Solar energy approaches the earth as electromagnetic radiation, with wavelengths ranging from 0.1 μm (x-rays) to 100 m (radio waves). The earth maintains a thermal equilibrium between the annual input of shortwave radiation (0.3 to 2.0 μm) from the sun and the outward flux of longwave radiation (3.0 to 30 μm). Only a limited band is considered in terrestrial applications, because 99% of the sun’s radiant energy has wavelengths between 0.28 and 4.96 μm. The current value of the solar constant (which is defined as the intensity of solar radiation on a surface normal to the sun’s rays, just beyond the earth’s atmosphere at the average earth-sun distance) is 433.4 Btu/h · ft² (ASTM Standard E490). Chapter 14 of the 2017 ASHRAE Handbook—Fundamentals has further information on the available extraterrestrial solar radiation.

The axis about which the earth rotates is tilted at an angle of 23.45° to the earth’s orbital plane and the sun’s equator. The earth’s tilted axis results in a day-by-day variation of the angle between the earth-sun line and the earth’s equatorial plane, called the solar declination δ. This angle varies with the date, as shown in Figure 1, and may be estimated by the following equation:

(1)

where N = day of year, with January 1 = 1.

Figure 1. Variation of Declination δ (degrees) and Equation of Time ET as Function of Day of Year

The relationship between δ and the date from year to year varies to an insignificant degree. The daily change in the declination is the primary reason for the changing seasons, with their variation in the distribution of solar radiation over the earth’s surface and the varying number of hours of daylight and darkness. Note that the following sections are based in the northern hemisphere; sites in the southern hemisphere will be 180° from the examples (e.g., a solar panel should face north).

The earth’s rotation causes the sun’s apparent motion (Figure 2). The position of the sun can be defined in terms of its altitude β above the horizon (angle HOQ) and its azimuth Φ, measured as angle HOS in the horizontal plane.

Figure 2. Apparent Daily Path of the Sun Showing Solar Altitude β and Solar Azimuth Φ

At solar noon, the sun is exactly on the meridian, which contains the south-north line. Consequently, the solar azimuth Φ is 0°. The noon altitude β_N is given by the following equation as

(2)

where LAT = latitude.

Because the earth’s daily rotation and its annual orbit around the sun are regular and predictable, the solar altitude and azimuth may be readily calculated for any desired time of day when the latitude, longitude, and date (declination) are specified. Apparent solar time (AST) must be used, expressed in terms of the hour angle H, where

(3)

Apparent solar time (AST) generally differs from local standard time (LST) or daylight saving time (DST), and the difference can be significant, particularly when DST is in effect. Because the sun appears to move at the rate of 360° in 24 h, its apparent rate of motion is 4 min per degree of longitude. The AST can be determined from the following equation:

(4)

All standard meridians are multiples of 15° east or west of the prime meridian, which is at the Royal Observatory in Greenwich, U.K. The longitude correction is a positive value for the western hemisphere and negative for the eastern hemisphere. The longitudes of the seven standard time meridians that affect North America are Atlantic ST, 60°W; Eastern ST, 75°W; Central ST, 90°W; Mountain ST, 105°W; Pacific ST, 120°W; Alaska ST, 135°W; and Hawaii-Aleutian ST, 150°W. Starting with the prime meridian through Greenwich, many European countries define their standard meridians based on legal, political, and economic, as well as purely physical or geographical, criteria. The longitudes of the three standard time meridians that affect Europe are western European ST (U.K., Ireland, and Portugal), 0°; central European ST, 15°E [e.g., Spain (except for Canary Islands) to the south, Serbia to the east, and Sweden to the north]; and eastern European ST, 30°E (e.g., Greece and Cyprus to the south, Turkey to the east, Finland to the north).

The equation of time (ET) is the measure, in minutes, of the extent by which solar time, as determined by a sundial, runs faster or slower than local standard time (LST), as determined by a clock that runs at a uniform rate. The equation of time may be estimated by the following equation:

(5)

where B = 0.989(N – 81).

Example 1.

Find AST at noon DST on July 21 for Washington, D.C., longitude = 77°W; for Chicago, longitude = 87.6°W; and for Athens, Greece, longitude = 23.75°E.

Solution: Noon DST is 11:00 am LST. Washington is in the eastern time zone, and the LST meridian is 75°W. From Equation (5), the equation of time for July 21 (N = 202) is −6.07 min. Thus, from Equation (4), noon DST for Washington is

Chicago is in the central time zone, and the LST meridian is 90°W. Thus, from Equation (4), noon central DST is

Athens is in the eastern European time zone, and the LST meridian is 30°E. Thus, from Equation (4), noon DST is

The hour angles H (see Figure 3) for these three examples are

To find the solar altitude β and the azimuth Φ when the hour angle H, latitude LAT, and declination δ are known, the following equations may be used:

(6)

(7)

or

(8)

The angle between the line normal to the irradiated surface (OP′ in Figure 3) and the earth-sun line OQ is called the incident angle θ. It is important in solar technology because it affects the intensity of the direct component of solar radiation striking the surface and the surface’s ability to absorb, transmit, or reflect the sun’s rays.

To determine θ, the surface azimuth ψ and the surface-solar azimuth γ must be known. The surface azimuth (angle POS in Figure 3) is the angle between the south-north line SO and the normal PO to the intersection of the irradiated surface with the horizontal plane, shown as line OM. The surface-solar azimuth, angle HOP, is designated by γ and is the angular difference between the solar azimuth Φ and the surface azimuth ψ. For surfaces facing east of south, γ = Φ − ψ in the morning and γ = Φ + ψ in the afternoon. For surfaces facing west of south, γ = Φ + ψ in the morning and γ = Φ − ψ in the afternoon. For south-facing surfaces, ψ = 0°, so γ = Φ for all conditions. The angles δ, β, and Φ are always positive.

For a surface with a tilt angle Σ (measured from the horizontal), the angle of incidence θ between the direct solar beam and the normal to the surface (angle QOP′ in Figure 3) is given by

(9)

Figure 3. Solar Angles with Respect to a Tilted Surface

For vertical surfaces, Σ = 90°, cos Σ = 0, and sin Σ = 1.0, so Equation (9) becomes

(10)

For horizontal surfaces, Σ = 0°, sin Σ = 0, and cos Σ = 1.0, so Equation (9) leads to

(11)

Example 2.

Find θ for a south-facing surface tilted upward 30° from the horizontal at 40° north latitude at 4:00 pm, AST, on August 21.

Solution: From Equation (3), at 4:00 pm on August 21,

From Equation (1) for August 21 (N = 233),

From Equation (6),

From Equation (7),

The surface faces south, so Φ = γ. From Equation (9),

Beyond the earth’s atmosphere, the effective blackbody temperature of the sun is 10,370°R. The maximum spectral intensity occurs at 0.48 μm in the green portion of the visible spectrum. Thekaekara (1973) presents tables and charts of the sun’s extraterrestrial spectral irradiance from 0.120 to 100 μm, the range in which most of the sun’s radiant energy is contained. The ultraviolet portion of the spectrum below 0.40 μm contains 8.73% of the total, another 38.15% is contained in the visible region between 0.40 and 0.70 μm, and the infrared region contains the remaining 53.12%.

In passing through the earth’s atmosphere, some of the sun’s direct radiation is scattered by nitrogen, oxygen, and other molecules, which are small compared to the wavelengths of the radiation; and by aerosols, water droplets, dust, and other particles with diameters comparable to the wavelengths (Gates 1966). This scattered radiation causes the sky to appear blue on clear days, and some of it reaches the earth as diffuse radiation.

Attenuation of the solar rays is also caused by absorption, first by the ozone in the outer atmosphere, which causes a sharp cutoff at 0.29 μm of the ultraviolet radiation reaching the earth’s surface (Figure 4). In the longer wavelengths, there are series of absorption bands caused by water vapor, carbon dioxide, and ozone. The total amount of attenuation at any given location is determined by (1) the length of the atmospheric path through which the rays travel and (2) the composition of the atmosphere. The path length is expressed in terms of the air mass m, which is the ratio of the mass of atmosphere in the actual earth-sun path to the mass that would exist if the sun were directly overhead at sea level (m = 1.0). For all practical purposes, at sea level, m = 1.0/sin β. Beyond the earth’s atmosphere, m = 0.

Before 1967, solar radiation data were based on an assumed solar constant of 419.7 Btu/h · ft² and on a standard sea-level atmosphere containing the equivalent depth of 2.8 mm of ozone, 20 mm of precipitable moisture, and 300 dust particles per cm³. Threlkeld and Jordan (1958) considered the wide variation of water vapor in the atmosphere above the United States at any given time, and particularly the seasonal variation, which finds three times as much moisture in the atmosphere in midsummer as in December, January, and February. The basic atmosphere was assumed to be at sea-level barometric pressure, with 2.5 mm of ozone, 200 dust particles per cm³, and an actual precipitable moisture content that varied throughout the year from 8 mm in midwinter to 28 mm in mid-July. Figure 5 shows the variation of the direct normal irradiation I_DN with solar altitude, as estimated for clear atmospheres and for an atmosphere with variable moisture content.

The ASHRAE clear-sky model described in previous editions of this chapter operated under several well-known limitations. For example, the clearness number was not universally available; its value varied between 0.85 and 1.20 according to location and season in the United States, and was often taken as unity for lack of better data in other countries. The model also lacked universal applicability and the values of its coefficients had to be altered according to location. In addition, the model was derived from a very limited number of measurements, and its applicability outside the United States had never been demonstrated. Finally, clear-sky diffuse irradiance was proportional to beam irradiance, a fact that runs contrary to intuition (i.e., hazier skies should lead to less direct but more diffuse solar irradiation). To overcome these limitations, ASHRAE research projects RP-1363 and RP-1453 developed a significant update of the model (Thevenard and Gueymard 2010). The objectives were to obtain a more accurate model that could enable calculation of clear-sky radiation for any location in the world for all 12 months of the year, while retaining a relatively simple formulation. The resulting model (Gueymard and Thevenard 2013) can be found in Chapter 14 of the 2017 ASHRAE Handbook—Fundamentals, along with the tabulated parameters required at different locations.

Figure 4. Spectral Solar Irradiation at Sea Level for Air Mass = 1.0

Figure 5. Variation with Solar Altitude and Time of Year for Direct Normal Irradiation

The total solar irradiation I_tθ of a terrestrial surface of any orientation and tilt with an incident angle θ is the sum of the direct component I_DN cos θ plus the diffuse component I_dθ coming from the sky plus whatever amount of reflected shortwave radiation I_r may reach the surface from the earth or from adjacent surfaces:

(12)

The diffuse component is difficult to estimate because of its wide variations and nondirectional nature. Figure 5 shows typical values of diffuse irradiation of horizontal and vertical surfaces. For additional information on calculating clear-sky solar radiation, see Chapter 14 of the 2017 ASHRAE Handbook—Fundamentals.

The maximum daily amount of solar irradiation that can be received at any given location is that which falls on a flat plate with its surface kept normal to the sun’s rays so it receives both direct and diffuse radiation. For fixed flat-plate collectors, the total amount of clear-day irradiation depends on the orientation and slope. As shown by Figure 6 for 40° north latitude, the total irradiation of horizontal surfaces reaches its maximum in midsummer, whereas vertical south-facing surfaces experience their maximum irradiation during the winter. These curves show the combined effects of the varying length of days and changing solar altitudes.

Figure 6. Total Daily Irradiation for Horizontal, Tilted, and Vertical Surfaces at 40° North Latitude

In general, flat-plate collectors are mounted at a fixed tilt angle Σ (above the horizontal) to give the optimum amount of irradiation for each purpose. Collectors intended for winter heating benefit from higher tilt angles than those used to operate cooling systems in summer. Solar water heaters, which should operate satisfactorily throughout the year, require an angle that is a compromise between the optimal values for summer and winter. Figure 6 shows the monthly variation of total day-long irradiation on the 21st day of each month at 40° north latitude for flat surfaces with various tilt angles.

NREL tables (rredc.nrel.gov/solar/pubs/redbook/) give the average solar irradiation of each month, at latitudes 24 to 64° north, on surfaces with the following orientations: normal to the sun’s rays (direct normal data do not include diffuse irradiation); horizontal; south-facing, tilted at (LAT−15), LAT, (LAT+15), and 90° from the horizontal. The day-long total irradiation for fixed surfaces is highest for those that face south, but a deviation in azimuth of 15 to 20° causes only a small reduction.

The preceding data apply to clear days. Irradiation for average days may be estimated for any specific location by referring to publications of the U.S. Weather Service. The Climatic Atlas of the United States website (NOA 2010; www.ncdc.noaa.gov/climateatlas/) gives maps of monthly and annual values of percentage of possible sunshine, total hours of sunshine, mean solar radiation, mean sky cover, wind speed, and wind direction. The European Solar Radiation Atlas (Scharmer and Grief 2000) is a database that provides spatial and temporal climatic information for different time scales, including irradiation (global and its components), sunshine duration, air temperature, precipitation, water vapor pressure, and air pressure for a number of stations. Chapter 14 in the 2017 ASHRAE Handbook—Fundamentals also provides several sources for obtaining solar data.

The total daily horizontal irradiation data reported by the U.S. Weather Bureau for approximately 100 stations before 1964 show that the percentage of total clear-day irradiation is approximately a linear function of the percentage of possible sunshine. The irradiation is not zero for days when the percentage of possible sunshine is reported as zero, because substantial amounts of energy reach the earth in the form of diffuse radiation. Instead, the following relationship exists for the percentage of possible sunshine (ratio of day-long horizon irradiation to clear-day total horizon irradiation):

(13)

where a and b are empirical constants for any specified month at any given location. See also Duffie and Beckman (2006) and Jordan and Liu (1977).

