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14 декабря, 2021
The described sensitivity analysis methods are implemented into the Genopt (Generic optimization program) [4] and coupled with the simulation program TRNSYS. For the first system, the influence of 16 parameters on the target function, describing the overall cost of the system in ct/kWhsolar, was investigated by the Morris method. Results of the analysis are presented in the Table 1.
Table 1. Ranking of the parameters by their influence on the cost target function by the Moris method. The
value of the mean /и estimates the overall influence of the parameter and the deviation a shows its non-linear
effect.
N |
Parameter |
Variation range |
и |
5 |
|
1 |
^dis, max |
Max. discharge spec. volume flow |
[10; 15] in L/m2h |
4.54 |
7.44 |
2 |
vsol, p |
Specific volume flow |
[6; 10] in L/m2h |
2.29 |
2.92 |
3 |
Dvive |
Pipe deameter |
[20; 30] in mm |
1.85 |
4.75 |
4 |
Vstore |
Volume of solar storage |
[4000; 8000] in Liter |
0.46 |
0.58 |
5 |
Aon |
Collector slope |
[30; 46] in o |
0.70 |
0.51 |
6 |
^Thyst |
Hyst. for contr. pump in sec. circ |
[1; 7] in K |
0.41 |
0.29 |
7 |
Hch1 |
Rel. pos. of inlet 1 |
[0.6; 1] |
0.30 |
0.77 |
8 |
Hch2 |
Rel. pos. of inlet 2 |
[0.1; 0.6] |
0.24 |
0.21 |
9 |
Sh1 |
Rel. pos. of temp. sensor 1 |
[0.1; 0.5] |
0.23 |
0.41 |
10 |
ATU |
Temp. diff. to switch off the pump |
[0; 7] in K |
0.16 |
0.23 |
11 |
Sh2 |
Rel. pos. of temp. sensor 2 |
[0.55; 0.75] |
0.18 |
0.26 |
12 |
UAshe |
UA value of the sol. heat exch. |
[70; 130] in W/m2K |
0.08 |
0.09 |
13 |
У coll |
Scaling factor |
[-5; 6] in o |
0.03 |
0.02 |
14 |
Ghyst |
Hyst. for contr. pump in sol. circ. |
[2; 50] in W/m2 |
0.02 |
0.02 |
15 |
Amin |
Switch-off threshold for pump |
[40; 200] in W/m2 |
0.01 |
0.02 |
16 |
Sh3 |
Rel. pos. of temp. sensor 3 |
[0.8; 1] |
0.00 |
0.00 |
In Fig. 3 the mean и of the distribution G; versus the standard deviation a of the distribution F is given. The larger the value of the mean и. the larger the overall influence of the parameter. Large values of the standard deviation a mean strong non-linear effect of the parameter or its interaction with other parameters. It is seen that parameters 1-3 (the maximal power of two pumps in charging and discharging circuits and the diameter of pipes) are the most important and influence the target function both linearly and non-linearly. Parameters 4-7 could be considered as average important and the other 9 parameters as not important.
The second system has been investigated with the FAST. The target function is chosen as the fractional thermal energy savings :
Table 2 shows the main effects on /avthenn of six parameters that were chosen by hand. The parameters have been changed in the given ranges. As the first test shows. the most influential parameter is the collector area (around 80% of all variation of /savtherm). In tests 2-4 the collector area is fixed at corresponding values and the importance of the other parameters is investigated. It is seen that the influence of the store volume and the mass flow grows with increasing the collector area.
Sensitivity indices (main effect)
|
The sensitivity analysis methods applied to the solar heating systems show that only some parameters have significant influence on the corresponding target functions. If the target function depends on many system parameters and only the most influential parameters should be identified then it seems to be computationally more efficient first to apply the Morris method and then the FAST algorithm.
Nomenclature
|
a — deviation of the distribution F
wi — Angular frequency
[1] A. Saltelli. S. Tarantola. K. Chan. Technometrics. 41(1) (1999). 39-56
[2] A. Saltelli. S. Tarantola. F. Campolongo. M. Ratto. (2004). Sensitivity Analysis in Practice. A Guide to Assessing Scientific Models. John Wiley & Sons publishers
[3] M. Krause. K. Vajen. F. Wiese. H. Ackermann. Solar Energy 73 (4) (2003). 217-225
[4] GenOpt. Generic Optimization Program. http://gundog. lbl. gov/GO/