Battery Systems Engineering

Christopher D. Rahn and Chao-Yang Wang The Pennsylvania State University, USA

1 Introduction 1 1.1 Energy Storage Applications 1 1.2 The Role of Batteries 4 1.3 Battery Systems Engineering 6 1.4 A Model-Based Approach 9 1.5 Electrochemical Fundamentals 10 1.6 Battery Design 12 1.7 Objectives of this Book 14 2 Electrochemistry 17 2.1 Lead-Acid 17 2.2 Nickel-Metal Hydride 21 2.3 Lithium-Ion 25 2.4 Performance Comparison 27 2.4.1 Energy Density and Specific Energy 27 2.4.2 Charge and Discharge 31 2.4.3 Cycle life 34 2.4.4 Temperature Operating Range 34 3 Governing Equations 35 3.1 Thermodynamics and Faraday's Law 35 3.2 Electrode Kinetics 39 3.2.1 The Butler-Volmer Equation 40 3.2.2 Double-Layer Capacitance 42 3.3 Solid Phase of Porous Electrodes 42 3.3.1 Ion Transport 44 3.3.2 Conservation of Charge 45 3.4 Electrolyte Phase of Porous Electrodes 47 3.4.1 Ion Transport 47 3.4.2 Conservation of Charge 52 3.4.3 Concentrated Solution Theory 54 3.5 Cell Voltage 54 3.6 Cell Temperature 55 3.6.1 Arrhenius Equation 56 3.6.2 Conservation of Energy 57 3.7 Side Reactions and Aging 58 4 Discretization Methods 67 4.1 Analytical Method 69 4.1.1 Electrolyte Diffusion 69 4.1.2 Coupled Electrolyte/Solid Diffusion in Pb Electrodes 79 4.1.3 Solid State Diffusion in Li-Ion and Ni-MH Particles 81 4.2 Pade Approximation Method 83 4.2.1 Solid State Diffusion in Li-Ion Particles 84 4.3 Integral Method Approximation 85 4.3.1 Electrolyte Diffusion 85 4.3.2 Solid State Diffusion in Li-Ion and Ni-MH Particles 88 4.4 Ritz Method 89 4.4.1 Electrolyte Diffusion in a Single Domain 89 4.4.2 Electrolyte Diffusion in Coupled Domains 91 4.4.3 Coupled Electrolyte/Solid Diffusion in Pb Electrodes 94 4.5 Finite Element Method 97 4.5.1 Electrolyte Diffusion 99 4.5.2 Coupled Electrolyte/Solid Diffusion in Li-Ion Electrodes 101 4.6 Finite Difference Method 102 4.6.1 Electrolyte Diffusion 103 4.6.2 Nonlinear Coupled Electrolyte/Solid Diffusion in Pb Electrodes 104 4.7 System Identification in the Frequency Domain 106 4.7.1 System Model 107 4.7.2 Least Squares Optimization Problem 107 4.7.3 Optimization Approach 109 4.7.4 Multiple Outputs 111 4.7.5 System Identification Toolbox 112 4.7.6 Experimental Data 112 5 System Response 115 5.1 Time Response 117 5.1.1 Constant Charge/Discharge 119 5.1.2 DST Cycle Response of the Pb-Acid Electrode 129 5.2 Frequency Response 130 5.2.1 Electrochemical Impedance Spectroscopy 130 5.2.2 Discretization Eciency 137 5.3 Model Order Reduction 144 5.3.1 Truncation Approach 146 5.3.2 Grouping Approach 147 5.3.3 Frequency Response Curve Fitting 148 5.3.4 Performance Comparison 148 6 Battery System Models 159 6.1 Lead-Acid Battery Model 160 6.1.1 Governing Equations 161 6.1.2 Discretization Using the Ritz Method 166 6.1.3 Numerical Convergence 170 6.1.4 Simulation Results 170 6.2 Lithium-Ion Battery Model 173 6.2.1 Conservation of Species 178 6.2.2 Conservation of Charge 180 6.2.3 Reaction Kinetics 181 6.2.4 Cell Voltage 182 6.2.5 Linearization 182 6.2.6 Impedance Solution 184 6.2.7 FEM Electrolyte Diffusion 188 6.2.8 Overall System Transfer Function 189 6.2.9 Time Domain Model and Simulation Results 189 6.3 Nickel-Metal Hydride Battery Model 193 6.3.1 Solid Phase Diffusion 197 6.3.2 Conservation of Charge 200 6.3.3 Reaction Kinetics 200 6.3.4 Cell Voltage 201 6.3.5 Simulation Results 202 6.3.6 Linearized Model 203 7 Estimation 213 7.1 State of Charge Estimation 215 7.1.1 SOC Modeling 218 7.1.2 Instantaneous SOC 221 7.1.3 Current Counting Method 222 7.1.4 Voltage Lookup Method 223 7.1.5 State Estimation 225 7.2 Least Squares Model Tuning 233 7.2.1 Impedance Transfer Function 233 7.2.2 Least Squares Algorithm 234 7.2.3 Ni-MH Cell Example 237 7.2.4 Identifiability 239 7.3 State of Health Estimation 243 7.3.1 Parameterization for Environment and Aging 244 7.3.2 Parameter Estimation 245 7.3.3 Ni-MH Cell Ex