In addition to the shortwave (0.3 to 2.0 μm) radiation it receives from the sun, the earth receives longwave radiation (4 to 100 μm, with maximum intensity near 10 μm) from the atmosphere. In turn, a surface on the earth emits longwave radiation q_Rs in accordance with the Stefan-Boltzmann law:

(14)

where

For most nonmetallic surfaces, the longwave hemispheric emittance is high, ranging from 0.84 for glass and dry sand to 0.95 for black built-up roofing. For highly polished metals and certain selective surfaces, e_s may be as low as 0.05 to 0.20.

Atmospheric radiation comes primarily from water vapor, carbon dioxide, and ozone (Bliss 1961); very little comes from oxygen and nitrogen, although they make up 99% of the air.

Approximately 90% of the incoming atmospheric radiation comes from the lowest 300 ft. Thus, air conditions at ground level T_at largely determine the magnitude of the incoming radiation. Downward radiation from the atmosphere q_Rat may be expressed as

(15)

The sky emittance e_at is a complex function of air temperature and moisture content. The dew point of the atmosphere near the ground determines the total amount of moisture in the atmosphere above the place where the dry-bulb (db) and dew-point (dp) temperatures of the atmosphere are determined (Reitan 1963). Bliss (1961) found that the sky emittance is related to the dew-point temperature, as shown by Table 1.

The apparent sky temperature T_sky is defined as the temperature at which the sky (as a blackbody) emits radiation at the rate actually emitted by the atmosphere at ground level temperature with its actual emittance e_at. Then,

(16)

or

(17)

Example 3.

Consider a summer night condition when ground-level temperatures are 65°F dew point and 85°F dry bulb. From Table 1, e_at at 65°F dew point is 0.87, and the apparent sky temperature is

Thus, T_sky = 526.0 − 459.6 = 66.4°F, which is 18.6°F below the ground-level dry-bulb temperature.

For a winter night in Arizona, when temperatures at ground level are 60°F db and 25°F dp, from Table 1, the sky emittance is 0.78, and the apparent sky temperature is 488.3°R or 28.7°F.

A simple relationship, which ignores vapor pressure of the atmosphere, may also be used to estimate the apparent sky temperature:

(18)

where T is in degrees Rankine.

If the temperature of the radiating surface is assumed to equal the atmospheric temperature, the heat loss from a black surface (e_s = 1.0) may be found from Figure 7.

Figure 7. Radiation Heat Loss to Sky from Horizontal Blackbody

Example 4.

For the conditions in the previous example for summer, 85°F db and 65°F dp, the rate of radiative heat loss is about 23 Btu/h · ft². For winter, 60°F db and 25°F dp, the heat loss is about 27 Btu/h · ft².

Where a rough, unpainted roof is used as a heat dissipater, the rate of heat loss rises rapidly as the surface temperature goes up. For the summer example, a painted metallic roof, e_s = 0.96, at 100°F (559.6°R) will have a heat loss rate of

This analysis shows that radiation alone is not an effective means of dissipating heat under summer conditions of high dew-point and ambient temperatures. In spring and fall, when both the dew-point and dry-bulb temperatures are relatively low, radiation becomes much more effective.

On overcast nights, when cloud cover is low, the clouds act much like blackbodies at ground-level temperature, and virtually no heat can be lost by radiation. Exchange of longwave radiation between the sky and terrestrial surfaces occurs in the daytime as well as at night, but the much greater magnitude of the solar irradiation masks the longwave effects.

The solar irradiation calculation methods presented in the previous sections may be used to estimate how much energy is likely to be available at any specific location, date, and time of day for collection by either a concentrating device, which uses only the direct rays of the sun, or by a flat-plate solar thermal collector (hereinafter called a flat-plate collector), which can use both direct and diffuse irradiation. Temperatures needed for space heating and cooling do not exceed 200°F, even for absorption refrigeration, and they can be attained with carefully designed flat-plate collectors.

A flat-plate collector generally consists of the following components (see Figure 8):

Collectors have been built in a wide variety of designs from many different materials (Figure 9). They have been used to heat fluids such as water, water plus an antifreeze additive, or air. Their major purpose is to collect as much solar energy as possible at the lowest possible total cost. The collector should also have a long effective life, despite the adverse effects of the sun’s ultraviolet radiation; corrosion or clogging because of acidity, alkalinity, or hardness of the heat transfer fluid; freezing or air binding in the case of water, or deposition of dust or moisture in the case of air; and broken glazing because of thermal expansion, hail, vandalism, or other causes. These problems can be minimized by using tempered glass.

Figure 8. Exploded Cross Section Through Double-Glazed Solar Water Heater

Glass has been widely used to cover flat-plate solar collectors because it can transmit as much as 90% of the incoming shortwave solar irradiation while transmitting very little of the longwave radiation emitted outward from the absorber plate. Glass with low iron content has a relatively high transmittance for solar radiation (approximately 0.85 to 0.90 at normal incidence), but its transmittance is essentially zero for the longwave thermal radiation (5.0 to 50 μm) emitted by sun-heated surfaces. Note that commercially available grades of window and greenhouse glass have normal incidence transmittances of about 0.87 and 0.85, respectively. For direct radiation, the transmittance varies markedly with the angle of incidence, as shown in Table 2, which gives transmittances for single and double glazing using double-strength clear window glass.

Plastic films and sheets also have high shortwave transmittance, but because most usable varieties also have transmission bands in the middle of the thermal radiation spectrum, their longwave transmittances may be as high as 0.40.

Plastics are also generally limited in the temperatures they can sustain without deteriorating or undergoing dimensional changes. Only a few kinds of plastics can withstand the sun’s ultraviolet radiation for long periods. However, they are not broken by hail and other stones and, in the form of thin films, they are completely flexible and have low mass.

The glass generally used in solar collectors may be either single-strength (0.085 to 0.100 in. thick) or double-strength (0.115 to 0.133 in. thick).

The 4% reflectance from each glass/air interface is the most important factor in reducing transmission, although a gain of about 3% in transmittance can be obtained by using water-white glass. Antireflective coatings and surface texture can also improve transmission significantly. The effect of dirt and dust on collector glazing may be quite small, and the cleansing effect of an occasional rainfall is usually adequate to maintain the transmittance within 2 to 4% of its maximum.

The glazing should admit as much solar irradiation as possible and reduce upward loss of heat as much as possible. Although glass is virtually opaque to the longwave radiation emitted by absorber plates, absorption of that radiation causes an increase in the glass temperature and a loss of heat to the surrounding atmosphere by radiation and convection. This type of heat loss can be reduced by using an infrared-reflective coating on the underside of the glass; however, such coatings are expensive and reduce the effective solar transmittance of the glass by as much as 10%.

In addition to serving as a heat trap by admitting shortwave solar radiation and retaining longwave thermal radiation, the glazing also reduces heat loss by convection. The insulating effect of the glazing is enhanced by using several sheets of glass, or glass plus plastic. Loss from the back of the plate rarely exceeds 10% of the upward loss.

The absorber plate absorbs as much of the irradiation as possible through the glazing, while losing as little heat as possible up to the atmosphere and down through the back of the casing. The absorber plates transfer retained heat to the transport fluid. The absorptance of the collector surface for shortwave solar radiation depends on the nature and color of the coating and on the incident angle, as shown in Table 2 for a typical flat-black paint.

By suitable electrolytic or chemical treatments, selective surfaces can be produced with high values of solar radiation absorptance α and low values of longwave emittance e. Essentially, typical selective surfaces consist of a thin upper layer, which is highly absorbent to shortwave solar radiation but relatively transparent to longwave thermal radiation, deposited on a substrate that has a high reflectance and a low emittance for longwave radiation. Selective surfaces are particularly important when the collector surface temperature is much higher than the ambient air temperature.

For fluid-heating collectors, passages must be integral with, or firmly bonded to, the absorber plate. A major problem is obtaining a good thermal bond between tubes and absorber plates without incurring excessive costs for labor or materials. Materials most frequently used for absorber plates are copper, aluminum, and steel. UV-resistant plastic extrusions are used for low-temperature application. If the entire absorber area is in contact with the heat transfer fluid, the material’s thermal conductance is not important.

Whillier (1964) concluded that steel tubes are as effective as copper if the bond conductance between tube and plate is good. Potential corrosion problems should be considered with the use of any metal. Bond conductance can range from 1000 Btu/h · ft² · °F for a securely soldered or brazed tube, to 3 Btu/h · ft² · °F for a poorly clamped or badly soldered tube. Plates of copper, aluminum, or stainless steel with integral tubes are among the most effective types available. Figure 9 shows a few of the solar water and air heaters that have been used with varying degrees of success.

Temperatures far above those attainable by flat-plate collectors can be reached if a large amount of solar radiation is concentrated on a relatively small collection area. Simple reflectors can markedly increase the amount of direct radiation reaching a collector, as shown in Figure 10A.

Figure 9. Various Types of Solar Collectors

Because of the apparent movement of the sun across the sky, conventional concentrating collectors must follow the sun’s daily motion. There are two methods by which the sun’s motion can be readily tracked. The altazimuth method requires the tracking device to turn in both altitude and azimuth; when performed properly, this method enables the concentrator to track the sun exactly. Paraboloidal solar furnaces (Figure 10B) generally use this system. The polar, or equatorial, mounting points the axis of rotation at the North Star, tilted upward at the angle of the local latitude. By rotating the collector 15° per hour, it tracks the sun almost perfectly (perfectly on March 21 and September 21). If the collector surface or aperture must be kept normal to the solar rays, a second motion is needed to correct for the change in the solar declination. This motion is not essential for most solar collectors.

The maximum variation in the angle of incidence for a collector on a polar mount is ±23.5° on June 21 and December 21; the incident angle correction then is cos 23.5° = 0.917.

Figure 10. Types of Concentrating Collectors

Horizontal reflective parabolic troughs, oriented east and west (Figure 10C), require continuous adjustment to compensate for changes in the sun’s declination. There is inevitably some morning and afternoon shading of the reflecting surface if the concentrator has opaque end panels. The necessity of moving the concentrator to accommodate the changing solar declination can be reduced by moving the absorber or by using a trough with two sections of a parabola facing each other, as shown in Figure 10D. Known as a compound parabolic concentrator (CPC), this design can accept incoming radiation over a relatively wide range of angles. By using multiple internal reflections, any radiation that is accepted finds its way to the absorber surface located at the bottom of the apparatus. By filling the collector shape with a highly transparent material having an index of refraction greater than 1.4, the acceptance angle can be increased. By shaping the surfaces of the array properly, total internal reflection occurs at the medium/air interfaces, which results in a high concentration efficiency. Known as a dielectric compound parabolic concentrator (DCPC), this device has been applied to the photovoltaic generation of electricity (Cole et al. 1977).

The parabolic trough of Figure 10E can be simulated by many flat strips, each adjusted at the proper angle so that all reflect onto a common target. By supporting the strips on ribs with parabolic contours, a relatively efficient concentrator can be produced with less tooling than the complete reflective trough.

Another concept applies this segmental idea to flat and cylindrical lenses. A modification is shown in Figure 10F, in which a linear Fresnel lens, curved to shorten its focal distance, can concentrate a relatively large area of radiation onto an elongated receiver. Using the equatorial sun-tracking mounting, this type of concentrator has been used to attain temperatures well above those that can be reached with flat-plate collectors.

One disadvantage of concentrating collectors is that, except at low concentration ratios, they can use only the direct component of solar radiation, because the diffuse component cannot be concentrated by most types. However, an advantage of concentrating collectors is that, in summer, when the sun rises and sets well to the north of the east-west line, the sun tracker, with its axis oriented north-south, can begin to accept radiation directly from the sun long before a fixed, south-facing flat plate can receive anything other than diffuse radiation from the portion of the sky that it faces. At 40° north latitude, for example, the cumulative direct radiation available to a sun tracker (on a clear day) is 3180 Btu/ft², whereas the total radiation falling on the flat plate tilted upward at an angle equal to the latitude is only 2220 Btu/ft² each day. Thus, in relatively cloudless areas, the concentrating collector may capture more radiation per unit of aperture area than a flat-plate collector.

To get extremely high inputs of radiant energy, many flat mirrors or heliostats using altazimuth mounts can be used to reflect their incident direct solar radiation onto a common target. Using slightly concave mirror segments on the heliostats, large amounts of thermal energy can be directed into the cavity of a steam generator to produce steam at high temperature and pressure.

The performance of collectors may be analyzed using a procedure originated by Hottel and Woertz (1942) and extended by Whillier (in Jordan and Liu 1977). The basic equation is

(19)

Equation (19) also may be adapted for use with concentrating collectors:

(20)

where

Figure 11. Variation of Absorptance and Transmittance with Incident Angle

The transmittance for single and double glazing and the absorptance for flat-black paint may be found in Table 2 for incident angles from 0 to 90°. These values, and the products of τ and α, are also shown in Figure 11. The solar-optical properties of the glazing and absorber plate change little for θ between 0° and 30°, but, because all values reach zero when θ = 90°, they drop off rapidly for values of θ beyond 40°.

For nonselective absorber plates, U_L varies with the temperature of the plate and the ambient air, as shown in Figure 12. For selective surfaces, which strongly reduce the emittance of the absorber plate, U_L is much lower than the values shown in Figure 12. Ask manufacturers of such surfaces for values applicable to their products, or consult test results that give the necessary information.

Figure 12. Variation of Overall Heat Loss Coefficient U_L with Absorber Plate Temperature and Ambient Air Temperatures for Single-, Double-, and Triple-Glazed Collectors

Example 5.

A flat-plate collector is operating in Denver, latitude = 40° north, on July 21 at noon solar time, and the total solar irradiation incident on the plane of the collector I_tθ is 306 Btu/h · ft². The atmospheric temperature is 85°F, and the average temperature of the absorber plate is 140°F. The collector is single-glazed with flat-black paint on the absorber. The collector faces south, and the tilt angle is 30° from the horizontal. Find the rate of heat collection and collector efficiency. Neglect losses from the back and sides of the collector.

Solution: From Equation (1) for July 21 (N = 202), δ = 20.4°.

From Equation (2),

From Equation (3), H = 0; therefore from Equation (7), sin Φ = 0 and thus, Φ = 0°. Because the collector faces south, ψ = 0°, and γ = Φ. Thus γ = 0°. Then Equation (9) gives

From Figure 11, for n = 1, τ = 0.87 and α = 0.96.

From Figure 12, for an absorber plate temperature of 140°F and an air temperature of 85°F, U_L = 1.3 Btu/h · ft² · °F.

Then from Equation (19),

Collector efficiency η is

The general expression for collector efficiency is

(21)

For incident angles below about 35°, the product τα is essentially constant and Equation (21) is linear with respect to the parameter (t_p − t_a)/I_tθ, as long as U_L remains constant.

ASHRAE (in Jordan and Liu 1977) suggested introducing an additional term, the collector heat removal factor F_R, to allow use of the fluid inlet temperature in Equations (19) and (21):

(22)

(23)

where F_R equals the ratio of the heat actually delivered by the collector to the heat that would be delivered if the absorber were at t_fi. F_R is found from the results of a test performed in accordance with ISO Standard 9806-2017. The Solar Rating and Certification Corporation (SRCC) conducts this test in the United States and publishes the results, along with day-long performance outputs. Similar organizations around the world (e.g., the International Organization for Standardization [ISO], the European Committee for Standardization [CEN], Commonwealth Scientific and Industrial Research Organization [CISRO]) provide similar test results. For additional information on SRCC ratings, see Chapter 37 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment.

The results of such a test are plotted in Figure 13. When the parameter is zero, because there is no temperature difference between fluid entering the collector and the atmosphere, the value of the y-intercept equals F_R(τα). The slope of the efficiency line equals the overall heat loss factor U_L multiplied by F_R. For the single-glazed, nonselective collector with the test results shown in Figure 13, the y-intercept is 0.82, and the x-intercept is 0.69 ft² · h · °F/Btu. This collector used high-transmittance single glazing, τ = 0.91, and black paint with an absorptance of 0.97, thus F_R = 0.82/(0.91 × 0.97) = 0.93.

Figure 13. Efficiency Versus (t_fi − t_at)/I_tθ for Single-Glazed Solar Water Heater and Double-Glazed Solar Air Heater

Assuming that the relationship between η and the parameter is actually linear, as shown, then the slope is −0.82/0.69 = −1.19; thus U_L = 1.19/F_R = 1.19/0.93 = 1.28 Btu/h · ft² · °F. The tests on which Figure 13 is based were run indoors. Wind speed and fluid velocity can affect measured efficiency.

Figure 13 also shows the efficiency of a double-glazed air heater with an unfinned absorber coated with flat-black paint. The y-intercept for the air heater B is considerably less than it is for water heater A because (1) transmittance of the double glazing used in B is lower than the transmittance of the single glazing used in A and (2) F_R is lower for B than for A because of the lower heat transfer coefficient between air and the unfinned metal absorber.

The x-intercept for air heater B is greater than it is for the water heater A because the upward loss coefficient U_L is much lower for the double-glazed air heater than for the single-glazed water heater. The data for both A and B were taken at near-normal incidence with high values of I_tθ. For Example 5, using a single-glazed water heater, the value of the parameter would be close to (140 − 85)/306 = 0.18 ft² · h · °F/Btu, and the estimated efficiency, 0.60, agrees closely with the test results.

When irradiation is below about 100 Btu/h · ft², losses from the collector may exceed the heat that can be absorbed. This situation varies with the temperature difference between the collector inlet temperature and the ambient air, as suggested by Equation (22).

When the incident angle rises above 30°, the product of the glazing’s transmittance and the absorber plate’s absorptance τα begins to diminish; thus, heat absorbed also drops. Losses from the collector are generally higher as time moves farther from solar noon, and consequently efficiency also drops. Thus, daylong efficiency is lower than near-noon performance. During early afternoon, efficiency is slightly higher than at the comparable morning time, because the ambient air temperature is lower in the morning than in the afternoon.

ISO Standard 9806-2017 describes the incident angle modifier, which may be found by tests run when the incident angle is set at 30, 45, and 60°. The incident angle modifier is the ratio of the actual (τα)_θ factor at some incidence angle θ to the normal (τα)_n factor at normal incident radiation; for normal angles of incidence, the modifier is unity. Simon (1976) showed that for many flat-plate collectors, the incident angle modifier is a linear function of the quantity (1/cos θ – 1). For evacuated tubular collectors, the incident angle modifier may grow with rising values of θ. For additional information on the incident angle modifier, see ISO Standard 9806-2017 and Chapter 37 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment.

The efficiency should be reported in terms of the gross collector area A_g rather than the aperture area A_ap. The reported efficiency is lower than that given by Equation (23), but the total energy collected is not changed by this simplification:

(24)

This section describes the major components involved in the collection, storage, transportation, control, and distribution of solar heat for a domestic hot-water (DHW) system.

Collectors. Flat-plate collectors are most commonly used for water heating because of the year-round load requiring temperatures of 80 to 180°F. For discussions of other collectors and applications, see Chapter 37 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment, and previous sections of this chapter. Collectors must withstand extreme weather (e.g., freezing, stagnation, high winds), as well as system pressures.

Heat Transfer Fluids. Heat transfer fluids transport heat from the solar collectors to the domestic water. There are potential chemical and mechanical problems with this transfer, primarily in systems in which a heat exchanger interface exists with the potable water supply. Both the chemical compositions of the heat transfer fluids (pH, toxicity, and chemical durability) and their mechanical properties (specific heat and viscosity) must be considered.

Except in unusual cases, or when potable water is being circulated, the energy transport fluid is nonpotable and could contaminate potable water. Even potable or nontoxic fluids in closed circuits are likely to become nonpotable because of contamination from metal piping, solder joints, and packing, or by the inadvertent installation of a toxic fluid at a later date.

Thermal Energy Storage. Heat collected by solar domestic and service water heaters is virtually always stored in a liquid in tanks. Storage tanks and bins should be well insulated. In domestic hot-water systems, heat is usually stored in one or two tanks. The hot-water outlet is at the top of the tank, and cold (makeup) water enters the tank through a dip tube that extends down to within 4 to 6 in. of the tank bottom. The outlet on the tank to the collector loop should be approximately 4 in. above the tank bottom to prevent scale deposits from being drawn into the collectors. Water from the collector array returns to the top of the storage tank. A plumbing arrangement connecting the collector array to the middle to lower portion of the tank may take advantage of thermal stratification, depending on the delivery temperature from the collectors and the flow rate through the storage tank.

Single-tank electric auxiliary systems often incorporate storage and auxiliary heating in the same vessel. Conventional electric water heaters commonly have two heating elements: one near the top and one near the bottom. If a dual-element tank is used in a solar energy system, the bottom element should be disconnected and the top left functional to take advantage of fluid stratification. Standard gas- and oil-fired water heaters should not be used in single-tank arrangements. In gas and oil water heaters, heat is added to the bottom of the tanks, which reduces both stratification and collection efficiency in single-tank systems.

Dual-tank systems often use the solar domestic hot-water storage tank as a preheat tank. The second tank is normally a conventional domestic hot-water tank containing the auxiliary heat source. Multiple tanks are sometimes used in large institutions, where they operate similarly to dual-tank heaters. Although using two tanks may increase collector efficiency and the solar fraction, it increases tank heat losses. The makeup water inlet is usually a dip tube that extends near the bottom of the tank.

Estimates for sizing storage tanks usually range from 1 to 2.5 gal per square foot of solar collector area. The estimate used most often is 1.8 gal per square foot of collector area, which usually provides enough heat for a sunless period of about a day. Storage volume should be analyzed and sized according to the project water requirements and draw schedule; however, solar applications typically require larger-than-normal tanks, usually the equivalent of the average daily load.

For details on thermal energy storage, see Chapter 37 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment.

Heat Exchangers. Indirect solar water heaters require one or more heat exchangers. Heat transfer from solar collectors to potable hot water has the potential for contaminating the water. Heat exchangers influence the effectiveness of energy collected to heat domestic water. They also separate and protect the potable water supply from contamination when nonpotable heat transfer fluids are used in the collector loop. For this reason, various codes regulate the need for and design of heat exchangers.

Heat exchanger selection should consider the following:

Heat exchanger selection depends on characteristics of fluids that pass through the heat exchanger and properties of the exchanger itself. Fluid characteristics to consider are fluid type, specific heat, mass flow rate, and hot- and cold-fluid inlet and outlet temperatures. Physical properties of the heat exchanger to consider are the overall heat transfer coefficient of the heat exchanger and the heat transfer surface area.

For most solar domestic hot-water designs, only the hot and cold inlet temperatures are known; the other temperatures must be calculated using the heat exchanger’s physical properties. Two quantities that are useful in determining a heat exchanger’s heat transfer and a collector’s performance characteristics when it is combined with a given heat exchanger are the (1) fluid capacitance rate, which is the product of the mass flow rate and specific heat of fluid passing through the heat exchanger, and (2) heat exchanger effectiveness, which relates the capacitance rate of the two fluids to the fluid inlet and outlet temperatures. Effectiveness is equal to the ratio of the actual heat transfer rate to the maximum heat transfer rate theoretically possible. Generally, a heat exchanger effectiveness of 0.4 or greater is desired.

Expansion Tanks. An indirect solar water heater operating in a closed collector loop requires an expansion tank to prevent excessive pressure. Fluid in solar collectors under stagnation conditions can boil, causing excessive pressure to develop in the collector loop, and expansion tanks must be sized for this condition. Expansion tank sizing formulas for closed-loop hydronic systems, found in Chapter 13 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment, may be used for solar heater expansion tank sizing, with the volume of water in the system defined as the total volume of fluid in the solar collectors and of any piping located above the collectors, if significant. This sizing method provides a passive means for eliminating fluid loss through overtemperature or stagnation, common problems in closed-loop solar systems. It results in a larger expansion tank than typically found in hydronic systems, but the increase in cost is small compared to the savings in fluid replacement and maintenance costs (Lister and Newell 1989).

Pumps. Pumps circulate heat transfer liquid through collectors and heat exchangers. In solar domestic hot-water heaters, the pump is usually a centrifugal circulator driven by a motor of less than 300 W. The flow rate for collectors generally ranges from 0.015 to 0.04 gpm/ft². Pumps used in drainback systems must provide pressure to overcome friction and to lift the fluid to the collectors.

Piping. Piping can be plastic, copper, galvanized steel, or stainless steel. The most widely used is nonlead, sweat-soldered L-type copper tubing. M-type copper is also acceptable if allowed by local building codes. If water/glycol is the heat transfer fluid, galvanized pipes or tanks must not be used because unfavorable chemical reactions will occur; copper piping is recommended instead. Also, if glycol solutions or silicone fluids are used, they may leak through joints where water would not. Piping should be compatible with the collector fluid passage material; for example, copper or plastic piping should be used with collectors having copper fluid passages.

Piping that carries potable water can be plastic, copper, galvanized steel, or stainless steel. In indirect systems, corrosion inhibitors must be checked and adjusted no less than annually, preferably every three months. Inhibitors should also be checked if the system overheats during stagnation. If dissimilar metals are joined, dielectric or nonmetallic couplings should be used. The best protection is sacrificial anodes or getters in the fluid stream. Their location depends on the material to be protected, anode material, and electrical conductivity of the heat transfer fluid. Sacrificial anodes of magnesium, zinc, or aluminum are often used to reduce corrosion in storage tanks. Because many possibilities exist, each combination must be evaluated. A copper-aluminum or copper-galvanized steel joint is unacceptable because of severe galvanic corrosion. Aluminum, copper, and iron have a greater potential for corrosion.

Elimination of air, accommodating thermal pipe expansion/contraction, and proper piping slope must be considered to avoid possible failures. Collector pipes (particularly manifolds) should be designed to allow expansion from stagnation temperature to extreme cold weather temperature. Expansion can be controlled with offset elbows in piping, hoses, or expansion couplings. Expansion loops should be avoided unless they are installed horizontally, particularly in systems that must drain for freeze protection. The collector array piping should slope 0.06 in. per foot for drainage (DOE 1978a).

Air can be eliminated by placing air vents at all piping high points and by air purging during filling. Flow control, isolation, and other valves in the collector piping must be chosen carefully so that these components do not restrict drainage significantly or back up water behind them. In systems without antifreeze, the collectors must drain completely.

Valves and Gages. Valves in solar domestic hot-water systems must be located to ensure system efficiency, satisfactory performance, and safety of equipment and personnel. Drain valves must be ball type; gate valves may be used if the stem is installed horizontally. Check valves or other valves used for freeze protection or for reverse thermosiphoning must be reliable to avoid significant damage.

Auxiliary Heat Sources. On sunny days, a typical solar energy system should supply water at a predetermined temperature, and the solar storage tank should be large enough to hold sufficient water for a day or two. Because of the intermittent nature of solar radiation, an auxiliary heater must be installed to handle hot-water requirements. If a utility is the source of auxiliary energy, auxiliary heater operation can be timed to take advantage of off-peak utility rates. The auxiliary heater should be carefully integrated with the solar energy heater to obtain maximum solar energy use. For example, the auxiliary heater should not destroy any stratification that may exist in the solar-heated storage tank, which would reduce collector efficiency.

Ductwork, particularly in systems with air-type collectors, must be sealed carefully to avoid leakage in duct seams, damper shafts, collectors, and heat exchangers. Ducts should be sized using conventional air duct design methods.

Control. Controls regulate solar energy collection by controlling fluid circulation, activate system protection against freezing and overheating, and initiate auxiliary heating when it is required. The three major control components are sensors, controllers, and actuators. Sensors detect conditions or measure quantities, such as temperature. Controllers receive output from the sensors, select a course of action, and signal a component to adjust the condition. Actuators, such as pumps, valves, dampers, and fans, execute controller commands and regulate the system. The trend is to maintain a near-constant temperature difference between the collector outlet and inlet, to maximize daily heat collection. Currently, controls operate in a user-adjustable temperature difference range.

