The present disclosure generally relates to a battery testing arrangement, and in particular, to a battery testing arrangement utilizing pulse voltammetry.
This section introduces aspects that may help facilitate a better understanding of the disclosure. Accordingly, these statements are to be read in this light and are not to be understood as admissions about what is or is not prior art.
Li-ion batteries are a ubiquitous part of the modern-day lifestyle, fulfilling a variety of applications ranging from portable electronics to electric vehicles, grid power, and the current development of urban air mobility such as electric vertical takeoff and landing vehicles (e-VTOL). Due to these ever-growing performance requirements, Li-ion batteries have progressively evolved and still have a scope for improvement by modification at a hierarchy of length scales. The current limitations to Li-ion batteries include rate capability during charge/discharge, energy/power density tradeoffs, sub-ambient temperature cycle life, and thermal safety characteristics.
These batteries go through a large number of charge-discharge cycles. Such dynamic cycling profiles of the battery are achieved at the cost of severe degradation to the cell components at various length scales. The electrodes undergo significant structural damage, such as the formation of cracks in active material particles due to rapid lithiation de-lithiation resulting in diffusion-induced stress damages. Additionally, parasitic side reactions also cause the loss of lithium inventory and electrolyte depletion, forming a passivating layer on electrode particles which further hinders the charge transfer kinetics.
For critical applications such as electric vehicles and electric-vertical takeoff landing vehicles, the user of the battery needs to be aware of the available useful life of the Li-ion battery for early decision-making and avoiding unforeseen circumstances. Physics-based models that can capture the dominant electrochemical physics and interactions of fields thereof are available, as long as a proper set of physical parameters are chosen. Various types of degradation-induced damages affect the charging/discharging behavior in dissimilar ways, but the large number of parameters involved in physics-based models make it difficult to deconvolute the effects of specific degradation modes from cycling data alone. Also, some of the simpler models such as circuit-based, and reduced-order models have difficulty in assigning physically relevant degradation modes, reducing their utility in predicting capacity and power fade over the life of the cell.
Examples of model-based methods of testing a battery are enumerated. First is a technique referred to as electro-impedance spectroscopy (EIS). This method includes applying a harmonic excitation signal. The frequency of these pulses usually varies between 1 mHz to 10 kHz. In response thereto the current response of the Li-ion battery is a measure. By plotting the current response vs. the input voltage, real and imaginary parts of an impedance are thus plotted based on a simplified equivalent circuit model representing a changing impedance. Based on this equivalent circuit the battery can be modeled. With battery aging, the impedance of the battery increases, thus signifying diminishing of the state of health of the battery.
The second and third model-based methods for the testing state of health of a battery are the galvanostatic intermittent titration technique (GITT) and potentiostatic intermittent titration technique (PITT). In these methods rectangular pulses are applied to a Li-ion cell. In GITT, the current pulses are applied for some amount of time followed by a period of rest for equilibrium attainment. The diffusion can be interpreted by the relaxation profile based on the formula noted in Eq. (1).
Similarly in PITT-based methods, potential pulses are applied for a brief time, followed by the current shutoff and repetition. This method is also used for solid-phase diffusivity calculations as shown in Eq. (2).
A fourth method utilized in determining battery health is referred to as the differential voltage analysis technique. This method requires a low-rate discharging voltage capacity data of the cell. In this method, the cell voltage is differentiated with respect to the capacity of the cell. The peaks in the full cell voltage curve are originating from either of the two electrodes. With the aging/degradation of the battery, these peaks shift towards the left or right. Based on tracking the shift of these peaks one can quantify the loss of active material and loss of Li-inventory.
However, all of the above-enumerated methods are based on rudimentary modeling of the battery. For example, the EIS technique is based on impedance characterization without regard as to how the impedance change is affected. Because these techniques do not effectively model the internal parameters of a battery, their accuracy is limited.
Therefore, there is an unmet need for a novel approach to determine the state of a battery based on a model that incorporates chemical and physical parameters of the battery.
A state of battery testing system is disclosed. The system includes a charger adapted to charge and test a battery having a positive and negative terminals, a load adapted to be selectively coupled across the positive and negative terminals of the battery, a controller having a processer executing software on a non-transient memory and adapted to apply a predetermined voltage pulse across the positive and negative terminals of the battery, selectively apply the load to the battery, measure current through the load, log the measured current as Iexp, and establish a model. The model is established based on establishing an initial estimation of state of the battery (θ0) based on a set of parameters including a) reaction rate constant for intercalation (k0) for electrodes of the battery, b) average particle size of active material Rs0, and c) a Li-intercalation fraction of the electrode (Y0), establishing a modeled state of battery (θi) based on a plurality of internal parameters of the battery. The model is adapted to output a model current (Imodel) through the load disposed between a modeled positive and negative terminals, inputting θ0 and the plurality of internal parameters to the model, thereby generating the Imodel, generate an objective function (f) based on a comparison of Imodel and Iexp, and iteratively optimize θi (θoptimal) in a loop based on the objective function f, and a gradient (g) of objective function f. The processor is further adapted to update θi (ki, Rsi, and Yi) based on direction of the steepest descent of f, and determine if change in θi as compared to values from an immediate previous iteration exceeds a predetermined limit: if no, then output θoptimal, and if yes, then update θ0 to θi and repeat the loop.
