System Design


At the level of this book, a system design evaluates the ability of alternative design options to meet the thermal energy demands of a potential application. The objective of this chapter is to allow the engineer to determine whether solar energy can be utilized effectively for a given application. In order to provide an answer, the engineer must execute a system design to estimate (1) the aperture area of solar collectors required, (2) the land area needed by the solar collectors, (3) storage requirements, and (4) the fraction of the fossil fuel that could reasonably be displaced by a solar thermal energy system.  In addition, a well-executed design allows approximation of the capital cost of the solar energy system needed to service the demand.


This chapter, using the control strategies outlined in SIMPLESYS, provides the tools to allow the designer to quickly sort through the various potential solar energy system designs and to choose one or two, if any, that have good potential for servicing the thermal energy demand cost-effectively.  As a result, the design serves as a screening tool. If the design reveals severe constraints in the solar energy system (e.g., insufficient land available for collector deployment), the application of solar energy to the process should be questioned before the detailed design process is begun. If the design indicates good compatibility between the solar energy system concept and the application, the design process described here serves as a foundation from which detailed processes can begin. Detailed design (pipe sizing, pipe support details, etc.) is beyond the scope of this book. 


Conceptually, the design process is not difficult. All that is really needed is a straightforward methodology for determining which combinations of components make sense. All the analytical tools have been developed so far in this text. The emphasis here is on integrating these tools into a computer program useful for system design. The stage was set in Chapter 14 with the discussion of SIMPLESYS. The system design programs (i.e., the generation of storage sizing graphs, see Section 15.2) will involve iteration and therefore significantly more computational capability.  Selected storage sizing graphs are provided here to allow the reader to do example design problems.


This chapter is divided into three sections:


·         Selection of a Collector Operating Temperature

o        Controlled Collector Operating Temperature

o        Constant Flow Rate Systems


·         Role of Thermal Energy Storage

o        Computation of Storage Capacity  The Storage Sizing Graph

o        The General Nature of Storage Sizing Graphs


·         The Design Process and Some Examples

o        Design Rules of Thumb

o        Summary of the System Design Method


Typically, the collector operating temperature is determined by the thermal energy demand characteristics (i.e., thermal energy should usually be produced at some desired temperature). The section discussing collector operating temperature examines how these temperatures are determined in both constant fluid flow and constant collector operating temperature systems. The section dealing with storage will show how to generate graphs that show the effect of including thermal energy storage on the overall performance of solar collectors. These graphs are used to select the appropriate size (energy capacity) of storage and collector area for a particular thermal energy demand. The techniques are illustrated by example in the last part of the chapter. This chapter specifically examines parabolic trough and dish system design but most concepts can be supplied to flat-plate collector and central receiver systems.

15.1          Selection of a Collector Operating Temperature

15.1.1    Controlled Collector Operating Temperature

Knowledge of the collector operating temperature is needed for computation of the thermal energy output from a solar collector. Most solar thermal collectors employ a heat-transfer fluid that does not change phase (e.g., boiling water to form steam) and that depends on a temperature increase in the heat-transfer fluid for the thermal energy collection process.


An exception would be thermal dishes and central receivers used to generate steam in their receivers. In these cases it would be reasonable to assume that the receiver temperature is approximately equal to the saturated steam temperature since vaporization is the largest endothermic process to occur during heat collection. Typically, some amount of superheating (5-10ºC) is provided to prevent condensation of the steam before expansion. Use of the saturated steam temperature as the operating temperature of a boiling water receiver does not, however, introduce much error in performance calculations since the performance of these collector concepts is not very sensitive to temperature.


This section illustrates how the temperature characteristics of the demand determine what the average collector operating temperature will be.  Two significantly different types of thermal energy demand are examined, each strongly influencing the solar energy system design: (1) a sensible heating system in which the thermal energy demand experiences large temperature swings and (2) a latent heat (phase-change) system, such as for steam production, which tends to operate within rather narrow temperature limits.

Sensible Heat DemandA sensible heat demand, in which the temperature of the demand varies over a wide range, is perhaps the type of demand most easily serviced by a solar thermal collector. This type of demand, which may, for example, involve heating of a heat-transfer fluid in an existing process heat system, closely matches the thermal characteristics of the solar collector field.  The collector field collects thermal energy through a sensible heat mechanism and, as a result, undergoes large temperature swings. Thus it is conceivable that the temperature in the collector field could be made to conform closely to the temperatures of the process heat-transfer fluid.  Design of the solar energy system can then proceed in a rather straightforward manner because the average operating temperature of the collector field is approximately equal to the average process temperature.  This is not the case with a latent heat demand such as a process steam system.


Actually, the use of a heat exchanger in the system would normally require that the collector heat-transfer fluid run about 10ºC hotter than the process fluid to allow good heat transfer.  Neglect of this temperature difference for computation of collector performance during design will not introduce significant error for most well-made mid- to high-temperature collectors.  This temperature increase could, of course, he included if the designer were interested.

Latent Heat Demand (Process Steam)  Process heat is most commonly delivered to an application in the form of steam. The design difficulty encountered with a process steam demand is the interfacing of a sensible heat collection system with a latent heat demand. The problem is illustrated schematically in Figure 15.1 for a hypothetical case in which 1.l MPa (150 psi) saturated steam at 182ºC (360ºF) is desired.


In transit to the point of use, the steam will suffer a small pressure drop and heat loss in the pipe. Any line condensate that results is usually removed by traps. These pressure and heat losses, however, are typically small and are not explicitly shown in Figure 15.1.


Following condensation of the steam by the process, the hot water is returned to the boiler for re-vaporization. Although the hot condensate may be used for preheating, this is not shown in Figure 15.1 in order to simplify the discussion at this point. The hot condensate is assumed to be saturated. The primary design problem here is how to interface the relatively constant temperature process steam system with a solar energy collection system that operates best with large swings in temperature. 