Temperature sensors measure the temperature of the absorber plate near the collector outlet and near the bottom of the storage tank. The sensors send signals to a controller, such as a differential temperature thermostat, for interpretation.

The differential thermostat compares signals from the sensors with adjustable set points for high and low temperature differentials. The controller performs different functions, depending on which set points are met. In liquid systems, when the temperature difference between the collector and storage reaches a high set point, usually 12 to 15°F, the pump starts, automatic valves are activated, and circulation begins. When the temperature difference reaches a low set point, usually 4°F, the pump is shut off and the valves are deenergized and returned to their normal positions. To restart the system, the differential temperature set point must again be met. If the system has either freeze or overheat protection, the controller opens or closes valves or dampers and starts or stops pumps or fans to protect the system when its sensors detect conditions indicating that either freezing or overheating is about to occur.

Sensors must be selected to withstand high temperature, such as may occur during collector stagnation. Collector loop sensors should be located as close as possible to the outlet of the collectors, either in or on a pipe above or near the collector, or in the collector outlet passage.

The storage temperature sensor should be near the bottom of the storage tank to detect the temperature of fluid before it is pumped to the collector or heat exchanger. Storage fluid is usually coldest at that location because of thermal stratification and the location of the makeup water supply. The sensor should be either securely attached to the tank and well insulated, or immersed inside the tank near the collector supply.

The freeze protection sensor, if required, should be located so that it detects the coldest liquid temperature when the collector is shut down. Common locations are the back of the absorber plate at the bottom of the collector, the collector intake or return manifolds, or the center of the absorber plate. The center absorber plate location is recommended because reradiation to the night sky freezes the collector heat transfer fluid, even though the ambient temperature is above freezing. Some system types, such as the recirculation system, have two sensors for freeze protection; others, such as the draindown, use only one.

Control of on/off temperature differentials affects system efficiency. If the differential is too high, the collector starts later than it should; if it is too low, the collector starts too soon. The turn-on differential for liquid systems usually ranges from 10 to 30°F and is commonly lower in warmer climates and higher in cold climates. For air systems, the range is usually 25 to 45°F.

The turn-off temperature differential is more difficult to estimate. Selection depends on a comparison between the value of the energy collected and the cost of collecting it. It varies with individual systems, but a value of 4°F is typical and generally the fixed default value in the control.

Water temperature in the collector loop depends on ambient temperature, solar radiation, radiation from the collector to the night sky, and collector loop insulation. Freeze protection sensors should be set to detect 40°F.

Sensors are important but often overlooked control components. They must be selected and installed properly because no control can produce accurate outputs from unreliable sensor inputs. Sensors are used in conjunction with a differential temperature controller and are usually supplied by the controller manufacturer. Sensors must survive the anticipated operating conditions without physical damage or loss of accuracy. Low-voltage sensor circuits must be located away from high-voltage lines to avoid electromagnetic interference. Sensors attached to collectors should be able to withstand the stagnation temperature.

Sensor calibration, which is often overlooked by installers and maintenance personnel, is critical to system performance; a routine calibration maintenance schedule is essential.

Another control option is to use a photovoltaic (PV) panel that powers a DC pump. A properly sized and oriented PV panel converts sunlight into electricity to run a small circulating pump. No additional sensing is required because the PV panel and pump output increase with sunlight intensity and stop when no sunlight (collector energy) is available. However, to prevent operation when the collector outlet temperature is lower than the storage tank, a DC-powered differential controller may be used. Cromer (1984) showed that, with proper matching of pump and PV electrical characteristics, PV panel sizes as low as 5 W per 40 ft² of thermal panel may be used successfully. Difficulty with late starting and running too long in the afternoon can be alleviated by tilting the PV panel slightly to the east during commissioning of the installed system. Electronic devices such as a maximum power point tracker and linear current booster can also improve pump performance at start-up (Bai et al. 2011).

Thermosiphon systems (Figure 14) heat potable water or a heat transfer fluid and rely on natural convection to transport it from the collector to storage. For direct systems, pressure-reducing valves are required when the city water pressure is greater than the working pressure of the collectors. In a thermosiphon system, the storage tank must be elevated above the collectors, which sometimes requires designing the upper level floor and ceiling joists to bear this additional load. Extremely hard or acidic water can cause scale deposits that clog or corrode the absorber fluid passages. Thermosiphon flow is induced whenever there is sufficient sunshine, so these systems do not need pumps.

A direct-circulation system (Figure 15) pumps potable water from storage to the collectors when there is enough solar energy available to warm it. It then returns the heated water to the storage tank until it is needed. Collectors can be mounted either above or below the storage tank. Direct-circulation systems are only feasible in areas where freezing is infrequent. Freeze protection is provided either by recirculating warm water from the storage tank or by flushing the collectors with cold water. Direct water-heating systems should not be used in areas where the water is extremely hard or acidic because scale deposits may clog or corrode the absorber fluid passages, rendering the system inoperable.

Figure 14. Thermosiphon System

Direct-circulation systems are exposed to city water line pressures and must withstand pressures as required by local codes. Pressure-reducing valves and pressure-relief valves are required when city water pressure is greater than the working pressure of the collectors. Direct-circulation systems often use a single storage tank for both solar energy storage and the auxiliary water heater, but two-tank storage systems can be used.

Figure 15. Direct Circulation System

Draindown Systems. Draindown systems (Figure 16) are direct-circulation water-heating systems in which potable water is pumped from storage to the collector array, where it is heated. Circulation continues until usable solar heat is no longer available. When a freezing condition is anticipated or a power outage occurs, the system drains automatically by isolating the collector array and exterior piping from the city water pressure and using one or more valves for draining. Solar collectors and associated piping must be carefully sloped to drain the collector’s exterior piping.

Indirect water-heating systems (Figure 17) circulate a freeze-protected heat transfer fluid through the closed collector loop to a heat exchanger, where its heat is transferred to the potable water. The most commonly used heat transfer fluids are water/ethylene glycol and water/propylene glycol solutions, although other heat transfer fluids such as silicone oils, hydrocarbons, and refrigerants can also be used (ASHRAE 1983). These fluids are nonpotable, sometimes toxic, and normally require double-wall heat exchangers. The double-wall heat exchanger can be located inside the storage tank, or an external heat exchanger can be used. The collector loop is closed and therefore requires an expansion tank and a pressure-relief valve. A one- or two-tank storage can be used. Additional overtemperature protection may be needed to prevent the collector fluid from decomposing or becoming corrosive.

Figure 16. Draindown System

Designers should avoid automatic water makeup in systems using water/antifreeze solutions because a significant leak may raise the freezing temperature of the solution above the ambient temperature, causing the collector array and exterior piping to freeze. Also, antifreeze systems with large collector arrays and long pipe runs may need a time-delayed bypass loop around the heat exchanger to avoid freezing the heat exchanger on start-up.

Figure 17. Indirect Water Heating

Drainback Systems. Drainback systems are generally indirect water-heating systems that circulate treated (typically demineralized water or 50% glycol/water) or untreated water through the closed collector loop to a heat exchanger, where its heat is transferred to the potable water. Circulation continues until usable energy is no longer available. When the pump stops, the collector fluid drains by gravity to a storage or tank. In a pressurized system, the tank also serves as an expansion tank, so it must have a temperature- and pressure-relief valve to protect against excessive pressure. In an unpressurized system (Figure 18), the tank is open and vented to the atmosphere.

The collector loop is isolated from the potable water, so valves are not needed to actuate draining, and scaling is not a problem. The collector array and exterior piping must be sloped to drain completely, and the pumping pressure must be sufficient to lift water to the top of the collector array.

Integral collector storage (ICS) systems use hot-water storage as part of the collector. Some types use the surface of a single tank as the absorber, and others use multiple long, thin tanks placed side by side horizontally to form the absorber surface. In this latter type of ICS, hot water is drawn from the top tank, and cold replacement water enters the bottom tank. Because of the greater nighttime heat loss from ICS systems, they are typically less efficient than pumped systems, and using selective surfaces (see Chapter 37 of the 2020 ASHRAE Handbook—Systems and Equipment) is strongly recommended. ICS systems are normally installed as a solar preheater without pumps or controllers. Flow through the ICS system occurs on demand, as hot water flows from the collector to a hot-water auxiliary tank in the structure.

Figure 18. Drainback System

SRCC provides annual performance results for these various types of systems at www.solar-rating.org.

Site-built, large-volume solar air- or water-heating equipment is used in commercial and industrial applications. These site-built systems are based on a transpired solar collector for air heating and shallow solar pond technologies.

Transpired Solar Collector. This collector preheats outdoor air by drawing it through small holes in a metal panel. It is typically installed on south-facing walls and is designed to heat outdoor air for building ventilation or process applications (Kutscher 1996). The prefabricated panel, made of dark metal with thousands of small holes, efficiently heats and captures fresh air by drawing it through a perforated adsorber, eliminating the cost and reflection losses associated with a glazing. The sun heats the metal panel, which in turn heats a boundary layer of air on its surface. Air is heated as it is drawn through the small holes into a ventilation system for delivery as ventilation air, for crop drying, or other process applications (Shukla et al. 2012).

Shallow Solar Pond. The shallow solar pond (SSP) is a large-scale ICS solar water heater (Figure 19) capable of providing more than 5000 gal of hot water per day for commercial and industrial use. These ponds are built in standard modules and tied together to supply the required load. The SSP module can be ground mounted or installed on a roof. It is typically 16 ft wide and up to 200 ft long. The module contains one or two flat water bags similar to a water bed. The bags rest on a layer of insulation inside concrete or fiberglass curbs. The bag is protected against damage and heat loss by greenhouse glazing. A typical pond filled to a 4 in. depth holds approximately 6000 gal of water.

Solar pool heaters do not require a separate storage tank, because the pool itself serves as storage. In most cases, the pool’s filtration pump forces the water through the solar panels or plastic pipes. In some retrofit applications, a larger pump may be required to handle the solar heater’s needs, or a small pump may be added to boost pool water to the solar collectors.

Figure 19. Shallow Solar Pond

Automatic control may be used to direct the flow of filtered water to the collectors when solar heat is available; this may also be accomplished manually. Normally, solar heaters are designed to drain down into the pool when the pump is turned off; this provides the collectors with freeze protection.

Four primary types of collector designs are used for swimming pool heat: (1) rigid black plastic panels (polypropylene), usually 4 by 10 ft or 4 by 8 ft; (2) tube-on-sheet panels, which typically have a metal deck (copper or aluminum) with copper water tubes; (3) an ethylene-propylene diene monomer (or ethylene-propylene terpolymer) (EPDM) rubber mat, extruded with water passages running its length; and (4) arrays of black plastic pipe, usually 1.5 in. diameter acrylonitrile butadiene styrene (ABS) plastic (Root et al. 1985).

Domestic hot-water (DHW) recirculation systems (Figures 20 and 21), which continuously circulate domestic hot water throughout a building, are found in motels, hotels, hospitals, dormitories, office buildings, and other commercial buildings. Recirculation heat losses in these systems are usually a significant part of the total water-heating load. In Figures 20 and 21, the three-way valve prevents heated water from returning to the solar storage tank when the return temperature is greater than the solar tank temperature. This ensures that heated water is used only when it is hot enough and prevents heating of the solar tank by the conventional heater. Using a cycle timer to control the DHW circulating pump that is synchronized with the building hot-water consumption profile can also help reduce circulation losses. The return line on the makeup preheat system can go directly to the conventional water heater to eliminate the three-way valve and prevent the solar tank from being heated by auxiliary energy.

Figure 20. DHW Recirculation System

A well-designed passive solar building needs (1) an appropriate thermal load (i.e., minimize heating loads first); (2) aperture, such as clear, glazed windows; (3) thermal storage (e.g., massive floors or walls, containers of water) to minimize overheating and to allow use of heat at night; (4) control, either manual or automatic, to address overheating; and (5) night insulation of the aperture so that there is not a net heat loss (Swift and Lawrence 2010). Passive systems may be divided into several categories. The first residence to which the name solar house was applied used a large expanse of south-facing glass to admit solar radiation; this is known as a direct-gain passive system. The solar collector (windows) and storage (e.g., floors, walls) are part of the occupied space and typically have the highest percent of heating load met by solar. The optimal amount of thermal mass is often around 8 in. thick high-density concrete for direct-gain floors over conditioned basements. Optimization requires a design concept that captures and stores the highest amount of solar energy without unnecessarily increasing cost or complexity. Direct-gain surfaces should have high absorptivity (dark color) and should not be covered by carpet, tile, much furniture, or other obstacles that prevent absorption of available solar radiation. To reduce heat losses, thermal mass should be well insulated from the outdoor environment or ground.

Indirect-gain passive systems use the south-facing wall surface or the roof to absorb solar radiation, which causes a rise in temperature that, in turn, conveys heat into the building in several ways. Pueblos and cliff dwellings built by indigenous peoples in what is now the southwestern United States used this principle. Glass has led to modern adaptations of the indirect-gain principle (Balcomb et al. 1977; Trombe et al. 1977; Wilson 1979).

By glazing a large south-facing, massive masonry wall, solar energy can be absorbed during the day, and heat conduction to the inner surface provides radiant heating at night. The wall’s mass and its relatively low thermal diffusivity delay the heat’s arrival at the indoor surface until it is needed. The glazing reduces heat loss from the wall back to the atmosphere and increases the system’s collection efficiency.

Openings in the wall near the floor and ceiling allow convection to transfer heat to the room. Air in the space between the glass and the wall warms as soon as the sun heats the outer surface of the wall. The heated air rises and enters the building through the upper openings. Cool air flows through the lower openings, and convective heat gain can be established as long as the sun is shining.

In another indirect-gain passive system, a metal roof/ceiling supports transparent plastic bags filled with water (Hay and Yellott 1969). Movable insulation above these water-filled bags is rolled away during the winter day to allow the sun to warm the stored water. The water then transmits heat indoors by convection and radiation. The insulation remains over the water bags at night or during overcast days. During the summer, the water bags are exposed at night for cooling by (1) convection, (2) radiation, and (3) evaporation of water on the bags. The insulation covers the water bags during the day to protect them from unwanted irradiation. Pittenger et al. (1978) tested a building for which water rather than insulation was moved to provide summer cooling and winter heating.

