Solar collectors capture incident solar radiation energy and either convert it to heat (thermal energy) or directly to electricity (photovoltaic cells). In Chapter 4 we developed the equations necessary to predict the amount of solar irradiance or energy falling on a solar collector. We looked at different cases of tilting and tracking the collectors to optimize the solar input. In this chapter, we study how a solar collector absorbs and converts solar energy into thermal energy or electricity as in the case of photovoltaic panels. The topics covered in this chapter are:

We will first look at solar thermal collectors and then at photovoltaic modules. Here we derive the energy balance for thermal collectors, without regards to the specific type; that will be dealt with in the following chapters. We will also understand the energy balance for a photovoltaic module, without going into the details of the electro-physics of the processes happening within the cells.

Prior to an examination of specific collector concepts, this chapter shows the development of a widely used yet simple model for prediction of the thermal energy output (i.e., performance) of various solar collectors. The model is applicable to all (including the central receiver with some extension) collector concepts and hence is discussed separately from any one collector concept to avoid the misunderstanding that the model is useful only for that one concept.

Although the presentation of a model for computation of collector performance before discussion of the individual collector design concepts may seem strange, system design can proceed if certain thermodynamic characteristics are known, without detailed knowledge of what the collector looks like. Usually, collector performance is determined from experimental data of prototype hardware. A particularly important feature of the performance models discussed in this chapter is that it exploits such data and extends it to different operating conditions. If experimental data are not available, the designer must resort to an analytical description of the collector’s performance, which is always risky.

In a similar manner, a simple model of photovoltaic panel performance is presented. Like the thermal collector performance model, it is based on experimental data that is modified for operating parameters different from a ‘standard’ condition.

To perform an energy balance on a solar thermal collector, one usually isolates the surface that absorbs the incoming radiation, and balances energy inflow and outflow to and from it. In a flat-plate collector, this is called the ‘absorber plate’ and for a concentrating collector, it is often called the ‘receiver’. In subsequent chapters we will describe many details of construction, surfaces for each type of collector, but for now, this is not important. The energy balance on a solar collector absorber or receiver can be written as;

where:

The ‘useful’ energy for a solar thermal collector is the rate of thermal energy leaving the collector, usually described in terms of the rate of energy being added to a heat transfer fluid passing through the receiver or absorber, i.e.:

where:

These losses are shown schematically in Figure 5.1.

Figure 5.1 Energy balance on a solar collector absorber / receiver.

where:

This solar resource is reduced by a number of losses as it passes from the aperture of the collector to the absorber. These processes depend on the type and design of the specific collector, but here we include the important optical loss mechanisms, and will drop the unimportant terms in future chapters as we discuss specific types of collectors. The rate of optical (short wavelength) energy reaching the absorber or receiver is the product of the incoming solar resource multiplied by a number of factors, all less than 1.0 describing this reduction:

where:

For parabolic trough collectors a glass tube surrounds the absorber tube for the same reason. High-temperature cavity receivers may incorporate a quartz glass cover to keep the gas in the receiver separate from outside air or to permit pressurization of the gas within the cavity. In all cases, the use of a cover sheet reduces the solar radiation passing to the receiver/absorber. Their benefit for reducing heat losses from the absorber must at least balance this reduction.

Transmittance of the cover also depends on the wavelength of light passing through it. Glass for example transmits most radiation in the visible spectrum, but does not transmit much in the infrared region. Therefore, an absorber covered with glass will receive most of the incoming, short wavelength radiation, but will not transmit much of the long wavelength radiation loss coming from the absorber. This characteristic of glass is the reason that glass greenhouses loose very little energy at nighttime. Carbon dioxide buildup gives our atmosphere a similar property and therefore the name ‘greenhouse effect’.

On the other hand, plastic covers have high transmittance values at very long wavelengths. Solar collectors using plastic covers can be used for nighttime cooling since radiation loss to the nighttime sky can be significant. This is also why greenhouses in warm climates use plastic rather than glass as a cover. Without nighttime long-wavelength radiation loss, the average temperatures would be too high for optimal plant growth.

In summary then, when performing an energy balance on the absorber plate or receiver of a solar collector, there are four important mechanisms that reduce the amount of solar energy that is incident on the collector aperture; imperfect reflection, imperfect geometry, imperfect transmission and imperfect absorption. This is a general statement, and different collector types will either include or not include these losses depending on the design.

