Calculation of battery bank capacity, c-rate, run-time, charge and discharge current
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Principle and definitions
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.
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.
A 0.5C or (C/2) charge loads a battery that is rated at, say, 1000 Ah at 500 A so it takes two hours to charge the battery at the rating capacity of 1000 Ah;
A 2C charge loads a battery that is rated at, say, 1000 Ah at 2000 A, so it takes theoretically 30 minutes to charge the battery at the rating capacity of 1000 Ah;
The Ah rating is normally marked on the battery.
Last example, a lead acid battery with a C10 (or C/10) rated capacity of 3000 Ah should be charge or discharge in 10 hours with a current charge or discharge of 300 A.
Why is it important to know the C-rate or C-rating of a battery
C-rate is an important data for a battery because for most of batteries the energy stored or available depends on the speed of the charge or discharge current. Generally, for a given capacity you will have less energy if you discharge in one hour than if you discharge in 20 hours, reversely you will store less energy in a battery with a current charge of 100 A during 1 h than with a current charge of 10 A during 10 h.
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
Cr = I / Er
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