Figure 15.1  Process steam cycle.

Sensible heat addition to the process steam generator is indicated in Figure 15.1 in the form of straight lines. As shown, several options are available with the constraint imposed by the second law of thermodynamics  the temperature of the collector fluid must at any given point be higher than the corresponding temperature of the process fluid in order for heat transfer from the collector fluid to the process fluid to occur. The two different heat addition lines for the collector fluid (lines PA and PB) represent different heat-transfer fluid temperature increases (ΔT values) across the collector field.


At first consideration, heat-addition line PA might appear best. This heat addition process would result in the lowest average collector temperature of both situations and, as discussed earlier, collector performance increases with decreasing operating temperature. There are however, system design considerations which can force a system design away from one in which the Δ T across the collector field is small and toward designs in which the ΔT is large, such as represented by line PB.


A system level consideration that favors a large collector field ΔT is storage.  Most storage concepts developed to the point where they would be used in near-term solar energy systems employ sensible heat. The ΔT across the storage system is essentially the ΔT across the collector field. As the sensible-heat storage ΔT increases (and thus the collector field ΔT increases), the volume of storage required to store a given quantity of energy decreases, resulting in decreased storage costs.


These tradeoff considerations are represented schematically in Figure15.2.  As the collector field ΔT increases, the collector field efficiency decreases, effectively increasing the cost of the collectors (i.e., more collectors are required to produce a given quantity of energy). On the other hand, as the collector field ΔT increases, storage costs decrease. The challenge for the designer is to find the conditions representing the most cost-effective system. We return to this point in the last section of this chapter.

Figure 15.2  Effect of collector ΔT on solar energy subsystem costs.

15.1.2    Constant Flow Rate Systems

Alternative to providing temperature control capability within the collector field, the heat-transfer fluid flow rate can be held constant (i.e., constant pump speed). In this situation, one does not control the temperature out of the collector field. This type of control is common in flat-plate collector systems where equipment and controls costs are kept to a minimum and some process heat systems where the solar collector system tends to act as a preheat (supplemental) heat system. Systems without temperature control are seldom recommended in high-temperature systems where either the heat-transfer fluid may degrade at temperatures only slightly above the desired collector outlet temperature or unexpected high pressures (e.g., in high-temperature water systems) may result in system damage.


Constant-flow-rate systems are usually supplied with a recommended flow rate from the manufacturer. The collector inlet temperature is determined, as described above, by the process demand temperatures. The computer program outlined in Chapter 14 (SIMPLESYSV) computes the collector operating temperature, if needed, as part of the program execution, and as a result, collector operating temperature is not an explicit input to the analysis.

15.2          Role of Thermal Energy Storage

There are typically two types of thermal energy storage provided in most solar thermal energy systems. A small amount of energy storage, called buffer storage, is usually provided to allow smooth startup and control of the collector field. This type of thermal energy storage is not discussed here. The focus of this chapter is on thermal energy storage provided for the purpose of increasing the amount of a given thermal energy demand, that can be displaced through the use of a solar thermal energy system. This chapter examines how the inclusion of thermal energy storage affects system design.


Figure15.3 illustrates the role of thermal energy storage in a solar thermal energy system by contrasting the energy production from various size solar collector fields (curves 1 through 5 in Figure 15.3a) and the demand for thermal energy.  Figures 15.3b and 15.3c plot the utilization of the collected solar energy both when no storage is available and when sufficient storage is available.  Let's not worry about the quantity of storage yet except to say that it is sufficient for our needs. We define what constitutes “sufficient” later in this section.


Figure 15.3 The role of storage in a solar energy system:


If a small collector area is deployed (curve 1), all the solar energy collected can be applied to the demand. As a result, both Figures 15.3b and 15.3c show utilizations of 1.0.  If the collector area is increased to curve 2 again the demand can absorb all the energy collected, and the utilizations shown in both Figures 15.3b and 15.3c are equal to 1.0. This continues until collector area 4 is deployed.  At this point, the collected solar energy exceeds the demand near noon.  If there is no storage (Figure 15.3b), this energy in excess of the demand must be discarded and the utilization decreases.  As illustrated in Figure 15.3c, however, the availability of storage allows this excess energy to be stored until a later time (e.g., after 2 PM), when the collected solar energy is less than the demand.  Since the excess solar energy collected near noon now does not have to be discarded, only stored for later use, the utilization in this case (see Figure 15.3c) remains equal to 1.0.  The difference between the storage and the no-storage cases becomes even more pronounced as the collector area increases further.


This rather conceptual analysis of the effect of storage on increasing the usefulness of collected solar energy can be made quantitative.  The following section describes a computer program to accomplish this.  This program is derived from SIMPLESYS (see Chapter 14).  The product of this program will be the data needed to construct graphs such as those illustrated in Figures 15.3b and 15.3c. These graphs are termed storage sizing graphs.


Before we go any further it will be to our advantage to restate several definitions originally made in Chapter 14 at this point and collect them here for easy reference.  The objective in making these definitions is to make the storage sizing graphs non-dimensional and thereby more general and easier to use.  The following is a definition of terms:


     where the solar and demand values are average daily values.


Note that the definition of design displacement is particularly useful since it, in effect, sizes the collector field required to meet a given demand:


    (m2)                    (15.1)


The actual displacement is related to the design displacement by the utilization:



15.2.1    Computation of Storage Capacity
The Storage Sizing Graph

To examine the effect of collector area and storage capacity on the utilization of the collected solar energy, one must study the hour-by-hour production of thermal energy by the collector field. This energy supply profile must then be contrasted with the application's hour-by-hour demand and the storage capacity available for storing excess solar derived thermal energy. The logic flow for a computer program to do this is similar to that for SIMPLESYS and is reformulated in Figure 15.4 for the specific task of generating the storage sizing graphs.




