Optimal Charging Profiles with Minimal Intercalation-Induced Stresses for Lithium-Ion Batteries Using Reformulated Pseudo 2-Dimensional Models

Abstract

This paper illustrates the application of dynamic optimization in obtaining the optimal current profile for charging a lithium-ion battery by restricting the intercalation-induced stresses to a pre-determined limit estimated using a pseudo 2-dimensional (P2D) model. This paper focuses on the problem of maximizing the charge stored in a given time while restricting capacity fade due to intercalation-induced stresses. Conventional charging profiles for lithium-ion batteries (e.g., constant current followed by constant voltage or CC-CV) are not derived by considering capacity fade mechanisms, which are not only inefficient in terms of life-time usage of the batteries but are also slower by not taking into account the changing dynamics of the system. Lithium-ion chemistries are attractive for many applications due to high cell voltage, high volumetric and gravimetric energy density (100 Wh/kg), high power density (300 W/kg), good temperature range, low memory effect, and relatively long battery life.1-3 Capacity fade, underutilization, and thermal runaway are the main issues that need to be addressed in order to use a lithium-ion battery efficiently and safely over a long life.In order to address the aforementioned issues and increase battery utilization, smarter battery management systems are required which can exploit the dynamics of a battery to derive better operational strategies. Recognizing the potential of reducing the weight and volume of these batteries by 20-25% for vehicular applications, the Department of Energy has recently initiated a $30M program through ARPA-E named Advanced Management and Protection of Energy Storage Devices (AMPED). 4 The use of physically meaningful models in deriving these strategies has received attention. Methekar et al. 5 looked at the problem of energy maximization for a set time with constraints on voltage using Control Vector Parametrization (CVP). Klein et al. 6 considered the minimum-time charging problem while including constraints on temperature rise and side reactions. Rahimian et al. 7 calculated the optimal charging current as a function of cycle number for a lithium-ion battery experiencing capacity fade using a single-particle model (SPM). Hoke et al.9 used a lithium-ion battery life-time model to reduce battery degradation in a variable electricity cost environment using the SPM. Previous efforts included the derivation of optimal charging profiles considering various phenomena that account for capacity fade separately (plating over-potential at the anode, 13 side reaction during charging, 6 thermal degradation, 10 intercalation-induced stress using SPM 11 etc.). Fracture of solid electrode particles due to intercalation induced stresses is one of the dominant capacity fade mechanics which affect the battery capacity in two ways: 12 (1) It leads to loss of solid phase due to isolation from the electronically conducting matrix of electrode. (2) It also increases the surface area, which lead to SEI * Electrochemical Society Student Member.* * Electrochemical Soci...

Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter

“…The derivation of matrices H x , H z and H u is trivial since the temperature is a differential state of the model and the voltage computation is straightforward from the algebraic state vector and the input vector. Equations (24), (25) and (28) constitute a state-space representation of the thermalelectrochemical P2D model. This representation is particularly convenient from a control engineering perspective and can be implemented in the ODE/DAEs MATLAB solver ode15s.…”

“…The EKF algorithm relies on a non-linear stochastic state-space model. Such a statespace representation of the P2D model can be derived from the state-space representation given by (24), (25) and (28) by adding process noise and measurement noise to the dynamics and measurement equations respectively according to:…”

“…Dao et al used the Galerkin spectral method on sinusoidal basis functions to discretise the electrolyte diffusion equation [21], while Cai and White applied orthogonal collocation on finite elements to all the equations of the P2D model [22]. Orthogonal collocation enforced at zeros of Jacobi polynomials was also applied to the full P2D model in [23] and solved using Maple and DASSL solvers using cosine basis functions and more recently Chebyshev polynomial basis functions for improved convergence at high currents [24]. In previous work, we applied Chebyshev orthogonal collocation to the isothermal P2D model and showed that computation time could be reduced by a factor of 10 to 100 compared to finite-difference for the same result accuracy [25].…”

Generic Model Control for Lithium-Ion Batteries

“…Suthar et al 12 proposed optimal charg- * Electrochemical Society Student Member. * * Electrochemical Society Member.…”

Introduction to Mechano-Electro-Chemical Coupling in Energy Related Materials and Devices

“…Examples of this include the stress-induced ferroelastic domain switching discussed in Kimura et al, 6 and the chemically induced changes in cation diffusion coefficients, and hence sintering kinetics, discussed in Ni et al 7 Under certain circumstances, MEC coupling can lead to undesirable results. For example, Chen et al, 8 Diercks et al, 9 KC et al, 10 Roberts et al, 11 Suthar et al, 12 Wang et al, 13 and Woodford et al, 14 show that the large stress caused by electrochemically induced stoichiometry changes can lead to mechanical shock and/or degradation unless special design considerations are utilized or new materials are developed. However, under other circumstances, MEC coupling can be beneficial.…”