Dynamic Modeling and Predictive Control in Solid Oxide Fuel Cells

Biao Huang University of Alberta, CanadaYutong Qi Corporate Electronics, CanadaAKM Monjur Murshed Shell Canada, Canada

• Preface xiAcknowledgments xiiiList of Figures xvList of Tables xxi1 Introduction 11.1 Overview of Fuel Cell Technology 11.1.1 Types of Fuel Cells 21.1.2 Planar and Tubular Designs 31.1.3 Fuel Cell Systems 41.1.4 Pros and Cons of Fuel Cells 51.2 Modelling, State Estimation and Control 51.3 Book Coverage 61.4 Book Outline 6Part I Fundamentals2 First Principle Modelling for Chemical Processes 112.1 Thermodynamics 112.1.1 Forms of Energy 112.1.2 First Law 122.1.3 Second Law 132.2 Heat Transfer 132.2.1 Conduction 142.2.2 Convection 152.2.3 Radiation 172.3 Mass Transfer 182.4 Fluid Mechanics 202.4.1 Viscous Flow 212.4.2 Velocity Distribution 212.4.3 Bernoulli Equation 212.5 Equations of Change 222.5.1 The Equation of Continuity 232.5.2 The Equation of Motion 232.5.3 The Equation of Energy 242.5.4 The Equations of Continuity of Species 262.6 Chemical Reaction 262.6.1 Reaction Rate 262.6.2 Reversible Reaction 282.6.3 Heat of Reaction 292.7 Notes and References 293 System Identification I 313.1 Discrete-time Systems 313.2 Signals 363.2.1 Input Signals 363.2.2 Spectral Characteristics of Signals 413.2.3 Persistent Excitation in Input Signals 443.2.4 Input Design 493.3 Models 503.3.1 Linear Models 503.3.2 Nonlinear Models 543.4 Notes and References 564 System Identification II 574.1 Regression Analysis 574.1.1 Autoregressive Moving Average with Exogenous Input Models 574.1.2 Linear Regression 594.1.3 Analysis of Linear Regression 604.1.4 Weighted Least Squares Method 614.2 Prediction Error Method 644.2.1 Optimal Prediction 654.2.2 Prediction Error Method 704.2.3 Prediction Error Method with Independent Parameterisation 744.2.4 Asymptotic Variance Property of PEM 754.2.5 Nonlinear Identification 764.3 Model Validation 794.3.1 Model Structure Selection 794.3.2 The Parsimony Principle 804.3.3 Comparison of Model Structures 814.4 Practical Consideration 824.4.1 Treating Non-zero Means 824.4.2 Treating Drifts in Disturbances 834.4.3 Robustness 834.4.4 Additional Model Validation 834.5 Closed-loop Identification 844.5.1 Direct Closed-loop Identification 854.5.2 Indirect Closed-loop Identification 874.6 Subspace Identification 924.6.1 Notations 924.6.2 Subspace Identification via Regression Analysis Approach 974.6.3 Example 1004.7 Notes and References 1025 State Estimation 1035.1 Recent Developments in Filtering Techniques for Stochastic Dynamic Systems 1035.2 Problem Formulation 1055.3 Sequential Bayesian Inference for State Estimation 1075.3.1 Kalman Filter and Extended Kalman Filter 1105.3.2 Unscented Kalman Filter 1125.4 Examples 1165.5 Notes and References 1206 Model Predictive Control 1216.1 Model Predictive Control: State-of-the-Art 1216.2 General Principle 1226.2.1 Models for MPC 1226.2.2 Free and Forced Response 1256.2.3 Objective Function 1256.2.4 Constraints 1266.2.5 MPC Law 1266.3 Dynamic Matrix Control 1276.3.1 Prediction 1276.3.2 DMC without Penalising Control Moves 1296.3.3 DMC with Penalising Control Moves 1306.3.4 Feedback in DMC 1306.4 Nonlinear MPC 1346.5 General Tuning Guideline of Nonlinear MPC 1366.6 Discretisation of Models: Orthogonal Collocation Method 1376.6.1 Orthogonal Collocation Method with Prediction Horizon 1 1376.6.2 Orthogonal Collocation Method with Prediction Horizon N 1406.7 Pros and Cons of MPC 1426.8 Optimisation 1426.9 Example: Chaotic System 1446.10 Notes and References 145Part II