The real-life solar energy systems are composed of a number of different components and units. Each of those components has specifics that require certain theoretical background and consideration. Several previous lessons introduced some theory behind those component models - heat transfer from the Sun to the collector; heat transfer from the collector to thermal fluid; concentration of solar radiation on optical devices, etc. While the basic calculations performed for those components can answer questions about what energy parameters can be output and what efficiency can be expected from each part of the system, the question still remains how those component models can be combined into a system model, that would allow optimization of the performance for a target application.

Overview of those component models is given in the first part of Chapter 10 if the D&B book. In these sections we can also read about the role of the **heat exchangers**, which provide interface between different components and allowheat transfer from one part of the system to another. Figure 10.2.1 from the D&B textbook shows a typical solar water heating system, containing a collector, heat exchanger, storage tank, pipes, and pumps. Throughout the system diagram, temperatures are noted. It is by these temperatures that the system component efficiencies can be calculated and subsequently integrated to find overall efficiency.

**Reading assignment**

Book chapter: Duffie, J.A. Beckman, W., *Solar Engineering of Thermal Processes*, Chapter 10, Sections 10.1-10.3.

These sections discuss the key parameters responsible for heat exchange between the system components. You can also quickly scan through Sections 10.4-10.8 to be aware of various conditional adjustments to component models.

"System models are assemblies of appropriate component models." When you put together the equations decribing each of the components into the system model, the simultaneous solving of all those equations may be a serious challenge. Sometimes it is advantageous to treat the systems of equations numerically, especially if some of them are non-linear. A number of computer simulation software have been developed to help with this task. Commonly, models cover annual cycle of system operation based on available meteorological data.

Thermal analysis performed for the whole system over significant period of time provide valuable information for assessing the economics of the project. There are a couple of useful parameters that we need to introduce here. The first one - **solar fraction ( f) **is the ratio of the solar energy obtained by the system to the total load:

*f _{i} = L_{S,i }/L_{i}*

where *L _{s}* is the amount of solar energy used in the load, and

*L*is the total load per unit of time.

_{i}Or in integrated form (over a year), the same concept will be expressed as annual solar fraction (*F*):

*F = L _{S}/L*

The second parameter useful from economical standpoint is **solar savings fraction ( F_{sav})**. It accounts for energy expenditures needed to run the solar system equipment (pumps, fans, controllers..) - so call "parasitic energy".

*F _{sav }= F - (C_{ef}ΔE)/L*

where *C _{ef}* is the ratio of cost of additional electricity for solar system operation to the cost of fuel;

*ΔE*is the amount of required "parasitic" electric energy. Read more about these metrics in the following source:

**Reading assignment**

Book chapter: Duffie, J.A. Beckman, W., *Solar Engineering of Thermal Processes*, Chapter 10, Sections 10.9-10.11.

In this lesson activity you will be asked to estimate these factors for an example solar water heating system using SAM modeling.

Equilibrium and steady state are two very different thermal states, but both provide a way to analyze the thermal status of a system. Recall that an object in outer space absorbing solar radiation could be analyzed at thermal equilibrium to calculate the temperature of the object in light of the radiative heat loss and solar gain. A steady state energy balance is a similar method that is used to analyze heat transfer in light of system dynamics. The Alleyne and Jain article from the *Mechanical Engineering* magazine gives an overview of basic transient system modeling for thermal systems in light of the application of steady state energy balance. This method is how TRNSYS works, under the hood. Note that to simulate a thermal system, at steady state, the energy balance is calculated iteratively across time, and results in a time dependent solution. By calculating and tracking the energy through the system at each interface or sub-system, we can obtain the overall energy balance of the whole system. Careful accounting is required to calculate an accurate energy balance. All energy gain (heat transfer into the system) must equal all energy loss (heat transfer out of the system). When all energy is accounted for, we find a series of energy balance equations and can solve them simultaneously to calculate unknown temperatures, heat flow, and thermal properties.

#### Supplemental reading:

**Journal article**: Alleyne A. and Jain N., Transient Thermal System, Focus on Dynamic Systems and Control, 2014, pp. 4-12.