Attached greenhouses (sunspaces) can be used as solar attachments when the orientation and other local conditions are suitable. The greenhouse can provide a buffer between the exterior wall of the building and the outdoors. During daylight, warm air from the greenhouse can be introduced into the house by natural convection or a small fan.

In most passive systems, control is accomplished by moving a component that regulates the amount of solar radiation admitted into the structure. Manually operated window shades or venetian blinds are the most widely used and simplest controls, but they may also be operated automatically.

Passive heating and cooling systems have been effective in field demonstrations A well-designed passive-solar-heated building may provide 45 to nearly 100% of daily heat requirements. Architectural design features can dramatically reduce air-conditioning loads through heat gain avoidance techniques and natural cooling, where climatically appropriate (Howard and Pollock 1982; Howard and Saunders 1989).

Passive solar daylighting has been shown to be cost effective, providing dual benefits: it both reduces electric power demand and lowers cooling costs in properly designed interiors and atrium spaces.

Active systems absorb solar radiation with collectors and convey it to storage using a suitable fluid. As heat is needed, it is obtained from storage via heated air or water. Control is exercised by several types of thermostats, the first being a differential device that starts the flow of fluid through the collectors when they have been sufficiently warmed by the sun. It also stops fluid flow when the collectors no longer gain heat. In locations where freezing occurs only rarely, a low-temperature sensor on the collector controls a circulating pump when freezing is impending. This process wastes some stored heat, but it prevents costly damage to the collector panels. This system is not suitable for regions where freezing temperatures persist for long periods.

The space-heating thermostat is generally the conventional double-contact type that calls for heat when the temperature in the controlled space falls to a predetermined level. If the temperature in storage is adequate to meet the heating requirement, a pump or fan starts to circulate the warm fluid. If the temperature in the storage subsystem is inadequate, the thermostat calls on the auxiliary or standby heat source.

Solar combi systems are solar heating installations providing space heating as well as domestic hot water for the building occupants (IEA Task 26). The primary energy sources are solar and an auxiliary source such as biomass, gas, oil, or electricity, either direct or with a heat pump. The solar contribution (the part of the heating demand met by solar energy) varies from 10% to 100%, depending on the size of the solar collector surface, storage volume, heat load, and climate. Europe has the most well-developed market for different solar thermal applications (Balaras et al. 2010). In 2016, around 2% of the global installed capacity supplied heat for both domestic hot water and space heating (solar combi systems). In Europe, the share of combi systems was about 19% of the total solar thermal market. The total capacity of glazed and evacuated tube solar collectors for solar combi systems already have a market share of 41% in Germany, 39% in Austria, and 21% in Switzerland (Weiss and Spork-Dur 2017).

Figure 25 shows one of the many systems for service hot water and space heating. In this case, a large, atmospheric-pressure storage tank is used, from which water is pumped to the collectors by pump P₁ in response to the differential thermostat T₁. Drainback is used to prevent freezing, because the amount of antifreeze required would be prohibitively expensive. Service hot water is obtained by placing a heat exchanger coil in the tank near the top, where, even if stratification occurs, the hottest water will be found.

An auxiliary water heater boosts the temperature of the sun-heated water when required. Thermostat T₂ senses the indoor temperature and starts pump P₂ when heat is needed. If water in the storage tank becomes too cool to provide enough heat, the second contact on the thermostat calls for heat from the auxiliary heater.

Figure 25. Solar Collection, Storage, and Distribution System for Domestic Hot Water and Space Heating

Standby heat becomes increasingly important as heating requirements increase. The heating load, winter availability of solar radiation, and cost and availability of the auxiliary energy must be determined. It is rarely cost effective to do the entire heating job for either space or service hot water by using the solar heat collection and storage system alone.

Electric resistance heaters have the lowest first cost, but often have high operating costs. Water-to-air heat pumps, which use sun-heated water from the storage tank as the evaporator energy source, are an alternative auxiliary heat source. The heat pump’s COP is 10 to 14. When both summer cooling and winter heating are needed, the heat pump is a logical solution, particularly in large systems where a cooling tower is used to dissipate the heat withdrawn from the system.

The system shown in Figure 25 may be retrofitted into a warm-air furnace. In such systems, the primary heater is deleted from the space heating circuit, and the coil is located in the return duct of the existing furnace. Full back-up is thus obtained, and the auxiliary heater provides only the heat not available at the storage temperature.

When solar energy is used for cooling as well as for heating, the absorption system shown in Figure 26 or one of its many modifications may be used. The collector and storage must operate at a temperature approaching 200°F on hot summer days when the water from the cooling tower exceeds 80°F, but considerably lower operating water temperatures may be used when cooler water is available from the tower. Controls for collection, cooling, and distribution are generally separated, with the circulating pump P₁ operating in response to the collector thermostat T₁. Thermostat T₂ senses the indoor air-conditioned space temperature. When T₂ calls for heating, valves V₁ and V₂ direct water flow from the storage tank through the unactivated auxiliary heater to the fan-coil in the air distribution system. The fan F₂ in this unit may respond to the thermostat also, or it may have its own control circuit so that it can bring in outdoor air when the temperature is suitable.

Figure 26. Space Heating and Cooling System Using Lithium Bromide/Water Absorption Chiller

When thermostat T₂ calls for cooling, the valves direct hot water into the absorption unit’s generator, and pumps P₃ and P₄ are activated to pump cooling tower water through the absorber and condenser circuits and chilled water through the cooling coil in the air distribution system. A relatively large hot-water storage tank allows the unit to operate when no sunshine is available. A chilled-water storage tank (not shown) may be added so that the absorption unit can operate during the day whenever water is available at a sufficiently high temperature to make the unit function properly. The COP of a typical lithium bromide/water absorption unit may be as high as 0.75 under favorable conditions, but frequent on/off cycling of the unit to meet a high variable cooling load may cause significant loss in performance because the unit must be heated to operating temperature after each shutdown. Modulating systems are analyzed differently than on/off systems.

Water-cooled condensers are required with the absorption cycles, because the lithium bromide/water cycle operates with a relatively delicate balance among the temperatures of the three fluid circuits (cooling tower water, chilled water, and activating water). Steam-operated absorption systems, from which solar cooling systems are derived, customarily operate at energizing temperatures of 230 to 240°F, but these are above the capability of most flat-plate collectors. The solar cooling units are designed to operate at considerably lower temperature, but unit ratings are also lowered.

Smaller domestic units may operate with natural circulation, or percolation, which carries the lithium bromide/water solution from the generator (to which the activating heat is supplied) to the separator and condenser; there, the reconcentrated LiBr is returned to the absorber while the water vapor goes to the condenser before being returned to the evaporator, where cooling occurs. Larger units use a centrifugal pump to transfer the fluid.

Absorption is the most popular heat-driven cooling technology, although different sorption technologies are also available (e.g. adsorption, see Chapter 32 of the 2017 ASHRAE Handbook—Fundamentals). Each technology has specific characteristics that match the building’s HVAC design, loads, and local climatic conditions. A good design must first exploit all available solar radiation and then cover the remaining loads from conventional sources (Henning 2007).

Proper calculations for collector and storage size depend on the solar cooling technology used. A hot-water storage may be integrated between the solar collectors and the heat-driven chiller to dampen fluctuations in the return temperature of the hot water from the chiller. Storage size depends on the application: when cooling loads mainly occur during the day, a smaller storage is necessary than when the loads peak in the evening. Strictly avoid heating the hot-water storage by the back-up heat source. The storage only exists to store excess heat of the solar system and to make it available when sufficient solar heat is not available.

The single-effect absorption machine gives best results with a heat supply temperature of 176 to 212°F. Double- and triple-effect machines require higher supply temperatures. Therefore, these machines require a higher-temperature collector. However, with a double-effect system, if the solar-supplied temperature drops below 212°F, the performance drops sharply, below that of a single-effect.

Most large-scale applications (85 ton and up) use LiBr/H₂O and produce chilled water at about 43 to 45°F; the COP is relatively higher than for H₂O/ammonia (NH₃). However, LiBr systems must be water cooled and thus usually require a cooling tower, whereas NH₃ systems can have an air-cooled condenser. Because of the large vapor volume of the water refrigerant, LiBr/H₂O chillers usually have large physical dimensions. For small cooling loads and for applications where it is not possible to use water cooling, an H₂O/NH₃ system is preferred.

In hot and sunny climates, the required solar collector area is approximately 114 to 152 ft²/ton. Higher heat supply temperature for multieffect chillers require higher-cost evacuated tube or concentrating collectors, and may need a high-temperature (i.e., thermochemical) storage.

In LiBr/H₂O systems, the refrigerant freezes at 32°F, so care is necessary while the machine is idle, especially in winter. Another potential problem is crystallization of the LiBr solution at high concentrations, which may result from high generator temperatures or from inadequate temperature control at other parts of the machine. Thus, the heat supply temperature from the solar collectors or heat storage must be adequately controlled. The cooling water temperature, particularly to the absorber, must also be monitored. Chiller capacity may be controlled by increasing the heat supply temperature or decreasing the cooling water temperature; both techniques increase capacity as well as the COP.

A fuel-fired boiler usually covers the need for a back-up system to heat the desorber of the heat-driven chiller. However, use caution because, during periods of low solar radiation availability, collectors connected in series with a back-up boiler can turn into a heat sink instead of a heat source. Alternatively, one may use a back-up conventional chiller alongside the solar-assisted machine, but this requires an additional full-sized chiller, which would be idle for long periods. A viable design solution for a single-effect absorption cycle is to incorporate an auxiliary desorber powered by the back-up, whereas the original desorber is powered by solar heat. The weak solution goes first to the solar-powered desorber, where it is concentrated as much as possible with the available solar heat, and then proceeds to the auxiliary desorber, where it is concentrated further using heat from the back-up source. Vapor from both desorbers is then supplied to the condenser.

The performance of any solar energy system is directly related to the (1) heating load, (2) amount of solar radiation available, and (3) solar energy system characteristics. Various calculation methods use different procedures and data when considering the available solar radiation. Some simplified methods consider only average annual incident solar radiation; complex methods may use hourly data.

Solar energy system characteristics, as well as individual component characteristics, are required to evaluate performance. The degree of complexity with which these systems and components are described varies from system to system.

The cost effectiveness of a solar domestic and service hot-water heating system depends on the initial cost and energy cost savings. A major task is to determine how much energy is saved. The annual solar fraction (the annual solar contribution to the water-heating load divided by the total water-heating load) can be used to estimate these savings. It is expressed as a decimal or percentage and generally ranges from 0.3 to 0.8 (30 to 80%), although more extreme values are possible.

A very simplified way to initially estimate the size of a solar heating system is to divide the average daily load by the daily output of a particular collector based on its SRCC rating for the application and solar conditions. This requires knowledge of the average daily incident solar radiation for the site and the type of collector best suited to the application. See Chapter 37 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment for more information.

Simplified analysis methods have the advantages of computational speed, low cost, rapid turnaround (especially important during iterative design phases), and ease of use by persons with little technical experience. Disadvantages include limited flexibility for design optimization, lack of control over assumptions, and a limited selection of systems that can be analyzed. Thus, if the application, configuration, or load characteristics under consideration are significantly nonstandard, a detailed computer simulation may be required to achieve accurate results. This section describes the f-Chart method for active solar heating and the solar load ratio method for passive solar heating (Dickinson and Cheremisinoff 1980; Klein and Beckman 1979; Lunde 1980).

The amount of hot water required must be estimated accurately because it affects component selection. Oversized storage may result in low-temperature water that requires auxiliary heating to reach the desired supply temperature. Undersizing can prevent the collection and use of available solar energy. Chapter 50 gives methods to determine the load.

Beckman et al. (1977) developed the f-Chart method using an hourly simulation program (Klein et al. 1976) to evaluate space heating and service water heating in many climates and conditions. The results of these analyses correlate the fraction f of the heat load met by solar energy. The correlations give the fraction f of the monthly heating load (for space heating and hot water) supplied by solar energy as a function of collector characteristics, heating loads, and weather. The standard error of the differences between detailed simulations in 14 locations in the United States and the f-Chart predictions was about 2.5%. Correlations also agree within the accuracy of measurements of long-term performance data. Beckman et al. (1977, 1981) and Duffie and Beckman (2006) discuss the method in detail.

The f-Chart method requires the following data:

The f-Chart assumes several standard systems and applies only to these liquid configurations. The standard liquid heater uses water, an antifreeze solution, or air as the heat transfer fluid in the collector loop and water as the storage medium (Figure 27). Energy is stored in the form of sensible heat in a water tank. A water-to-air heat exchanger transfers heat from the storage tank to the building. A liquid-to-liquid heat exchanger transfers energy from the main storage tank to a domestic hot-water preheat tank, which in turn supplies solar-heated water to a conventional water heater. A conventional furnace or heat pump is used to meet the space heating load when energy in the storage tank is depleted.

Figure 28 shows the assumed configuration for a solar air heater with a pebble-bed storage unit. Energy for domestic hot water is provided by heat exchange from air leaving the collector to a domestic water preheat tank, as in the liquid system. The hot water is further heated, if necessary, by a conventional water heater. During summer operation, a seasonal, manually operated storage bypass damper is used to avoid heat loss from the hot bed into the building.

Figure 27. Liquid-Based Solar Heating System (Adapted from Beckman et al. 1977)

The standard solar domestic water heater collector heats either air or liquid. Collected energy is transferred by a heat exchanger to a domestic water preheat tank that supplies solar-heated water to a conventional water heater. The water is further heated to the desired temperature by conventional fuel if necessary.

