How to Calculate Inverter Power Rating and Inverter Battery Backup Time

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Inverter systems are a common feature in our homes and workplace where they play a prominent role in the ensuring uninterruptible power to sensitive loads and devices. For home applications, there is the need to adequately size your inverter to be able to meet the expected load demand. 

Inverters convert DC voltage to AC voltage. They have a battery system which provide adequate backup time to provide continuous power in the home. The inverter system then converts the battery voltage to AC voltage through electronic circuitry. The inverter system also has some charging system that charges the battery during utility power. During utility power, the battery of the inverter is charged and at the same time power is supplied to the loads in the house. When utility power fails, the battery system begins to supply power via the inverter to the loads in the home as shown below:

How to Size and Calculate the Inverter Power Requirement
Inverter power is rated in VA or KVA.
Power in VA = AC Voltage x AC Current in Amps
Power in KVA = AC Voltage x AC Current in Amps/1000
Power in Watts = AC Voltage x AC Current in Amps x PF
Where PF = power factor 
Power in KW = AC Voltage x AC Current in Amps x PF/1000
Also  Power in W = Power in VA x PF
         Power in KW = Power in KVA x PF

Suppose we want to size an inverter to carry the following loads:
1. Lighting load, 300W
2. 3 Standing fans of 70W, each
3. 2 LCD TV, 100W
4. 1 Home Theatre Music System, 200W
5. 1 Juice extractor, 150W

Applying Power in KW = Power in KVA x PF
Power in KVA  = Power in KW/PF = Power in KW/0.8    (Nominal PF = 0.8, which is standard for homes)

Total load in Watts = 300 + (3 x 70) + 200 + 200 + 150 = 1060W = 1.06KW
Power in KVA = 1.06/0.8 = 1.325
An inverter of standard rating 1.5KVA is required to carry the loads above.

How to Calculate Inverter Battery Backup Time
The backup time for batteries in an inverter system depends on the number of batteries as well as their capacity in Amp-hours.

Inverter battery backup time is calculated as:
Back up time = Battery Power in Watt hour (Wh)/Connected Load in Watts (W)
Battery Power in Wh = Battery Capacity in AH x Battery Voltage (V) x Number of Batteries

Let us shorten the formula by using the following Symbols:
Let BUT = battery backup time in hours
            C = battery capacity in AH 
    V = battery voltage in volts
    N = Number of batteries in series or parallel as the case may be.
    $P_L$ = connected load in watts (W)


$$BUT = {\frac{C*V*N}{ P_L}}$$

In our example above, suppose we have selected a 24V, 1.5KVA inverter system that is to use two 12V batteries in series connection and suppose further that the capacity of our batteries are 200AH each, then :

C = 200AH
V = 12V
N = 2
$P_L$   = 1,060W

$$BUT = {\frac{200 * 12 * 2}{1060}} = 4.53 hrs$$