battery pack configuration calculator

 


Capacity and energy of a battery or storage system

The capacity of a battery or accumulator is the amount of energy stored according to specific temperature, charge and discharge current value and time of charge or discharge.

Configuration of batteries in series and in parallel : calculate global energy stored (capacity) according to voltage and AH value of each cell

To get the voltage of batteries in series you have to sum the voltage of each cell in the serie.

To get the current in output of several batteries in parallel you have to sum the current of each branch .

Example :
- 2 batteries of 1000 mAh,1.5 V in series will have a global voltage of 3V and a current of 1000 mA if they are discharged in one hour. Capacity in Ampere-hour of the system will be 1000 mAh (in a 3 V system). In Wh it will give 3V*1A = 3 Wh
- 2 batteries of 1000 mAh,1.5 V in parallel will have a global voltage of 1.5V and a current of 2000 mA if they are discharged in one hour. Capacity in Ampere-hour of the system will be 2000 mAH (in a 1.5 V system). In Wh it will give 1.5V*2A = 3 Wh

That is why it is better to speak in Wh (Watt-hour) rather than Ah (ampere hour) when you speak of capacity of a pack of batteries with elements in series and parallel, because capacity in Watt-hour is not linked to the voltage of the system whereas capacity in Ampere-hour is linked to the voltage of the pack of batteries.

Rating capacity and C-rate

C-rate is used to scale the charge and discharge current of a battery. For a given capacity, C-rate is a measure that indicate at what current a battery is charged and discharged to reach its defined capacity.
A 1C (or C/1) charge loads a battery that is rated at, say, 1000 Ah at 1000 A during one hour, so at the end of the hour the battery reach a capacity of 1000 Ah; a 1C (or C/1) discharge drains the battery at that same rate.

Formula to calculate Current available in output of the battery system

How to calculate output current, power and energy of a battery according to C-rate?
The simplest formula is :

I = Cr * Er
or
Cr = I / Er
Where
   Er = rated energy stored in Ah (rated capacity of the battery given by the manufacturer)
   I = current of charge or discharge in Amperes (A)
   Cr = C-rate of the battery
Equation to get the time of charge or charge or discharge "t" according to current and rated capacity is :
t = Er / I
t = time, duration of charge or discharge (runtime) in hours
Relationship between Cr and t :
Cr = 1/t
t = 1/Cr


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