- Energy Calculations and Units
- Siting a Solar Water-heating System
- Sizing a Solar Water-heating System
Visible light (insolation) is the main energy source collected by systems that provide space heat, water heat, and electricity for homes. Because of the Earth’s axial tilt, the amount of solar insolation incident at any one spot on the Earth’s surface varies throughout the year. On a daily and a seasonal basis, the amount of light energy incident on a surface varies from sunrise to sunset. The atmospheric conditions and elevation at the site are also factors that influence the amount of light reaching the Earth’s surface.
For sites above and below the equator, seasonal variations are commonly marked by the spring and fall equinoxes and the summer and winter solstices. The equinoxes are defined as the time of year when the sun crosses the equator (March and September 21/22). At this time there are an equal number of hours of daylight and nighttime. The summer and winter solstices are defined as the time when the sun reaches its highest/lowest latitude. In the northern latitudes, the summer solstice in June 21/22 and the winter solstice is December 21/22. The summer solstice is the date when the number of daylight hours is the longest and the winter solstice has the shortest number of daylight hours. In the southern hemisphere, the solstices are just the opposite.
Before installing a solar water-heating system, you must first consider the site's solar resource, since the efficiency and design of a solar water-heating system depend on how much of the sun's energy reaches the building site. You’ll also have to properly size the system to ensure that it meets the hot-water needs of the home. In this lesson, you will learn how to site and size a solar water-heating system.
Energy Calculations and Units
We have to be able to measure and compare energy and other quantities to be able to estimate the size of solar water-heating and solar electric systems. We, therefore, need to gain an understanding of the energy calculations and energy units we use to make these estimates.
British Thermal Unit (Btu): the amount of energy to raise 1 pound of water 1 degree Fahrenheit
Therm: 100,000 Btu
DekaTherm (DKT): 1,000,000 Btu
Natural gas contains about 1 DKT of energy in 1000 cubic feet of gas.
Electric Power and Energy
1 Watt = 1 Volt*1 Amp in purely resistant circuits
1000 Watts = 1 Kilowatt (KW) (this is Power)
1 KW* 1 Hour = 1 Kilowatt-Hour (this is energy)
Siting a Solar Water-heating System
Geographic orientation and collector tilt can affect the amount of solar radiation the system receives.
Solar water-heating systems use both direct and diffuse solar radiation. Despite being a colder, northern climate, Pennsylvania still offers an adequate solar resource. Generally, if the installation site is un-shaded from 9 a.m. to 3 p.m. and faces south, it's a good candidate for a solar water-heating system.
PVWatts (www.pvwatts.org) is a useful on-line calculator that helps to understand the solar resource at a given location. The table below shows average summer, winter, and annual solar radiation for Wilkes-Barre, Pennsylvania. PVWatts can help you determine the solar resource available at your specific site, and also help you estimate the size of solar system needed to provide the necessary solar energy for either solar water-heating or solar electric systems. (Tip: To convert from Kilowatt-hours to Btu, multiply by 3413. To convert square meters to square feet, multiply by 10.76).
Average Daily Solar Radiation
|Tilt Angle||Azimuth Angle||January||July||Yearly|
Collector orientation is critical in achieving maximum performance from a solar energy system. In general, the optimum orientation for a solar collector in the northern hemisphere is true south (azimuth of 1800). However, recent studies have shown that, depending on the location and collector tilt, the collector can face up to 90º east or west of true south without significantly decreasing its performance.
Local climatic conditions can play a significant role in whether to orient the collectors east or west of true south, as well as in determining the proper tilt angle for the collectors. The building’s roof orientation and slope, shading factors, perceived aesthetics, and local covenants also play significant roles in the installation of the solar system’s collection hardware.
You must also consider factors such as roof orientation (if you plan to mount the collector on the roof), local landscape features that shade the collector daily or seasonally, and local weather conditions (foggy mornings or cloudy afternoons, for example), as these factors also can affect the collector's optimal orientation.
Most residential solar collectors are flat panels that can be mounted on a roof or on the ground. Called flat-plate collectors, these are typically fixed in a tilted position correlated to the latitude of the location. This allows the collector to best capture the sun. These collectors can use both the direct rays from the sun and reflected light that comes through a cloud or off the ground. Because they use all available sunlight, flat-plate collectors are the best choice for many northern states.
Optimal tilt angle for solar collector is an angle equal to the latitude.
Although the optimal tilt angle for the collector is an angle equal to the latitude, mounting the collector flat on an angled roof will not result in a big decrease in system performance and is often desirable for aesthetic reasons. You will, however, want to take roof angle into account when sizing the system.
As previously mentioned, solar collectors should be installed at a site that is un-shaded from 9 a.m. to 3 p.m. and faces south. Shading from mountains, trees, buildings, and other geographical features can significantly reduce the collectors’ performance. Before installing a solar energy system, you should first complete a sun path diagram to estimate the impact of shading on annual system performance.
Sizing a Solar Water-Heating System
To properly size a solar water-heating system, you’ll need to determine the total collector area and the storage volume needed to meet 90 to 100 percent of the household's hot water needs during the summer. One software tool that is available to calculate solar water heating system sizing is RetScreen (www.retscreen.net/ang/home.php). If you plan on designing a number of solar water heating systems, you can choose to download the Solar Hot Water software from www.retscreen.net/ang/t_software.php. This software can be used to size solar water-heating systems, and we will use it to verify our “Rule of Thumb” calculation example below.
