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Dr. Song-Yul Choe Professor Auburn University

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**High Resolution Modeling of Lithium Ion Battery and its Applications**

Auburn University Mechanical engineering Advanced Propulsion Research Lab. Song-Yul (Ben) Choe

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**Trend of advanced propulsion systems**

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**Energy storage with battery**

Nominal Capacity (Amp-hours): 15.7 Nominal Cell Voltage 3.73 Cell Dimensions (mm) 5.27 Cell Dimensions w/ terminals (mm) X 249.6 Maximum Cell Temperature (°C) 75 Positive Lithium Metal Oxide Negative Carbon Electrolyte Organic Material Separator SRS

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**Typical models for battery**

Models base on equivalent electrical circuit Statics: resistors in series to a voltage source Dynamics: a capacitor connected in parallel to a resistor Ignored effects : Electrical behavior of the terminal as a function of SOC , T and material degradation, and OCV as a function of hysteresis and SOC. Battery calendar life as a function of cycles and load profile Heat generation as a function of SOC , change of entropy and I (charge and discharge), heat transfer Various temperature effects caused by gradients of ion concentrations and side reactions

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**Modeling of LiPB cell ce Φe Φs ηSEI T cs Y Separator LixC6 LiyMO2**

Current collector (Cu) Current collector (Al) Electrolyte Positive electrode area Negative electrode area Electrode particle L T X

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**Principle: Current, Concentration and State of Charge**

Current in micro cell current = Electron current - + - Ion current + - + Credit: huangqing SOC (state of charge) and cs (concentration in solid) - + - + - + Low SOC Medium SOC charging High SOC Credit: huangqing

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**Electrochemical Thermal Mechanical Model**

Charging and discharging processes: Heat generation, Elasticity and Degradation Multi scale and Multi-physics coupled problems

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**Overview of model Single cell model Initial conditions: Initial SOC**

Load profile Initial temperature distribution Ambient temperature Cell voltage Temp. distribution SOC Overpotentials Reaction rate Concentration Efficiency Energy conservation Heat transfer Charge conservation Temperature distribution Potential distribution Micro cell model Micro cell model Micro cell model Butler-Volmer Heat source Parameters: Battery geometry Maximum capacity Concentration Activity coefficient Diffusion coefficient Change of enthalpy Conductivity etc. Reaction rate Standard potential Current Overpotential Nernst equ. Mass balance In electrolyte In solid Concentration

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**Static and dynamic behavior of the battery**

Static and dynamic behavior of the battery Characteristics at different current rates (T=300K and SOC=100%)

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**Transient behavior of ion concentration (Discharging behavior at a step current of 10C)**

At 1sec At 80 sec At 20 sec At 180 sec As lithium ion leaves from negative electrode and deposited in positive electrode, concentration at the interface of the negative electrode drops rapidly when compared with that of inners, while opposite phenomena occurs in the positive electrode.

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**Potentials/Current density at positive and negative current collector**

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**Validation of a single pouch cell at 1C/2C/5C discharge/charge**

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**Thermal validation – 5C cycle 2D**

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**Heat generation using the model and calorimeter**

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**Measurement of Thickness**

4/10/2017 Measurement of Thickness The change of battery thickness caused by the volume change of electrodes is calculated by the model. In experiment, thickness of the battery is measured by measuring both sides of the battery during cycling.

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**Mechanical stress of cells at 0.5C, 1C and 2C cycling**

4/10/2017 Mechanical stress of cells at 0.5C, 1C and 2C cycling

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4/10/2017 Maximum Stress as a Function of Position during discharge (at one instant) Separator Anode current collector Cathode current collector The plotted stress at each position is the maximum value of the stress in the local electrode particle. The highest stress is found in the electrode near the separator.

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**Fracture is Observed near the Separator**

4/10/2017 Fracture is Observed near the Separator Q. Horn and K. White, 2007 [8] J. Christensen, 2010 [7] Other researchers took SEM images at the cross-section of cell, where fractures are found in the electrode near the separator [7] [8]. Our simulation shows that the highest stress locates at the electrode near the separator, where fractures are most likely to happen.

