Battery Model Parametrization

Accurate battery models are the basis for reliable cell selection, system design and battery management. Whether for stationary storage or electric mobility, a model is only as good as the measurements and the parametrization behind it. This article outlines how battery models are set up and parametrized, for cylindrical, prismatic and pouch cells alike.

From measurement to a validated model

Setting up a battery model follows a sequence of steps, from describing the electrical behaviour of the cell to the final model parametrization:

Fig. 1: Steps of battery model setup and parametrization

Electrochemical impedance spectroscopy (EIS)

Electrochemical impedance spectroscopy (EIS) is a suitable method for identifying the dynamic behaviour of lithium-ion batteries. The battery is excited with a signal, typically sinusoidal, and the resulting system response is measured. Two variants are distinguished:

• Galvanostatic impedance spectroscopy: a current is applied and the resulting voltage response is measured.

• Potentiostatic impedance spectroscopy: a voltage signal is prescribed and the resulting current response is captured.

In galvanostatic impedance spectroscopy, the sinusoidal current (RMS value Iac) is often superimposed with different direct currents (Idc) to capture the electrochemical behaviour of the battery under different current loads.

A prerequisite for impedance spectroscopy is that the system under investigation is linear and time-invariant. Batteries, however, show highly nonlinear behaviour over the state-of-charge range. During EIS measurements it must therefore be ensured that the state of charge does not change significantly, so that sufficient linearity around the operating point is maintained.

The impedance is determined from the relationship between the voltage and current signals and describes amplitude amplification and phase shift. It is measured at frequencies from several kilohertz down to the millihertz range to capture the full impedance spectrum. Figure 2 shows a characteristic impedance spectrum of an LTO/NMC lithium-ion cell.

Fig. 2: Typical Nyquist plot of an LTO/NMC lithium-ion cell at −20 °C and 50 % state of charge, frequency range 5 kHz – 1 mHz

Model parametrization

The individual components of the equivalent circuit must be parametrized according to the required dependencies on temperature, state of charge and current. The open-circuit voltage (OCV) curve is typically stored in the model as a state-of-charge-dependent table, from which the open-circuit voltage is interpolated based on the current state of charge. For the dynamic effects, suitable lookup tables or approximation functions (e.g. polynomials) that include the relevant dependencies must also be determined.

Depending on the available measurement equipment, the maximum test duration and the accuracy requirements, two parametrization methods are commonly used.

1. Electrochemical impedance spectroscopy

Capturing the battery parameters with EIS is the most complex parametrization method, as the measurements take comparatively long and the equipment is expensive. It is particularly suitable for highly dynamic processes such as the SEI passivation layer, charge transfer and double-layer capacitance. Diffusion effects are difficult to capture with this method, as they require frequencies below 1 mHz and therefore very long measurement times.

Fig. 3: Ohmic resistance of new and aged LTO/NMC cells: a) dependence on temperature, b) dependence on state of charge

2. Parametrization using current pulses

The second common method is the analysis of voltage responses to current pulses (e.g. HPPC tests). From the rise and decay of the overvoltages caused by the various dynamic effects, the resistance values and time constants of the RC elements can be determined. In principle, this works for both high and low frequencies. Limitations only apply to effects with very short time constants, such as the SEI layer, if the measurement equipment cannot record the voltage response with a sampling rate in the kilohertz range.

As with impedance spectroscopy, current pulses are applied at different states of charge, temperatures and current levels to capture the relevant dependencies. In both methods, the model parameters are identified by nonlinear optimization.

Verification and validation of battery models

To validate a battery model, the simulation results are compared with real measurement data. Datasets different from those used for parametrization must be used for this.

The following example (Figure 4) considers a model consisting of a state-of-charge-dependent voltage source, a resistor and an RC element. The parametrization was carried out using EIS and HPPC tests to determine the total resistances and to parametrize the RC element, which mainly represents charge-transfer effects. The parameters were stored in current-dependent lookup tables.

Fig. 4: Nonlinear first-order lithium-ion battery model commonly used in battery management systems

Summary

Reliable battery models require a structured approach: OCV measurement, identification of the dynamic behaviour with EIS and current pulses, parametrization over temperature, state of charge and current, and validation with independent measurement data. FA Battery Engineering supports development teams in e-mobility and stationary energy storage with advanced systems engineering, modelling and simulation methods, drawing on more than a decade of experience in battery system engineering.

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