Step 3: Array Sizing
Now that we have calculated loads and storage, next calculate the array size in watts, and the number of PV modules needed. The array calculations must include Wh per day (calculated from the average daily load), the location’s solar resource, expressed in daily peak sun-hours, battery efficiency losses (about 20%), module temperature losses (about 12%), possible array shading, and a conservative derate multiplier to account for things like wire losses, module soiling, and production tolerance.
Peak sun-hours are the equivalent number of hours per day when solar irradiance (intensity) averages 1,000 watts per square meter, as derived from the National Solar Radiation Database (http://rredc.nrel.gov/solar/pubs/redbook/). Dividing the Wh required by the location’s peak sun-hours leaves us with the initial PV array watts needed. For this sizing example, the solar data for Concord, New Hampshire (at 43.2°N) provides the closest estimate of the solar resource for Pawlet, Vermont (at 43.3°N) at an array tilt angle equal to latitude. Since this system is using a backup generator, the average daily peak sun-hours can be used (4.6), as the generator can cover energy shortages during periods of low insolation or high energy consumption—or both. If less generator run time is desired, the array size must be increased or daily energy consumption must be reduced appropriately (or both).
Battery efficiency: Since batteries are not 100% efficient in converting electrical energy into chemical energy and back again, the array size must be increased to account for energy lost in the storage process. A common battery efficiency is 80%.
PV temperature losses: Module standard test conditions (STC) ratings, which are based upon a cell temperature of 77°F (25°C), don’t reflect real-world operating conditions. To account for losses due to higher cell temperatures, a derating value of 0.88 can be used. This assumes an average daytime ambient temperature of 68ºF and an estimated cell temperature of 122°F. (Another way to calculate temperature losses would be to use the specific module’s maximum power temperature coefficient, in conjunction with a cell temperature based on the record high daytime local temperature.)
Shading coefficient: Although 9 a.m. to 3 p.m. is often considered the ideal solar window, site-specific shading should always be evaluated for the whole day. Even moderate shading can have a substantial impact on array output. In the case of this sizing example, with a shade-free solar window of 8 a.m. to 4 p.m., an average shading coefficient of 0.90 was determined with a Solar Pathfinder array siting tool.
Derate factor: A 0.85 derate factor (from NREL’s PVWatts online performance calculator) accounts for other system losses, including module production tolerances, module mismatch, wiring losses, dust/soiling losses, etc. An experienced designer can adjust this value to reflect conditions for your specific site. See the table for a summary of these values.
2,360 Wh daily load ÷ 4.6 peak sun hours ÷ 0.8 battery efficiency ÷ 0.88 temp. losses ÷ 0.9 shading coefficient ÷ 0.85 system derate = 953 W peak array
953 ÷ 80 W STC individual module = 12 modules needed
48 V nominal array voltage ÷ 12 V nominal module voltage = 4 modules per string, 3 strings total
The resulting 12-module array will have a capacity of 960 W STC, rounded up slightly from the 953 W specified in the calculations. Although the DC system voltage and the battery bank are 24 VDC, this array can be wired at a higher voltage of 48 VDC, because of the “step-down” feature of the charge controller being used. Since the modules are nominally rated at 12 V, they will have to be wired into three series-strings of four modules each.
If these calculations seem conservative, it is because they are. It is imperative to design a system that will operate reliably and efficiently—and that will produce, on average, the expected amount of energy required. In other words, it is the designer’s job to give the system manager/homeowner a realistic idea of what to expect.