Step 2: Battery Bank Sizing
The average daily load is then used to calculate the battery requirements. The batteries must be able to store the total daily load, in addition to the extra energy lost by inverting from direct current (DC) to alternating current (AC). Dividing the AC average daily load by the inverter efficiency (90% standard), inflates the average daily load that the batteries must store to account for efficiency losses from the inverter. While inverter manufacturers will commonly list “peak efficiency” (generally ranging from about 92% to 95%), we use a more conservative 90% to account for the fact that the actual operating efficiency depends on the AC load, which is constantly fluctuating. Hence, an inverter will rarely operate at the load level which results in peak efficiency.
The battery bank’s ambient operating temperature is also taken into consideration, since temperature affects a flooded lead-acid battery’s internal resistance and ability to hold a charge. As temperatures fall below 80°F, battery capacity is reduced. A battery temperature multiplier table can be used—check with the battery manufacturer for their specific correction factors.
Days of autonomy is also an important design criterion, as it dictates how many days the battery bank will need to sustain the average daily load when there is little or no sunshine to recharge it. It’s a compromise between having energy during overcast spells, how much time the generator will run, and the added cost of a larger battery bank. The more days of autonomy desired, the larger the battery bank. Generally three to five days of autonomy provides a good balance. Keep in mind that the larger the battery bank, the larger the PV array will need to be to recharge the bank sufficiently on a regular basis—or the more the generator will be needed to pick up the slack.
The last major design criterion for sizing batteries is the depth of discharge (DOD). While deep-cycle lead-acid batteries are designed to discharge 80% of their capacity, the deeper they are discharged on a regular basis, the fewer charge/discharge cycles they can provide over their lifetime. When choosing a DOD, strike a balance between longevity, cost, and the significant hassle of replacement. Many system designers will specify a 50% DOD to be used in the worksheet. Because several days of autonomy are accounted for, which increases the battery bank size, the actual depth of discharge during sunny weather will often be less than 20%. The DOD design value can greatly affect the cost of the battery bank. (For simplicity, the numbers from the load table have been rounded in the following equations.)
(1,800 AC Wh Avg. Daily Load ÷ 0.9 Inv. Eff.) + 360 DC Wh Avg. Daily Load = 2,360 Wh/day
2,360 Wh/day ÷ 24 DC System Volts = 98.3 Avg. Ah per day
98.3 x 1.11 battery temperature multiplier x 3 days autonomy ÷ 0.5 DOD = 654.7 total system Ah
654.7 ÷ 225 Ah individual battery capacity = 3 parallel battery strings (rounded up from 2.9)
24 V system voltage ÷ 6 V battery voltage = 4 batteries in series
3 parallel strings x 4 batteries in series = 12 total batteries
The battery calculations indicate that a battery bank made up of 12 of the chosen 6 V, 225 Ah, flooded lead-acid batteries will provide adequate storage to meet daily energy requirements, inverter efficiency losses, operating temperature effects, days of autonomy, and the desired average depth of discharge. The number of batteries or series-strings of batteries connected in parallel should be kept to a minimum, preferably three or less. This minimizes the chance of unequal charging from one battery or string to the next. While using higher-capacity batteries would have resulted in fewer parallel strings, the Ackerman-Leists chose lower-capacity batteries for budgetary reasons.
Batteries are rated by their capacity in amp-hours and at the rate that they are charged/discharged. In most PV systems, the appropriate Ah rating to use is based on a discharge over 20 hours. Unlike shallow-cycle vehicle batteries, deep-cycle batteries in PV systems are charged and discharged over 24 hours, and the weather, level of solar irradiance, and energy usage patterns all influence the charge/discharge scheme. In this system example, the battery could provide 225 Ah of stored energy—if discharged 100% over 20 hours. If it were discharged faster, the capacity would be less, and vice versa. Be sure to check with the battery manufacturer, as they provide battery-specific Ah capacity values based on different charge/discharge rates. Choose the 20-hour rate when sizing and selecting batteries, unless a specific load profile dictates otherwise.