Battery knowledge · Charging and discharging

Relaxation

The slow recovery of a cell’s voltage towards open-circuit voltage after current stops, as concentration gradients inside the electrodes level out. It takes minutes to hours, which is why OCV measurements need a rest period.

Also called
rest

Example

Voltage response and relaxation

At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.

Two separate analytical experiments; normalized voltage, not measured data.

Explore the graph

One time constant completes about 63% of a first-order voltage change.

First-order voltage response
First-order voltage responseTime (s) versus Fraction of voltage change. Step response; Separate relaxation experiment. Interpretation follows the graphs.000.263450.525900.7881351.05180Time (s)Fraction of voltagechange
Step responseSeparate relaxation experiment (dashed)

At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.

τ = RC; step response = 1 − e^(−t/τ)

Illustrative model. Two separate analytical experiments; normalized voltage, not measured data.

Use in Lemonergy

Design protocol or analysis tool

Inspect pulse characterization

HPPC alternates pulses, moves SOC and includes long rests.

Equation or tool to use

  1. Rest

    Allows relaxation

    Inputs & settings
    • s
  2. Pulse

    Excites charge/discharge

    Inputs & settings
    • a
    • pulseS / restS
  3. Repeat

    Repeats SOC points

    Inputs & settings
    • count

This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.

  1. Open HPPC pulse characterization.
  2. Compare immediate voltage change and recovery.

Example. 0.2 V change after a 10 A step gives 20 mΩ by ΔV/ΔI on the same cell/pack basis.

Observe. Long rests differ from the immediate resistive jump.

The estimate depends on timing, temperature and state; this is not AC impedance spectroscopy.

Open Design → Protocol bench →

References & further reading

Further reading on this topic

These sources provide broader context; they are not presented as citations for every statement in this entry.

  1. Lithium-ion battery fast charging: A review

    Anna Tomaszewska et al. · eTransportation · 2019

    Topic background · CC-CV and alternative charging protocols, transport limitations, degradation and thermal implications; results depend on cell and test conditions. Software behavior is documented separately in Lemonergy block references.