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Consisting of two main parts, the first offers a detailed review of three-phase power electronics, electrical machines, carrier-based pulse width modulation, optimized pulse patterns, state-of-the art converter control methods and the principle of MPC. The second part is an in-depth treatment of MPC methods that fully exploit the performance potential of high-power converters. These control methods combine the fast control responses of deadbeat control with the optimal steady-state performance of optimized pulse patterns by resolving the antagonism between the two.
MPC is expected to evolve into the control method of choice for power electronic systems operating at low pulse numbers with multiple coupled variables and tight operating constraints it. Model Predictive Control of High Power Converters and Industrial Drives will enable to reader to learn how to increase the power capability of the converter, lower the current distortions, reduce the filter size, achieve very fast transient responses and ensure the reliable operation within safe operating area constraints.
Targeted at power electronic practitioners working on control-related aspects as well as control engineers, the material is intuitively accessible, and the mathematical formulations are augmented by illustrations, simple examples and a book companion website featuring animations. Readers benefit from a concise and comprehensive treatment of MPC for industrial power electronics, enabling them to understand, implement and advance the field of high-performance MPC schemes.
Consisting of two main parts, the first offers a detailed review of three-phase power electronics, electrical machines, carrier-based pulse width modulation, optimized pulse patterns, state-of-the art converter control methods and the principle of MPC. The second part is an in-depth treatment of MPC methods that fully exploit the performance potential of high-power converters. These control methods combine the fast control responses of deadbeat control with the optimal steady-state performance of optimized pulse patterns by resolving the antagonism between the two.
MPC is expected to evolve into the control method of choice for power electronic systems operating at low pulse numbers with multiple coupled variables and tight operating constraints it. Model Predictive Control of High Power Converters and Industrial Drives will enable to reader to learn how to increase the power capability of the converter, lower the current distortions, reduce the filter size, achieve very fast transient responses and ensure the reliable operation within safe operating area constraints.
Targeted at power electronic practitioners working on control-related aspects as well as control engineers, the material is intuitively accessible, and the mathematical formulations are augmented by illustrations, simple examples and a book companion website featuring animations. Readers benefit from a concise and comprehensive treatment of MPC for industrial power electronics, enabling them to understand, implement and advance the field of high-performance MPC schemes.
Tobias Geyer joined ABB's Corporate Research Center as a deputy group leader and principal scientist in 2012. In this role, he is building up a dedicated research team focusing on Model predictive control (MPC) for power electronic systems. After obtaining his PhD at ETH Zurich, he spent three years in GE's Corporate Research Center in Munich as a project leader for high-power electronics and drives. He subsequently worked at the intersection of academia and industrial research, fully funded by ABB and part of an ABB research team, whilst being employed by the University of Auckland as a Research Fellow. During this time, his focus was on the development of a new generation of drive control schemes that is intended to replace ABB's currently used schemes in their medium-voltage drive portfolio. Tobias Geyer has been working on MPC for power electronics since 2002, and was one of the first researchers who began working in this field. During the past 12 years he has written approximately 100 peer-reviewed journal and conference publications and patent applications. He is also an Associate Editor of Transactions on Power Electronics and Transactions on Industry Applications.
