in bias_time[0]:pos_flag = -1else:pos_flag = 1bias_minute = int(bias_time[0])bias_second = int(bias_time[1])bias = pos_flag * (abs(bias_minute) + bias_second / 60)minute_sun_down = true_time_down - bias - 4 * (longitude - longitude_time)minute_sun_up = true_time_up - bias - 4 * (longitude - longitude_time)return time_sun, minute_sun_up, minute_sun_downdef calculate_irradiance_base(day_year, minute_day, latitude, longitude, tilt, azimuth, longitude_time):"""根据给定的日期与时间，计算当前位置的大气外理论辐照度,只适用于南北回归线之外的情况，假定电站方位角为0北纬为正，东经为正latitude:电站所在维度longitude:电站所在经度tilt:电站光伏板安装角度azimuth:电站斜面方位角longitude_time:电站所采用时区的中心经度"""G_0 = 1368  # 取太阳常数为1368（W/m2）k = 1 + 0.034 * (math.cos(2 * math.pi / 365 * day_year))        # 计算日地距离修正系数delta = 23.45 / 180 * math.pi * math.sin(2 * math.pi * (284 + day_year) / 365)    # 计算太阳赤纬(弧度)# 计算偏差时间bias_time = dif_true_solar_time(day_year).split(':')if '-' in bias_time[0]:pos_flag = -1else:pos_flag = 1bias_minute = int(bias_time[0])bias_second = int(bias_time[1])bias = pos_flag * (abs(bias_minute) + bias_second / 60)true_time = minute_day + 4 * (longitude - longitude_time) + bias     # 计算真太阳时omega = (true_time / 60 - 12) * 15 / 180 * math.pi      # 计算太阳时角(弧度)latitude = latitude / 180 * math.pi                     # 纬度转换为弧度# theta为天顶角cos_theta = math.sin(delta)*math.sin(latitude) + math.cos(delta)*math.cos(latitude)*math.cos(omega)h = math.pi / 2 - math.acos(cos_theta)  # 太阳高度角# 当天顶角cos<=0时，认为无光# if cos_theta <= 0:#     G = 0if tilt != 0:tilt = tilt / 180 * math.piazimuth = azimuth / 180 * math.picos_alpha = (math.sin(h) * math.sin(latitude) - math.sin(delta)) / (math.cos(h) * math.cos(latitude))alpha = math.acos(cos_alpha)    # 计算太阳方位角# 不用sin的原因是，asin无法分辨alpha大于90°的情况# sin_alpha = -math.cos(delta) * math.sin(omega) / math.cos(h)# if sin_alpha > 1:#     sin_alpha = (math.sin(h) * math.sin(latitude) - math.sin(delta)) / (math.cos(h) * math.cos(latitude))# alpha = math.asin(sin_alpha)    # 计算太阳方位角if true_time > 60 * 12:         # 使下午的太阳方位角正常alpha = -alpha# 计算对于斜面的太阳入射角cos_i = math.cos(tilt) * math.sin(h) + math.sin(tilt) * math.cos(h) * math.cos(alpha - azimuth)G = k * G_0 * cos_ielse:G = k * G_0 * cos_thetaif G < 0:G = 0return Gdef calculate_irradiance(time_str, latitude, longitude, tilt, azimuth, longitude_time):"""从datetime类型的时间计算当前大气外理论辐照度"""cur_time = datetime.strptime(time_str, '%Y-%m-%d %H:%M:%S')day_year = int(datetime.strftime(cur_time, '%j'))   # j是积日hour = int(datetime.strftime(cur_time, "%H"))minute = int(datetime.strftime(cur_time, "%M"))minute_day = 60 * hour + minute                     # 计算当前时刻的日分钟数return calculate_irradiance_base(day_year, minute_day, latitude, longitude, tilt, azimuth, longitude_time)def dif_true_solar_time(day_year):sun_array = list(range(0, 366))# <editor-fold