how to get the parameters α, β, ∆Q/∆T and ∂E/∂T

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Marouen Ben Said
Marouen Ben Said on 30 Jan 2023
Answered: Kartik on 17 Apr 2023

Answers (1)

Kartik
Kartik on 17 Apr 2023
Hi,
The Battery block documentation in MATLAB provides the equations used to calculate the parameters α, β, ∆Q/∆T, and ∂E/∂T. Here are the relevant equations:
α = 1 / (R * C_nom) β = -1 / C_nom ∆Q/∆T = I_gain * C_nom ∂E/∂T = (OCV_gain * R * C_nom) / (2 * F)
where:
  • R is the battery resistance parameter
  • C_nom is the nominal battery capacity parameter
  • I_gain is the gain for the current measurement sensor
  • OCV_gain is the gain for the open-circuit voltage measurement sensor
  • F is the Faraday constant
These equations are derived from the following equations, which describe the battery model used in the Battery block:
V = OCV(T) - i*R Q = ∫i dt C_nom * ∂V/∂t + V = Q
where:
  • V is the battery voltage
  • OCV(T) is the open-circuit voltage as a function of temperature
  • i is the battery current
  • R is the battery resistance
  • Q is the battery charge
  • C_nom is the nominal battery capacity
The equations for α and β come from linearizing the battery model about a nominal operating point (i.e., a small-signal analysis). The equations for ∆Q/∆T and ∂E/∂T come from taking partial derivatives of the battery model with respect to temperature.
For more information and details, please refer to the MATLAB documentation for the Battery block : https://www.mathworks.com/help/sps/powersys/ref/battery.html

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