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Battery voltage model

The voltage model is similar for lead-acid and li-ion technologies.

The base voltage is the open-circuit voltage VocBattery, described separately.
In the linear region, the Voc voltage is mainly modified by the Internal resistance. The main difference between technologies is overcharging behavior: gassing in lead-acid batteries and internal resistance increase in li-ion.

The basic model takes the simple form :

\(Vbattery = Voc_{battery} + ResInt * Ibattery\)

For lead-acid batteries, above the overcharging threshold, a gassing voltage correction must be added:

\(Vbattery = Voc_{battery} + ResInt * Ibattery + VGassing\)

where:

  • Voc_battery is a function of SOC, with temperature correction for lead-acid
  • ResInt is constant for lead-acid. For li-ion, temperature correction applies, as well as exponential correction in overcharging and deep discharge regions,
  • VGassing applies only to lead-acid batteries.
  • IBattery is positive during charging and negative during discharging.

The graphs compare lead-acid and li-ion voltage models for a discharge rate of 10 hours (C10). Ohmic loss is significantly lower in li-ion due to better internal resistance. The gassing curve is visible for lead-acid, and the effect of ResInt increase at high SOC is evident in li-ion. Other characteristics are very similar.

Battery voltage model

State of charge determination

This model is often used to determine SOC from voltage for charging/discharging control. For a given voltage, SOC determination is highly current-dependent, especially for lead-acid batteries. Lead-acid voltage variation (13.5% for SOC = 0...1) is greater than li-ion LFP variation (4.8%). Additionally, lead-acid voltage is temperature-dependent, which introduces significant measurement uncertainty in field conditions.

Detection of overcharging and deep discharge is facilitated by current deviation enhancements at these extremes. Reconnection must use the VocBattery voltage curve, which is insensitive to current when the charger or load is disconnected. Therefore, controllers must use a large voltage hysteresis to avoid oscillations.

Polarization

With lead-acid batteries in open circuit, measured voltage is often poorly defined: voltage drift depends on immediately preceding operating conditions. This characteristic time is less than one hour and affects only very-low-current states. PVsyst does not account for this effect.