Figure 15.4  Logic used with COLECTK to prepare storage sizing graphs.

To produce storage sizing graphs described below, a computer program called COLECTK was developed.  Functionally, it looked much like the solar energy system model shown in the previous chapter as Figure 14.1.  It used hour-by-hour TMY irradiation data described in Chapter 2, a sun-collector incident angle calculation model similar to the sun angle calculator developed as part of Chapter 3, and collector performance data as described in Chapter 4.  With a control system as developed for SIMPLESYS, energy balances were calculated for every hour of the year and the system output determined.


It is beyond the scope of this book to provide such a program, but the examples below are given so that the reader can see what types of design analysis can be done once such a program is developed.  Results are presented here only for Albuquerque, New Mexico, however hour-by-hour solar irradiation data are available for many sites throughout the world.


The collector output per unit area is first computed for the time period of interest (typically 1 year) and the results stored.  Next, the hourly thermal demand, (QL in SIMPLESYS), is set equal to the annual collector output per unit area divided by the yearly total hours of demand.  Thus, for a 24-h/day demand, the annual per unit area collector output is divided by 8760 hours.  This is done for convenience only.  Actually any thermal demand could be used, but the use of a demand equal to the average hourly collector output per unit area places all computations on a per unit area collector basis directly.


At this point the program enters a nested loop that increments storage fraction and design displacement. As in SIMPLESYS, at each hour, the energy output from the collector field is compared with the demand.  If the demand is less than the thermal energy output of the collector field, the thermal energy in excess of the demand is placed in storage (mode 3 in SIMPLESYS), if available.  If the storage capacity is exceeded, the excess energy is considered to be discarded and acts as a debit against the utilization of the collected solar energy (mode 4 in SIMPLESYS).  If the demand for thermal energy by the process is greater than the collector output, energy is withdrawn from storage to help to satisfy the demand (modes 5 and 6 in SIMPLESYS).  If the combined collector output and the thermal energy in storage is insufficient to meet the demand of the application, fossil fuel is consumed in order to satisfy the demand (modes 1 and 2 in SIMPLESYS), resulting in decreased actual displacement of the fossil fuel by the solar installation. An efficiency for fossil fuel combustion could be incorporated here if desired.


This analysis is repeated hourly for the time period under study, and design displacement and storage fraction is incremented as indicated in Figure 15.4.  Referring back to Figure 15.3, we are generating curves similar to 15.3b and 15.3c except for a much wider range of storage sizes.  All the curves will be plotted on a single graph called a storage sizing graph.

Example Storage Sizing Graph  Daytime DemandsPerhaps it would be a good idea to stop at this point and consider a specific example of a storage sizing graph generated as described in the preceding paragraphs. Suppose that we have an application with a constant one-shift demand (8 AM to 5 PM) for 232ºC (450ºF) steam, 365 days per year. Assume further that we wish to evaluate an E/W-oriented field of parabolic troughs located in Albuquerque and that, as described in Section 15.1, we have concluded that the average collector operating temperature will be 288ºC (550ºF).  To keep the example simple and not divert attention from the interaction of the storage and the collectors, heat losses from the field piping, pipe heat-up energy, and storage loss (QF, EP, and SL in SIMPLESYS) are set equal to zero and collector shadowing will be neglected.


Figure 15.5 shows the storage sizing graph for this situation with storage fractions ranging from 0.0 (no storage) to 0.5 (storage equal to 50 percent of the total average daily demand). Several interesting features are evident from Figure 15.5.  First, with no storage, one can increase the solar energy collected (i.e., increase the design displacement) up to about 50 percent of the demand before being faced with the need to discard (i.e., the utilization drops below 1.0) any of the collected solar energy. This corresponds to curve 3 in Figure 15.3a.  Beyond this point, collected solar energy must be discarded when there is no storage.

Figure 15.5  Storage sizing graph for E/W trough field, daytime demand in Albuquerque, NM.

With the inclusion of storage capacity equal to 20 percent of the daily demand (i.e., storage fraction equals 0.2) however, we can collect enough solar energy to meet approximately 70 percent of the daily demand before we must discard any of the collected solar energy (i.e., the utilization drops below 1.0).  Note, however, that we cannot simply increase storage capacity and collector area indefinitely and still reap equivalent benefits. As we increase the storage fraction to 0.4 and then to 0.5, we do not really gain that much. In fact, the last two curves are almost superimposed.


In addition, we can see from Figure 15.5 that we cannot displace much more than 80 percent (design displacement equal to 0.80) of the demand and still maintain 100 percent utilization of the collected solar energy even with large storage fractions.  This is denoted as the maximum displacement point in Figure 15.5.


Above a storage fraction of about 0.3 - 0.4, additional increments of storage have diminishing impact on the utilization of the collected solar energy. One reason for this can be observed in Figure 5.4, which shows that the thermal energy produced by an E/W parabolic trough located in Albuquerque varies about +/ 10 percent around the annual average from season to season. Increasing the actual displacement (without having to discard collected solar energy) above about 80 percent for an E/ W parabolic trough collector field in Albuquerque would thus require seasonal storage. Up to the maximum displacement point, the combination of collectors and storage serve mainly to displace the recurring daily overnight thermal demand.


Note that we can achieve an actual displacement above 0.9 if we are willing to discard some of the collected solar energy. One combination that would achieve an actual displacement of above 0.9 is:


                                                               Design displacement  =   1.0

                                                                     Storage fraction  =   0.3

                                                 Utilization (from Figure 15.5)  =   0.94

Recall that:

Actual displacement = (design displacement) X (utilization)

It should be remembered that Albuquerque has a reasonably clear climate with little cloud cover. In cloudy climates, the maximum displacement point will occur at smaller values of design displacement as a result of the many cloudy days throughout the year. As storage sizing graphs for these sites would indicate, sometimes only rather small actual displacements are reasonable in such climates.


