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:

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:

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.


Article ID: 463
Created: October 31, 2012
Last Updated: October 31, 2012
Author: Beth Bartel

Online URL: https://kb.unavco.org/article/power-calculations-for-solar-arrays-and-battery-backup-463.html