A Comparison of Different Methods for Physically Motivated Parameterization of High Power Lithium-Ion Battery Cells

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The development of lithium-ion batteries with high power density is currently being driven by their potential applications in mild hybrid vehicles. A 48 V electrical system in passenger cars can provide an efficiency advantage and reduce CO_2 emissions by about 10 % to 15 %. Pouch bag cells having a lithium-titanate (Li_4Ti_5O_12) anode and a nickel-manganese-cobalt (NMC) cathode provide good cell chemistry for high-performance applications.
Electrochemical impedance spectroscopy (EIS) has proven to be a promising, non-invasive method for the physically motivated parameterization of lithium-ion cells. By differentiation of relaxation times using EIS measurement data, electrochemical processes with short time constants ranging down to 10 mHz can separately be identified. In the equivalent circuit model (ECM), every process gets an element that can be parametrized individually.
Since the resistances of high-performance cells are small (values at 0.1 to 1 mΩ), there are difficulties getting a proper EIS measurement for low frequencies that has to be used for the parametrization of ECM elements with slow time constants.
The lower the frequency of the sinusoidal excitation, the longer the charging and discharging phases. Accordingly, the amplitude of the current excitation must be reduced in order not to change the state of charge of the cell in such a way that an LTI system can no longer be assumed. If the current amplitude is too small, a valid interpretation of the EIS measurement is no longer possible due to the poor signal-to-noise ratio.
Therefore, a hybrid parameterization method is proposed in this work for the elements with slow time constants. Such a hybrid parameterization method uses measurement data from the time domain to modify and supplement the parameters with time constants slower than 10 mHz in the ECM with parameters of the EIS method. The time-domain measurement data shows the combined behavior of all electrochemical processes with different time constants. Therefore, the ECM elements with slow time constants can be parametrized by using this data.
In this work, a physically motivated ECM, parameterized exclusively with the EIS method, is compared with an ECM parameterized with two types of hybrid parameterization methods. One hybrid method is using the time domain measurements of a relaxation phase, and the other uses the time domain measurements of charge and discharge pulses.
For validation, a current profile is used that represents the load of the “Worldwide harmonized Light vehicles Test Procedure“ (WLTP), measured for a single cell in a 48 V system. A model parameterized with the hybrid method with pulses shows the least error between the voltage curves measured in reality and simulated.

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