A battery testing method is also disclosed. The method includes charging a battery having a positive and negative terminals, applying a predetermined voltage pulse across the positive and negative terminals of the battery, selectively coupling a load across the positive and negative terminals of the battery, measuring current through the load, logging the measured current as Iexp, establishing a model based on establishing an initial estimation of state of the battery (θ0) based on a set of parameters including a) reaction rate constant for intercalation (k0) for electrodes of the battery, b) average particle size of active material Rs0, and c) a Li-intercalation fraction of the electrode (Y0), establishing a modeled state of battery (θi) based on a plurality of internal parameters of the battery, wherein the model is adapted to output a model current (Imodel) through the load disposed between a modeled positive and negative terminals, and inputting θ0 and the plurality of internal parameters to the model, thereby generating the Imodel. The model further includes generating an objective function (f) based on a comparison of Imodel and Iexp, and iteratively optimizing θi (θoptimal) in a loop based on objective function f, and gradient (g) of objective function f, updating θi (ki, Rsi, and Yi) based on direction of the steepest descent of f, and determining if change in θi as compared to values from an immediate previous iteration exceeds a predetermined limit. If no, then outputting θoptimal. If yes, then updating θ0 to θi and repeating the loop.
For the purposes of promoting an understanding of the principles of the present disclosure, reference will now be made to the embodiments illustrated in the drawings, and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of this disclosure is thereby intended.
In the present disclosure, the term “about” can allow for a degree of variability in a value or range, for example, within 10%, within 5%, or within 1% of a stated value or of a stated limit of a range.
In the present disclosure, the term “substantially” can allow for a degree of variability in a value or range, for example, within 90%, within 95%, or within 99% of a stated value or of a stated limit of a range.
A novel approach is presented herein to determine the state of a battery based on a model that incorporates chemical and physical parameters of the battery. To resolve the shortcomings of known techniques, a differential pulse voltammetry (DPV) method is disclosed herein which inherently contains the kinetic and thermodynamic information of a Li-ion battery, facilitating the development of accurate state of battery estimations and evaluations. This estimation method's superiority lies in application of a voltage pulse train and coupling it with a detailed physics-based model of battery, capturing the physically relevant degradation modes. The method is capable of testing batteries aged under variety of scenarios allowing for in-situ quantification and tracking of the degradation mechanisms occurring inside of the cell, making it relevant for various critical applications.
Referring to
Referring to
As discussed above, the method relies on detailed physics-based battery model, such that tracking of parameters is directly applicable to state of battery modeling and decision making. Specifically, to describe the battery model according to the present disclosure (denoted as the macro-homogenous model), four separate sub-models are defined based on i) mass conservation, ii) intercalation kinetics, iii) charge conservation, and iv) energy conservation as shown in
The macro-homogenous model 252 including the four-enumerated sub-models: Mass Conservation: 252A, Intercalation Kinetics: 252B, Charge Conservation: 252C, and Energy Conservation: 252D as shown in
The primary electrochemical reaction occurring during the Li-ion cell operation is based upon the intercalation reaction. The reaction dynamics of an intercalation reaction at both electrodes are modeled based on the Butler-Volmer formulation with symmetric charge transfer. These equations are part of the intercalation kinetics sub-model are referenced in 252B in
The charge conservation sub-model is based on the electroneutrality within the solid and electrolyte phase as referenced in 252C in
The energy conservation sub-model is referenced in 252D in
Each of the battery sub-models have a dependence on the battery's physio-chemical parameters including the input parameter set I1 . . . In and the estimation parameter set θ. The simultaneous solution of these sub-models described from Eq. (3) through Eq. (6) using the above-described parameters results in the electrolyte concentration (Ce), solid-phase Li-concentration (Cs), solid-phase potential (ϕs) and electrolyte potential (ϕe) field within the battery computational domain. Based on this solution the model current (Imodel) can be determined by the gradient of the solid phase potential at the electrode-current collector interface through a relation specified in Eq. (7).
An objective function (f) is introduced to measure the closeness between the experimental (Iexp) and model current (Imodel). It is expressed based on the fit between the two currents (Iexp and Imodel) and measured using the coefficient of determination (R2). The objective function (f) is the logarithm of the complement of R, as shown in Eq. (8).
The state of the battery can be inferred from θoptimal, indicating the condition of battery e.g., how fast the battery can be safely charged, charge left in the battery. Once the optimal battery parameter θoptimal is determined from previous steps, it is passed on along with battery input parameter Ito a prediction engine consisting of the macrohomogeneous model of battery to generate graphs as shown in
Referring to
Those having ordinary skill in the art will recognize that numerous modifications can be made to the specific implementations described above. The implementations should not be limited to the particular limitations described. Other implementations may be possible.
The present non-provisional patent application is related to and claims the priority benefit of U.S. Provisional Patent Application Serial No. 63/345,302, entitled METHOD AND SYSTEM UTILIZING PULSE VOLTAMMETRY FOR TESTING BATTERY which was filed May 24, 2022, the contents of which are hereby incorporated by reference in its entirety into the present disclosure.
This invention was made with government support under contract number W911NF-19-C-0084 awarded by the Army Research Office. The government has certain rights in the invention.
Number | Date | Country | |
---|---|---|---|
63345302 | May 2022 | US |