# Battery Sizing for AC system

1. Jul 24, 2017

### Jeza43

Hi,

Interested in sizing some DC lithium-ion batteries (through a controller) to power the following system: 90KVA, 200/115 Volts AC, 400 Hz, 3-phase.

The current approaches I've taken have been drastically oversized so I'm clearly missing something.

Cheers,
J.

2. Jul 24, 2017

### Staff: Mentor

How long does it need to produce 90 kva?

My understanding is that Tesla does 88kvah by paralleling thousands of small standard cells...

3. Jul 24, 2017

### CWatters

Perhaps show us your calculations. They might be correct.

4. Jul 24, 2017

### Jeza43

It needs to produce for around two hours, yes I'm currently looking at utilizing Nissan Leaf battery packs which have a capacity of approximately 24 kWh.

5. Jul 24, 2017

### Jeza43

To elaborate, CWatters, I'll step you through my process back to front. To obtain the effective power derived from the AC system I calculated the rms current and voltage, which then using a power factor of 0.9 (assumption as cannot find specific to the system) and a added factor of sqrt(3) for the three-phase aspect provided the following:

V_rms=V_max / sqrt(2) = 200 V/sqrt(2)=141.4 V
I_rms=90 KVA / V_rms = 636.4 A
P_eff = V_rms * I_rms * PF * sqrt(3) = 140 kW

Which would indicate for two hours of operation I would need a capacity of at least 280 kWh.

Any feedback would be appreciated, come from a mechanical background so am not confident with my methodology.
Cheers,
J.

6. Jul 24, 2017

### Staff: Mentor

I would think you are given voltage in RMS (it almost always is), but I'm not familiar with a 200V system...

In either case, since you already have kVa, you don't need to do anything other than correct it for power factor: 90*.9=81 kW....and for 2 hours, is 162 kWh.

7. Jul 24, 2017

### Jeza43

Thanks for the feedback russ_waters, still larger than I was expecting but it's good to know the maths is sound.
Cheers,
J.

8. Jul 27, 2017

### Windadct

Not enough info:

What is the "system" - 90 KVA may be the rating but at what rate does it use real power, not just Watts vs LVA, but I doubt it runs at FULL power for 2 hours. That spec looks like a UPS? -- The UPS, if it is controlling the battery, needs to be connected to the same battery technology. So if it was built for Lead Acid - you can not just change it to LiPO. The issue is the charging of the LiPo - discharge not as much of a concern.

The load - may use 90 KVA and use very little power - so the system can be running at maximum rating, but the battery supplying little power.

In an AC system - KVA can be "no" real power, but a confusing point is that in a DC system ( battery) - VA is effectively the real power. Batteries are rated in Amp-Hours, but you have to look at the datasheet to see where this rating was developed, the RATE of discharge affects the total A-H delivered, and the rating is to what Voltage.

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