Development of a reduced order electrochemical and thermal model for Lithium battery with blended cathode

Abstract

Accurate and fast estimation of state of charge (SOC) and state of health (SOH) during operations plays a pivotal role in prevention of overcharge or undercharge and accurately monitoring the state of cell degradation, which requires a model that can be embedded in the battery management system (BMS). Currently available models are based on either empirical equations or electric equivalent circuit components with voltage sources or a combination of the two. The models are relatively simple, but limited to represent a narrow range of operating behaviors not including the effects of temperature, SOC and degradation. On the other hand, Full Order Models (FOM) are multi-dimensional or multi-scale models based on electrochemical and thermal principles capable of representing the details of cell behavior, but impractical for real time applications, because they require high computational time. Therefore, there is a need for the development of a model with an intermediate performance and real time capability, which is accomplished by reducing the FOM into a Reduced Order Model (ROM). Two FOMs are developed for LiMnxCoyNizO2 (NMC)/Carbon batteries and LiFePO4 (LFP)/Carbon batteries separately. After that, the two FOMs are coupled to simulate the behavior of NMC/LFP blended cathode batteries. The reduction of the models is carried out in three parts: the ion concentration in the electrode is reduced using the polynomial approach, the ion concentration in the electrolyte is reduced using the state space method, and potentials and electrochemical kinetics are reduced by linearization. In addition, the energy equation is used to calculate the cell temperature, on which the diffusion coefficient and the Solid Electrolyte Interphase (SEI) resistance are dependent. The computational time step is determined based on the total computational time and errors at a given SOC range and different current rates. ROM responses are compared with those of the FOM and experimental data at a single cycle and multiple cycles under different operating conditions. The results show that calculation time of the ROM is reduced to approximately one fifteenth of the FOM, while the accuracy can be maintained. The working mechanism of the cells with blended cathode of NMC and LFP is very complex and hard to understand. In addition, characteristics of the blended cells, particularly the plateau, history and path dependence of LFP materials, make it extremely difficult to estimate the SOC and SOH using classical electric equivalent circuit models. Therefore, a reduced order model based on electrochemical and thermal principles is developed with objectives for real time applications and validated against experimental data collected from a large format pouch type of lithium ion polymer battery. The model for LFP is based on a shrinking core model along with moving boundary and then integrated into NMC model. Responses of the model that include terminal voltage and temperature are compared with those of experiments at CC/CV charging and CC discharging at various operating conditions. In addition, the model is used to analyze effects of mass ratios between two materials on terminal voltage and heat generation rate; and the model is used to estimate the SOC based on Extended Kalman filter.