desc="真平太阳时差的赋值">sun_array[0] = "-3:9"sun_array[1] = "-3:38"sun_array[2] = "-4:6"sun_array[3] = "-4:33"sun_array[4] = "-5:1"sun_array[5] = "-5:27"sun_array[6] = "-5:54"sun_array[7] = "-6:20"sun_array[8] = "-6:45"sun_array[9] = "-7:10"sun_array[10] = "-7:35"sun_array[11] = "-7:59"sun_array[12] = "-8:22"sun_array[13] = "-8:45"sun_array[14] = "-9:7"sun_array[15] = "-9:28"sun_array[16] = "-9:49"sun_array[17] = "-10:9"sun_array[18] = "-10:28"sun_array[19] = "-10:47"sun_array[20] = "-11:5"sun_array[21] = "-11:22"sun_array[22] = "-11:38"sun_array[23] = "-11:54"sun_array[24] = "-12:8"sun_array[25] = "-12:22"sun_array[26] = "-12:35"sun_array[27] = "-12:59"sun_array[28] = "-13:10"sun_array[29] = "-13:19"sun_array[30] = "-13:37"sun_array[31] = "-13:44"sun_array[32] = "-13:50"sun_array[33] = "-13:56"sun_array[34] = "-14:1"sun_array[35] = "-14:5"sun_array[36] = "-14:9"sun_array[37] = "-14:11"sun_array[38] = "-14:13"sun_array[39] = "-14:14"sun_array[40] = "-14:15"sun_array[41] = "-14:14"sun_array[42] = "-14:13"sun_array[43] = "-14:11"sun_array[44] = "-14:8"sun_array[45] = "-14:5"sun_array[46] = "-14:1"sun_array[47] = "-13:56"sun_array[48] = "-13:51"sun_array[49] = "-13:44"sun_array[50] = "-13:38"sun_array[51] = "-13:30"sun_array[52] = "-13:22"sun_array[53] = "-13:13"sun_array[54] = "-11:4"sun_array[55] = "-12:54"sun_array[56] = "-12:43"sun_array[57] = "-12:32"sun_array[58] = "-12:21"sun_array[59] = "-12:8"sun_array[60] = "-11:56"sun_array[61] = "-11:43"sun_array[62] = "-11:29"sun_array[63] = "-11:15"sun_array[64] = "-11:1"sun_array[65] = "-10:47"sun_array[66] = "-10:32"sun_array[67] = "-10:16"sun_array[68] = "-10:1"sun_array[69] = "-9:45"sun_array[70] = "-9:28"sun_array[71] = "-9:12"sun_array[72] = "-8:55"sun_array[73] = "-8:38"sun_array[74] = "-8:21"sun_array[75] = "-8:4"sun_array[76] = "-7:46"sun_array[77] = "-7:29"sun_array[78] = "-7:11"sun_array[79] = "-6:53"sun_array[80] = "-6:35"sun_array[81] = "-6:17"sun_array[82] = "-5:58"sun_array[83] = "-5:40"sun_array[84] = "-5:22"sun_array[85] = "-5:4"sun_array[86] = "-4:45"sun_array[87] = "-4:27"sun_array[88] = "-4:9"sun_array[89] = "-3:51"sun_array[90] = "-3:33"sun_array[91] = "-3:16"sun_array[92] = "-2:58"sun_array[93] = "-2:41"sun_array[94] = "-2:24"sun_array[95] = "-2:7"sun_array[96] = "-1:50"sun_array[97] = "-1:33"sun_array[98] = "-1:17"sun_array[99] = "-1:1"sun_array[100] = "0:46"sun_array[101] = "0:30"sun_array[102] = "0:16"sun_array[103] = "0:1"sun_array[104] = "0:13"sun_array[105] = "0:27"sun_array[106] = "0:41"sun_array[107] = "0:54"sun_array[108] = "1:6"sun_array[109] = "1:19"sun_array[110] = "1:31"sun_array[111] = "1:42"sun_array[112] = "1:53"sun_array[113] = "2:4"sun_array[114] = "2:14"sun_array[115] = "2:23"sun_array[116] = "2:33"sun_array[117] = "2:41"sun_array[118] = "2:49"sun_array[119] = "2:57"sun_array[120] = "3:4"sun_array[121] = "1:10"sun_array[122] = "3:16"sun_array[123] = "3:21"sun_array[124] = "3:26"sun_array[125] = "3:30"sun_array[126] = "3:37"sun_array[127] = "3:36"sun_array[128] = "3:39"sun_array[129] = "3:40"sun_array[130] = "3:42"sun_array[131] = "3:42"sun_array[132] = "3:42"sun_array[133] = "3:42"sun_array[134] = "3:41"sun_array[135] = "3:39"sun_array[136] = "3:37"sun_array[137] = "3:34"sun_array[138] = "3:31"sun_array[139] = "3:27"sun_array[140] = "3:23"sun_array[141] = "3:18"sun_array[142] = "3:13"sun_array[143] = "3:7"sun_array[144] = "3:1"sun_array[145] = "2:54"sun_array[146] = "2:47"sun_array[147] = "2:39"sun_array[148] = "2:31"sun_array[149] = "2:22"sun_array[150] = "2:13