A Computationally Efficient Coupled Electrochemical-Thermal Model for Large Format Cylindrical Lithium Ion Batteries

Abstract

We present a one-dimensional, radial, coupled degradation-electrochemical-thermal (DET) model of a large format cylindrical lithium ion cell. The model consists of reduced order equations that describe the electrochemical phenomena, including that associated with degradation, coupled with an approximate model of thermal behavior. The reduced order electrochemical model, which is approximated from the pseudo-two-dimensional (P2D) electrochemical model using a Padé approximation method, computes the variation of electrochemical variables and heat generation terms. Simultaneously, a coupled thermal model computes the temperature distribution in the radial direction of the cell. The results from DET model compare favorably to those obtained from solving the 1D radial coupled degradation-electrochemical-thermal partial differential equations in COMSOL Multiphysics, however the DET model returns these results in significantly reduced computational times. Importantly, the model capability in providing insightful information of cell degradation and temperature in a computationally efficient manner paves the way for the health-conscious, real-time optimal control of large format cylindrical cells. Lithium ion batteries are now commonly used for the storage of energy in large, renewable energy generation systems, such as wind and photovoltaic systems, to eliminate their inherent intermittency. This is due to the fact that the battery storage systems are capable of providing a rapid response to counteract the fluctuations and filter out the vari-abilities associated with renewable generation and therefore enhance stabilize grid performance and maximize system security benefits. 1 Large format cylindrical lithium ion cells with high energy have been developed and implemented in those energy storage systems. For example , "CH75" cylindrical cells developed by Hitachi have capacity of 75Ah/cell. 2 These cells can compose a large energy battery pack using relatively small number of cells, which can reduce the total number of components and therefore, increase the reliability of the pack. 2 In order to operate batteries optimally, with the intention of maintaining safety and extending battery life, a battery management system (BMS) is essential. 3 Two critical functions of a BMS are the thermal management and degradation monitoring. These functions become more essential for large format cylindrical batteries in which non-uniformities in temperature and degradation occur during operation. 4 Furthermore, such non-uniformities exacerbate further degradation and temperature gradients within the battery. Information on heat generation is fundamentally important for managing thermal issues such as thermal runaway, electrical cell imbalance within the battery pack and poor performance at low temperatures. 5 However, heat generation inside a cell is a complex process that requires the knowledge of the physical characteristics of the cell during its operation. Total heat generation is due to irreversible and reversible processes, Joule heating in the solid and electrolyte and heating from the electrode/current collector contact resistance. 6 It is accompanied by changes in the elec-trochemical properties of the cell, such as entropy, solid and elec-trolyte concentrations due to chemical and electrochemical reactions and changes in the solid and electrolyte potentials. Battery degradation is mainly caused by the formation and growth of the solid electrolyte interphase layer (SEI) layer, which scavenges active lithium ions and electrolyte materials and increases battery resistance, leading to capacity and power fade, respectively. 7 SEI growth is also coupled with the thermal behavior of the cell as higher temperatures increase the SEI growth rate which in turn causes higher SEI resistance and ohmic heat * Electrochemical Society Student Member. z generation, which elevates further the temperature. 8 Current BMSs rely significantly on equivalent circuit models due to their simplicity and low computational requirement. 9 However, equivalent circuit models have limited insight on the electrochemical characteristics of a battery and therefore, given the intimate coupling between the two, they are not able to model battery thermal behavior precisely. 6 Alternatively, the pseudo-two-dimensional electrochemical model (P2D), first developed by Doyle, Fuller, and Newman, 10,11 does provide insight into battery electrochemical behavior coupled with thermal properties. 6 The P2D model, however, consists of five partial differential equations (PDEs) and one algebraic equation, which cannot be practically implemented in embedded BMS applications, without simplification or order reduction, due to their high computational requirement. 9 A simplified electrochemical model that has low computational overheads, whilst maintaining precision in a specific range of operation would therefore be ideal to facilitate accurate, real-time resolution and control of battery operation. There are several reduced electrochemical models in the literature. 12-16 The single particle model (SPM) embodies one of the approaches that is used to reduce the complexity of P2D model into a single PDE and an algebraic equation. 17-19 However, the SPM model assumes that the electrolyte concentration is constant and that the current in the electrolyte does not vary spatially, which results in poor voltage prediction capability. 12 Cai and White 20 developed a reduced order model using proper orthogonal decomposition to compute the electrochemical variables at discretized locations along the model domains. Subramanian et al. 13 developed approximations of the microscale diffusion of lithium ion in the solid phase, which have been well-adapted in macroscale models in the literature. In another paper, Subramanian et al., 21 used finite difference approximations and polynomial representations to reduce a system of 12 coupled PDEs into a system of Differential Algebraic Equations (DAEs), which are amenable to be used in battery control. Smith et al. 22 derived analytic transfer functions, in the Laplace domain, for a number of electrochemical variables in a linearized P2D model. Lee et al. 9 proposed an improvement of this approach by developing a complete set of transcendental transfer functions for the linearized P2D model. These authors then used the discrete-time realization algorithm (DRA) 23 to convert these transfer functions into an optimal discrete-time state-space model which can be used in real-time applications. However, extended computational time is required to rerun the DRA to produce a new state-space model when the electrochemical parameters of the P2D change. 9 Alternatively, Padé approximations provide a way of greatly simplifying complicated transcendental transfer functions) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 172.250.202.96 Downloaded on 2019-09-15 to IP