Physical models used > Batteries - General model description > Lithium-ion voltage model

(go directly to the help section of the form, "Lithium-ion : Internal Resistance")

The resistance model considers 2 corrections, a correction as a function of temperature, which is the main correction, and a correction as a function of SOC which is a minor one.

•Internal resistance vs Temperature

Resistance (T°C) = Resistance (T°CRef) . EXP((Activation Energy/8.315)*(1/(273+T°C)-1/(273+T°CRef)))

with :

Resistance (T°C) =	the resistance at given T°C
Resistance (T°CRef) =	the resistance at reference temperature
Activation Energy =	the activation energy for the underlying thermally activated mechanism (in kJ/Mol)

The validity of this Arrhenius relationship (Ref. Lundgren 2016) has been checked against many experimental discharge curves. It was observed that the law was giving very good satisfaction for the modeling purpose in PVSyst.

•Internal resistance vs SOC

PVSyst applies an empirical correction factor to catch the increase of voltage at the the end of charge. This correction is applied as well at the beginning of discharge.

Correction Factor = 1 + A*exp(-B*(1-SOC))

with

A	Pre-exponential correction
B	coefficient to set the SOC range where the correction shall be applied

This correction is then applied as follow :

Charge :	VBatt(SOC,T°C,I) = OCV(SOC) + Correction Factor . Resistance (T°C) . I
Discharge :	VBatt(SOC,T°C,I) = OCV(SOC) + Correction Factor . Resistance (T°C) . I - 2 . Resistance (T°C) . I

Note that this correction was set for display purposes only, in the form. It has no impact on the battery behaviour as the SOC range concerned is extremely small.