Preface xvii
Acknowledgments xix
List of Abbreviations xxi
About the Companion Website xxvii
Part I Introduction
1 Introduction 3
1.1 Industrial Power Electronics 3
1.1.1 Medium-Voltage, Variable-Speed Drives 3
1.1.2 Market Trends 5
1.1.3 Technology Trends 6
1.2 Control and Modulation Schemes 7
1.2.1 Requirements 7
1.2.2 State-of-the-Art Schemes 8
1.2.3 Challenges 9
1.3 Model Predictive Control 11
1.3.1 Control Problem 11
1.3.2 Control Principle 12
1.3.3 Advantages and Challenges 16
1.4 Research Vision and Motivation 19
1.5 Main Results 19
1.6 Summary of this Book 21
1.7 Prerequisites 25
References 26
2 Industrial Power Electronics 29
2.1 Preliminaries 29
2.1.1 Three-Phase Systems 29
2.1.2 Per Unit System 31
2.1.3 Stationary Reference Frame 33
2.1.4 Rotating Reference Frame 36
2.1.5 Space Vectors 40
2.2 Induction Machines 42
2.2.1 Machine Model in Space Vector Notation 42
2.2.2 Machine Model in Matrix Notation 44
2.2.3 Machine Model in the Per Unit System 45
2.2.4 Machine Model in State-Space Representation 48
2.2.5 Harmonic Model of the Machine 50
2.3 Power Semiconductor Devices 51
2.3.1 Integrated-Gate-Commutated Thyristors 51
2.3.2 Power Diodes 53
2.4 Multilevel Voltage Source Inverters 54
2.4.1 NPC Inverter 54
2.4.2 Five-Level ANPC Inverter 62
2.5 Case Studies 68
2.5.1 NPC Inverter Drive System 68
2.5.2 NPC Inverter Drive System with Snubber Restrictions 70
2.5.3 Five-Level ANPC Inverter Drive System 71
2.5.4 Grid-Connected NPC Converter System 72
References 75
3 Classic Control and Modulation Schemes 77
3.1 Requirements of Control and Modulation Schemes 77
3.1.1 Requirements Relating to the Electrical Machine 77
3.1.2 Requirements Relating to the Grid 80
3.1.3 Requirements Relating to the Converter 83
3.1.4 Summary 83
3.2 Structure of Control and Modulation Schemes 84
3.3 Carrier-Based Pulse Width Modulation 85
3.3.1 Single-Phase Carrier-Based Pulse Width Modulation 86
3.3.2 Three-Phase Carrier-Based Pulse Width Modulation 94
3.3.3 Summary and Properties 101
3.4 Optimized Pulse Patterns 103
3.4.1 Pulse Pattern and Harmonic Analysis 104
3.4.2 Optimization Problem for Three-Level Converters 107
3.4.3 Optimization Problem for Five-Level Converters 112
3.4.4 Summary and Properties 117
3.5 Performance Trade-Off for Pulse Width Modulation 117
3.5.1 Current TDD versus Switching Losses 118
3.5.2 Torque TDD versus Switching Losses 120
3.6 Control Schemes for Induction Machine Drives 121
3.6.1 Scalar Control 122
3.6.2 Field-Oriented Control 123
3.6.3 Direct Torque Control 130
Appendix 3.A: Harmonic Analysis of Single-Phase Optimized Pulse Patterns 139
Appendix 3.B: Mathematical Optimization 141
3.B.1 General Optimization Problems 142
3.B.2 Mixed-Integer Optimization Problems 142
3.B.3 Convex Optimization Problems 143
References 145
Part II Direct Model Predictive Control With Reference Tracking
4 Predictive Control with Short Horizons 153
4.1 Predictive Current Control of a Single-Phase RL Load 153
4.1.1 Control Problem 153
4.1.2 Prediction of Current Trajectories 154
4.1.3 Optimization Problem 156
4.1.4 Control Algorithm 156
4.1.5 Performance Evaluation 158
4.1.6 Prediction Horizons of more than 1 Step 161
4.1.7 Summary 163
4.2 Predictive Current Control of a Three-Phase Induction Machine 164
4.2.1 Case Study 164
4.2.2 Control Problem 165
4.2.3 Controller Model 166
4.2.4 Optimization Problem 167
4.2.5 Control Algorithm 168
4.2.6 Performance Evaluation 170
4.2.7 About the Choice of Norms 175
4.2.8 Delay Compensation 178
4.3 Predictive Torque Control of a Three-Phase Induction Machine 183
4.3.1 Case Study 183
4.3.2 Control Problem 184
4.3.3 Controller Model 184
4.3.4 Optimization Problem 185
4.3.5 Control Algorithm 186
4.3.6 Analysis of the Cost Function 187
4.3.7 Comparison of the Cost Functions for the Torque and Current Controllers 188
4.3.8 Performance Evaluation 191
4.4 Summary 193
References 194
5 Predictive Control with Long Horizons 195
5.1 Preliminaries 196
5.1.1 Case Study 196
5.1.2 Controller Model 197
5.1.3 Cost Function 197
5.1.4 Optimization Problem 198
5.1.5 Control Algorithm based on Exhaustive Search 200
