Skip to content

Battery Model

System (external) point of view

Any PV system can use an Energy Storage System as a energy buffer between the energy production and the energy consumption. This buffer is almost exclusively made up of an electrochemical battery, usually referred to by the name Battery Energy Storage System (BESS).

The charge and discharge strategy may change based on the system type and other external factors, but they all need the same key variables:

  • The charging power - EBatCh
  • The discharging power - EBatDis
  • The possible losses (internal resistance, faradic efficiency, self-discharge)
  • The State of Charge - SOC

The charging and discharging power are relatively simple to measure. They represent the energy going to and from the battery terminals.

The losses cannot be measured directly, but can be determined during a full battery cycle with the difference between the charging and discharging energy.

The SOC represents the % of energy remaining in the battery at a given time.

Internal operation

PVsyst battery model is split into 3 different parts:

  • Loss Model
  • Capacity Model
  • Ageing Model

Loss Model

The loss model is used to estimate how much energy is lost when charging or discharging the battery.

This model considers:

The internal resistance ResInt acts on the battery voltage \(V_{\textsf{Battery}}\):

\[V_{\textsf{Battery}} = V_\textsf{OC,Battery}(\textsf{SOC}) + \textsf{ResInt} \cdot I_{\textsf{Battery}}\]

with \(V_{\textsf{Battery}}\) being the measurable voltage at the battery terminals, and the \(V_\textsf{OC}\) representing the effective voltage for the battery. When charging (\(I_{\textsf{Battery}} > 0\)), the external voltage is higher than the \(V_\textsf{OC}\), and it is lower when discharging.

The Faradic or Coulombic efficiency (i.e. the charge/discharge current balance) named EfficI is applied when charging

\[I_{\textsf{Battery,internal}}\,\mathrm{[A]} = I_{\textsf{Battery}}\,\mathrm{[A]} \cdot \textsf{EfficI}\]

The corresponding current loss is named IBEffL in PVsyst.

The battery gassing applies on Lead-Acid batteries at high SOC.

\[I_\textsf{gassing} = I_\textsf{o,gass} \cdot \exp(\Delta \cdot dV_\textsf{gassing})\]

All these effects on the current and voltage are applied before computing the internal energy variation.

The self-discharge is a permanent discharging current, named IBSelf in PVsyst, dependent on the temperature. It is currently only used for StandAlone systems.

Please see Battery efficiency for details.

Capacity

The battery effective capacity is not constant, and depends on the discharging rate (or current), the temperature, the battery wear state.

The battery capacity current dependency is especially important with lead-acid batteries. At C100 (charge in 100 hours, i.e. \(I_{\textsf{Charge}} = \textsf{Capacity}/100\)), the capacity may be about 40% higher than at C10. This variation is much less pronounced with Li-Ion batteries (about 4%).

The battery capacity variation is not a loss, and will only impact the "visible" energy for the controller.

Ageing

The battery characteristics may change with time and usage conditions. The most impacting factors being the number of cycles, the charging and discharging rates and the operating temperature.

Battery controllers

For Grid connected systems, the battery controller is always based on the SOC.

For Stand Alone systems, the battery controller may be based on the battery SOC or Voltage.

Variable names in PVsyst simulation

When you want to analyse detailed simulation data, the variables names in PVsyst are simplified. For example: ECharge is named EBatCh, EDischarge is EBatDis, ESOCBalance is ESOCBal, the battery voltages are named U_Batt, UBatCh, UBatDis, etc. For StandAlone systems, you can have simultaneous values EBatCh and EBatDis within the simulation time step. This means the operating status have changed during the time step. The operating times will be given by ChargeON and DischON. The effective capacity used during the time step is also accessible under the name CapaEff. When both charge and discharge occurs during the step, the CapaEff value will be the discharging capaEff (the capacity during charge being constant)