Figure 28. Solar Air Heating System (Adapted from Beckman et al. 1977)

Computer simulations correlate dimensionless variables and the long-term performance of the systems. The fraction f of the monthly space- and water-heating loads supplied by solar energy is empirically related to two dimensionless groups. The first dimensionless group X is collector loss; the second Y is collector gain:

(27)

(28)

where

Ac	=	area of solar collector, ft2
Fr	=	collector heat exchanger efficiency factor
FR	=	collector efficiency factor
UL	=	collector overall energy loss coefficient, Btu/h · ft2 · °F
Δθ	=	total number of hours in month
t̄a	=	monthly average ambient temperature, °F
L	=	monthly total heating load for space heating and hot water, Btu
H̄T	=	monthly averaged daily radiation incident on collector surface per unit area, Btu/day · ft2
N	=	number of days in month
	=	monthly average transmittance-absorptance product
(τα)n	=	normal transmittance-absorptance product
tref	=	reference temperature, 212°F

F_RU_L and F_R(τα)_n are obtained from collector test results. The ratios F_r/F_R and are calculated using methods given by Beckman et al. (1977). The value of t̄_a is obtained from meteorological records for the month and location desired. H̄_T is calculated from the monthly averaged daily radiation on a horizontal surface by the methods previously discussed in this chapter or in Duffie and Beckman (2006). The monthly load L can be determined by any appropriate load-estimating method, including analytical techniques or measurements. Values of the collector area A_c are selected for the calculations. Thus, all the terms in these equations can be determined from available information.

Transmittance τ of the transparent collector cover and the absorptance α of the absorber plate depend on the angle of incidence of solar radiation on the collector surface. Collector tests are usually run with the radiation nearly perpendicularly incident on the collector. Thus, the value of F_R(τα)_n determined from these tests ordinarily corresponds to the transmittance and absorptance values for radiation at normal incidence. Depending on collector orientation and time of year, the monthly average values of transmittance and absorptance can be significantly lower. The f-Chart method requires knowledge of the ratio of the monthly average to normal incidence transmittance-absorptance.

The f-Chart method for liquid systems is similar to that for air systems. The fraction of the monthly total heating load supplied by the solar air heating system is correlated with the dimensionless groups X and Y, as shown in Figure 29. To determine the fraction of the heating load supplied by solar energy for a month, values of X and Y are calculated for the collector and heating load in question. The value of f is determined at the intersection of X and Y on the f-Chart, or from the following equivalent equations.

Figure 29. Chart for Air System (Adapted from Beckman et al. 1977)

Air system:

(29)

Liquid system:

(30)

This is done for each month of the year. The solar energy contribution for the month is the product of f and the total heating load L for the month. Finally, the fraction F of the annual heating load supplied by solar energy is the sum of the monthly solar energy contributions divided by the annual load:

(31)

Example 6.

Calculating the heating performance of a residence, assume that a solar heating system is to be designed for use in Madison, WI, with two-cover collectors facing south, inclined 58° with respect to the horizontal. The air heating collectors have the characteristics F_RU_L = 0.50 Btu/h · ft² · °F and F_R(τα)_n = 0.49. The t̄_a is 19.4°F, the total space and water-heating load for January is 34.1 × 10⁶ Btu), and the solar radiation incident on the plane of the collector is 1.16 × 10³ Btu/day · ft². Determine the fraction of the load supplied by solar energy with a system having a collector area of 538.2 ft².

Solution: For air systems, there is no heat exchanger penalty factor and F_r/F_R = 1. The value of is 0.94 for a two-cover collector in January. Therefore, the values of X and Y are

Then the fraction f of the energy supplied for January is 0.19. The total solar energy supplied by this system in January is

The annual system performance is obtained by summing the energy quantities for all months. The result is that 37% of the annual load is supplied by solar energy.

The collector heat removal factor F_R that appears in X and Y is a function of the collector fluid flow rate. Because of the higher cost of power for moving fluid through air collectors rather than through liquid collectors, the capacitance rate used in air heaters is ordinarily much lower than that in liquid heaters. As a result, air heaters generally have a lower F_R. Values of F_R corresponding to the expected airflow in the collector must be used to calculate X and Y.

Increased airflow rate tends to improve collector performance by increasing F_R, but it tends to decrease performance by reducing the degree of thermal stratification in the pebble bed (or water storage tank). The f-Chart for air systems is based on a collector airflow rate of 2 scfm per square foot of collector area. The performance with different collector airflow rates can be estimated by using the appropriate values of F_R in both X and Y. A further modification to the value of X is required to account for the change in degree of stratification in the pebble bed.

Air system performance is less sensitive to storage capacity than that of liquid systems for two reasons: (1) air systems can operate with air delivered directly to the building in which storage is not used, and (2) pebble beds are highly stratified and additional capacity is effectively added to the cold end of the bed, which is seldom heated and cooled to the same extent as the hot end. The f-Chart for air systems is for a nominal storage capacity. Performance of systems with other storage capacities can be determined by modifying the dimensionless group X as described in Beckman et al. (1977).

With modification, f-Charts can be used to estimate performance of solar water heating operating in the range of 120 to 160°F. The main water supply temperature and minimum acceptable hot-water temperature (i.e., desired delivery temperature) both affect the performance of solar water heating. The dimensionless group X, which is related to collector energy loss, can be redefined to include these effects. If monthly values of X are multiplied by a correction factor, the f-Chart for liquid-based solar space- and water-heating systems can be used to estimate monthly values of f for water heating. Experiments and analysis show that the load profile for a well-designed heater has little effect on long-term performance. Although the f-Chart was originally developed for two-tank systems, it may be applied to single- and double-tank domestic hot-water systems with and without collector tank heat exchangers. The standard f-Chart method is not designed to provide performance estimates of thermosiphon and ICS systems.

For industrial process heating, absorption air conditioning, or other processes for which the delivery temperature is outside the normal f-Chart range, modified f-Charts are applicable (Klein et al. 1976). The concept underlying these charts is that of solar usability: the fraction of the total solar energy that is useful in the given process. This fraction depends on the required delivery temperature as well as collector characteristics and solar radiation. The procedure allows the energy delivered to be calculated in a manner similar to that for f-Charts. An example of applying this method to solar-assisted heat pumps is presented in Svard et al. (1981).

The relative areas method, based on correlations of the f-Chart method, predicts annual rather than monthly active heating performance (Barley and Winn 1978). An hourly simulation program was used to develop the monthly solar-load ratio (SLR) method, another simplified procedure for residential systems (Dickinson and Cheremisinoff 1980). Based on hour-by-hour simulations, a method was devised to estimate performance based on monthly values of horizontal solar radiation and heating degree-days. This SLR method has also been extended to nonresidential buildings for a range of design water temperatures (Dickinson and Cheremisinoff 1980; Schnurr et al. 1981).

A widely accepted simplified passive space heating design tool is the solar-load ratio (SLR) method (Balcomb et al. 1984; DOE 1980/1982). It can be applied manually, although, like the f-Chart, software is also available. The SLR method for passive systems is based on correlating results of multiple hour-by-hour computer simulations, the algorithms of which have been validated against test cell data for the following generic passive heating types: direct gain, thermal storage wall, and attached sunspace. Monthly and annual performance, as expressed by the auxiliary heating requirement, is predicted by this method. The method applies to single-zone, envelope-dominated buildings. A simplified, annual-basis distillation of SLR results, the load collector ratio (LCR) method, and several simple-to-use rules have grown out of the SLR method. Several hand-held calculator and microcomputer programs have been written using the method (Nordham 1981).

The SLR method uses a single dimensionless correlating parameter (SLR), which Balcomb et al. (1982) define as a particular ratio of solar energy gains to building heating load:

(32)

A correlation period of 1 month is used; thus the quantities in the SLR are calculated for a 1 month period.

The parameter that is correlated to the SLR, the solar savings fraction (SSF), is defined as

(33)

The SSF measures the energy saving expected from the passive solar building, relative to a reference nonpassive solar building.

In Equation (33), the net reference load is equal to the degree-day load DD of the nonsolar elements of the building:

(34)

where NLC is the net load coefficient, which is a modified UA coefficient computed by leaving out the solar elements of the building. The nominal units are Btu/°F · day. The term DD is the temperature departure in degree-days computed for an appropriate base temperature. A building energy analysis based on the SLR correlations begins with a calculation of the monthly SSF values. The monthly auxiliary heating requirement is then calculated by

(35)

Annual auxiliary heat is calculated by summing the monthly values.

By definition, SSF is the fraction of the heat load of the nonsolar portions of the building met by the solar element. If the solar elements of the building (south-facing walls and window in the northern hemisphere) were replaced by other elements so that the net annual flow of heat through these elements was zero, the building’s annual heat consumption would be the net reference load. The savings achieved by the solar elements would therefore be the net reference load in Equation (34) minus the auxiliary heat in Equation (35), which gives

(36)

Although simple, in many situations and climates, Equation (36) is only approximately true because a normal solar-facing wall with a normal complement of opaque walls and windows has a near-zero effect over the entire heating season. In any case, the auxiliary heat estimate is the primary result and does not depend on this assumption.

The hour-by-hour simulations used as the basis for the SLR correlations are done with a detailed model of the building in which all the design parameters are specified. The only parameter that remains a variable is the solar collector area, which can be expressed in terms of the load collector ratio (LCR):

(37)

Performance variations are estimated from the correlations, which allow the user to account directly for thermostat set point, internal heat generation, glazing orientation, and configuration, shading, and other solar radiation modifiers. Major solar system characteristics are accounted for by selecting one of 94 reference designs. Other design parameters, such as thermal storage thickness and conductivity, and the spacing between glazings, are included in a series of sensitivity calculations obtained using hour-by-hour simulations. The results are generally presented in graphic form so that the designer can see the effect of changing a particular parameter.

Solar radiation correlations for the collector area have been determined using hour-by-hour simulation and typical meteorological year (TMY) weather data. These correlations are expressed as ratios of incident-to-horizontal radiation, transmitted-to-incident radiation, and absorbed-to-transmitted radiation as a function of the latitude minus mid-month solar declination and the atmospheric clearness index (i.e., ratio between the actual clear-day direct irradiation intensity at a specific location and the intensity calculated for the standard atmosphere for the same location and date).

Performance predictions of the SLR method have been compared to predictions made by the detailed hour-by-hour simulations for a variety of climates in the United States. The standard error in the prediction of the annual SSF, compared to the hour-by-hour simulation, is typically 2 to 4%.

The annual solar savings fraction calculation involves summing the results of 12 monthly calculations. For a particular city, the resulting SSF depends only on the LCR of Equation (37), system type, and the temperature base used in calculating the temperature departure. Thus, tables that relate SSF to LCR for various systems and for various degree-day base temperatures may be generated for a particular city. Such tables are easier for hand analysis than are the SLR correlations.

Annual SSF versus LCR tables have been developed for 209 locations in the United States and 14 cities in southern Canada for 94 reference designs and 12 base temperatures (Balcomb et al. 1984). Fernandez-Gonzalez (2007) evaluates the thermal performance of five passive solar strategies (direct gain, Trombe wall, water wall, sunspace, and roof pond) under severe winter climates with predominant overcast sky conditions.

Example 7.

(Abstracted from the detailed version in Balcomb et al. [1982].) Consider a small office building located in Denver, Colorado, with 3000 ft² of usable space and a sunspace entry foyer that faces due south; the vertically projected collector area A_p is 420 ft². A sketch and preliminary plan are shown in Figure 30. Distribution of solar heat to the offices is primarily by convection through the doorways from the sunspace. The principal thermal mass is in the common wall that separates the sunspace from the offices and in the sunspace floor. Even though lighting and cooling are likely to have the greatest energy costs for this building, heating is a significant energy item and should be addressed by a design that integrates passive solar heating, cooling, and lighting.

Solution: Table 3 shows calculations of the net load coefficient. Then,

and the total load coefficient includes the solar aperture

From Equation (37), the load collector ratio is

If the daily internal heat is 130,000 Btu/day, and the average thermostat setting is 68°F, then

(Note that solar gains to the space are not included in the internal gain term as they customarily are for nonsolar buildings.)

In this example, the solar system is type SSD1, defined in Balcomb et al. (1982, 1984). It is a semiclosed sunspace with a 12 in. masonry common wall between it and the heated space (offices). The aperture is double-glazed, with a 50° tilt and no night insulation. To achieve a vertically projected area of 420 ft², a sloped glazed area of 420/sin 50° = 548 ft² is required.

The SLR correlation for solar system type SSD1 is shown in Figure 31. Values of the absorbed solar energy S and heating degree-days DD to base temperature 60°F are determined monthly. For S, the solar radiation correlation presented in Balcomb et al. (1984) for tabulated Denver, CO, weather data is used. For January, the horizontal surface incident radiation is 840 Btu/ft² · day. The 60°F base degree-days are 933. Using the tabulated incident-to-absorbed coefficients found in Balcomb et al. (1984), S = 43,681 Btu/ft². Thus S/DD = 46.8 Btu/ft² · °F · day. From Figure 31, at an LCR = 30 Btu/ft² · °F · day, the SSF = 0.51. Therefore, for January,

Repeating this calculation for each month and adding the results for the year yields an annual auxiliary heat of 19.94 × 10⁶ Btu.

Figure 30. Commercial Building in Example 7

Table 3 Calculations for Example 7

	Area A, ft2	U-Factor, Btu/h · ft2 · °F	UA, Btu/h · °F
Opaque wall	2000	0.04	80
Ceiling	3000	0.03	90
Floor (over crawl space)	3000	0.04	120
Windows (E, W, N)	100	0.55	55
Subtotal			345
Infiltration			180
Subtotal			525
Sunspace (treated as unheated space)			151
Total			676
ASHRAE procedures are approximated with V = volume, ft3; c = heat capacity of Denver air, Btu/ft3 · °F; ACH = air changes/h; equivalent UA for infiltration = VcACH. In this case, V = 24,000 ft3, c = 0.015 Btu/ft3 · °F, and ACH = 0.5.

