Electrical Energy Storage Technology

# Electrical, Thermal, and Lifetime Modeling

We require reliable simulation models to properly and accurately design energy storage devices for equipment like electric and hybrid powered vehicles or for stationary equipment (e.g. temporary storage for photo-voltaic or for wind-powered devices). Using the electrical and thermal characteristics provided by these models, it is possible to predict the lifetime of a battery. Battery management systems also use model-based methods to estimate the state of the system and the cells. Various modeling concepts are used:

Technische Universität Berlin
Electrical Energy Storage Technology
Institute of Energy and Automation Technology
Faculty IV
Office code EMH 2
Einsteinufer 11
D-10587 Berlin

## Impedance-based modeling

The aim of impedance-based modeling is to develop an equivalent circuit for the electrical characteristics of an energy storage device. Equivalent circuit models contain simple models consisting of a variable voltage source, an internal resistance, inductance, multiple RC elements as well as fractional models, which are capable of modeling special impedance characteristics by using Warburg elements or constant-phase elements. Other models are designed especially for the high frequency behavior of a cell. The equivalent circuits and the values for the various elements can be determined through impedance spectroscopy or the evaluation of the voltage response to a current pulse (for further information about characterization see Electrical characterization). By fitting the impedance spectra and the voltage responses, the model parameters can be extracted.

For all battery types the impedance spectrum/voltage response is altered by a variety of external influencing factors, primarily DC ripple current, temperature and state of charge. As a result, a broad range of measurements are required for the various tasks performed by a battery. A further issue is the size of batteries and the associated irregularity in temperature, power distribution, etc.

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## Physical-chemical modeling

In contrast to an impedance-based model, a physical-chemical model is not based on measurements from an equivalent circuit but rather on emulating the expiring processes. The model parameters are established by means of geometrical data and material characteristics. The advantage of this approach is that you can also simulate new battery concepts without actually having a battery. On the other hand all relevant processes must be known and modeled for the model to exhibit accurate behavior. Likewise the interior structure must be known, which often requires a battery to be opened. The aging process also has to be incorporated into the model so that any influences from e.g. operating strategies or the effects of internal structures on the different aging mechanisms can be examined. Physical-chemical models include the electrode average model, the single particle model and the pseudo two-dimensional model, which are programmed in Matlab, as well as finite element models, which are modeled in special multiphysics software solutions.

## Thermal models

Thermal models are essential for determining the temperature in a battery system model as well as for simulating a battery’s thermal characteristics. These are needed to design cool and hot system applications and determine the aging behavior. These models can be based on thermal equivalent circuits or finite element models and are parameterized by conducting special thermal measurements or by using the material data. In virtually all battery technologies, increasing the temperature accelerates the aging process. However, extremely low temperatures can also cause harm to the device.

## Aging models

Aging models are categorized into two different model types: physical-chemical and semi-empirical models. The latter is based on the determination of capacity and internal resistance over the course of the aging process. These two factors are determined in aging tests, where the different influencing factors are varied to quantify the influence. These are the most common models for designing battery systems and estimating battery cell aging in battery management systems.

The aim of physical-chemical modeling is to identify and reproduce aging processes, whereas the aim of semi-empirical modeling is to reveal the different influencing factors on the aging processes and how those factors affect aging. The primary objective of this work is to discover the largely unknown reciprocal influences of different factors.

## System models

The knowledge acquired from single cell modeling can be applied to model battery systems, allowing us to model cell connections and the electrical, thermal and aging behavior in particular. The system model is used for research on current distributions, resulting thermal behavior and possible inhomogeneous aging. Contact and conductor resistances can also be taken into account.