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Summary
Summary
The high temperature solid oxide fuel cell (SOFC) is identified as one of the leading fuel cell technology contenders to capture the energy market in years to come. However, in order to operate as an efficient energy generating system, the SOFC requires an appropriate control system which in turn requires a detailed modelling of process dynamics.
Introducting state-of-the-art dynamic modelling, estimation, and control of SOFC systems, this book presents original modelling methods and brand new results as developed by the authors. With comprehensive coverage and bringing together many aspects of SOFC technology, it considers dynamic modelling through first-principles and data-based approaches, and considers all aspects of control, including modelling, system identification, state estimation, conventional and advanced control.
Key features:
Discusses both planar and tubular SOFC, and detailed and simplified dynamic modelling for SOFC Systematically describes single model and distributed models from cell level to system level Provides parameters for all models developed for easy reference and reproducing of the results All theories are illustrated through vivid fuel cell application examples, such as state-of-the-art unscented Kalman filter, model predictive control, and system identification techniques to SOFC systemsThe tutorial approach makes it perfect for learning the fundamentals of chemical engineering, system identification, state estimation and process control. It is suitable for graduate students in chemical, mechanical, power, and electrical engineering, especially those in process control, process systems engineering, control systems, or fuel cells. It will also aid researchers who need a reminder of the basics as well as an overview of current techniques in the dynamic modelling and control of SOFC.
Author Notes
Biao Huang University of Alberta, Canada
Yutong Qi Corporate Electronics, Canada
AKM Monjur Murshed Shell Canada, Canada
Table of Contents
Preface | p. xi |
Acknowledgments | p. xiii |
List of Figures | p. xv |
List of Tables | p. xxi |
1 Introduction | p. 1 |
1.1 Overview of Fuel Cell Technology | p. 1 |
1.1.1 Types of Fuel Cells | p. 2 |
1.1.2 Planar and Tubular Designs | p. 3 |
1.1.3 Fuel Cell Systems | p. 4 |
1.1.4 Pros and Cons of Fuel Cells | p. 5 |
1.2 Modelling, State Estimation and Control | p. 5 |
1.3 Book Coverage | p. 6 |
1.4 Book Outline | p. 6 |
Part I Fundamentals | |
2 First Principle Modelling for Chemical Processes | p. 11 |
2.1 Thermodynamics | p. 11 |
2.1.1 Forms of Energy | p. 11 |
2.1.2 First Law | p. 12 |
2.1.3 Second Law | p. 13 |
2.2 Heat Transfer | p. 13 |
2.2.1 Conduction | p. 14 |
2.2.2 Convection | p. 15 |
2.2.3 Radiation | p. 17 |
2.3 Mass Transfer | p. 18 |
2.4 Fluid Mechanics | p. 20 |
2.4.1 Viscous Flow | p. 21 |
2.4.2 Velocity Distribution | p. 21 |
2.4.3 Bernoulli Equation | p. 21 |
2.5 Equations of Change | p. 22 |
2.5.1 The Equation of Continuity | p. 23 |
2.5.2 The Equation of Motion | p. 23 |
2.5.3 The Equation of Energy | p. 24 |
2.5.4 The Equations of Continuity of Species | p. 26 |
2.6 Chemical Reaction | p. 26 |
2.6.1 Reaction Rate | p. 26 |
2.6.2 Reversible Reaction | p. 28 |
2.6.3 Heat of Reaction | p. 29 |
2.7 Notes and References | p. 29 |
3 System Identification I | p. 31 |
3.1 Discrete-time Systems | p. 31 |
3.2 Signals | p. 36 |
3.2.1 Input Signals | p. 36 |
3.2.2 Spectral Characteristics of Signals | p. 41 |
3.2.3 Persistent Excitation in Input Signals | p. 44 |
3.2.4 Input Design | p. 49 |