 5.1.2 Heat Loss Mechanisms

Once the solar energy resource (short wavelength radiation) has made its way down to the surface of the absorber or receiver of a collector, it raises the temperature of the absorber above ambient temperature. This in turn starts a process of heat loss from the absorber as with any surface heated above the temperature of the surroundings. These loss mechanisms are convection, radiation and conduction, and all are dependent on, among other things, the difference in temperature between the absorber and the surroundings.

Because a solar thermal collector is designed to heat a fluid, there is a balance between the rate of heat being removed by the heat transfer fluid and the heat loss by radiation, convection and conduction as defined by Equation (4.1). Since heat loss increases with temperature, this balance between heat removal and heat loss defines the operating temperature of the collector.

If the heat transfer fluid removes too much heat, the temperature of the absorber decreases, reducing heat loss. If not enough heat is removed from the absorber, the absorber temperature increases, increasing the rate of heat loss. This can pose a major problem for concentrating collectors, because when not enough heat is being removed (as can happen if the flow of heat transfer fluid is interrupted), the temperature of the absorber can increase to its melting temperature.

Convection Loss - Convective heat loss of a solar collector receiver is proportional to the surface area of the absorber or receiver, and the difference in temperature between the absorber surface and the surrounding air. It can be written in general terms as:

where:

As with the other heat loss equations below, this is a simplified, instructive model. Usually there are a number of convective processes that cause an absorber or receiver to loose heat to the surroundings. For example, a flat-plate collector often has a glass cover sheet between the absorber plate and outside ambient air. There is one convection process between the hot absorber and the cover sheet, and a second between the cover sheet and outside air. Also, wind increases the heat transfer coefficient on the cover sheet and must be included in any serious analysis of convective heat loss.

For parabolic dish concentrators, the absorbing surface is typically placed inside of a cavity. This protects it from wind, and naturally driven air currents. Little is known about convective heat loss from an open cavity, but it is clear that the position of the cavity and its internal temperature, along with wind speed and direction all affect the rate of heat loss from a cavity (Stine & McDonald, 1989, Paitoonsurikarn et. al., 2003).

Even with all of these imperfections, it is instructive to consider the convective heat loss as being proportional to surface area and the difference between some average temperature, and ambient temperature.

Since convective heat loss is the major heat loss term for most solar collectors, inventors and designers have incorporated many features to collector design to reduce this term. Examples that will be discussed under the different collector designs are; multiple transparent cover sheets for flat-plate collectors, glass tubes surrounding linear absorbers with a vacuum drawn in the intervening space, concentration of solar energy so that the absorber area is small relative to the capture area, absorbers within cavities incorporating glass windows, just to name a few.

Radiation Loss - Radiation heat loss is important for collectors operating at temperatures only slightly above ambient, and becomes dominant for collectors operating at higher temperatures. Figure 5.2 illustrates this transition for a black vertical surface in still air. The rate of radiation heat loss is proportional to the emittance of the surface and the difference in temperature to the fourth power. Described in equation form, we have:

where:

Figure 5.2 Comparison of radiation and convection heat loss for a black, vertical surface in free air at 25^oC.

Terms in this equation over which the collector designer has some control, are the surface emittance and receiver. Surfaces that have a low emittance often have a low absorptance as well, reducing the absorbed solar energy as described in Equation (4.4). However there is a class of surface coatings called ‘selective coatings, that have low values of emittance when the surface is at relatively low temperatures, but high values of absorptance for solar energy. These surfaces are discussed in Section 4.1.4 below.

The other term, which may be minimized, is the receiver surface area. As with convection loss, concentration of solar energy is the main design tool for reducing radiation heat loss by reducing receiver surface area. In addition, cavity receivers can be used since they have small openings through which concentrated solar energy passes, onto larger absorbing surfaces.

Since solar collectors operate out of doors, and generally face the open sky, they exchange radiation with the sky. The equivalent radiation temperature of the sky depends on the air density and its moisture content. When the relative humidity is high and at sea level, the sky temperature can be assumed to be the same as ambient air temperature. However, for low relative humidity or at high altitudes, the sky radiation temperature can be 6 to 8^oC less than ambient temperature. Of course if there is no atmosphere as with space applications, the equivalent sky temperature approaches 0K.

Conduction Loss - The final mode of heat loss to consider in collector design is heat conduction. This is generally described in terms of a material constant, the thickness of the material and its cross-section area:

where:

Conduction loss is usually small compared to convection and radiation losses and therefore is combined with the convection loss term in most analyses. However, it is displayed here for completeness, and to emphasize the importance of ensuring that this mode of heat loss is minimum in any collector design.

