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Revision 974 - (show annotations) (download) (as text)
Tue Dec 19 11:00:57 2006 UTC (13 years, 7 months ago) by johnpye
File MIME type: text/x-ascend
File size: 7453 byte(s)
Fixed 'testcmslv2' test case.
Fixed 'sunpos5' test case.
One can now type 'python test.py TestSolver' and all current tests pass.
1 REQUIRE "atoms.a4l";
2
3 (*
4 Using the equations given in Duffie & Beckman (1980)
5 the following model allows calculation of the angle of incidence of
6 sunlight onto an inclined surface
7
8 The equation of time has been changes to the Duffie & Beckman 2nd edition
9 form, cited as coming from Iqbal 1983. The equation for 'B' has also
10 been changed to the 2nd Ed D&B form.
11
12 For the longitude correction we use the spherical geometry convention
13 of making east positive. D&B are americocentric, obviously :-)
14
15 by John Pye, 2006
16 *)
17 MODEL sunpos;
18 t IS_A time; (* starting at zero at midnight on 1 Jan *)
19
20 L_st IS_A angle; (* standard meridian for the current time zone *)
21 L_loc IS_A angle; (* local longitude *)
22 phi IS_A angle; (* latitude, north positive *)
23
24 E IS_A time; (* 'Equation of time' correction *)
25 E = 229.2{min}*(0.000075 + 0.001868*cos(B) - 0.032077*sin(B)
26 - 0.014615*cos(2*B) - 0.04089*sin(2*B) );
27 (* where *) B IS_A angle;
28 B = t*360{deg}/365{day};
29
30 t_solar IS_A time; (* solar time *)
31 t_solar = t - 4{min/deg}*(L_st - L_loc) + E;
32 t_long IS_A time;
33 t_long = 4{min/deg}*(L_st - L_loc);
34 t_corr IS_A time;
35 t_corr = E - t_long;
36
37 delta IS_A angle; (* solar declination *)
38 delta = 23.45{deg}*sin(360{deg}*(285{day}+t)/(365{day}));
39
40 theta IS_A angle; (* angle of incidence of sun onto inclined surface *)
41 omega IS_A angle; (* hour angle, noon=0, afternoon positive *)
42 gamma IS_A angle; (* surface azimuth angle, south=0, west positive *)
43 beta IS_A angle; (* surface inclination, horiz=0, +90deg=vertical *)
44
45 omega = (t_solar - 12{h})*(360{deg}/1{d});
46 omega_RHP IS_A angle;
47 omega_RHP = arccos(cos(omega));
48
49 omega_s IS_A angle;
50 omega_s = arccos( - tan(phi)*tan(delta) );
51
52 theta = arccos(
53 sin(delta)*sin(phi)*cos(beta) - sin(delta)*cos(phi)*sin(beta)*cos(gamma)
54 + cos(delta)*cos(phi)*cos(beta)*cos(omega)
55 + cos(delta)*sin(phi)*sin(beta)*cos(gamma)*cos(omega)
56 + cos(delta)*sin(beta)*sin(gamma)*sin(omega)
57 );
58
59 theta_z IS_A angle; (* zenith angle of the sun *)
60 theta_z = arccos(
61 cos(delta)*cos(phi)*cos(omega) + sin(delta)*sin(phi)
62 );
63
64 costheta IS_A factor;
65 costheta = cos(theta);
66 costhetaz IS_A factor;
67 costhetaz = cos(theta_z);
68
69 Gsc IS_A real_constant; (* solar constant *)
70 Gsc :== 1353 {W/m^2};
71
72 (* extraterrestrial irradiance on a normal surface*)
73 Gon IS_A irradiance;
74 Gon = Gsc*(1 + 0.033*cos(
75 300{deg}/365{day}*(1{day}+t))
76 );
77
78 R_b IS_A factor; (* ratio of beam radiation, inclined : horizontal *)
79 R_b = cos(theta) / cos(theta_z);
80
81 METHODS
82 METHOD default_self;
83 t := 0{day};
84 L_st := -120{deg}; (* USA Pacific time *)
85 L_loc := -(116{deg}+47{arcmin}); (* Daggett, California, home of SEGS *)
86 END default_self;
87 METHOD on_load;
88 RUN default_self;
89 RUN reset;
90 RUN values;
91 END on_load;
92 METHOD specify;
93 FIX t, L_st, L_loc, phi; (* time and location *)
94 FIX beta, gamma; (* surface orientation *)
95 END specify;
96 METHOD values;
97 (* values for Duffie & Beckman examples 1.5.1 ff *)
98 L_st := -90{deg}; (* USA Central time*)
99 L_loc := -89.4{deg};
100 phi := +43{deg};
101 (* t := 32.4375 {d}; *)
102 t := 32{d} + 10{h}+30{min};
103
104 (* surface orientation *)
105 beta := 45{deg};
106 gamma := 15{deg};
107
108 END values;
109 END sunpos;
110
111 (*
112 Total daily extraterrestrial radiation, from sunrise to sunset.
113
114 Set 't' to the start of the day in question.
115 *)
116 MODEL dailyextraterrestrial REFINES sunpos;
117 (* extraterrestrial irradiance on a horizontal surface -- problems coz it goes negative! *)
118 (* Go IS_A irradiance;
119 Go = Gsc*(1 + 0.033*cos( 300{deg}/365{day}*(1{day}+t)) )*cos(theta_z); *)
120
121 (* day's-total extraterrestrial radiation on a horizontal surface *)
122 Ho IS_A irradiation;
123 Ho = 1{d}*Gon*(
124 1/1{PI} * (cos(phi)*cos(delta)*sin(omega_s) + omega_s*sin(phi)*sin(delta))
125 );
126 END dailyextraterrestrial;
127
128 (*------------------------------------------------------------------------------
129 EXAMPLES
130
131 The following examples come from chapter one of Duffie and Beckman (1980)
132 *)
133
134 (*
135 For Madison (Wisconsin), calculate the angle of incidence of beam radiation
136 on a surface at 10:30 AM solar time on February 13, if the surface is
137 tilted 45 from the horizontal and pointed 15 degrees west of south.
