19 December 2010


To calculate the Total Number of DC Amp Hours per Day Required to power the system:
DC Load Amps = kW ) DC System Voltage
Total Daily Load [Amp Hours] = (No. of Amps X No. of Hrs.) / Day of Operation
0.12 kW ) 48 VDC = 2.5 A.
Total Daily Load = (2.5 A. X 24 Hrs.) / Day of Operation = 60 AH/Day of Operation
For non-continuous DC Loads establish the duty cycle in time of operation per Day
(70% of day at xx Amps) + (30% of day at yy Amps) = Total AH Consumed/Day
(70% X 5 A. X 24 Hrs.)/Day + (30% X 10 A. X 24 Hrs.)/Day = 156 AH/Day
Total Daily Load = 84 AH + 72 AH = 156 AH/Day


When an inverter is used to power 120 or 240 VAC appliances, such as pumps, refrigerators,
lighting, etc. the AC voltage must be converted to the Battery’s DC voltage and the efficiency
of the inverter must be considered.
If the inverter AC voltage is 120 VAC and the battery DC voltage is 24 VDC then the
conversion factor is 5.0. For every AC amp drawn there will be 5 times as many DC amps.
Also, the inverter’s conversion efficiency from DC to AC is not 100%. There is an internal loss
in the inverter which is normally about 10 to 15% [See inverter/charger manufacturer’s
efficiency specifications].
AC Load = 6 kWh/Day ) 120 VAC = 50 AH/Day @ 120 VAC
Convert to DC Battery Load. Inverter’s Charger is 48 VDC. Therefore, the conversion factor is
2.5 to 1 and the efficiency is 90%.
DC Load = 50 AH/Day X 2.5 [conversion factor] = 125 AH/Day ) 0.9 [efficiency] = 139 AH/Day battery
Note: When sizing the battery for non-continuous loads, or for larger loads for short periods of
time per day, it may not be possible to use the 20, 24 or 120 hr. rate of discharge for the
battery’s capacity. When discharged at different rates, a battery’s capacity will vary. The
higher the rate of discharge the lower the capacity of the battery.

The sun does not shine with equal intensity every day, at night and during inclement weather.
Cloud cover, rain, snow, etc, diminish the daily Insolation (Insolation measured is the amount
of solar energy delivered to the earth’s surface. Insolation is measured in kWatts/meter2). A
storage factor must be employed to allow the photovoltaic battery system to operate reliably
throughout these periods.
In addition, it is desired to obtain the best service life of the battery by limiting its average daily
depth of discharge. This storage factor is commonly referred to as “Number of Days of Battery
Autonomy”. The number of days is established by evaluating the Peak Hours of Sun per Day
[(kW/m2)/day] for the lowest Insolation month of the year; with the solar array oriented for
maximum output during that month.
The minimum number of days that should be considered is 5 days of storage for even the
sunniest locations on earth. In these high sun locations there will be days when the sun is
obscured and the desired battery’s average daily depth of discharge is limited to 20%.
Therefore, the recommended days of autonomy storage are listed on the following chart:

 Recommended Days of Autonomy Storage
kW/m2/day               Days of Storage
4.5+                                  5
3.5 to 4.5                           6
2.7 to 3.5                           7
2.0 to 2.7                           8
<2.0                           Up to 14*

The temperature of the battery can be a major factor in sizing the system. Lead acid battery
capacity is reduced in cold temperatures. Lead acid battery life is shortened in high
It should be noted that the temperature of the battery itself and ambient temperature can be
vastly different. While ambient temperatures can change very quickly, battery temperature
change is much slower. This is due the mass of the battery. It takes time for the battery to
absorb temperature and it takes time for the battery to relinquish temperature.
The battery’s temperature is normally the average temperature for the past 24 hours plus or
minus a few degrees. In many cases it can be difficult or impossible to heat or cool the battery
and we must take temperature into consideration. A battery that is required to operate
continuously at 0º F. (-18º C.) will provide about 60% of its capacity. This same battery
operated continuously in a 95º F. (35º C.) environment can lose half its expected life.
The earth is a great heat sink which provides great insulation in high or low temperatures. By
burying the battery in the ground we can increase its capacity in cold temperatures and
increase the life of the battery in high temperatures. The battery with only 60% of its capacity
at 0º F. [-18º C.] can be brought up to 85% to 90% capacity by burying it. With life cut in half
at 95º F. [35º C.], burying the battery can bring it back to near normal life expectancy.

Many battery manufacturers will advise sizing the battery for cyclic applications to a maximum
depth of discharge of 50%. That would mean doubling the size of the battery. Some batteries
have trouble recovering from deep discharges. That would mean for the 60 AH/Day load with
5 days of autonomy or 300 AH that they would advise using a 600 AH battery.
 consider that the battery is replaceable when it does not provide 80% of its original capacity. Therefore, recommend that the same 300 AH requirement be divided by 0.80 to provide a reliable battery system. We would recommend using a 375 AH battery. That represents a significant savings.


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