Impedance is an important feature of linear two-port networks. As a system with strong nonlinearity and time-variation, the impedance of the battery needs to be obtained under conditions satisfying causality, stability, and linearity, otherwise, the obtained impedance is difficult to resolve or loses physical significance. Therefore, it is common to apply unbiased weak disturbances (such as the applied disturbance voltage or response voltage of about 10mV) to the positive and negative electrodes after the battery is sufficiently stationary. A current disturbance or a voltage disturbance can be applied. However, considering that the battery impedance is very small, the current disturbance is usually used to avoid overcurrent. There is no limit to the waveform of the perturbation.
Lithium-ion batteries are a very complex electrochemical system that contains many electrochemical and physical processes, mainly solid-liquid diffusion processes, solid-liquid phase conductance processes, and interface processes. Charged particles, including lithium ions, are involved in these processes. These processes differ in time constants and therefore dominate impedance in different frequency intervals on the impedance spectrum. In the low-frequency region, it is dominated by the slowest ion diffusion process, the medium and high-frequency impedance is dominated by the electrochemical reaction process of ion intercalation, in the high-frequency region, it is mainly dominated by SEI impedance, the charge transfer of the solid-liquid phase determines the size of the ohmic resistance, and in the ultra-high frequency it is dominated by parasitic inductances such as wires and current collectors. The correspondence between EIS and different processes enables it to characterize different process characteristics, and EIS, therefore, has rich information content.
Difference from internal resistance
The impedance is calculated by frequency domain analysis, while the internal resistance is calculated by relying on only a few feature points in the waveform. From the internal principle, the impedance of different frequencies corresponds to the process with different time constants inside the battery, which is a more refined process research method. The internal resistance reflects the change in terminal voltage during continuous current loading. The internal resistance cannot clearly distinguish between the different internal processes and is more suitable for describing the power characteristics of the battery. Therefore, impedance is widely used in mechanistic research, forming a systematic methodology.
Models of impedance
There are many models of impedance that are used to represent the behavior of various electrical components. Examples include the electrochemical model and equivalent circuit model. Each model is used to represent the behavior of different components, such as capacitors, inductors, and resistors, in different electrical circuits.
Electrochemical impedance model
(1) Electrochemical model. Based on the porous electrode theory, simplified P2D models and SPM models are widely used to describe the main physicochemical processes inside the battery. In the P2D model, the positive and negative solid-phase particles are equivalent to spherical particles, and the electrode processes of the main solid-liquid phase and their interface are included in the electrode thickness direction and particle radius direction, which can accurately simulate the battery characteristics. Compared with the P2D model, the SP model is simpler, and the positive and negative electrodes are equivalent to a spherical particle, which often ignores the solid-liquid phase conduction and liquid phase diffusion processes of the battery. The effect of the neglected process on the potential is described by the resistance of the lumped parameter.
(2) Electrochemical impedance model. The electrochemical impedance model can be obtained directly from the electrochemical model of the battery. Since electrochemical impedance is mostly measured under very small excitation, the SP model describing the charge-discharge characteristics of small magnification has been reported for impedance analytical derivation. The SP model has less coupling process, and the impedance analysis expression is easy to establish. For more universal and complex P2D models, impedance is obtained more through simulation, and there are often processes closer to the mechanism, such as DL models and agglomerate models added to impedance simulations based on P2D models. In short, the electrochemical impedance model can couple the influence of battery temperature, state of charge, aging state, and other changes on battery electrode parameters, so that the impedance in different states can be studied.
(3) Illegal pulling process. Under normal circumstances, in addition to the intercalation and detachment reaction of lithium ions at the electrode interface, there is also the charging and discharging process of equivalent capacitors, which is an illegal pull-up process, mainly including SEI film capacitors and DL capacitors. This is also the reason why EIS exhibits an approximate arc in the mid-high frequency region, and the description of the membrane capacitance model at the interface will affect the accuracy of the impedance description in this region. Many equivalent forms of membrane capacitance have also been reported.
Equivalent circuit model
(1) Equivalent components. The equivalent circuit model uses a combination of resist-capacitor elements, normal-phase angle elements, etc. to obtain the broadband impedance of the battery. These components generally correspond to the electrode process inside the battery and are used to equivalently the impedance of this part. The equivalent capacitance of the membrane is generally described in terms of ideal capacitance or more of a normal angular element (CPE) that considers the diffusion effect of the porous electrode.
(2) Equivalent circuit model. Ershler and Randles were the first scholars to use equivalent circuit models. So far, a large number of battery-equivalent circuit models have been proposed to characterize battery impedance. The equivalent circuit model is simpler than the electrochemical impedance model and is more suitable for control-oriented applications. However, due to the lack of physical meaning, the components are equivalent, resulting in insufficient accuracy and universality of the model.
(3) Equivalent circuit model selection. A large number of equivalent circuit models have been reported, and it is important to select the appropriate equivalent circuit model to analyze the battery impedance. Different equivalent components have significant impedance characteristics, so it is easy to choose the equivalent components. The key is to determine the number of parallel links of R-C or R-CPE, which is one of the main differences in ECM reported in the literature. Links with different time constants are considered to correspond to different processes inside the battery. The DRT analysis method can help determine the equivalent circuit model used to analyze impedance by determining the number of selected parallel links by determining the time constant distribution in the impedance spectrum.
Through the review of the progress in impedance modeling, it can be seen that impedance is frequently reported in battery management research and has broad application prospects, but there are still many engineering and scientific problems to be solved. The electrochemical impedance model is complex and has many parameters, and the equivalent circuit model is more suitable for control-oriented applications. However, the equivalent circuit model forms are ever-changing, and it is necessary to reasonably select the impedance model with clear physical significance and accuracy, and propose a control-oriented parameter identification method to realize the analysis of the obtained impedance.
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