138
139 checked, this looks OK -- JP
140 *)
141 MODEL example_1_6_1 REFINES sunpos;
142 METHODS
143 METHOD specify;
144 RUN sunpos::specify;
145 FREE t;
146 FIX t_solar;
147 END specify;
148 METHOD values;
149 RUN sunpos::values;
150 t_solar := 43{d} + 10{h} + 30{min};
151 beta := 45 {deg};
152 gamma := 15 {deg};
153 L_st := -90{deg}; (* USA Central time*)
154 L_loc := -89.4{deg};
155 phi := +43{deg};
156 END values;
157 METHOD self_test;
158 ASSERT abs(theta-35.0{deg}) < 0.15{deg};
159 ASSERT abs(delta-(-13.80{deg})) < 0.02{deg};
160 END self_test;
161 END example_1_6_1;
162
163 (*
164 Calculate the zenith angle of the sun at 9:30 AM solar time in Madison on
165 Feb 13.
166
167 checked, this looks OK -- JP
168 *)
169 MODEL example_1_6_2 REFINES sunpos;
170 METHODS
171 METHOD specify;
172 RUN sunpos::specify;
173 FREE t;
174 FIX t_solar;
175 END specify;
176 METHOD values;
177 RUN sunpos::values;
178 t_solar := 43{d} + 9{h} + 30{min};
179 L_st := -90{deg}; (* USA Central time*)
180 L_loc := -89.4{deg};
181 phi := +43{deg};
182 END values;
183 METHOD self_test;
184 ASSERT abs(theta_z-66.0{deg}) < 0.4{deg};
185 END self_test;
186 END example_1_6_2;
187
188 (*
189 What is the ratio of beam radiiation for the surface and time specified in
190 Example 1.6.1 to that on a horizontal surface?
191
192 checked, this looks OK -- JP
193 *)
194 MODEL example_1_7_1 REFINES example_1_6_1;
195 METHODS
196 METHOD self_test;
197 ASSERT abs(R_b-1.6577) < 0.013;
198 END self_test;
199 END example_1_7_1;
200
201 (*
202 Calculate Rb for a surface at latitude 40 N, at a tilt 30 degrees toward
203 the south, for the hour 9 to 10 (solar time) on Feb 16.
204
205 checked, this looks OK -- JP
206 *)
207 MODEL example_1_7_2 REFINES example_1_6_1;
208 METHODS
209 METHOD values;
210 phi := 40{deg};
211 beta := 30{deg};
212 gamma := 0{deg};
213 t_solar := 46{d} + 9.5{h};
214 END values;
215 METHOD self_test;
216 ASSERT abs(delta - (-13{deg})) < 0.5{deg};
217 ASSERT abs(R_b-1.61) < 0.005;
218 END self_test;
219 END example_1_7_2;
220
221 (*
222 As for Example 1.7.2, but with a surface inclined at 50 degrees
223
224 checked, this looks OK
225 *)
226 MODEL example_1_7_3 REFINES example_1_7_2;
227 METHODS
228 METHOD values;
229 RUN example_1_7_2::values;
230 beta := 50{deg};
231 END values;
232 METHOD self_test;
233 ASSERT abs(delta - (-13{deg})) < 0.5{deg};
234 ASSERT abs(R_b-1.80) < 0.05;
235 END self_test;
236 END example_1_7_3;
237
238 (* checked, looks OK (although the error in Ho is a little high) *)
239 MODEL example_1_8_1 REFINES dailyextraterrestrial;
240 METHODS
241 METHOD values;
242 phi := 43{deg};
243 t := 104{d};
244 END values;
245 METHOD self_test;
246 ASSERT abs(omega_s - 98.9{deg}) < 0.05 {deg};
247 ASSERT abs(Ho - 33.4{MJ/m^2}) < 0.4{MJ/m^2};
248 END self_test;
249 END dailyextraterrestrial;
250
251 (*
252 NOTE
253 although these calcs are very useful, we are now starting to see why it
254 might be a good idea to do them outside ASCEND in an external library.
255
256 The reason is that when integrating around the clock, some of these
257 functions go unphysically negative, eg radiation on a horizontal surface.
258 Using external functions we can easily apply such constraints without
259 even necessarily needing to cause nonsmoothness in the 'G' values.
260
261 Another reason is that using the sun position calculations enable smarter
262 time-wise interpolation of TMY data, preventing non-physical situations
263 from arising, eg sun after sunset.
264
265 --
266
267 REFERENCES
268
269 Duffie & Beckman (1980) Solar Engineering of Thermal Processes,
270 1st ed., Wiley
271
272 Duffie & Beckman (1991) Solar Engineering of Thermal Processes,
273 2nd ed., Wiley
274
275 Iqbal (1983) An Introduction to Solar Radiation, Academic Press, Toronto.
276 *)

john.pye@anu.edu.au
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