Tubular SOFC7 Dynamic Modelling of Tubular SOFC: First-Principle Approach 1497.1 SOFC Stack Design 1497.2 Conversion Process 1507.2.1 Electrochemical Reactions 1507.2.2 Electrical Dynamics 1537.3 Diffusion Dynamics 1557.3.1 Transfer Function of Diffusion 1567.3.2 Simplified Transfer Function of Diffusion 1577.3.3 Dynamic Model of Diffusion 1587.3.4 Diffusion Coefficient 1597.4 Fuel Feeding Process 1607.4.1 Reforming/Shift Reaction 1607.4.2 Mass Transport 1627.4.3 Momentum Transfer 1647.4.4 Energy Transfer and Heat Exchange 1657.5 Air Feeding Process 1667.5.1 Mass Transport in the Cathode Channel 1667.5.2 Cathode Channel Momentum Transfer 1677.5.3 Energy Transfer in the Cathode Channel 1687.5.4 Air in Injection Channel 1687.6 SOFC Temperature 1697.6.1 Dynamic Energy Exchange Process 1697.6.2 Conduction 1707.6.3 Convection 1717.6.4 Radiation 1727.6.5 Cell Temperature Model 1747.6.6 Injection Tube Temperature Model 1747.7 Final Dynamic Model 1757.7.1 I/O Variables 1757.7.2 State Space Model 1767.7.3 Model Validation 1807.8 Investigation of Dynamic Properties through Simulations 1817.8.1 Dynamics of Diffusion 1827.8.2 Dynamics of Fuel Feeding Process 1847.8.3 Dynamics of Air Feeding Process 1867.8.4 Dynamics due to External Load 1887.9 Notes and References 1908 Dynamic Modelling of Tubular SOFC: Simplified First-Principle Approach 1938.1 Preliminary 1938.1.1 Relation of Process Variables 1948.1.2 Limits to Power Output 1948.2 Low-order State Space Modelling of SOFC Stack 1958.2.1 Physical Processes 1958.2.2 Modelling Assumptions 1978.2.3 I/O Variables 1978.2.4 Voltage 1988.2.5 Partial Pressures 1998.2.6 Flow Rates 2008.2.7 Temperatures 2038.3 Nonlinear State Space Model 2048.4 Simulation 2058.4.1 Validation 2058.4.2 Step Response to the Inputs 2078.4.3 Step Responses to the Disturbances 2098.5 Notes and References 2119 Dynamic Modelling and Control of Tubular SOFC: System Identification Approach 2139.1 Introduction 2139.2 System Identification 2139.2.1 Selection of Variables 2139.2.2 Step Response Test 2149.2.3 Non-typical Step Response 2179.2.4 Input Design 2189.2.5 Linear System Identification 2209.2.6 Nonlinear System Identification 2349.3 PID Control 2419.3.1 Set Point Tracking 2439.3.2 Disturbance Rejection 2439.3.3 Internal Model Control for Discrete-time Processes 2439.3.4 Application of Discrete-time IMC to Multi-loop Control of SOFC 2549.4 Closed-loop Identification 2579.5 Notes and References 263Part III Planar SOFC10 Dynamic Modelling of Planar SOFC: First-Principle Approach 26710.1 Introduction 26710.2 Geometry 26810.3 Stack Voltage 26810.4 Mass Balance 27010.5 Energy Balance 27110.5.1 Lumped Model 27210.5.2 Detail Model 27310.6 Simulation 27710.6.1 Steady-state Response 27710.6.2 Dynamic Response 27810.7 Notes and References 28011 Dynamic Modelling of Planar SOFC System 28311.1 Introduction 28311.2 Fuel Cell System 28311.2.1 Fuel and Air Heat Exchangers 28411.2.2 Reformer 28611.2.3 Burner 28711.3 SOFC along with a Capacitor 28711.4 Simulation Result 28911.4.1 Fuel Cell System Simulation 29011.4.2 SOFC Stack with Ultra-capacitor 29211.5 Notes and References 29212 Model Predictive Control of Planar SOFC System 29512.1 Introduction 29512.2 Control Objective 29612.3 State Estimation: UKF 29712.4 Steady-state Economic Optimisation 29812.5 Control and Simulation 30112.5.1 Linear MPC 30112.5.2 Nonlinear MPC 30312.5.3 Optimisation 30512.6 Results and Discussions 30612.7 Notes and References 307Appendix A Properties and Parameters 309A.1 Parameters 309A.2 Gas Properties 309References 315Index 321