Differential Expansion and Voltage Model for Li-ion Batteries at Practical Charging Rates

Abstract

Differential voltage analysis (DVA) is a conventional approach for estimating capacity degradation in batteries. During charging, a graphite electrode goes through several phase transitions observed as plateaus in the voltage response. The transitions between these plateaus emerge as observable peaks in the differential voltage. The DVA method utilizes these peaks for estimating cell degradation. Unfortunately, at higher C-rates (above C/2) the peaks flatten and become unobservable. In this work, we show that, unlike the differential voltage, the peaks in the 2nd derivative of the expansion with respect to capacity remain observable up to 1C and thus make possible diagnostic algorithms at these charging rates. To understand why that is the case, we have developed an electrochemical and expansion model suitable for model-based estimation. In particular, we demonstrate that the single particle modeling methodology is not able to capture the peak smoothing effect, therefore a multi-particle approach for the graphite electrode is needed. Additionally, model parameters are identified using experimental data from a graphite/NMC pouch cell. The proposed model produces an excellent fit for the observed electric and mechanical swelling response of the cells and could enable physics-based data-driven degradation studies at practical charging rates.

Accelerated battery lifetime simulations using adaptive inter-cycle extrapolation algorithm

“…The algorithms introduced in this work are intended to be general and work with any degradation model based on porous-electrode theory. For demonstration purposes, we will show the numerical improvements which are the main focus of the paper in a case study degradation model, namely the Single Particle Model with SEI formation [28] and loss of active material [29,30] due to particle swelling [31,32]. More complicated models can also be used without modification to the algorithms that we introduce below.…”

“…Particle mechanics, assuming maximum stress at the particle surface and zero minimum stress [29,30,31,32]:…”

“…Parameter values are as in [32] with additional degradation parameters given in Table 2. After spatial discretization (for example using finite volumes), the discretized state vector is…”

“…Degradation parameters of the model. Other parameters are as in[32]. The three remaining degradation parameters are different for each case as shown in Table3.…”

Experimental Characterization of Lithium-Ion Cell Strain Using Laser Sensors

“…Macroscopic swelling of LIB can be detected experimentally both as a displacement of the surfaces or as a force exerted on the battery constraints. The force is commonly measured with load cells [13][14][15], on the other hand displacement is measured with different techniques, such as eddy current device [16], Bragg fibre sensor [17], dial gauge [18][19][20][21] and strain gauge [22]. Other authors tried to compute the internal strain directly on electrode via in situ measurements with optical fibre sensor [8,23,24] and digital image correlation (DIC) [25].…”