The maximum displacement point in Figure 15.5 and all other storage sizing graphs has design significance in that it represents a design goal for solar energy systems incorporating storage. In general, if the economic decision is made to incorporate storage in a solar energy system, there is no additional economic penalty for deploying the collectors and storage concomitant with the maximum displacement point. The decision is really whether to include any storage at all! If storage is to be included, the maximum displacement point indicates the appropriate quantity to assess the potential for auxiliary fuel displacement.


The logic that drives the design of a solar energy system to the maximum displacement point is reduced to graphical form in Figure 15.6. This graph plots a term called the incremental storage ratio against design displacement.  The incremental storage ratio is defined as the ratio of a given increase in storage fraction to the resultant increase in actual displacement as derived from Figure 15.5. The incremental storage ratio is a measure of how effective a given amount of added storage is in increasing actual displacement.


Figure 15.6  Effect of storage on displacement.

Example:  Let’s generate the points plotted in Figure 15.6, using Figure 15.5.  If you increase the collector area in order to increase the design displacement from 0.5 to about 0.6, a concomitant increase in storage fraction of 0.1 provides an increase in actual displacement (design displacement × utilization) from 0.5 to 0.6 (a net change of 0.1). Thus the incremental storage ratio associated with going from a design displacement of 0.5 to 0.6 is 1.0 and is plotted in Figure 15.6.  The other points shown in Figure 15.6 were all calculated in this manner and show that the incremental storage ratio does not change significantly until the maximum displacement point is approached. 

At this point, a further increase in the design displacement leads to a sharp increase in the incremental storage ratio.  In fact, to keep the plot on scale, an increase in design displacement of only 0.04 was used.  The situation quickly worsens from this point. The basic problem is that, beyond the maximum displacement point, we are not deploying enough collectors to fill up the extra storage capacity.  At the maximum displacement point, the role of storage changes from diurnal to long term (i.e., seasonal).

In system design, the maximum displacement point will identify the design point for assessing the maximum practical potential a solar energy system has for displacing an auxiliary fuel. Although the selection of the proper storage-collector combination will be determined by economics, the maximum displacement point represents a good initial selection of collector area and storage capacity.

    Example Storage Sizing Graph  Demands Longer than Daytime OnlyThe appropriate storage capacity for any constant demand which lasts longer than the 8 AM to 5 PM time period discussed earlier can be approximated from the daytime-only storage sizing graphs. The daytime-only storage sizing graphs give the storage fraction required for daytime operation. Any operation outside the 8 AM to 5 PM period must be done exclusively from storage. As an example of how the daytime-only storage sizing graphs can be used to predict storage capacities for demands with longer duration, consider a constant demand that lasts 24 hours and is serviced by a field of E/W troughs in Albuquerque (i.e., a situation similar to the preceding one except that now the demand duration is 24 h/day).

Example.  If a constant daily demand of 30 MWh/day is assumed and a design displacement of 0.8 is desired, the quantity of demand that occurs outside the 8 AM to 5 PM period is:

Demand (outside 8AM to 5 PM) = (15/24) × (30 MWh) = 18.75 MWh

From Figure 15.5, it is seen that a storage fraction of about 0.2 to 0.3 is sufficient to provide near 100 percent utilization for the daytime-only portion of the demand.  The 8 AM to 5 PM portion of the demand is:

Demand ( from 8AM to 5PM) = (9/24) × (30 MWh) = 11.25 MWh

Thus the storage capacity required for the 8 AM to 5 PM portion of the constant 24-hour demand can be calculated as:

Storage Capacity (for 8AM to 5PM demand) = (11.25 MWh) × (0.2) = 2.25 MWh

The resultant total storage capacity for a design displacement of 0.8 with near 100 percent utilization of the constant 24-hour demand is:

Total Storage Capacity = 0.8 × 18.75 + 2.25 = 17.25 MWh

This corresponds to a storage fraction of:

Storage Fraction = 17.25 / 30 = 0.58


This, in fact, corresponds with what would have been found from computing the storage sizing graph for this situation.


Note that there is an inherent assumption behind this simple calculation.  That assumption is that we have approximately 100 percent utilization of the collected solar energy and that we are at the maximum displacement point.  In reality, we are sizing storage so that part of the year when the collector output is high (i.e. we can satisfy the complete daily demand) there will be no discarded solar energy.  During other times of the year (i.e. collector output falls off as a result of seasonal effects) the storage capacity will be somewhat larger than needed.

Example Storage Sizing Graph  Demands That Are Not Constant. The storage sizing graphs for constant thermal energy demands can also be used to allow system design to proceed in cases where the demand can be considered a composite of the constant demands discussed earlier.  If, for example, the demand of an application had the profile illustrated in Figure 15.7, the solar energy system to service this demand may be considered to be two separate systems.

Figure 15.7  A stepped demand profile.

The increased daytime demand is considered a separate demand serviced by a particular collector area and storage combination, whereas the constant 24-hour demand is considered separately and serviced by a different collector area and storage combination.  The solar energy system servicing the entire demand is the total collector area plus the total storage capacity of the two separately analyzed demands. An example illustrating design of a solar energy system servicing such a stepped demand profile is presented later in this chapter in Section 15.3.

15.2.2    The General Nature of Storage Sizing Graphs

It is important to realize that the storage sizing graphs are rather general in nature.  These graphs report the time-dependent interaction of a solar collector field, storage, and a demand for thermal energy.  The graphs are not dependent on collector performance as long as the collector performance does not affect the time-dependent profile of the collected solar energy.  For a given location and operating temperature, therefore, all E/W parabolic troughs, for example, will have the same storage sizing graph. In truth, even changes in collector operating temperature will not significantly change the storage sizing graphs.


