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Power - Calculations for Solar Arrays and Battery Backup
Calculations for Solar Arrays and Battery Backup
Please feel free to use the calculator below to do your own calculations for solar arrays and battery backup.
Equations
Use the following equations to determine solar array size and battery backup requirements based on 12V nominal system voltage.
| Power consumption for each piece of equipment | Power = voltage × current | W = V × A |
|---|---|---|
| Daily amp-hour load for each piece of equipment | Amp-hour load = power / voltage × hours of operation per day (h) Add up amp-hour load for whole system. | Ah = W / V × hours of operation per day (h) |
| Efficiency and loss-corrected load for whole system | Corrected load = amp-hour load / 0.8 | Ah(corr) = Ah / 0.8 |
| Worst case equivalent sun hours (ESH) (h) | Determine from charts or meteorological data. | |
| Solar array current requirement (A) | Solar current req. = Corrected load / ESH (h) | A = Ah(corr) / ESH (h) |
| Number of solar panels in parallel (N) | No. of panels = solar current req. / current output per panel | N(panel) = A / A/panel |
| Autonomy or reserve time (Ah) | Autonomy = no. of days × corrected load / % discharge rate | Ah(res) = N(days) × Ah(corr) / % discharge rate |
| Battery bank (backup) size | Battery bank = autonomy (Ah) / Ah per battery | Bank = Ah(res) / Ah/battery |
Calculator
Example
A permanent station with a Trimble receiver, cellular phone, modem, and computer located in Boulder, Colorado, approximately at latitude 40´02´´ N, 105´14´´ W, elevation 1602 meters.
Power consumption:
| Equipment | Power | Hours/day |
| Trimble 4000SSi receiver | 9W | 24 |
| Cellular phone | 15W | 4 |
| Cellular phone modem | 10W | 4 |
| Computer | 20W | 4 |
Daily amp-hour load:
| Equipment | Calculation | Ah |
| Trimble 4000SSi receiver | 9W/12V x 24h | 18.0 |
| Cellular phone | 15W/12V x 4h | 5.0 |
| Cellular phone modem | 10W/12V x 4h | 3.33 |
| Computer | 20W/12V x 4h | 6.67 |
| Total | 33.0 |
Efficiency and loss-corrected load:
33 Ah / 0.8 = 42 Ah.
Worst case equivalent sun hours (ESH) for Boulder, CO:
3.5 hours
Solar array current requirement:
42 Ah / 3.5 h = 12A
Number of solar panels in parallel:
Three solar modules are currently being used in UNAVCO designs:
-
Siemens PC-4JF rated at 75W (4.4 A
17.0 V) -
Siemens M75 rated at 48W (3.02 A
15.9 V) -
Solarex MSX-30 rated at 30W (1.68 A
17.8 V)
Choosing the M75 module, four panels are needed to cover the solar array current requirements: 12A / 3.02A per panel = 3.97 panels
Autonomy or reserve time:
Choosing five days of autonomy with 50% maximum discharge:
5 × 42 Ah / 50% = 420Ah battery bank
Battery bank (backup) size:
Three types of sealed deep cycle batteries are currently being used in UNAVCO designs:
-
Deka 90Ah
-
Deka 66Ah
-
Deka 30Ah
As an example, if you choose the Deka 90Ah, five batteries are needed to provide the required autonomy. 420Ah / 90Ah per battery = 4.67 batteries.