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**Block Diagram for battery management system (BMS)**

Block Diagram for battery management system (BMS) Battery Pack/Module SENSOR Current Voltage Temperature Predefined Map Ri(SOC) Ri(Charging) TRAY Temp. Voc(SOC) Voc(Charging) Cooling Control Thermal Management Imean Charging/Discharging Control Aging Coefficient & SOC Calculation Accumulated SOC Error Comp. HCU I,V(SOC) Vaverage & Temp. Compensation Health monitoring & Protection Temperature Charging/Discharging power User Interface Voltage Imbalance detection Diagnosis Search IVSOC by IV Voltage MAP

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**Review of models for Battery**

High Intermediate Low Improvement of cell designs Full order of Electrochemical, thermal and mechanical Model (ETMM: FOM): Electrochemical kinetics, Potential theory, energy and mass balance, and charge conservation , Ohm’s law, Empirical OCV and elasticity BMS Functionalities Reduced order of Electrochemical thermal Model (ETM: ROM ): Empirical OCV Polynomial, State space, Páde approx., POD, Galerkin Reformulation and others Electric equivalent circuit Model (EECM): Randles models with the 1st, 2nd and 3rd order Empirical Model: Peukert’s equation Comp. time Accuracy Low Moderate High

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**Reduced order of the model (ROM) for real time applications**

Parameters: Cell geometry Kinetic and transport properties Initial conditions: Terminal voltage Load profile Ambient temperature Cell voltage Temperature SOC Ion concentration in electrolyte Ce Ion concentration in electrodes Cs Potentials Φ SOC estimation Input: Output: Battery : Steps Approaches Results Order reduction Ce State space approach Cs Polynomial approach Φ Parameters simplification Higher accuracy with less computational time Implicit method to solve PDEs Optimization of the ROM for real time applications

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**Validation of the ROM 1. Test condition: 2. Test condition:**

Mode: Depleting Cycle #: 5 Temperature: 0ºC, 25ºC, 45ºC Current: 1C, 2C, 5C Initial SOC: 0% 2. Test condition: Mode: Depleting Cycle #: 2 Temperature: 25ºC Current: 1C, 2C, 5C Initial SOC: 0%

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**SOC estimation using Extended Kalman Filter**

Error of SOC 7-10% Initial errors of BMS Feedback controls and real time model Output: Battery Measurement update Time update with the ROM SOC calculation Input:

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**Results of the estimation based on ROM + EKF**

Current: Voltage: SOC: Current: Voltage: Error of SOC: Test condition: Mode: JS Temperature: 25ºC Initial SOC: 100% Initial error: 0.2V (30% SOC) Test condition: Mode: Depleting Temperature: 25ºC Initial SOC: 0% Initial error: 0.5V (6.5% SOC)

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**Health monitoring of battery**

SOH SOHQ SOHP Capacity fade Power fade Other mechanism Research interests for SOH SOH Current i Battery pack ROM Model & SOH detection algorithm Output states value ( V T ) States estimation (Vt SOC T ) Compare Aging parameters estimation ( as ɛs ) error

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4/10/2017 Estimation of SOHQ The simulation of Qmax is calculated by the semi-empirical model whose aging parameters are obtained from curve fitting.

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**Fast charging: limiting factors**

Fast charging: limiting factors The reaction on the negative electrode is described as: When operated improperly, Li-ions are deposited on the anode surface instead of intercalating during charging: Reference: C. J. Mikolajczak, J. Harmon, From Lithium plating to Lithium –ion cell runaway Exponent [Ex(40)]annual report, 2009 Observed Li plating Cause of Lithium plating: Large current rate during charging, especially at high Li ion concentration Low temperature Effects of Lithium plating: Capacity Irreversible loss of active Lithium Safety Dendrites can cause shorting within the electrodes Heat generation A mat of dead lithium and dendrites can increase the chances minor shorts will lead to thermal runway

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**Comparison of simulation results and experimental results: Charging**

Test condition: Temperature=25°C Initial Vt= 2.9V Charge current: 1C/2C/5C rate Surface Concentration (mol/cm3) Terminal Voltage (V)

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**New Charging method - Battery i(t) + ROM Model**

Positive Terminal Estimated concentrations, SOC and temperature + - ROM Model Ambient Temperature; T Terminal Voltage: VT Charging/Discharging current Negative Terminal Reference: Maximum allowed concentrations and temperature, and desired SOC Pulse generator Two level or Three level

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**Experimental Data for Charging at 4C**

Qmax by CC and CV charging and the proposed charging method

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**Fast Charging Algorithm**

Test conditions: Benefits: Less capacity losses after 100 cycles; 0.34Ah by the CC and CV. 0.24Ah losses by the proposing method Estimate losses at 500 cycles: 0.5 Ah Less temperature rise Reduction of charging time Cell No. 1 2 Ambient temperature (°C) 25 Charging method CC/CV Pulse Charging current (C) 4 Discharging current (C) Rest time (min) 10 Cycles 100 If there is no significant degradation, Qmax = Cycle*P1 + P2

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**Diagnosis and Prognosis**

Summary Multi-scale and Multi-physics high resolution electrochemical, thermal and mechanical modeling considering degradations of materials. Modeling Design Diagnosis and Prognosis Cell design System design Series and parallel connection Cooling systems Controls SOC estimation Temperature controls Rapid charging and discharging Health monitoring (Growth of SEI, Change of conductivities, Losses of active materials and others) Power fade Capacity fade

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Dr. Song-Yul Choe Professor Auburn University

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