Thus, once you have generated a storage sizing graph for a given generic type (e.g., trough, dish, flat plate) and orientation of collector and daytime demand, there is no need to construct a new storage sizing graph even if you wish, for example, to do a design with a similar collector having a different ΔT/I curve.  The work by Harrigan (1981) contains a compendium of storage sizing graphs for E/W- and N/S-oriented parabolic trough collectors for different locations in the U.S.


We have included below seven more storage sizing graphs.  Including Figure 15.5, these make up a set that may be useful for some example system designs.  As indicated on the graphs, Albuquerque TMY meteorological data were used and both 9-hour per day (daytime) and 24-hour per day constant demands were considered.  Typical collector orientations, including east/west and north/south tracking axis orientations for parabolic trough fields, 2-axis tracking parabolic dish fields, and flat-plate collector field with the collectors tilted toward the south at the latitude angle are represented.  For illustrative purposes, the concentrating collectors were assumed to be operating at 288oC (550oF) while the flat-plate collectors at 50oC (122oF).  Typical collector efficiency curves were used but as noted here, the storage sizing graphs are not very sensitive to there particular assumptions.


Figure 15.8  Storage sizing graph for E/W trough field, 24-hour demand in Albuquerque, NM.

Figure 15.9  Storage sizing graph for N/S trough field, daytime demand in Albuquerque, NM.

Figure 15.10  Storage sizing graph for N/S trough field, 24-hour demand in Albuquerque, NM.

Figure 15.11  Storage sizing graph for parabolic dish field, daytime demand in Albuquerque, NM.

Figure 15.12  Storage sizing graph for parabolic dish field, 24-hour demand in Albuquerque, NM.

Figure 15.13  Storage sizing graph for a flat plate field, latitude tilt, daytime demand in Albuquerque, NM.

Figure 15.14  Storage sizing graph for a flat plate field, latitude tilt, 24-hour demand in Albuquerque, NM.

15.3          The Design Process and Some Examples

The basic characteristics of both the collectors and storage have been defined to the extent necessary to execute a system design.  This section assembles the methods discussed previously for predicting collector performance and storage capacity into a procedure for achieving a system design of a solar thermal energy system.  At this stage in the design process, the objective is to determine the ability of the solar energy system to interface with a demand for thermal energy.  Of primary importance is an approximation of the collector and land areas needed and the portion of the fossil fuel demand that can reasonably be displaced by the solar energy system. If the concept appears feasible at this point, the more detailed design stage leading to construction can be started. This latter design stage is outside the scope of this book. 


To help start off the design process, a series of design Rules of Thumb have been formulated and are presented here.  Although specific recommendations are made for selecting appropriate collector area and storage capacities in the form of design Rules of Thumb, other rules could, of course, be formulated.  There is sufficient information in the storage sizing graphs for determination of the collector area and storage capacity needed to achieve almost any reasonable displacement of fossil fuel desired.  In areas having low availability of insolation, a designer may, for example, elect to deploy a larger collector area than suggested by the maximum displacement point in order to achieve a larger actual displacement.


The design Rules of Thumb are derived from the concept of the maximum displacement point simply to help define a reasonably cost-effective deployment of collector and storage capital equipment. Other designs could be developed that would have higher storage and collector costs but that might better suit the particular needs of a given application.  Thus, the design Rules of Thumb should be treated as reasonable starting points for the design process and not as “cast in concrete.”  The logic flow followed in achieving a system design is presented following the design Rules of Thumb. This chapter ends with several examples to illustrate the design process.

15.3.1    Design Rules of Thumb

The first step in the analysis of a solar collector field is to determine the collector operating temperature.  If a constant flow rate system is to be evaluated, there is no problem.  The collector operating temperature is computed as part of its operation or, as in the case of a flat-plate collector, the ΔT/I curve is in the form of Tin.  If a constant-temperature system is to be evaluated, however, we need to know at what temperature we want the collector to operate (or, more accurately, the average collector operating temperature).  The first Rules of Thumb address the question: “How do we know at what temperature the collectors will be operating?”

Latent Heat Demand (Process Steam)

Typically, flat-plate collectors are not used for steam generation. Thus, these Rules of Thumb apply particularly to sensible heat parabolic troughs and dishes where steam is not generated in the receiver.

Rule I: Collector Field ΔT With Sensible-Heat Storage.  If significant storage capacity is to be provided in a solar energy system, the collector field ΔT will be approximately 140ºC (252ºF) or the difference between 315ºC (600ºF) and the saturated steam temperature, whichever is smaller.

This Rule of Thumb is a result of the desire to reduce storage costs by increasing the ΔT across storage.  Whereas the proper ΔT would typically be determined through an economic optimization, changes in the average collector operating temperature due to changes in the collector field ΔT usually affect storage costs more than collector costs. This Rule of Thumb yields a good starting point for design. In the absence of collector operating temperature limitations, therefore, the least cost storage will result when the collector field ΔT is maximized.  Because of the pinch point (see Figure 15.1), the minimum temperature experienced by the collector field heat-transfer fluid will be, as discussed in Section 15.1, close to the saturated steam temperature.  The 315ºC (600ºF) temperature limit is imposed by fluid stability.  Most of the organic heat-transfer fluids (e.g., Therminol 66®) currently in use in high-temperature collector fields and sensible heat storage are not recommended for use much above 315ºC.  Some silicone fluids have upper temperature limits of about 370 - 400ºC and have been used with parabolic dishes (e.g., Shenandoah dish installation  see Chapter 16).  In this case an upper limit of 400ºC (752ºF) would be used.