Figure 31. Monthly SSF Versus Monthly S/DD for Various LCR Values

Most solar components are the same as those in HVAC and hot-water systems (pumps, piping, valves, and controls), and their installation is not much different from a conventional installation. Solar collectors are the most unfamiliar component in a solar heater. They are located outdoors, which requires penetration of the building envelope. They also require a structural element to support them at the proper tilt and orientation toward the sun.

The site must be taken into account. Collectors should be (1) located so that shading is minimized and (2) installed so that they are attractive both on and off site. They should also be located to minimize vandalism and to avoid a safety hazard.

Collectors should be placed near the storage tank to reduce piping cost and heat loss. The collector and piping must be installed so that they can be drained without trapping fluid in the system.

For best annual performance, collectors should be installed at a tilt angle above the horizontal that is appropriate for the local latitude. In the northern hemisphere they should be oriented toward true south, not magnetic south. Small variations in tilt (±10°) and orientation (±20°) do not reduce performance significantly.

The following checklist is for designers of solar heating and cooling systems. Specific values have not been included because these vary for each application. The designer must decide whether design figures are within acceptable limits for any particular project (see DOE [1978b] for further information). The review order listed does not reflect their precedence or importance during design.

Solar photovoltaic (PV) systems, unlike solar thermal systems, convert solar radiation into electricity, rather than heat. Therefore, instead of pumps, piping, and valves, a PV system’s energy transmission elements are comprised of wires, switches, fuses, power conversion equipment (e.g., inverters, charge controllers), and other electrical equipment. Chapter 37 of the 2020 ASHRAE Handbook—HVAC Systems and Equipment discusses the fundamentals of PV operation and key system components.

Photovoltaics are used for electricity generation to power remotely located communication equipment, remote monitoring, lighting, water pumping, battery charging, and cathodic protection. In the built environment, PV systems are designed to reduce non-renewable energy consumption, reduce peak power demand, and/or enhance energy resiliency. The first step before designing a PV application is to analyze electric loads and minimize them wherever possible. The size of a PV array can be reduced substantially with an energy-conserving building design and by implementing energy efficiency measures such as high-efficiency HVAC equipment, appliances, motors, and plug loads.

 Grid-Connected Systems

This section describes PV system applications that are connected to the electric utility and allow for bidirectional flow of electricity between the client (e.g., a building with on-grid PV system) and the power grid (Figure 32).

Grid-Connected Systems. Grid-connected (also known as grid-tied) PV systems use string inverters or microinverters that convert DC power from the PV array to AC. The AC output power is then fed to the AC load circuit. The inverters are designed to synchronize their AC output (phase, frequency, and voltage) with the electric utility.

Figure 32. Grid-Connected (Left) and Grid-Interactive (Right) Photovoltaic Applications for Buildings (Natural Resources Canada 2018)

A typical grid-connected PV system uses no battery storage. Excess power generated during the day is fed back to the utility grid. Grid power is used when the PV system does not generate enough energy to fulfill the building’s electricity requirements. During a power outage, a grid-tie inverter automatically disconnects, so no solar power is fed to the AC load circuit or to the grid until grid power is restored.

The main objective is to reduce energy consumption from the grid. However, this system could also include a small battery storage system to reduce peak power demand.

Grid-Interactive Systems. These are advanced configurations of a grid-connected system that can also function in isolated mode (when the grid is down) or in a parallel-to-the-grid mode by using grid-interactive inverters (Figure 32). A grid-interactive inverter can regulate or form its own local grid, thus allowing the PV system to feed the AC load circuit with power for emergency loads even when the grid is down. It may also be able to perform advanced inverter functions at the request of the utility, such as improving voltage or reactive power characteristics. In areas where energy resiliency and emergency operation are of importance (e.g., areas vulnerable to earthquakes, hurricanes, heat waves, ice storms, etc.), the use of grid-interactive inverters is recommended. A typical grid-interactive system incorporates battery storage and aims to reduce end-use utility energy consumption, reduce peak power demand, and enhance energy resiliency.

 PV for Buildings

Photovoltaic modules can be installed on flat roofs, sloped roofs, facades, and shading elements. In all cases, the PV system should be designed and installed without compromising any requirements or functions of the building envelope.

Building-Applied PV. In building-applied PV (BAPV) applications, the PV modules are mounted on the building to generate solar electricity. If the BAPV system is removed, the building envelope will still perform as designed. Rack-mounted photovoltaic systems on roofs or facades are typical examples. In these applications, the PV modules are mounted either parallel to the building surface or at optimal tilt and azimuth angles to maximize energy yield.

Building-Integrated PV. In building-integrated PV (BIPV) applications, the PV modules act as a building envelope product or system in addition to generating solar electricity. If a BIPV system is removed, the building envelope performance is compromised and the BIPV will need to be replaced by an appropriate envelope product or system. Typical applications include flat or inclined BIPV roofing and skylights, opaque and transparent BIPV curtain walls, double-skin BIPV facades, and exterior BIPV shading elements. Depending on the application, a BIPV system might influence daylighting, passive solar gains, and visual as well as thermal and acoustic comfort. As a result, the building heating, cooling, and electric lighting loads are also affected (Figure 33). Ideally, design of a BIPV system should take place in conjunction with the design of the HVAC system and the building envelope.

PV with Thermal Energy Recovery. PV modules typically convert 5 to 22% of the incident solar radiation into electricity; a small fraction is reflected while the rest is absorbed and converted into thermal energy (in some cases where the PV module is transparent, a portion of the incident solar radiation is also transmitted). In a photovoltaic module with thermal energy recovery (PVT), a fraction of this thermal energy is recovered either actively or passively by a heat recovery fluid (air, a liquid, or a refrigerant). As a result, PVT collectors produce both thermal and electrical energy using the same surface area.

Figure 33. Representation of Major Interactions Between BIPV Application, Building Systems, and Occupants (Natural Resources Canada 2018)

Thermal energy can also be recovered from BIPV systems. Such systems are called building-integrated photovoltaics with thermal energy recovery (BIPVT). Air-based PVT or BIPVT systems have an open-loop configuration and use air as the heat recovery fluid. A ventilation cavity is created by installing the photovoltaic modules at a certain distance from the facade or roof on which they are mounted. A fan located downstream of the ventilation cavity draws ambient air through the cavity from one or multiple inlets. The air circulates behind the photovoltaic array to recover some of the heat generated by the modules before entering the building through one or multiple ducts in a plenum. In most PVT or BIPVT systems, air flows from bottom to top to avoid going against natural buoyancy and increasing the system pressure drop. Other airflow patterns are possible, however, such as double-pass flow.

The thermal energy collected can be used directly, as preheated fresh air, or for space or domestic hot-water heating through an air-to-water heat exchanger or heat pump (Figure 34). For all applications, however, the thermal energy generated is not useable at all times. Thus, a well-designed BIPVT roof or facade should have a venting system for the air to escape the cavity naturally when thermal energy is not required and the BIPVT mechanical ventilation system is off. The same design approach also applies on PVT systems. This natural ventilation prevents the cells from overheating. Both forced and natural ventilation operating modes should be considered when selecting the ventilation cavity thickness. Under natural convection, the Nusselt number inside the cavity increases with cavity thickness, enhancing the cooling of the modules. Under mechanical ventilation conditions, however, the convective heat transfer coefficient between the air and the back surface of the module decreases as the cavity thickness increases due to reduced air velocity.

Note that, by operating a PVT or BIPVT roof system during the night, the outdoor air can be precooled by nocturnal radiation and introduced into the building for night cooling.

Figure 34. Air-Based PVT System (Natural Resources Canada 2018)

General design considerations are similar to solar thermal collectors, with orientation in the northern hemisphere generally facing south at a similar tilt to the latitude (LAT ± 15°), for latitudes below 65°. PV systems with other orientations and tilt angles will still generate solar electricity, but with lower energy yield. This is due to reduced irradiance (e.g., an east- or west-facing BIPV facade receives significantly less solar radiation than an equatorial-facing one, on an annual basis), soiling, or snow accumulation. However, nonoptimal angles may be desired for aesthetic, economic, or generation profile tuning reasons.

 PV Design Considerations

An on-site visit and site survey are essential for the proper design, installation and performance of a PV system. The final system design should be performed by a certified professional. The design must comply with local electrical codes. Local building codes may also apply, as well as fire safety regulation and other legislation.

Shading. During the design of any PV system, attention should be given to routine shading (e.g., self-shading, shading due to surrounding buildings, vegetation, topography) or temporary shading (e.g., shading due to vegetation, snow, soiling). A shadow cast on a PV system has higher impact on its energy yield than it would for a solar thermal system because PV is reliant on direct photon energy. Ideally, a PV array should be installed in a shadow-free environment to avoid impact on yield and damage to the PV modules. In reality, shading losses are hard to avoid in an urban or suburban environment. A shading analysis should be carried out to minimize these losses. In the case of a building, a shading analysis also indicates the surfaces with the highest solar potential. Several tools and techniques are available to assist with a shading analysis, including existing building or PV performance simulation tools. For BIPV curtain wall applications, the mounting hardware (mullions) might introduce some shading. Thus, low-profile (or flushed) mullions are recommended.

For crystalline silicon (c-Si) PV systems, mounting in landscape orientation helps to minimize shading losses due to the location of the bypass diodes on the module circuit. The diodes protect the PV cells from damaging reverse-current flow when a PV cell is shaded. However the diodes are prone to failure, and attempts should be made to minimize routine shading. PV-module level inverters or maximum power point trackers can help reducing power losses by optimizing the power output of each PV module individually, so that a low-performing PV module does not impact others in the system.

Soiling and Snow. The amount, type, and characteristics of soiling depend on location. Soiling can cause a reduction in power output between 2% and, in extreme cases, 25%. In most locations, losses due to soiling represent less than 5%, because most soiling is removed by rainfall. Tilt angles of 12^o or higher also allow for more self cleaning with rain. Uniform shading reduces power output. It does not typically damage the PV modules, however, because all cells are uniformly affected. Sometimes, a “dirt dam,” which can shade a row of PV cells, may form at the lower edge of a framed PV module. Bird droppings and leaves are frequent causes of localized shading. Localized shading can damage a PV module, especially if the protective bypass diode is malfunctioning. In areas where snow accumulation might be a concern, tilt angles of 45^o and higher are recommended. In this case, precautions should be taken to ensure pedestrian safety in case of sliding snow.

PV Mounting. General mounting considerations are similar to solar thermal collectors (see the section on Collector Mounting). Mounting tilt, azimuth angle, and module layout influence the maximum electricity production potential. The layout should avoid routine inter-row racking shading and other known shading obstacles. The building and racking system must be able to handle increased loads from the PV system as well as resulting wind and snow loading. Seismic calculations may be needed for earthquake-prone areas. The roof/building condition should have an estimated lifetime at least as long as the PV system (20 years or more).

Care must be taken to ensure that any roof penetration for BAPV and BIPV installations is sealed to prevent water ingress. For ballasted systems, the roofing membrane must be protected from damage due to the weight and possible movement of the system. In addition, adequate rear ventilation is required for most PV modules to ensure product safety and performance. This is typically 4 in. minimum clearance at the rear side of the PV module. An exception is PV modules rated for building integrated installations. Care should be taken when racking and/or module-level electronics may impede ventilation. In all cases, refer to the temperature rating and installation recommendations given by the equipment manufacturer. Clearance should also be given to allow for water drainage and leaf/debris clearing.

Seasonal and daily expansion and contraction of metal components, PV modules, and cabling should be accounted for. Direct contact between dissimilar metals (e.g., steel and aluminum) should be avoided due to galvanic corrosion; stainless steel is often used as an intermediary, especially between aluminum PV module frames and copper grounding/bonding wires.

Ideally, there are access paths to allow servicing of equipment. In some jurisdictions, fire codes require certain setbacks. For sloped-roof installations and carport/canopy applications, sliding snow may present a hazard to pedestrians.

PV equipment staging before installation and structural calculations should also be considered at the design stage.

Wiring Management. PV systems are often comprised of both AC and DC wiring. In AC circuits, electron flow changes direction multiple times every second at a given frequency. However, with DC electricity, electrons flow in one direction only, similar to air moving from higher to lower pressure. Therefore, because the current never crosses zero in a DC circuit, electrical arcing from DC faults can last longer than AC arcs. For this reason, AC switchgear and protection devices cannot be substituted for DC purpose. Special care must also be provided to avoid degraded contact resistance in wiring components due to mechanical stress or corrosion. Ratings for outdoor cables are different than for indoor applications. Cable selection must account for their exposure to the elements, service and installation temperature, and exposure to sunlight. Means must be provided to secure the wiring, avoid abrasion from sharp corners and movement due to wind or other vibrations, and withstand load from snow or freezing rain. Similarly, connectors should be supported and provided with drip loops to avoid water ingress. In some locations, mechanical screening methods are used to protect the DC wiring from rodents.

For BIPV. Depending on the BIPV application, performance and design considerations extend beyond solar electricity generation. Design considerations related to common envelope assemblies (Chapter 45) also apply to BIPV systems.

For BIPV roof applications (the use of typical PV modules), PV shingles or lightweight flexible PV modules can serve as a waterproofing membrane. The design should consider thermal expansion of both modules and cabling.

For BIPV curtain wall applications, BIPV arrays can serve as a face-sealed or rain screen system. A drained/vented air cavity behind the BIPV module should be designed to (1) minimize rain entry in the wall and outward drainage of the cavity and (2) prevent module overheating by allowing natural ventilation in the cavity.

For BIPV fenestration applications, BIPV modules should always be the outermost layer of the glazing unit to maximize solar electricity generation and minimize overheating. The selection of optical, thermal, and electrical properties of the BIPV fenestration product should be the result of an integrated design approach where solar gains, solar electricity generation, visual and thermal comfort, and acoustic and thermal insulation are assessed through building performance simulations. Chapter 60 discusses the integrated design approach that should be followed in the design and realization of BIPV system applications.

For BIPV shading applications, BIPV modules should be oriented to provide the building or building facade with the desired shading while limiting routine or temporary shading on the modules.