"sun_array[151] = "2:4"sun_array[152] = "1:54"sun_array[153] = "1:44"sun_array[154] = "1:34"sun_array[155] = "1:23"sun_array[156] = "1:12"sun_array[157] = "1:0"sun_array[158] = "0:48"sun_array[159] = "0:36"sun_array[160] = "0:24"sun_array[161] = "0:12"sun_array[162] = "0:1"sun_array[163] = "0:14"sun_array[164] = "0:39"sun_array[165] = "0:52"sun_array[166] = "1:5"sun_array[167] = "1:18"sun_array[168] = "1:31"sun_array[169] = "1:45"sun_array[170] = "1:57"sun_array[171] = "2:10"sun_array[172] = "2:23"sun_array[173] = "2:36"sun_array[174] = "2:48"sun_array[175] = "3:1"sun_array[176] = "3:13"sun_array[177] = "3:25"sun_array[178] = "3:37"sun_array[179] = "3:49"sun_array[180] = "4:0"sun_array[181] = "4:11"sun_array[182] = "4:22"sun_array[183] = "4:33"sun_array[184] = "4:43"sun_array[185] = "4:53"sun_array[186] = "5:2"sun_array[187] = "5:11"sun_array[188] = "5:20"sun_array[189] = "5:28"sun_array[190] = "5:36"sun_array[191] = "5:43"sun_array[192] = "5:50"sun_array[193] = "5:56"sun_array[194] = "6:2"sun_array[195] = "6:8"sun_array[196] = "6:12"sun_array[197] = "6:16"sun_array[198] = "6:20"sun_array[199] = "6:23"sun_array[200] = "6:25"sun_array[201] = "6:27"sun_array[202] = "6:29"sun_array[203] = "6:29"sun_array[204] = "6:29"sun_array[205] = "6:29"sun_array[206] = "6:28"sun_array[207] = "6:26"sun_array[208] = "6:24"sun_array[209] = "6:21"sun_array[210] = "6:17"sun_array[211] = "6:13"sun_array[212] = "6:8"sun_array[213] = "6:3"sun_array[214] = "5:57"sun_array[215] = "5:51"sun_array[216] = "5:44"sun_array[217] = "5:36"sun_array[218] = "5:28"sun_array[219] = "5:19"sun_array[220] = "5:10"sun_array[221] = "5:0"sun_array[222] = "4:50"sun_array[223] = "4:39"sun_array[224] = "4:27"sun_array[225] = "4:15"sun_array[226] = "4:2"sun_array[227] = "3:49"sun_array[228] = "3:36"sun_array[229] = "3:21"sun_array[230] = "3:7"sun_array[231] = "2:51"sun_array[232] = "2:36"sun_array[233] = "2:20"sun_array[234] = "2:3"sun_array[235] = "1:47"sun_array[236] = "1:29"sun_array[237] = "1:12"sun_array[238] = "0:54"sun_array[239] = "0:35"sun_array[240] = "0:17"sun_array[241] = "0:2"sun_array[242] = "0:21"sun_array[243] = "0:41"sun_array[244] = "1:0"sun_array[245] = "1:20"sun_array[246] = "1:40"sun_array[247] = "2:1"sun_array[248] = "2:21"sun_array[249] = "2:42"sun_array[250] = "3:3"sun_array[251] = "3:3"sun_array[252] = "3:24"sun_array[253] = "3:45"sun_array[254] = "4:6"sun_array[255] = "4:27"sun_array[256] = "4:48"sun_array[257] = "5:10"sun_array[258] = "5:31"sun_array[259] = "5:53"sun_array[260] = "6:14"sun_array[261] = "6:35"sun_array[262] = "6:57"sun_array[263] = "7:18"sun_array[264] = "7:39"sun_array[265] = "8:0"sun_array[266] = "8:21"sun_array[267] = "8:42"sun_array[268] = "9:2"sun_array[269] = "9:22"sun_array[270] = "9:42"sun_array[271] = "10:2"sun_array[272] = "10:21"sun_array[273] = "10:40"sun_array[274] = "+10:59"sun_array[275] = "+11:18"sun_array[276] = "+11:36"sun_array[277] = "+11:36"sun_array[278] = "+11:53"sun_array[279] = "+12:11"sun_array[280] = "+12:28"sun_array[281] = "+12:44"sun_array[282] = "+12:60"sun_array[283] = "+13:16"sun_array[284] = "+13:16"sun_array[285] = "+13:31"sun_array[286] = "+13:45"sun_array[287] = "+13:59"sun_array[288] = "+14:13"sun_array[289] = "+14:26"sun_array[290] = "+14:38"sun_array[291] = "+14:50"sun_array[292] = "+15:1"sun_array[293] = "+15:12"sun_array[294] = "+11:21"sun_array[295] = "+15:31"sun_array[296] = "+15:40"sun_array[297] = "+15:48"sun_array[298] = "+15:55"sun_array[299] = "+16:1"sun_array[300] = "+16:7"sun_array[301] = "+16:12"sun_array[302] = "+16:16"sun_array[303] = "+16:20"sun_array[304] = "+16:22"sun_array[305] = "+16:24"sun_array[306] = "+16:25"sun_array[307] = "+16:25"sun_array[308] = "+16:24"sun_array[309] = "+16:23"sun_array[310] = "+16:21"sun_array[311] = "+16:17"sun_array[312] = "+16:13"sun_array[313] = "+16:9"sun_array[314] = "+16:3"sun_array[315] = "+15:56"sun_array[316] = "+15:49"sun_array[317] = "+15:41"sun_array[318] = "+15:32"sun_array[319] = "+15:22"sun_array[320] = "+15:11"sun_array[321] = "+14:60"sun_array[322] = "+14:47"sun_array[323] = "+14:34"sun_array[324] = "+14:20"sun_array[325] = "+14:6"sun_array[326] = "+13:50"sun_array[327] = "+13:34"sun_array[328] = "+13:17"sun_array[329] = "+12:59"sun_array[330] = "+12:40"sun_array[331] = "+12:21"sun_array[332] = "+12:1"sun_array[333] = "+11:40"sun_array[334] = "+11:18"sun_array[335] = "+10:56"sun_array[336] = "+10:33"sun_array[337] = "+10:9"sun_array[338] = "+9:45"sun_array[339] = "+9:21"sun_array[340] = "+8:55"sun_array[341] = "+8:29"sun_array[342] = "+8:3"sun_array[343] = "+7:36"sun_array[344] = "+7:9"sun_array[345] = "+6:42"sun_array[346] = "+6:14"sun_array[347] = "+5:46"sun_array[348] = "+5:17"sun_array[349] = "+4:48"sun_array[350] = "+4:19"sun_array[351] = "+3:50"sun_array[352] = "+3:21"sun_array[353] = "+2:51"sun_array[354] = "+2:22"sun_array[355] = "+1:52"sun_array[356] = "+1:22"sun_array[357] = "+0:52"sun_array[358] = "+0:23"sun_array[359] = "+0:7"sun_array[360] = "+0:37"sun_array[361] = "-1:6"sun_array[362] = "-1:36"sun_array[363] = "-2:5"sun_array[364] = "-2:34"sun_array[365] = "-3:3"# </editor-fold>return sun_array[day_year - 1]# # 函数测试
# # Latitude 39.1319° [°N], Longitude -77.2141° [°E], Elevation 138 m [m])
tilt = 20pd_data = pd.DataFrame(np.arange(1, 60*24+1, 30), columns=['minute_day'])
pd_data['day_year'] = 142
pd_data['G'] = pd_data.apply(lambda x: calculate_irradiance_base(int(x['day_year']), x['minute_day'], 40, 110, 0, 0, 120), axis=1)
pd_data['tilt_G'] = pd_data.apply(lambda x: calculate_irradiance_base(int(x['day_year']), x['minute_day'], 40, 110, tilt, 0, 120), axis=1)print(pd_data)time_str = '2008-06-23 14:35:22'
G = calculate_irradiance(time_str, 30, 122, tilt, 0, 120)
print(G)[time_sun, minute_sun_up, minute_sun_down] = calculate_sun_time(time_str, 30, 122, tilt, 0, 120)
print(G)

参考：
[1] https://wenku.baidu.com/view/0989752c3169a4517723a3d8.html
[2] https://www.pveducation.org/zh-hans/pvcdrom/%E4%BB%BB%E6%84%8F%E6%9C%9D%E5%90%91%E5%92%8C%E5%80%BE%E6%96%9C%E5%BA%A6
[3] 王飞, 并网型光伏电站发电功率预测方法与系统, 2013, 华北电力大学.

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地外水平/斜面的太阳理论辐照度计算及其python实现

地外水平/斜面的太阳理论辐照度计算及其python实现

引入

水平理论辐照度

任意斜面的太阳辐照度

代码

地外水平/斜面的太阳理论辐照度计算及其python实现相关推荐

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