Sizing Collector Area
A good rule of thumb for sizing collector area in northern climates such as Pennsylvania is to allow 20 square feet (2 square meters) of collector area for each of the first two family members, and 12 to 14 square feet for each additional person.
Sizing Storage Volume
A small (50- to 60-gallon) storage tank is usually sufficient for one to two people. A medium (80-gallon) storage tank works well for three to four people. A large tank (120-gallon) is appropriate for four to six people.
For active solar water-heating systems, the size of the solar storage tank increases with the size of the collector—typically 1.5 gallons per square foot of collector. This helps prevent the system from overheating when the demand for hot water is low.
The Solar Rating and Certification Corporation website has thermal performance results for tested solar collectors at www.fsec.ucf.edu/solar/testcert/collectr/tprdhw.htm. The site has performance data within the temperature range that is appropriate for picking a collector for heating the hot water demand. The following is a page from this site. Bear in mind that these collectors are certified based upon Florida conditions. A trial and error procedure is necessary to get to the right collector sizing for Pennsylvania.
Comparing the daily hot water heat demand with the tested collector thermal performance numbers, we want to choose solar collectors that will produce the 45,081 Btu/day. Looking in the Btu/day column, we see that we will need two collectors to match our load, each collector being able to provide about 22,541 Btu/day. An Alternate Energy Technologies AE-32 collector is rated at 27,500 Btu/day. These collectors each have an area of close to 32 square feet. This example compares favorably with the general guidelines presented earlier for the number of solar collectors to install – 20 square feet of collector area for the first two people and 12 square feet for each additional occupant.
For Pennsylvania, the water storage tank to couple to 64 square feet of solar collector should be at least 80 gallons, but a tank with a capacity of 90+ gallons would be better.
- Using the RETScreen software, the AET AE-32 collectors will produce .98 MWh from June-August, or 36,347 Btu per day. This is short of our design water-heating load, so we need to pick a different collector. Since we are short about 8,734 Btu per day, or 24%, we need to pick collectors about 24% larger than our original estimate. We will try a 40-square-foot collector, the AET AE-40. Using the RET Screen software, we see that the AE-40 collectors will produce 1.08 MWh from June to August or about 40,055. What happened? Why do we increase the solar collector area by 25% and only get 10% more hot water? The answer lies in the fact that, as the amount of energy produced gets close to the amount of energy used, the efficiency of the system drops because the higher system temperatures result in more heat loss. The system with the two AE-32 collectors has a system efficiency of 35 percent, while supplying 86% of the energy needed in the summertime (the 86% is called solar fraction). The system with the two AE-40 collectors has a system efficiency of 31% while supplying 95% of the energy needed in the summertime. Remember, we started out by sizing the system to provide 100% of summertime water-heating energy.
The other system design parameter we need to look at is the size of solar water storage tank. Using RETScreen, the previous analysis was done assuming a 120-gallon storage tank. What would the efficiency and solar fraction be if we were to install an 80-gallon storage tank? The RETScreen model predicts that using an 80-gallon storage tank, the solar fraction drops to 93%, and the efficiency stays at 31% for the summer time. A smaller storage tank therefore decreases the system solar fraction.
How does our system perform on an annual basis?
Average Daily Solar Radiation
for the months of January and July and yearly for various tilts and azimuth angles in Wilkes Barre, PA (kWh/m2/day)
Source: PV Watts Website
Tilt Angle Azimuth Angle January July Yearly 25 180 2.50 5.58 4.19 25 210 2.40 5.81 4.12 25 270 1.72 5.52 3.59 40 180 2.81 5.47 4.19 40 210 2.66 5.45 4.09 40 270 1.69 5.08 3.37 55 180 2.89 4.82 3.98 55 210 2.79 4.85 3.88 55 270 1.62 4.55 3.09
- Using the data for Wilkes Barre in the table above, what is the percent difference in the yearly average daily solar insolation incident on a surface facing true south (azimuth angle 1800) with a tilt of 25 degrees versus that with a 55 degree tilt? For a 25-degree tilt versus a 40-degree tilted surface?
- What is the percent difference between the yearly average value for a surface tilted at 25 degrees facing true south versus the same surface, same tilt but with an azimuth angle of 210 degrees?
- What is the percent difference between the yearly average value for a surface tilted at 25 degrees facing true south versus the same surface, same tilt with an azimuth angle of 270 degrees? For surfaces with 40 and 55 degree tilts?
- Given the percent differences shown in question 3, which tilt angle is more reasonable to accept if you had no choice but to install a solar system with an azimuth angle of 270 degrees? Please explain your answer.
- If you lived in Wilkes Barre and wanted to maximize the collection of solar insolation in the winter, what tilt and azimuth angles would you mount the solar collectors? Conversely, if you wanted to maximize the summer solar collection, what tilt and azimuth angles would you mount the solar collectors?
- In the solar system sizing example, the total daily heat energy demand for 80 gallons of hot water was calculated at 45,081 Btus. What would the total heat energy demand be for 80 gallons with the hot water temperature set at 1400F with the same cold water temperature?
- What would the auxiliary energy demand be for 80 gallons of hot water with the hot water temperature set at 1200F and a solar water heating system providing 1000F water to the cold water inlet of the conventional domestic hot water heater? Assume the heat losses for the 120 degree set temperature from the conventional heater when making the calculation.