The 140ºC (252ºF) limit on ΔT comes from current collector designs typically not allowing a greater ΔT because of the high pumping power required for long delta-T strings in parabolic trough fields and the receiver tubing in thermal dishes.  Typical parabolic trough collector designs, for example, provide for a fluid temperature rise of about 0.3ºC (0.5ºF) per linear foot of trough when the fluid flow is just above the turbulent flow region. Recommendations of the collector manufacturer should, of course, be used if available.

Rule 2: Collector Field ΔT with No Storage.  In the absence of storage, the collector field ΔT will be approximately 5585ºC (100155ºF) or the difference between 315 ºC (600 ºF) and the steam delivery temperature, whichever is smaller.

In the absence of storage, the lowest collector field ΔT (and, hence, average collector field operating temperature) compatible with reasonable pumping power requirements (and good heat transfer in the receiver) and thermal losses from the field is desirable. This will usually lead to a collector field ΔT of about 55-85ºC (100-155ºF) based on the parabolic trough development program.  As can be seen in Figure 15.1, the lowest temperature the collector field heat-transfer fluid can normally achieve approximates the saturated steam temperature because of the pinch point.

Rule 3: Collector Operating Temperature.  The collector operating temperature will be one-half the collector field ΔT above the saturated steam temperature.

The average collector temperature is simply the average between the collector inlet and outlet temperatures. This Rule of Thumb-of-thumb follows from the collector inlet temperature being defined by the steam temperature (see Rules of Thumb 1 and 2).

Sensible Heat Demands

 These Rules of Thumb include flat-plate collectors since, in fact, this is the most common application for these collectors. For flat-plate collectors in which inlet temperature, and not average operating temperature, information is desired, see Rule of Thumb 6. Distinctions between flat-plate, parabolic trough, and parabolic dish collectors are indicated when appropriate.

Rule. 4: Collector Field ΔT with No Storage. When a solar energy system services a process heat demand that uses a sensible heating mechanism (i.e., not a process steam system), the collector field ΔT will be approximately the process ΔT, or for concentrators (i.e., parabolic troughs and dishes), 55-85ºC (100-155º F) or the process ΔT, whichever is greater.


In a process heat system with no storage that uses sensible heat, the temperature of the collector field tends to closely follow the process temperatures.  If the process ΔT is small, the minimum collector field ΔT for concentrators will be about 5585ºC (100-155ºF) in order to keep pumping parasitics within reason (i.e., in a collector the fluid must be pumped faster to lower the collector ΔT).


Rule 5: Collector Field ΔT  with Sensible Heat Storage. If significant storage capacity is to be provided in the solar energy system, the collector field ΔT will be approximately the difference between the process low temperature and (a) 315ºC (600ºF) if the collector is a concentrator, or (b) the manufacturer- recommended upper operating temperature (60-70ºC is a good guess if you have no data) if the collector is a flat plate.  If the collector is a concentrator, the maximum collector fluid ΔT is 140ºC (252ºF).


As in Rule of Thumb 1, the cost of storage tends to drive the collector field ΔT as large as possible without allowing the collector fluid to exceed 315 ºC (600 ºF) for concentrators.  This upper temperature limit can be extended to 400ºC (752ºF) if silicone fluids are used.  The 140ºC (252ºF) limit on the ΔT is discussed in Rule of Thumb 1 for concentrating collectors.

Rule 6: Collector Operating Temperature. The collector operating temperature will be one-half the collector field ΔT above the process low temperature.

As discussed earlier, the average collector operating temperature is simply the average between the collector inlet and outlet temperatures.  For flat-plate collectors in which knowledge of the collector inlet temperature may be required, the inlet temperature is approximately equal to the process low temperature at the point at which the flat-plate system interfaces with the process.


Rule 7: Land Area Requirements. The land area required for the deployment of solar collectors is approximately 2.0-3.5 times the total aperture area of the collectors.

Land area requirements are based on tradeoff analyses of collector shading and thermal heat losses from the field piping.

Rule: 8: Storage Capacity.  If storage is to be incorporated into the system design and there is no a priori reason for limiting collector area, the proper collector area and storage capacity combination is that associated with the maximum displacement point on the appropriate storage sizing graph.

The justification for this Rule is presented in Section 15.2.

Rule 9: Decrease of Collector Output.  The thermal energy output from an installed collector field will be 75-85 percent of the output from a clean, as-tested, isolated collector.

Thermal losses from field piping, dirt on the collectors and to a lesser extent inter-collector shading will reduce the collector field thermal energy output calculated using test data.  Experience has shown that this reduction will be about 15-25 percent for a typical field.  Although these losses are not explicitly evaluated in the design process presented in this chapter, the application of a correction factor of 0.75-0.85 to the calculated output will provide a realistic approximation of actual installed collector field performance.  If you have knowledge of the magnitude of specific losses, they can be incorporated into system analysis as indicated in the discussion of SIMPLESYS in Chapter 14.


This Rule of Thumb is presented here as a warning as much as anything.  A 25 percent performance degradation may appear excessive, but it must be kept in mind that published collector performance data are normally “best-case” data that have been obtained under ideal conditions by skilled technicians. Real-world installations will not be as fortunate.

15.3.2    Summary of the System Design Method

The procedure for arriving at a system design is fast and easily applied when the design Rules of Thumb listed in Section 15.3.1 are employed. The application of these Rules of Thumb, when employed in conjunction with the storage sizing graphs, quickly yields a credible conceptual design. The logic path from definition of the demand characteristics through achievement of a design is outlined in Figure 15.15. Where appropriate, the design Rule of Thumb is indicated. 


Figure 15.15  Logic flow for the design process.

The design process starts with the definition of the demand characteristics.  The temporal profile of the demand, when taken together with the desire to have a system that either does or does not include storage, defines the collector field ΔT.  Typically, both storage and no-storage designs are performed to evaluate the relative economics. 


