Analysis Approach

The purpose of the performance analysis is two-fold:

• to establish and optimize the performance of the solar heating system,

• to test the MINSUN program in its present form, for as far as the system simulation and optimization are concerned.

The performance analysis carried out has been as follows:

First, via best guess and trial and error methods a so-called "Base case" system has been identified. This is the system previously described in the first and second sections above.

After a careful examination of the results with the help of the daily time profiles, the variables for a sensitivity analysis were chosen.

The chosen variables are:

• Collector surface

• Storage volume

• Duct density

• Duct diameter

• Thickness of insulation layer on top of the storage

The performance indicators chosen for this analysis are:

• Total annual costs per MWh

• Solar fraction

• C. O.P. of the heatpump

• Maximum and minimum storage temperature

Since for reasons explained in the third section above, the graph option and optimizer could not be used, the analysis has been done point for point. That is, starting from the base case, for each run, one variable was changed in value and the others were kept as in the base case.

In Table 1 the variables and their values are listed.

TABLE 1 SYSTEM PARAMETERS USED FOR OPTIMIZATION coll. surf. stor. vol. duct den. duct diam insulation 3,000 30,000 1.0 0.01 2.0 5,000 40,000 .75 .02 1.5 ************************************************************** BASE CASE; 7,000 50,000 .5 .05 1.0 ************************** ************ ************ ************ 9,000 70,000 .3 .1 .5 11,000 90,000 .25 .25 12,000 _ .20 _ 15,000 _ .1 — —

The cost parameters were kept constant.

Results

The results of this sensitivity analysis are given in Figures 2 to 6.

From Figure 2 it can be seen that there is a minimum in the cost curve, but not very sharp. However the collector surface chosen for the reference case is too small*

The storage volume shows a very flat minimum in the cost curve, around the 40,000 m3 (Figure 3).

Remarkable is the sharp minimum found in Figure 4, which shows the influence of the tube density on the system performance.

In Figure 5, the system cost curve is given for different duct diameters. The cost per duct, was kept constant, which is not the case in a real situation. In reality it might be that the costs decreases with decreasing tube diameter, since the costs per borehole will decrease.

However Figure 5 shows that the system performance is rather insensitive to the borehole diameter, when the diameter is more than.025 m.

The influence of the thickness of the insulation layer is given in Figure 6. As could be expected for a low temperature storage which is located about 2 m under the ground surface, the insulation thickness has little effect.

Using these figures a new reference case has been defined which gives better results then the previous one. The results are given in Table 2.

One could again do a sensitivity analysis, using this case as reference case. This has not been done here, for reasons of time.

TABLE 2 IMPROVED REFERENCE CASE Collector surface 10,000 m2 Storage volume 90,000 m3 Duct density .25 duct/m3 Duct diameter .05 m Insulation . 1 m Solar fraction 63 % Annual syst. costs 71.80 US$/MWh Max store temp. 52 °С Min store temp. 10 °С C. O.P. heatpump 3.8

In order to compare the costs of the solar system with the costs of a traditional system, a run was made with 10 m2 of solar collectors and 10 m3 of storage. These were the smallest values the program could deal with.

The annual costs for auxiliary energy were found to be 65.49 US$/MWh. Which is about 10% less than the costs of the solar system. The solar fraction was zero.