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I am doing battery calculations for off-grid solar panel. I don't get that why battery guides on Internet always ignore Peukert's Law for batteries of solar panel. I want to have good approximations not perfect. So, don't answer too complex please.

I want to know

  1. What AH battery use
  2. What is its charging time
  3. Discharging time

If I have a 1KW load and I want to have its backup for 3 hours. That makes energy 3KWH. That means I need to generate this energy. Furthermore, 1 KW requires 4.54 current for a single phase at homes in Pakistan (220 AC at 50 Hz). This current can also be called discharging current of battery.

Id = 1000/220
Id = 4.54 A

Battery to use:

That means we require

AH = Id * Battery voltage
Let's take it 12 V
AH =   4.54 * 12
AH = 54.48

We should have DOD 50%, so that our battery drains only 50% and it gets the chance to charge again and doesn't go ever below 5o%. Doing so, enhances the battery life.

AH = 54.58/0.5
AH = 109.16

Is it economical to use such a huge battery for only 1 KW load?

Discharging time:

Note that batteries come with 20 HR (hour rate). That means a battery shows its mentioned capacity if discharged in 20 hours. Otherwise so many losses occur and decreases the battery capacity. So here comes a complex pukerts formula.

Pukers law formula

where k=pukers number. But batteries don't come with pukerts no. Do they? I never ever saw written pukerts number written on any battery. Guides say that its usually between 1.1 to 1.4. But 1.1 and 1.4 makes a huge difference in calculations.

Anyway, let's choose k=1.4

It tells us that when:

C=54.48
H=20
I=4.54
then t=9.78 hours

and when C=109.16 AH
then t=25.88 hours.

I feel like I have used extra AH battery because I dont need backup for 26 hours. I need for 3 hours only.

Charging time:

Charging current should be 10% of the battery capacity. Therefore, 1/10th of 109.16 is 10.916 A.

Charging current should be 10.916 A and it will take t=109.16/10.916=10 hours to charge?

Please improve my calculations where lackings are. And correct me where I am wrong.

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    \$\begingroup\$ Your amp number is wrong - 4.5A at mains voltage requires considerably more on the 12V side. electronics.stackexchange.com/questions/28847/… ; 3kWh is a lot for a battery system, that's half of the Tesla Powerwall 1 capacity of 6kWh at a cost of $3000. \$\endgroup\$ – pjc50 Oct 9 '18 at 15:24
  • \$\begingroup\$ @pjc50 Can you please tell me where are you exactly referring me to in this link? Plus I dont get how my 4.5 A is wrong and it requires more on the 12 V side? \$\endgroup\$ – Muhammad Naufil Oct 9 '18 at 15:31
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    \$\begingroup\$ You will have to supply the same power from the battery as you will consume at 240VAC (more, actually because of losses.) 1kW at 240VAC is around 4A. 1kW at 12V is 83A. So, you need at least 83Ah for one hour of operation. \$\endgroup\$ – JRE Oct 9 '18 at 16:16
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    \$\begingroup\$ According to this site, " Peukert’s law is exponential; the readings for lead acid are between 1.3 and 1.5 and increase with age. Temperature also affects the readings." [emphasis added]. This is probably why you're not finding Peukert's number on data sheets. \$\endgroup\$ – The Photon Oct 9 '18 at 16:22
  • \$\begingroup\$ That number is useless for everyday calculation. C however is not and often provided \$\endgroup\$ – PlasmaHH Oct 9 '18 at 16:52
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1 KW requires 4.54 current for a single phase at homes in Pakistan (220 AC at 50 Hz). This current can also be called discharging current of battery.

Not unless the battery is a 220 volt battery. If it's a 12-volt battery (as JRE commented) then for 1 KW you need about 83 amps. Power equals voltage times current, remember?

Then 3 kWh requires 3 x 83.3 amps, or 250 Ah. Assuming a 50% discharge limit, the battery capacity required is 500 Ah.

Is it economical to use such a huge battery for only 1 KW load?

Well, that's up to you, isn't it? How badly do you want to provide that 1 kW load? What is the price of the alternative?

And, for what it's worth, as pjc commented 1 kW from a battery system is a very large draw. It's made worse by your miscalculation of the required current, too.

Now, as for your original question about Peukert's Law, the answer is pretty simple. It is ignored because it's not particularly useful. When designing a battery system the load is hardly ever precisely known, so attempting to precisely define battery life is pretty much a hopeless cause. And that is before adding in the effects of varying temperature and operational life. So what people do is use the "standard" ratings and, particularly if the load current is expected to be high, add a safety factor. The situation is made even worse by the fact the charging efficiency decreases as a battery reaches full charge. And that effect is also affected by charge current level, temperature and battery life.

Battery performance is nastily complex to calculate, so nobody does.

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