3.3 Models | p. 50 |
3.3.1 Linear Models | p. 50 |
3.3.2 Nonlinear Models | p. 54 |
3.4 Notes and References | p. 56 |
4 System Identification II | p. 57 |
4.1 Regression Analysis | p. 57 |
4.1.1 Autoregressive Moving Average with Exogenous Input Models | p. 57 |
4.1.2 Linear Regression | p. 59 |
4.1.3 Analysis of Linear Regression | p. 60 |
4.1.4 Weighted Least Squares Method | p. 61 |
4.2 Prediction Error Method | p. 64 |
4.2.1 Optimal Prediction | p. 65 |
4.2.2 Prediction Error Method | p. 70 |
4.2.3 Prediction Error Method with Independent Parameterisation | p. 74 |
4.2.4 Asymptotic Variance Property of PEM | p. 75 |
4.2.5 Nonlinear Identification | p. 76 |
4.3 Model Validation | p. 79 |
4.3.1 Model Structure Selection | p. 79 |
4.3.2 The Parsimony Principle | p. 80 |
4.3.3 Comparison of Model Structures | p. 81 |
4.4 Practical Consideration | p. 82 |
4.4.1 Treating Non-zero Means | p. 82 |
4.4.2 Treating Drifts in Disturbances | p. 83 |
4.4.3 Robustness | p. 83 |
4.4.4 Additional Model Validation | p. 83 |
4.5 Closed-loop Identification | p. 84 |
4.5.1 Direct Closed-loop Identification | p. 85 |
4.5.2 Indirect Closed-loop Identification | p. 87 |
4.6 Subspace Identification | p. 92 |
4.6.1 Notations | p. 92 |
4.6.2 Subspace Identification via Regression Analysis Approach | p. 97 |
4.6.3 Example | p. 100 |
4.7 Notes and References | p. 102 |
5 State Estimation | p. 103 |
5.1 Recent Developments in Filtering Techniques for Stochastic Dynamic Systems | p. 103 |
5.2 Problem Formulation | p. 105 |
5.3 Sequential Bayesian Inference for State Estimation | p. 107 |
5.3.1 Kalman Filter and Extended Kalman Filter | p. 110 |
5.3.2 Unscented Kalman Filter | p. 112 |
5.4 Examples | p. 116 |
5.5 Notes and References | p. 120 |
6 Model Predictive Control | p. 121 |
6.1 Model Predictive Control: State-of-the-Art | p. 121 |
6.2 General Principle | p. 122 |
6.2.1 Models for MPC | p. 122 |
6.2.2 Free and Forced Response | p. 125 |
6.2.3 Objective Function | p. 125 |
6.2.4 Constraints | p. 126 |
6.2.5 MPC Law | p. 126 |
6.3 Dynamic Matrix Control | p. 127 |
6.3.1 Prediction | p. 127 |
6.3.2 DMC without Penalising Control Moves | p. 129 |
6.3.3 DMC with Penalising Control Moves | p. 130 |
6.3.4 Feedback in DMC | p. 130 |
6.4 Nonlinear MPC | p. 134 |
6.5 General Tuning Guideline of Nonlinear MPC | p. 136 |
6.6 Discretisation of Models: Orthogonal Collocation Method | p. 137 |
6.6.1 Orthogonal Collocation Method with Prediction Horizon 1 | p. 137 |
6.6.2 Orthogonal Collocation Method with Prediction Horizon N | p. 140 |
6.7 Pros and Cons of MPC | p. 142 |
6.8 Optimisation | p. 142 |
6.9 Example: Chaotic System | p. 144 |
6.10 Notes and References | p. 145 |
Part II Tubular SOFC | |
7 Dynamic Modelling of Tubular SOFC: First-Principle Approach | p. 149 |
7.1 SOFC Stack Design | p. 149 |
7.2 Conversion Process | p. 150 |
7.2.1 Electrochemical Reactions | p. 150 |
7.2.2 Electrical Dynamics | p. 153 |
7.3 Diffusion Dynamics | p. 155 |
7.3.1 Transfer Function of Diffusion | p. 156 |
7.3.2 Simplified Transfer Function of Diffusion | p. 157 |
7.3.3 Dynamic Model of Diffusion | p. 158 |
7.3.4 Diffusion Coefficient | p. 159 |
7.4 Fuel Feeding Process | p. 160 |
7.4.1 Reforming/Shift Reaction | p. 160 |
7.4.2 Mass Transport | p. 162 |
7.4.3 Momentum Transfer | p. 164 |
7.4.4 Energy Transfer and Heat Exchange | p. 165 |
7.5 Air Feeding Process | p. 166 |
7.5.1 Mass Transport in the Cathode Channel | p. 166 |
7.5.2 Cathode Channel Momentum Transfer | p. 167 |
7.5.3 Energy Transfer in the Cathode Channel | p. 168 |
