2.3.2. Selection of Test Frequencies

In a Li-ion battery cell, charged particles containing lithium ions are always involved in the electrode process. It is generally believed that the time constants of the movement or reaction of charged particles in these processes are different. Thus, impedance at different frequencies is related to different processes [52]. The influence of mass transfer, whose time constant is slower, is dominant at impedance at lower frequencies. Mass transfer (including diffusion) becomes faster as the temperature is higher and as the concentration of Li-ions increases (as DoD is lower). Faster transfer speed can be interpreted as lower impedance. On the other hand, the lower the cell temperature or the higher the DoD, the slower the mass transport [53], which appears to be a higher impedance in the lower frequency. This means that impedance at lower frequency can be more advantageous as it is used for cell SoC estimation. Studies on battery cell impedance consistently show that impedance at lower frequencies is more dependent on changes in cell SoC. However, since the frequency is the reciprocal of the period, the lower the frequency, the longer the period required to measure each continuous impedance. For example, if 1 mHz is used for the measurement, it takes about 17 min to collect only one period of signal. Therefore, the test frequency should be selected considering the time interval required for state estimation depending on the battery application. There is one more problem: the longer the measurement of one period, the greater the change in the internal state of the cell such as SoC and cell internal temperature. This also increases the error in impedance measurements. In this paper, 1 Hz where one period of signal can be collected per second is used as an example for SoC estimation.

There are also some considerations for higher frequencies to be used. In this case, the achievable sampling rate in the hardware can be a constraint. In theory, satisfying the Nyquist-Shannon criteria is sufficient for the signal to be restored, but, generally, oversampling is required due to noise and non-ideal properties in analog filters. Another problem is that the cell impedance is generally lower at higher frequencies, which can lead to the same problems when the test amplitude is too low. Most cell degradation results in an increase in internal resistance [54–57], and the 1 kHz impedance of the cell used in this paper represents the ohmic resistance of the cell in which the imaginary part of the impedance becomes 0. In paper [46], the accuracy of SoH estimation with impedance at different frequencies is compared, which shows that impedance at higher frequencies is more advantageous for use in SoH estimation, which is less affected by cell SoC and temperature. In this paper, a frequency of 1 kHz is used for SoH estimation as an example.