When BIPV systems are located in areas prone to hurricanes, cyclones, or earthquakes or the application requires blast or impact live load protection, they should be designed to satisfy the relevant safety and performance standards.

Depending on building size, “blanks” are sometimes used to mimic the visual aesthetics of PV modules to fill gaps in the PV system and achieve the electrical wiring configuration required. Because these are typically not exact replicas, they should be symmetrically positioned to maintain aesthetics.

For BIPVT. In PVT or BIPVT systems, the thermal yield influences the electrical yield and vice versa. Most PV technologies operate with higher efficiency at lower temperature. Therefore, a more efficient thermal system removing more heat allows the PV to generate more electricity. In a BIPVT air system, performance is affected not only by the cavity thickness, but also by its configuration and the solar cell technology used. In addition, the thermal and electrical yield of BIPVT air systems depends on the weather and operating conditions that typically affect both air solar thermal collectors and photovoltaic modules. These variables include incident solar radiation, ambient air temperature, wind speed, air flowrate, and second-order effects, such as solar angle of incidence and air mass. Generally, useful performance metrics for BIPVT air systems consist of thermal efficiency, air temperature rise, and electrical efficiency. The effects of irradiance and wind speed on the thermal efficiency, air temperature rise, and PV modules back-surface temperature of a nearly 15 ft long BIPVT system with a 1.6 in. cavity thickness are shown in Figures 35 and 36.

Figure 35. Air-Based BIPVT Thermal Efficiency, Temperature Rise, and Back-Surface Temperature as Function of Specific Flowrate and Incident Irradiance (Natural Resources Canada 2018)

Figure 36. Air-Based BIPVT Thermal Efficiency, Temperature Rise, and Back-Surface Temperature as Function of Specific Flowrate and Wind Speed (Natural Resources Canada 2018)

Heat recovery in BIPVT systems can be improved with heat enhancement strategies such as fins and roughness elements. Fins create a larger surface area for heat transfer, but usually increase pressure drop inside the cavity and, as a result, the fan power requirements. The purpose of roughness elements is to generate local turbulence to increase the heat transfer coefficient locally, limiting the impact on the pressure losses. The design of such roughness elements is challenging, however, because the operating flowrate strongly affects their efficiency. The addition of thermal boosters is also an option to achieve higher temperatures in a BIPVT system. These boosters are similar to glazed air solar thermal collectors and are generally added at the top section of a BIPVT roof or facade to increase the air temperature prior to entering the building.

Fan Power Requirements. To estimate the total pressure drop in a BIPVT system, consider the pressure losses associated with the following components of the system: (1) the actual BIPVT roof or facade, (2) the dampers, (3) the plenum, and (4) the ducts and fittings required to bring the preheated air to its final end usage.

Pressure losses associated with the BIPVT roof or facade are generally much less than those of the other components, especially the ducts and fittings bringing the preheated air in the plenum. However, this depends on the BIPVT configuration. For example, a small cavity thickness or the presence of heat transfer enhancement strategies such as fins can significantly increase the pressure drop of the actual BIPVT roof or facade. Chapter 21 of the 2017 ASHRAE Handbook—Fundamentals examines this subject in greater detail.

Batteries. Off-grid and grid-connected systems may contain batteries. The design, size, and ratings depend on the application. Deep-cycle batteries can be discharged to a higher capacity, and the number of cycles indicates how often this can occur. Racking must be robust and appropriate for the battery type. Ventilation or insulation requirements and temperature ratings depend on the battery technology and installation location. Hazardous DC voltages and significant short-circuit capacity may be present. Initial charging may be necessary before first use, and routine maintenance for some technologies may be impractical for certain applications.

 PV, BAPV, and BIPV Electrical Performance

A number of methods can predict the performance of PV and BIPV systems. Though distinct in complexity and accuracy of prediction offered, all have something in common: all require the incident solar radiation and the PV cell operating temperature as minimum inputs. For additional information on calculating incident solar radiation from first principles, see Chapter 14 of the 2017 ASHRAE Handbook—Fundamentals.

PV Modules. The simplified model presented provides an estimate of the electrical yield of PV modules (excluding inverter and balance of system), based on typical meteorological data. Note that PV specifications are typically given in international SI units; care should be taken when using I-P conversions. The solar power generation is calculated based on Evan’s model (reported in watts):

(38)

where

c	=	unit correction coefficient, 0.293 W · h/Btu
I	=	incident total irradiance, Btu/h · ft2
Pmod	=	electrical output of PV modules, W
tcell	=	operating cell temperature, °F
tref	=	reference temperature, usually at 77°F
ηref	=	electrical efficiency under reference conditions (typically to 317 Btu/h·ft2, PV module temperature of 77°F and solar spectrum of air mass 1.5), available through manufacturer’s data sheet of solar module
μP,mp	=	temperature coefficient at maximum power point, available through manufacturer’s data sheet of solar module, °F−1

Module reference efficiency and power temperature coefficient are usually provided in the PV manufacturer’s data sheet. Table 4 provides typical values for various photovoltaic module technologies available on the market. These values may vary depending on solar cell technology, module assembly, and manufacturer.

Table 4 Typical Values and Range of Module Electrical Efficiency (η_ref) and Temperature Coefficient at Maximum Power Point (μ_P,mp), for Various Photovoltaic Technologies

Photovoltaic Technology	ηref		μP,mp (%/°F−1)()
	Typical	Range	Typical	Range
Monocrystalline silicon	0.157	0.084 to 0.221	−0.252	−0.499 to −0.126
Polycrystalline silicon	0.149	0.062 to 0.204	−0.253	−0.377 to −0.191
Silicon heterostructures (HIT)	0.173	0.126 to 0.197	−0.185	−0.261 to +0.001
Amorphous silicon (a-Si)	0.064	0.053 to 0.088	−0.145	−0.195 to −0.119
Micromorphous silicon (a-Si/μc-Si)	0.082	0.063 to 0.104	−0.178	−0.219 to −0.101
Cadmium telluride (CdTe)	0.139	0.094 to 0.170	−0.159	−0.234 to −0.092
Copper indium (gallium) selenide (CI[G]S)	0.117	0.055 to 0.167	−0.198	−0.288 to −0.120

The calculation of the PV power generation also requires the PV operating cell temperature t_t,cell as an input. King’s model (King et al. 2004) uses an implicit correlation between the measured back-surface temperature t_t,back and operating cell temperature:

(39)

In a typical PV module, the back-surface temperature refers to the rear side of the module. In a BIPV window, the back-surface temperature refers to the rear side of the BIPV window, which is the surface of the insulated glazing unit facing the indoor environment (e.g., surface 4 on a double glazing window). When the back-surface temperature is unknown or cannot be measured directly, the following empirical model can be used:

(40)

where

a	=	empirically determined coefficient indicating upper temperature limit under low wind speeds and high solar irradiance
b	=	empirically determined coefficient indicating rate at which back-surface temperature drops with wind speed, mph−1
c1	=	unit correction coefficient, 5.68 h · °F · ft2/Btu
Iref	=	reference solar irradiance, typically 317 Btu/h·ft2
tt,back	=	back-surface PV module temperature, °F
ta	=	ambient air temperature, °F
Umet	=	wind speed measured at standard 33 ft height, mph
Δt	=	tcell – tback, temperature difference between cell and module back surface at irradiance level of 317 Btu/h·ft2

Table 5 provides representative coefficient values for PV and BIPV systems, using crystalline silicon PV cells. The empirically determined coefficients may vary depending on PV module assembly, mounting arrangement, and location.

Example 8.

Estimate (1) the average operating cell temperature and (2) the PV modules’ power generation for a 100 ft² micromorphous double glazing BIPV curtain wall system under I = 250 Btu/h · ft², t_a = 70°F, and U_met = 3 mph.

Solution. Using Tables 4 and 5, the average back-surface temperature of a micromorphous double glazing BIPV window system can be calculated with Equation (40):

(1) From Equation (39) and Table 5, the average operating cell temperature of the BIPV window system is:

Table 5 Typical Values for Coefficients a, b, and Δt in Prediction of PV or BIPV Electrical Yield

Type of PV Application	a	b, mph−1	Δt, °F
Open rack PV, BAPV or BIPV with good rear ventilation	−3.47	−0.0266	5.4
BAPV or BIPV with medium rear ventilation	−2.98	−0.0211	1.8
BAPV or BIPV with poor rear ventilation	−2.81	−0.0203	0
Double glazing BIPV window with low emissivity coating (surface 2 or 3)	−2.85	−0.0157	16.2
Triple glazing BIPV window with low emissivity coatings (surfaces 2 and 4 or 3 and 5)	−2.88	−0.0143	19.8
Sources: Adapted from Kapsis (2016) and King et al. (2004).

Table 6 Typical Values and Range of PV System Electric Losses Due to Various Factors

Electric Loss Factor, ELi	Typical	Range
Shading	0.00	0.00–1.00
Soiling	0.05	0.02–0.25
PV module nameplate DC rating	0.00	0.00–0.15
Initial light-induced degradation	0.02	0.01–0.10
Inverter	0.04	0.04–0.07
Transformers	0.03	0.02–0.04
Mismatch	0.02	0.02–0.03
DC wiring	0.02	0.01–0.03
AC wiring	0.01	0.01–0.02
Diodes and connections	0.005	0.00–0.01
Source: Adapted from Marion et al. (2005).

(2) From Equation (38) and Table 4, the estimated solar power generation is:

PV Systems. Besides PV modules, photovoltaic systems are comprised of a number of supporting equipment, which serves to make them operational. Depending on the system configuration, the Balance of system (BoS) may include inverters, DC and AC wiring, relays, transformers, charge/load controllers, and a battery bank. When compared to the PV module power output, the total output of a PV system is reduced due to losses related to BoS components, mismatch, wiring, and more. Table 6 provides a range of PV system losses for AC power rating due to various factors. Nevertheless, losses are specific to each installation and location. Loss factors influenced by meteorological conditions also vary daily, seasonally, and annually. Taking into account the various losses, the PV system solar power generation is estimated as follows (reported in watts):

(41)

where

ELtotal	=	(1 − EL1)(1 − EL2)…(1 − ELi), total electric loss factor
Pel	=	electrical output of PV system, W
ELi	=	electric losses due to factor i

Example 9.

Considering the PV installation from Example 8, calculate the PV system’s power generation assuming total wiring losses of 3%, inverter losses of 4%, mismatch losses of 2%, losses due to soiling of 5%, and losses due to shading of 5%.

Solution. Considering the above loss factors, the PV system’s power generation is calculated using Equation (41):

Preliminary PV Sizing and Design. The simplified approach presented here can be used to inform the preliminary design stages of a PV system, which consist of the following steps:

• Estimating the annual electrical load to be offset by the PV system (E_annual).

• Calculating the average daily electricity E_daily to be generated by the PV system.

  (42)

• Estimating the sun hours (i.e., equivalent number of hours which a particular location would be exposed to, if the sun was shining at I_STC = 317 Btu/h · ft²) per day available for the location of interest. For the United States, this information is available through NREL’s website at rredc.nrel.gov/solar/pubs/redbook/, and for Canada, through NRCan’s website at www.nrcan.gc.ca/18366.

  (43)

• Calculating the PV array installed capacity required.

  (44)

• Calculating the number of PV modules required.

  (45)

  where

  Eannual	=	annual electrical load to be offset by PV system, kWh
  Edaily	=	daily average electricity to be generated by PV system, kWh
  Esun	=	daily average solar energy that strikes surface per unit area, for given location, Btu/day
  ISTC	=	solar irradiance under standard testing conditions, 317 Btu/h · ft2
  Nmod	=	number of PV panels required
  PSTC	=	power rating of module under standard testing conditions, W
  SHD	=	sun hours per day, h

Example 10.

A two-story apartment building (8 apartments) in Phoenix, AZ, has an annual energy consumption of 112,000 kWh. The building owner would like to have 40% of the annual energy requirement delivered by a flat roof-mounted solar PV system. Calculate the number of PV panels required to generate 40% of the building’s annual energy requirement.

Site Specifications:

• Array orientation (solar azimuth Φ): south (180°)

• Array tilt angle (Σ): 18°

• Site latitude (LAT): 33.43°N

Selected PV System Characteristics:

• Rated power of PV module under standard testing conditions: 310 W

• Module length: 61.4 in.

• Module width: 41.2 in.

• Module depth: 1.81 in.

• PV electric loss factor: 0.86

Solution

Step 1: Calculate the annual electrical load that needs to be offset by the PV system:

Step 2: Estimate daily average energy usage:

Step 3: For Phoenix, AZ, the SHD ≈ 6.4 h. The SHD is approximated by using the value for LAT-15° (rredc.nrel.gov/solar/pubs/redbook/).

The PV array installed capacity required is

Step 4: Calculate number of PV panels required:

Example 11.

Based on PV module characteristics listed in Example 10, calculate the minimum spacing required between rows to avoid inter-row shading on December 21 (during the winter season).

Solution. Assuming six hours of sunlight on December 21 (from 9:00 am to 3:00 pm), the solar altitude and solar azimuth at 9:00 am on December 21 are β = 19° and ψ = 139° respectively, as calculated using Equations (6) and (7). From Figure 37, the PV array height h can be calculated by simple trigonometry as follows:

Similarly, the PV shadow SH is calculated as follows:

Thus, the minimum inter-row spacing IS is

Note that the last calculation takes into account the correction of the solar azimuth.

Figure 37. Side View and Top View of Tilted PV Array Mounted on Flat Building Roof

PV modules are generally smaller and lighter than solar thermal collectors. Nevertheless, they should be handled carefully due to their thin rear-insulating layer. Damage to the delicate PV cells may not be visible, but can reduce system performance significantly.

Proper installation is critical to the long-term reliability and performance of a PV system. Even with an appropriate design, a system’s safety and power production can be negatively impacted by inadequate installation procedures. The crew performing the installation should, at minimum, be led by someone trained, qualified, and experienced in PV installation and system design. Depending on the jurisdiction, a certified electrician may be required for all or portions of the installation. A proper installation should not compromise any building envelope warranties.