7.5.4 Air in Injection Channel | p. 168 |
7.6 SOFC Temperature | p. 169 |
7.6.1 Dynamic Energy Exchange Process | p. 169 |
7.6.2 Conduction | p. 170 |
7.6.3 Convection | p. 171 |
7.6.4 Radiation | p. 172 |
7.6.5 Cell Temperature Model | p. 174 |
7.6.6 Injection Tube Temperature Model | p. 174 |
7.7 Final Dynamic Model | p. 175 |
7.7.1 I/O Variables | p. 175 |
7.7.2 State Space Model | p. 176 |
7.7.3 Model Validation | p. 180 |
7.8 Investigation of Dynamic Properties through Simulations | p. 181 |
7.8.1 Dynamics of Diffusion | p. 182 |
7.8.2 Dynamics of Fuel Feeding Process | p. 184 |
7.8.3 Dynamics of Air Feeding Process | p. 186 |
7.8.4 Dynamics due to External Load | p. 188 |
7.9 Notes and References | p. 190 |
8 Dynamic Modelling of Tubular SOFC: Simplified First-Principle Approach | p. 193 |
8.1 Preliminary | p. 193 |
8.1.1 Relation of Process Variables | p. 194 |
8.1.2 Limits to Power Output | p. 194 |
8.2 Low-order State Space Modelling of SOFC Stack | p. 195 |
8.2.1 Physical Processes | p. 195 |
8.2.2 Modelling Assumptions | p. 197 |
8.2.3 I/O Variables | p. 197 |
8.2.4 Voltage | p. 198 |
8.2.5 Partial Pressures | p. 199 |
8.2.6 Flow Rates | p. 200 |
8.2.7 Temperatures | p. 203 |
8.3 Nonlinear State Space Model | p. 204 |
8.4 Simulation | p. 205 |
8.4.1 Validation | p. 205 |
8.4.2 Step Response to the Inputs | p. 207 |
8.4.3 Step Responses to the Disturbances | p. 209 |
8.5 Notes and References | p. 211 |
9 Dynamic Modelling and Control of Tubular SOFC: System Identification Approach | p. 213 |
9.1 Introduction | p. 213 |
9.2 System Identification | p. 213 |
9.2.1 Selection of Variables | p. 213 |
9.2.2 Step Response Test | p. 214 |
9.2.3 Non-typical Step Response | p. 217 |
9.2.4 Input Design | p. 218 |
9.2.5 Linear System Identification | p. 220 |
9.2.6 Nonlinear System Identification | p. 234 |
9.3 PID Control | p. 241 |
9.3.1 Set Point Tracking | p. 243 |
9.3.2 Disturbance Rejection | p. 243 |
9.3.3 Internal Model Control for Discrete-time Processes | p. 243 |
9.3.4 Application of Discrete-time IMC to Multi-loop Control of SOFC | p. 254 |
9.4 Closed-loop Identification | p. 257 |
9.5 Notes and References | p. 263 |
Part III Planar SOFC | |
10 Dynamic Modelling of Planar SOFC: First-Principle Approach | p. 267 |
10.1 Introduction | p. 267 |
10.2 Geometry | p. 268 |
10.3 Stack Voltage | p. 268 |
10.4 Mass Balance | p. 270 |
10.5 Energy Balance | p. 271 |
10.5.1 Lumped Model | p. 272 |
10.5.2 Detail Model | p. 273 |
10.6 Simulation | p. 277 |
10.6.1 Steady-state Response | p. 277 |
10.6.2 Dynamic Response | p. 278 |
10.7 Notes and References | p. 280 |
11 Dynamic Modelling of Planar SOFC System | p. 283 |
11.1 Introduction | p. 283 |
11.2 Fuel Cell System | p. 283 |
11.2.1 Fuel and Air Heat Exchangers | p. 284 |
11.2.2 Reformer | p. 286 |
11.2.3 Burner | p. 287 |
11.3 SOFC along with a Capacitor | p. 287 |
11.4 Simulation Result | p. 289 |
11.4.1 Fuel Cell System Simulation | p. 290 |
11.4.2 SOFC Stack with Ultra-capacitor | p. 292 |
11.5 Notes and References | p. 292 |
12 Model Predictive Control of Planar SOFC System | p. 295 |
12.1 Introduction | p. 295 |
12.2 Control Objective | p. 296 |
12.3 State Estimation: UKF | p. 297 |
12.4 Steady-state Economic Optimisation | p. 298 |
12.5 Control and Simulation | p. 301 |
12.5.1 Linear MPC | p. 301 |
12.5.2 Nonlinear MPC | p. 303 |
12.5.3 Optimisation | p. 305 |
12.6 Results and Discussions | p. 306 |
12.7 Notes and References | p. 307 |
Appendix A Properties and Parameters | p. 309 |
A.1 Parameters | p. 309 |
A.2 Gas Properties | p. 309 |
References | p. 315 |
Index | p. 321 |