Battery knowledge · Thermal management and heat transfer
Heat generation
The heat a cell produces in operation: an irreversible part equal to current times overpotential, and a reversible part from the entropy change, I·T·dE/dT. The Bernardi equation sums them and feeds every thermal model. [1]
- Also called
- Bernardi equation
- Unit
- W
- Relationship
- q = I(V − E_OCV) + I·T·(dE/dT)
Example
Keep reversible and irreversible heat separate
With charging current +5 A and terminal voltage 0.10 V above OCV, the irreversible term is 0.50 W. At 300 K with dE/dT = +0.1 mV/K, the reversible contribution is +0.15 W, giving 0.65 W under this sign convention.
Explore the graph
Double the current and ohmic heating increases fourfold.
At 5 A: 0.5 W. At 10 A: 2 W.
P_heat = I²R
Illustrative model. Resistance is constant; reversible entropic heat and other losses are excluded.
Use in Lemonergy
Lemonergy Studio blocks
Compare grid and battery energy
Separate energy and loss signals make efficiency visible.
Blocks to use
- Regulated CC/CV charger
Regulates current and voltage
Inputs & settings
- currentA
- voltageV
- cutoffCurrentA / cutoffHoldS
- Electrical ports p and n
- Battery with SOC-dependent OCV
Stores charge and supplies terminal voltage
Inputs & settings
- capacityAh
- initialSoc
- emptyVoltageV / fullVoltageV
- resistanceOhm
- Electrical ports p and n
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Keep battery settings fixed.
- Change converter efficiency.
Example. 7 kW battery-side power at 95% efficiency requires about 7.37 kW grid power and produces about 0.37 kW converter loss.
Observe. Battery I²R loss differs from converter loss.
A loss signal is not a predicted temperature. This network takes external temperature.
Open the Studio example →References & further reading
Technical references
- A General Energy Balance for Battery Systems
Dawn Bernardi, Ellen Pawlikowski, John Newman · Journal of The Electrochemical Society · 1985
Technical reference · Battery energy balance and irreversible and reversible heat contributions. Reduced thermal models require explicit assumptions and current-sign conventions.
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- University Physics Volume 2, §1.6: Mechanisms of Heat Transfer
OpenStax, Rice University
Topic background · Conduction, convection, radiation and thermal resistance.