The power forecast is a central task in the battery management system, which should always determine the
maximum power of the battery. An inaccurate forecast can affect the safety and lifetime of the energy storage
system, as the forecasted power will overload the storage system. The battery impedance is an important
parameter here, which, due to the chemical and physical processes, depends not only on the state of charge, but
more importantly on the temperature of the cell. Therefore, it is crucial to know it precisely.
In the automotive sector, lithium-ion battery cells in low-voltage storage systems are often exposed to high
charging and discharging currents, for example through recuperation when braking or accelerating the vehicle.
These high currents can lead to increased heat development within the cells as well as in the battery pack.
Various publications show that local temperature increases can occur at electrode contacts or at the edges of the
electrodes due to the concentrated current flow, which is why some areas can be warmer than others. Using
different cooling concepts, such as a cooling plate on the bottom or at the side of the cells, can further increase
this inhomogeneous temperature distribution. In-car measurements have shown that this can lead to temperature
gradients of up to 20°C within the cell.
Depending on the position of the temperature sensor, a temperature can be measured that is warmer or colder
than in other areas of the cell. On the one hand, this can lead to the battery management system allowing higher
charging currents, which can increase lithium plating and the formation of dendrites in the colder areas of the
cell. On the other hand, the warmer zones can be disproportionately loaded, which results in increased ageing of
these areas.
Model-based state-of-power algorithms use electrical battery models to determine the impedance and thus to
calculate the maximum permissible current and the available power. The parameters of these electrical battery
models depend on the state of charge, current and temperature of the cell and are usually stored in look-up tables.
Data-based state-of-power algorithms based on power maps, for example, record the battery's performance at
different operating points of temperature, state of charge and current levels. The system can use this information
to predict how the battery will perform under certain conditions. 
Both approaches require temperature information of the cell and usually consider a temperature value for the
entire cell, often the locally measured temperature. In combination with temperature gradients, this can lead to
problems, as both the warmer and colder zones of the cell should not be loaded with a too high current.
An electrical model based on volume elements, which considers temperature gradients within a cell to determine
the maximum permissible current, will be developed. However, this requires information on the current
temperatures of the cell.
The aim of this work is to create a temperature model which can be used to determine the inhomogeneous
temperature within a cell can be determined.
For this purpose, different thermal models are presented and compared to each other. The respective advantages
and disadvantages are discussed.
Finally, a model is selected which offers an optimum between accuracy and complexity and thus considers the
limited computing power of the BMS in automotive applications.