In constant-temperature solar collector fields, Rules of Thumb 1 and 2 apply to process steam systems and Rules of Thumb 4 and 5, to sensible heat demands.  The collector field ΔT, in turn, defines the collector operating temperature, which, together with the collector performance characteristics, provides the average annual collector performance. In constant-flow collector systems no a priori knowledge of collector operating temperature is needed.


The storage sizing graphs are used to determine the relationship between needed collector output, storage capacity, and demand.  As a first choice, only solar energy systems that provide near 100 percent utilization of the collected solar energy are selected.  Sensitivity around this design point can be examined if desired. In the case of systems incorporating storage, the design point is the maximum displacement point.  Multiplication of the design displacement by the demand yields the quantity of energy displaced by the solar energy system.


Division of the quantity of energy displaced by the per unit area collector output and adjustment for field losses (Rule of Thumb 9) yields the required collector area. Finally, multiplication of the storage fraction by the average daily demand yields the required storage capacity.  If the estimates of storage costs (Chapter 11) and collector costs are available, total storage-collector subsystem costs can be approximated. The net results of the system design are the displacement of fossil fuel, the collector area, and storage capacity needed to achieve this displacement of fossil energy; the approximate land area needed for collector deployment; and an estimate of the total capital costs.

Example Design 1: E/W Parabolic Trough System. To illustrate the preceding design procedures, we have defined a hypothetical 1.1 MPa (150-psi) process steam system and will design a retrofit solar energy system to service the demand for thermal energy. Figure 15.16 outlines the thermal energy flow paths of the fossil fuel energy system, located in Albuquerque, together with the important temperatures and pressures needed to define the system.  The solar retrofit, consisting of an E/W parabolic trough collector field and sensible-heat storage, is also shown with the fossil fuel system retained for backup.  The first demand profile considered will be constant, 24 hours per day, 365 days per year.  The temperatureentropy (T-s) diagram in Figure 15.17 traces the thermal characteristics of the process steam supply.

Figure 15.16  Thermal energy flows in example problem.

Figure 15.17  Temperature-entropy diagram for example problem.  Adapted from Keenan et al. (1978).

Two basic choices are available for the solar energy system  a system including storage and a system without storage.  Typically, both options are considered at the initial design stage.  This example illustrates the design of both storage and no-storage systems. 


A hypothetical parabolic trough performance will be assumed.  The performance of this collector is plotted in Figure 15.18 and is denoted as example collector.  This plot of collector efficiency versus ΔT/I is typically of the form in which collector performance data are published for commercial collectors.



Figure 15.18 Performance characteristics of example collector used in “Design Example 1.”

No-storage caseRecall that we have already generated the storage sizing graph for an E/W parabolic trough located in Albuquerque (see Figure 15.5).  Although this graph is for the 8 AM to 5 PM time period, we can adjust the graph to 24 hours per day as was illustrated in Section 15.2.1 in the subsection titled “Example Storage Sizing Graph  Demands Longer than Daytime Only” (the 24-h/day storage sizing graph is also included here as Figure 15.8 for comparison).


As observed in the storage sizing graphs included here, for this type of demand profile, the main effect of having no storage in a solar thermal energy system is to restrict the amount of the demand that can be displaced to a small fraction of the total demand.  In the case of Albuquerque, only about 20 percent of the demand can be displaced with near100 percent utilization by an E/W collector field having no thermal energy storage.


Calculation for the no-storage cases illustrating this is as follows:

From the storage sizing graph for 8 AM to 5 PM, the design displacement for 8 AM to 5 PM time period (100 percent utilization) is 0.5.  Thus the design displacement for a 24-hour demand (100 percent utilization) is:


According to design Rule of Thumb 2 for a no-storage system, the average operating temperature of the collector field will be about 210ºC (410ºF), reflecting a ΔT of 56ºC (100ºF) across the collector field.


Given a 24-h/day demand of 30 MWh per day and an average collector operating temperature of 210ºC (410ºF), the aperture area of E/W collector that best services the demand can be determined. From the storage sizing graph (Figure 15.5), it was observed that, at best, only about 50 percent of the daytime portion of the demand could be displaced while maintaining near 100 percent utilization.  Thus the collector field should be sized to provide


The average annual thermal energy output of the example collector at 210ºC (410ºF) is, as computed by using COLECTK, 3.15 kWh/m2 per day. This results in a required collector aperture area of 1780 m2.  If Rule of Thumb 9 is applied to account for field losses, the required collector aperture area is 2370 m2.


If greater displacement of the fossil fuel energy is desired, additional collectors could, of course, be deployed.  If no storage is added along with the additional collectors, utilization of the collected solar energy falls rapidly.  The land area required for collector deployment, in accordance with Rule of Thumb 7, is about 2.5 times the collector aperture area or approximately 6000 m2.


With sensible-heat storage. The addition of storage to the solar thermal energy system described above allows consideration of deploying larger fields of solar collectors to displace more than 20 percent of the demand (50 percent of daytime demand). The decision to add storage is an economic one.  If the value of the additional fossil fuel energy displaced is greater than the cost of the extra collectors and storage required, the increase in fossil fuel displacement is worthwhile.  The selection of the proper quantity of storage is not too sensitive to the cost of storage as long as the decision is made to include more than the small amount typically used for control purposes. Once the decision is made to include storage, the form of the dependence of the solar energy utilization on storage capacity tends to drive the design to the maximum displacement point of the appropriate storage sizing graph regardless of cost (see Section 15.2.1).


Thus the design can proceed in the absence of cost figures since, for a given displacement of the demand, a preferred storage capacity can be identified.  As capital costs are factored into the evaluation, the costs associated with providing more than nominal fossil fuel displacement would become evident.


