Cell Thermal Modeling: Heat Generation

In this document we are trying to model cell heat generation as a function of current, ambient temperature, and humidity.

Research Articles:

https://www.mdpi.com/2227-9717/11/12/3450#B7-processes-11-03450

Experimental and numerical studies on lithium-ion battery heat generation behaviors

Relevant Documentation:

- Cell Data Sheet

Variables:

• Q (J/s) - total heat generated by battery pack

• I (A) - current run through cell

• U_wv (V) - working voltage of cell

• U_ocv (V) - open circuit voltage of cell

• T_batt (C) - cell temperature

• T_env (C) - environmental temperature

• R_o (Ω) - ohmic resistance of cell

• R_p (Ω) - polarized resistance of cell

• R_i (Ω) - internal resistance of cell

• n - number of cells

• m (kg) - mass of cell

• Q_h (J) - total chemical reaction heat

• F (C/mol) - faraday constant

• M (kg/mol) - molar mass

• Q_J (J) - joule heat

• Q_P (J) - polarized heat

• Q_R (J) - reaction heat

• Q_S (J) - side reaction heat

• σ - (J/K) - entropy coefficient

Simplified Heat Generation of a Battery Pack Ignoring Temperature and Humidity

According to D. Bernardi’s battery heat generation theory, there are four components of heat generated by a battery pack, which are joule heat, polarization heat, reaction heat, and side reaction heat. Side reaction will be ignored since over charging/discharging will not be taken into account.

Q = Q_J + Q_P + Q_R + Q_S

Q = Q_J + Q_P + Q_R

Q = I²R_o + I²R_p + nmQ_hI/MF

Q = I²(R_o + R_p) + nmQ_hI/MF

Q = I²R_i + nmQ_hI/MF

Alternative Derivation: