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