Another important mode of conduction loss is the way the high-temperature absorber is attached to the frame and support structure. Use of low conductance materials such as stainless steel can reduce conduction loss into the frame or support casing. However, since most design issues around conduction can be handled without reducing the solar input, the term is generally combined with the convective heat loss term.

In order to provide a single expression for the useful energy produced from a solar collector based on an energy balance of the receiver or absorber, we can combine Equations (4.1) through (4.8) into a single equation. This equation will be repeated in the next few chapters as we develop an understanding of how and why specific types of collectors are designed the way they are.

where:

This equation states that the rate of useful energy produced by a solar collector equals the optical (short wavelength) energy absorbed on the absorber surface, minus the rate of heat loss from the absorber. We have combined the convection heat loss term with the convection term for simplicity.

 5.1.4 Selective Surfaces

where the subscript indicates that these are ‘spectral’ properties and must be integrated over all wavelengths to represent the properties used in Equations (4.4) and (4.7). If the spectrums are different, the integrated properties can be different.

In solar collectors, the spectrum of the energy being absorbed is from a 6,050K black body emitter with peak intensity at a wavelength of 0.48 microns (see Table 2.3). The spectrum of the energy being emitted by the absorber / receiver is defined by the temperature of the absorber surface, T_r which is considerably less. For example if the receiver surface temperature is 80^oC, the peak intensity is at a wavelength of 8.21 microns.

Selective surfaces have a high absorptance (and emittance) for short wavelength (visible) light and have low average absorptance and emittance for long wavelength radiation (thermal or infra-red radiation). They do not violate Kirchoff’s law, however, we say that they have ‘high absorption and low emittance’ meaning high absorption for short wavelength radiation, and low emittance for long wavelength radiation. The end result is a surface that absorbs solar energy well, but does not radiate thermal energy very well.

The concept of a selective surface is illustrated in Figure 5.3. Consider a hypothetical surface with 0.95 absorptance at wavelengths shorter than 5 microns and 0.25 for longer wavelengths. Since 99.5% of solar energy occurs at wavelengths below 5 microns as discussed in Chapter 2, Section 2.1.2, the effective absorptance of such a surface is 0.945. The integrated emittance for this hypothetical surface depends on its temperature. If this surface is 80^oC as is typical for hot water system collectors, 99.1% of its radiant energy is at wavelengths above microns and the integrated emittance for this surface is 24.8%.

On the other hand, the effect of using a selective surface is less dramatic on higher temperature absorbers. If the absorber surface is at a temperature of 700^oC as is typical for receivers in parabolic dish concentrating collectors, only 43.6 % of its radiated energy is at wavelengths above 5 microns and the integrated emittance is 64.5%.

Figure 5.3 Radiation properties of a hypothetical selective surface.

Selective absorbers have been developed that employ composite coating to produce absorbers with the combined properties of high absorptance in the solar spectrum and low emittance in the IR part of the spectrum.

The coating is deposited, as microscopic particles of chromium metal that, because of their geometry, effectively trap the incident light, making the coating look black. Although the black chrome coating is highly absorbing in the visible spectrum, it is transparent in the IR region. Thus the receiver takes on the lower emittance of the bright nickel substrate. The resultant composite bright nickel-black chrome coating thus has high absorptance (approximately equal to 0.95) for the incident solar radiation and low emittance (less than 0.25) in the infrared region.

One final loss mechanism to consider, which is particular to parabolic troughs, is called end-loss. This is the fraction of energy being reflected from the trough that falls beyond the receiver. This loss is proportional to the angle of incidence. End-loss will be illustrated in Chapter 9 of this text.

An energy balance on a photovoltaic panel provides less useful information to the solar energy system designer. However since the photovoltaic cell efficiency decreases with increases in panel temperature, it is important for the rate of heat loss from the panel to be high rather than low! In other words, while the solar thermal panel must be hot to provide useful energy, photovoltaic panels should remain cool to maximize their output of useful energy (electricity in this case).

An energy balance of a photovoltaic cell incorporated within a panel can be written as:

where:

There is a physical limit to the fraction of useful energy that can be produced from the incident optical radiation. Depending on the type and design of the cell this can be from 1 percent to 30 percent. This requires that the rest of the remaining 70% to 99% of the incident energy, be lost through heat loss mechanisms.

 5.2.1 Optical Energy Capture

 5.2.2 Heat Loss

Heat loss from the panel follows the same three paths, convection, radiation and conduction. Optimizing those factors that increase heat loss without increasing cell temperature are important for well designed photovoltaic panels. Maximizing heat loss for concentrating PV collectors is more difficult due to the reduced cell surface area resulting from concentration.

