# Battery power required for a 2HP Motor AC at 1800 rpm, 56Hz?

So I will be using an Inverter to convert DC(12V) to AC(220v)(50Hz).

The 2HP*(746w) = 2.3 kW / .85 power factor = 2.7 kW / 220V = 12.27A

If I want it to run for 5 hours that's 62 Ah.

Can I use a single 100 Ah battery or even a 50 Ah batter rated at 12V?

The maths

2.3 kW / .85 power factor = 2.7 kW / 220 V = 12.27 A.

Yes, at 220 V.

At 12 V ...

2.3 kW at 12 V: $I = \frac {P}{V} = \frac {2300}{12} \approx 200~A$.

For 5 hour run time you would need 1000 Ah capacity with a 100% efficient inverter. Assuming you could find an 80% efficient inverter and you decide to only discharge the batteries by 75% to prolong their life then required battery capacity:

$$Ah = \frac {1000}{80\% \times 75\%} = \frac {1000}{0.8 \times 0.75} = 1666~Ah$$

As you can see, your 50 Ah is not going to work.

Selecting battery voltage

When designing high-powered inverters and UPS the standard technique is to use a high voltage battery bank rather than a 12 V bank. This has several advantages:

• The current is lower.
• Conductor sizes can be reduced.
• Power loss through the switching devices (e.g., transistors) is less because of the reduced current. This reduces the heatsinking requirements.

Basic inverter calculations:

$$P_{OUT} = \eta P_{IN}$$

where $\eta$ is the inverter efficiency.

To get 12.27A at 220V from an inverter running off a 12V battery you would need about 225A from the 12V battery - assuming if the inverter is 100% efficient.

So No, is the short answer; you would need a 12V battery rated at more than 1350 Ah