## Step by step explanation

By calculating the free energy that each collector can contribute and by taking the cost of installing each additional collector into account, it is possible to make an accurate calculation of the exact number of collectors that makes the Optimum solar system economic. In this way it quickly becomes obvious that the traditional technical limit represented by collector area (linked to overheating problems experienced by conventional "pressurized" systems) needs to be exceeded for the system to be more economical and generate additional savings.

Using powerful simulation tools and data from each project, it is possible to determine with accuracy the amount of energy that will be produced by a given solar thermal system. In order to analyze the optimum surface to install as accurately as possible, we carry out numerous simulations. The results are then analyzed.

The more Sunoptimo solar thermal collectors installed, the more annual energy requirements for water heating are covered. It can be seen, however, that the curve reaches a ceiling at a given moment. The additional m² added to a small area of solar thermal collectors covers a greater portion of the energy required than the same additional area added to a solar thermal collector surface area that is already larger. The first 10 m² covers 5% of energy needs while 10 m² above 300 m² will only supply an additional 2 to 3%.

Let's look at the impact of the choice of solar thermal collector area from another angle: the supplementary energy still necessary (energy the solar system cannot provide) over a certain period of analysis. The more Sunoptimo solar thermal collectors installed, the more the total cost of the supplementary energy still necessary will decrease. In the same way that the solar fraction reaches a ceiling, the reduction in the cost of the supplementary energy will reach a floor.

Adding the net cost of the solar installation (depending on the surface area installed) to the cost of the supplementary energy still necessary (solid green curve), we have a curve (green dotted line) that represents the total cost of heating water for a given period of analysis.

It should be noted that this curve descends very sharply at the beginning, then reduces less and less to flatten out and finally ends up by rising slightly. This therefore means that to start with, each additional m² of solar thermal collector generates very great savings, then less and less, and finally, after a long "flat spot", extra cost.

To better understand this curve representing the total cost of water heating, here is another graph where the whole green zone corresponding to the cost of the supplementary energy still required, and in yellow, the additional cost linked to the Sunoptimo solar thermal system can easily be seen. The whole therefore forms the total cost of water heating over the period analyzed.

By comparing this with the cost represented by water heating without the Sunoptimo solar system (dark dotted line), the savings that can be made can be calculated easily: the difference between the total cost without the Sunoptimo solar thermal system and the total cost of water heating with a Sunoptimo solar thermal system. The dark blue dot corresponds to the surface area of Sunoptimo solar thermal collectors needed to generate the maximum savings.

### Conclusion

By studying this curve, we can draw several lessons:

- It is very cost-effective to install a Sunoptimo solar thermal system. It will allow you to generate big savings.
- The flat part of the curve shows that the total cost of water heating remains relatively "identical" for a wide variation in area of Sunoptimo solar thermal collectors. In our example, between 250 m² and 450 m², the total cost of water heating is almost the same.
- It is preferable to be too far to the right of the curve than too far to the left. Therefore, to have installed too many collectors rather than not enough. In our example, installing 50 m² (too far to the left) instead of 500 m² (too far to the right), means an additional cost of almost €185,000!
- As so-called conventional "pressurized" systems are limited technically by overheating problems, sizing does not allow you to generate the savings that can be generated by Sunoptimo solar systems.

Got a solar thermal project in mind?