In each solar energy system, there are supply and demand of energy, which, ideally, should be matched. The supply of solar energy depends on the available solar resource, the technology to convert solar radiation to the usable heat, losses, properties of materials, and system design. The energy demand depends on applications connected to the collectors - let it be water stoarge tank to be heated for domestic or industrial use, a space, a swimming pool, etc. Both supply and demand are time dependent. It is understandable that the solar energy varies on the daily basis, usually peaking during the day and diminishing over the night. The use of available energy also varies over time based on human activities or technical processes involved in the system. Here we use the term "*load*" to define a time-dependent energy need. Load is the amount of energy obtained from the source to do the work.

In a certain system, we can have a solar collector and another system - the *auxiliary* - to meet energy demand requirements. The solar system alone is not sometimes sufficient and requires such a backup to make sure the application in use does not run out of energy. The auxiliary can be represented by an on-site natural gas combustion system or grid, for example. Then the system load can be represented as:

*L = L _{s} + L_{a}*

with subscripts *s* and *a* standing for solar and auxiliary, respectively.

It is also useful to define the load rates (e.i. demanded power). The load rate is

*L' = dL/dt*

Note L' (rate) is denoted in the D&B book as L with a dot. Load rates are useful because the load are highly variable, and we may see times when the demands are met by solar energy and times when theya are met by auxiliar energy. The one important purpose of system modeling is to determine the hour-by-hour energy performance of the system, match it with loads, and decide how much auxiliary energy must be secured or purchased.

Here we can also define heating and cooling loads. Those depend on system thermal requirements. For example, if a building is too cold and requires some heating to meet a certain standard, then we deal with a *heating load*. On the contrary, if the building is too warm, due to internal gains and losses, then we deal with a *cooling load, *in other words we need to remove energy from the space.

How can loads be estimated?

Please refer to the following reading to understand what heat gains and losses should be taken into account and what equations can be used.

#### Reading assignment

Book chapter: Duffie, J.A. Beckman, W., *Solar Engineering of Thermal Processes*, Chapter 9.

This text explains more detail about the hot-water loads, space-heating and cooling loads. Also you will be introduced to such terms as degree-days, balance temperature, building loss coefficient, and building energy storage capacity.

One commonly used method for calculating the heating and cooling requirements of a building is to calculate degree days (DD) as discussed in Section 9.3 of the D&B textbook. The rate of energy transfer from the building to the exterior environment makes up a significant piece of the energy balance calculation. This rate of energy transfer is considered to be directly proportional to degree days. The following video (3:36) provides a brief explanation on the calculation of degree days, showing how the number of degree days is directly calculated by a difference in temperature over a period of time.

OK, so this is a much shorter video than the last one, based on it example 9.3.1, which focuses on heating degree days. I just want to chat a bit about heating degree days, do one simple calculation, and talk about some of meaning behind it. So in this example, we're given a base temperature of 18 degrees Celsius and we're in Madison, Wisconsin. The example goes into much more detail on calculating heating degree days for different months, but at the real basic level we're going to calculate just December's here. Heating degree days are calculated simply by the number of days in the month and the base temperature and the month's ambient average temperatures, so t ambient bar is t average for the month. So for December, there's 31 days in the month, the base temperature's 18, and this is given a negative 5. It's pretty cold in Wisconsin. So what we end up with is 31 times 23.3, which is 722 heating degree days. So it's pretty high number. And again, I just want to chat a bit about what this means and why it's important. And essentially this number gives you an idea for how often you are far away from the reasonable temperature for your indoor space. So if it's really cold, then you'll get a high number, and that means you need to be heating a lot. Whereas, if your ambient temperature is close in temperature, if t ambient was 18 degrees right here, if this was 18 you get zero. Once you'd have zero. You would end up with zero degree days. So that means you don't need any heating that month if your month's average temperature was 18 degrees Celsius. So that's really the essence of what heating degree days are. And then in the summer months when you need cooling it goes the other way around where then you would end up with some degree days. If you're in a location that required cooling and they would be cooling degree days. So if your t ambient was very hot, then you would end up with a different number there as well. So again, that these numbers are used essentially to calculate overall heating cooling loads and how much a specific location would need in light of the ambient temperature. All right, thanks for listening.