The detailed energy balance for a photovoltaic cell in a panel can be written in a manner similar to Equation (4.9), replacing the receiver/absorber temperature term with the temperature of the cell:

where:

Performance of a photovoltaic panel or concentrating photovoltaic collector can be described in terms of its voltage and current output. The electrical power output from the panel is the product of these two variables. Voltage and current vary with the intensity of the solar irradiance and the temperature of the cell, all of which are described in the following figures. These figures were derived from real data taken on a commercial photovoltaic panel of approximately 0.65 m². However, only the trends are important here and the solar designer should obtain similar information from the manufacturer of the specific panel or concentrator to be used in their design.

The I-V Curve - The fundamental performance of a photovoltaic panel is represented by Figure 5.4, called an I-V curve. It is a plot of the voltage across the panel for different values of current. Since the voltage is a product of the current and the load resistance, lines of constant load resistance are shown to complete the description.

Figure 5.4 Photovoltaic panel output current as a function of the voltage across the panel. These I-V curves are shown for different levels of insolation. Also superimposed on graph are lines of constant load resistance. Data are for a cell temperature of 25^oC and an air mass of 1.5.

It can also be seen that the short-circuit current is also directly proportional to the level of solar irradiance. This characteristic is why photovoltaic cells can be used as a transducer to measure solar irradiance as discussed in Chapter 2.

As the load resistance increases, the current decreases slightly until a point is reached where the cell can no longer maintain a high current level, and it falls to zero. The point at which the panel current falls to zero represents an infinite resistance or an open circuit. The voltage across the panel at zero current is called the open-circuit voltage, V_oc, and represents the output of the unloaded panel. Note that the open-circuit voltage varies only a small amount as a function of solar irradiance (except at very low levels).

A single silicon photovoltaic cell produces an open-circuit voltage of slightly over 0.55 volts. The voltage produced by a photovoltaic panel is a function of how many cells are connected in series. In the case of the panel described below, there must be about 36 photovoltaic cells connected in series in order to produce over 20 volts.

Figure 5.5 Power output of a photovoltaic panel at different levels of solar irradiance. The notation PPP defines the peak power point. Data are for a cell temperature of 25^oC and an air mass of 1.5.

Note that the peak power output occurs at a panel voltage of about 80% of the maximum open-circuit voltage, for a wide range of solar irradiance levels. In order to maintain maximum electrical power output from a photovoltaic panel, the load resistance should match this point. As can be seen on Figure 5.4, the load resistance must increase as solar irradiance decreases in order to maintain maximum power output from the panel.

Since the resistance of most electrical loads are fixed (except for electrical motors and batteries), special consideration must be taken in the system design to ensure that the maximum potential of the solar panel is utilized. There are electronic devices, called peak power trackers that ensure that the panels are operating close to their peak power point.

Figure 5.6 Effect of cell temperature on photovoltaic panel output. Data shown are for an irradiance of 1,000 W/m² and an air mass of 1.5.

All of the data presented so far have been for photovoltaic cells at a temperature of 25^oC. In a real system design, this is seldom the case. Photovoltaic cells are usually encapsulated in a panel to provide rigidity and physical protection of the front surface. Since panels must reject 80% to 90% of the solar energy incident upon them, and usually this transfer is to the ambient air, both the air temperature and the wind speed and direction have great effects on this.

The concept of a normal operating cell temperature (NOCT) has been defined in order to provide some sense of the ability of a specific panel to reject heat and provides a design guideline for system performance analysis. Normal operating cell temperature is the cell temperature under ‘standard operating conditions’, ambient air temperature of 20^oC, solar irradiance of 800 W/m² and wind speed of 1 m/s. NOCT values are specific to a particular panel or collector, but generally are about 50^oC for flat-plate panels.

All data presented above are for an air mass of 1.5 (AM=1.5). The concept of air mass was introduced in Chapter 2, Section 2.2.2. The air mass is an indication of the path length that solar irradiance travels through the atmosphere. An air mass of 1.0 means the sun is directly overhead and the radiation travels through one atmosphere (thickness). The air mass is approximately equal to the reciprocal of the cosine of the zenith angle and an air mass of 1.5 would represent a zenith angle of 48.2 degrees or an altitude angle of 41.8 degrees.

At this point in our discussion of how solar energy is collected, we will define the basic performance parameter, collector efficiency. We will then describe how this is measured and then how these measurements can be combined into an analytical model to predict collector output. This is done in general terms, applicable to flat-plate and concentrating collectors for either thermal or photovoltaic applications.

where: