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Issue #2 = The pack is always under load, how do we get the OCV?
Battery modelling!
TLDR: Lots of math I had fun with, we use this equation for the RC circuit:
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We can model our battery pack with either a 2RC or RC model. For simplicity, I will stick to an RC model.
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The circuit can be modelled with the equation:
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In the S-Domain it is modelled as:
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Two ideas to model this equation for the firmware:
1. First-order Taylor series approximation of ex
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So OCV voltage can be estimated using this:
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2. Transfer function with Inverse Laplace Transform (S domain → Time domain)
https://www.youtube.com/watch?v=nkq4WkX7CFU
The transfer function for the RC circuit (eq 1) can be converted into the time domain using reverse Laplace transform (eq 2)
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Discretized for embedded systems, the equation can be written as:
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This is what will be implemented in our firmware, it is more accurate than the first-order Taylor series approx.
TO BE CONTINUED….
Resources:
https://www.analog.com/en/resources/technical-articles/a-closer-look-at-state-of-charge-and-state-health-estimation-tech.html
https://www.linkedin.com/pulse/li-ion-battery-rc-modeling-what-how-done-part-1-testing-techlanz-lscyc/