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I am doing a case study on battery back up of a wind system with the following specification:

  • System size: 10 kW which runs continuously for 5 hours per day.

Battery Calculations:

  • Battery type: lead acid
  • Energy generated per day: 50,000 Wh
  • Back-up days: 1
  • Depth of discharge: 50%, so 50000 Wh/0.5 = 100,000 Wh

Battery de-rate factor based on temperature (NJ max. = 63°F)

De-rate factor = 1.04, so 100,000 Wh x 1.04 = 104,000 Wh

Battery voltage: 48 V.

104000 Wh/48 V = 2166 Ah.

The next size up is 2200 Ah.

Can some one help me verify my calculations and also how to calculate the charging time and discharging time for this battery?

Thanks any guidance is much appreciated

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There are numerous errors in your calculations.

50000/0.5 = 100,000 Wh

Dividing two dimensionless quantities can't result in a value of Wh.

Again:

100,000 x 1.04 = 104,000 Wh

And again:

104000/48 = 2166 Ah

There is no point looking at the numeric values when the units are wrong.

For charging and discharging time, you need to know the current or power. You already know the discharge time, since you used it to size the battery bank. It will take 5 hours to discharge to a depth of 50%, since you designed it to be so.

For charging time, do the reverse. Find how long your power source takes to produce 50 kWh. You also need to derate that to the efficiency of the battery. Since the battery isn't 100% efficient, you need to put more energy in to charge it than you get out when you discharge it. Any battery will also have a maximum charge rate. See the battery datasheet.

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  • \$\begingroup\$ Thanks @Olin Lathrop for your constructive feedback. \$\endgroup\$ – TheElectrician Oct 7 '18 at 18:30

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