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Capacity as function of the discharge rate

The capacity is highly varying according to the charge/discharge rate, i.e. the current.

NB: The discharge rate [hours] is the time for fully discharging the battery at a given current. In PVsyst, the nominal capacity is specified at C10, i.e a discharge in 10 hours. This corresponds to a current of 0.1 x capacity, sometimes noted 0.1C.

Lead-acid batteries

The capacity variation is very important: we observe a ratio of about 40 % between C10 and C100 ! In PVsyst, this behavior is defined as a profile.

Discharge rate, lead-acid

This will have deep consequences on the battery balance and efficiency when using the battery in a simulation.

Lithium-Ion batteries

The capacity variation is less prononced. The capacity increase at C100 is about 4%.

Discharge rate, lead-acid

Peukert model

Here the capacity evolution is obtained by a model. The correction of capacity according to the discharge rate is done through the peukert coefficient K, which is specified in the battery's parameters (usual value K = 1.02):

\(Capacity [Ah] = CapNomC10 * (DischRate / DischRateRef) ^{(1-K)}\)

or

\(Capacity [Ah] = CapNomC10 * (CurrentRef / Current) ^{(1-K)/K}\)

Where:

  • CapNomC10 [Ah] = nominal capacity, defined for the discharge time of 10 hours
  • DischRateRef [hours] = 10 hours here
  • CurrentRef [A] = current at C10 = capacity [Ah] / 10 [hours]

NB: The Peukert model may also be applied to the lead-acid batteries. This corresponds to a Peukert coefficient of 1.12 to 1.13.