By employing Rule of Thumb 1, a collector ΔT of 133ºC (240ºF) is chosen and is represented in Figure 15.17 by line PB. This results in an average collector temperature (in accordance with Rule of Thumb 3) of 249ºC (480ºF). Since a collector with the performance characteristics of the example collector is assumed, the average daily collector output is, as computed by using COLECTK, about 2.8 kWh/m2 per day.  Following Rule of Thumb 8, the solar energy system will be designed to the maximum displacement point in the storage sizing graph shown in Figure 15.5. Sizing of the collector field follows directly.


The design displacement associated with the maximum displacement point in Figure 15.5 is 0.8.  Note that the maximum displacement point occurs at 0.8 design displacement in both the 24-hour and daylight-only storage sizing graphs.  This results because the maximum displacement point is a seasonal, not hourly phenomenon.)  The quantity of thermal energy storage required is, as discussed in Section 15.2.1, the sum of the storage needed for the daytime operation represented by Figure 15.5 plus the capacity needed for the demand that occurs outside the normal daylight hours for a total of 17.25 MWh.  (See section titled “Example Storage Sizing Graph  Demands Longer than Daytime Only” in Section 15.2.1.)


The quantity of thermal energy that must, on the average throughout the year, be provided by the E/W parabolic trough field is:




Table 15.1. Results of Example Design 1 (Demand = 30 MWh/day, Constant)














   Fossil Fuel





   2370 m2




   5.6 MWh/day


   6000 m2







11,430 m2

17.25 MWh

 24 MWh/day

28,575 m2








Division of this daily output by the average per unit area collector output (2.8 kWh/m2 per day) and 0.75 to account for the field losses yields a necessary collector aperture area of 11,430 m2. Following Rule of Thumb 7, the required land area is 2.5 times the collector aperture area or about 28,575 m2.  Table 15.1 summarizes the results for these two designs.


An approximation of the capital costs for this solar energy system (based on 1980 dollars) can be obtained with the help of Chapter 11.  If it is assumed that the collectors could be purchased and installed for $215/ m2, the capital cost for the collector field is $2.45 million dollars.  Based on Chapter 11 (see Equation11.4), storage costs are estimated to be $229,000 (assuming a storage efficiency of 100 percent) for oil that costs about $950/m2 ($3.60/gallon) and a collector field ΔT of 133ºC (240ºF) this results in a total storage-collector subsystem capital cost of about $2.68 million dollars.


The assumption of 100 percent storage efficiency above, is not realistic since storage tanks lose heat and suffer degradation in energy quality by other mechanisms.  However, there is a general lack of information on the efficiency of thermal energy storage systems.  Since the purpose here is to illustrate the design techniques and not suggest the status of storage technology development, 100 percent efficiency has been chosen for this example.



Example Design 2: A Stepped Demand Profile.  As an example of how a stepped demand profile is handled, consider the demand profile shown in Figure 15.19.  The application is assumed identical to that defined earlier for “Example Design 1” except for the demand profile.  The demand for this example will be assumed constant at 1.25 MW between midnight and 8 AM and between 5 PM and midnight. During the hours between 8 AM and 5 PM the demand is assumed to double to 2.5 MW. 

Figure 15.19 Example of stepped demand profile.

This stepped demand can be regarded as the superposition of two distinct demands.  One demand is constant, 24 h/day, 365 days/ yr, whereas the other is also constant but present only during daylight hours. The 24-hour part of the demand is equal to 30 MWh/day.  This is the demand of “Example Design 1.”  The separate daytime-only part of the demand is equal to:




The constant 24-hour part of the demand serviced by an E/W example collector has already been examined and need not be repeated.  Thus a design need be performed only for the daytime demand and the resulting collector area and the storage capacity added to that of the 24-hour demand design.


The maximum displacement point in Figure 15.5, as discussed earlier, occurs at a design displacement of 0.8 and storage fraction of 0.2.  Thus the appropriate aperture area of the example collector, which has an average thermal energy output of 2.8 kWh/m2 per day, is:


The capacity of the thermal storage is obtained by multiplying the storage fraction (0.2) at the maximum displacement point by the separate daytime demand of 11.25 MWh  per day.  This results in a required storage capacity of 2.25 MWh.


When the collector field sizes and the storage capacities for the two designs are added, the resultant design consists of 19.5 MWh storage capacity coupled with 15,720 m2 of example collector.  If the same unit collector and storage capital costs are assumed as in Example Design 1, the total storage-collector capital costs for the E/W solar energy system servicing the stepped demand of Figure 15.19 is $3.60 million dollars.

15.4          Summary

It should be clear by now that the process of performing a first-level design of a solar thermal energy system is actually relatively simple if a computer code such as COLECTK is developed.  The real trick is to generate the appropriate storage sizing graph for the situation under study.  The storage sizing graphs graphically display all the time-varying interactions within the solar thermal energy system and allow the designer to select the appropriate conditions that best meet the important system requirements.  Access to the storage sizing graphs and the code that computes them allows maximum flexibility in design. 


If you don't like some of the design procedures outlined here (e.g., perhaps one or two of the design Rules of Thumb seem inappropriate or you wish to include additional system specific information), change them. You have the necessary tools.  Regardless, you will progress through the same basic steps in your design, which will be to generate storage sizing graphs (or their equivalents) followed by selecting appropriate storage capacities and collector area.


Harrigan, R. W. (1981), Handbook for the Conceptual Design of Parabolic Trough Solar Energy Systems. Process Heal Applications, SAND81-0763, Sandia National Laboratories, Albuquerque, July.

Keenan, J. H., F. G. Keyes, P. G. Hill, and J. G. Moore (1978), Steam Tables: Thermodynamic Properties of Water Including Vapor, Liquid and Solid Phases, John Wiley & Sons, New York.