5.2 Integer Quadratic Programming Formulation 201
5.2.1 Optimization Problem in Vector Form 201
5.2.2 Solution in Terms of the Unconstrained Minimum 202
5.2.3 Integer Quadratic Program 202
5.2.4 Direct MPC with a Prediction Horizon of 1 203
5.3 An Efficient Method for Solving the Optimization Problem 204
5.3.1 Preliminaries and Key Properties 205
5.3.2 Modified Sphere Decoding Algorithm 205
5.3.3 Illustrative Example with a Prediction Horizon of 1 207
5.3.4 Illustrative Example with a Prediction Horizon of 2 209
5.4 Computational Burden 211
5.4.1 Offline Computations 211
5.4.2 Online Preprocessing 211
5.4.3 Sphere Decoding 212
Appendix 5.A: State-Space Model 213
Appendix 5.B: Derivation of the Cost Function in Vector Form 214
References 216
6 Performance Evaluation of Predictive Control with Long Horizons 217
6.1 Performance Evaluation for the NPC Inverter Drive System 218
6.1.1 Framework for Performance Evaluation 218
6.1.2 Comparison at the Switching Frequency 250 Hz 220
6.1.3 Closed-Loop Cost 223
6.1.4 Relative Current TDD 225
6.1.5 Operation during Transients 231
6.2 Suboptimal MPC via Direct Rounding 232
6.3 Performance Evaluation for the NPC Inverter Drive System with an LC Filter 234
6.3.1 Case Study 235
6.3.2 Controller Model 237
6.3.3 Optimization Problem 237
6.3.4 Steady-State Operation 239
6.3.5 Operation during Transients 243
6.4 Summary and Discussion 245
6.4.1 Performance at Steady-State Operating Conditions 245
6.4.2 Performance during Transients 246
6.4.3 Cost Function 246
6.4.4 Control Objectives 247
6.4.5 Computational Complexity 247
Appendix 6.A: State-Space Model 248
Appendix 6.B: Computation of the Output Reference Vector 248
6.B.1 Step 1: Stator Frequency 248
6.B.2 Step 2: Inverter Voltage 249
6.B.3 Step 3: Output Reference Vector 250
References 251
Part III Direct Model Predictive Control With Bounds
7 Model Predictive Direct Torque Control 255
7.1 Introduction 255
7.2 Preliminaries 257
7.2.1 Case Study 257
7.2.2 Control Problem 259
7.2.3 Controller Model 259
7.2.4 Switching Effort 262
7.3 Control Problem Formulation 263
7.3.1 Naive Optimization Problem 263
7.3.2 Constraints 264
7.3.3 Cost Function 265
7.4 Model Predictive Direct Torque Control 266
7.4.1 Definitions 267
7.4.2 Simplified Optimization Problem 268
7.4.3 Concept of the Switching Horizon 268
7.4.4 Search Tree 274
7.4.5 MPDTC Algorithm with Full Enumeration 275
7.5 Extension Methods 277
7.5.1 Analysis of the State and Output Trajectories 278
7.5.2 Linear Extrapolation 279
7.5.3 Quadratic Extrapolation 280
7.5.4 Quadratic Interpolation 282
7.6 Summary and Discussion 284
Appendix 7.A: Controller Model of the NPC Inverter Drive System 286
References 287
8 Performance Evaluation of Model Predictive Direct Torque Control 289
8.1 Performance Evaluation for the NPC Inverter Drive System 289
8.1.1 Simulation Setup 290
8.1.2 Steady-State Operation 290
8.1.3 Operation during Transients 298
8.2 Performance Evaluation for the ANPC Inverter Drive System 300
8.2.1 Controller Model 301
8.2.2 Modified MPDTC Algorithm 303
8.2.3 Simulation Setup 304
8.2.4 Steady-State Operation 305
8.2.5 Operation during Transients 312
8.3 Summary and Discussion 314
Appendix 8.A: Controller Model of the ANPC Inverter Drive System 315
References 316
9 Analysis and Feasibility of Model Predictive Direct Torque Control 318
9.1 Target Set 319
9.2 The State-Feedback Control Law 320
9.2.1 Preliminaries 321
9.2.2 Control Law for a Given Rotor Flux Vector 322
9.2.3 Control Law along an Edge of the Target Set 331
9.3 Analysis of the Deadlock Phenomena 331
9.3.1 Root Cause Analysis of Deadlocks 332
9.3.2 Location of Deadlocks 335
9.4 Deadlock Resolution 337
9.5 Deadlock Avoidance 340
9.5.1 Deadlock Avoidance Strategies 340
9.5.2 Performance Evaluation 343
9.6 Summary and Discussion 347
9.6.1 Derivation and Analysis of the State-Feedback Control Law 347
9.6.2 Deadlock Analysis, Resolution, and Avoidance 347
References 348
10 Computationally Efficient Model Predictive Direct Torque Control 350
10.1 Preliminaries 351
10.2 MPDTC with Branch-and-Bound 352
10.2.1 Principle and Concept 352
10.2.2 Properties of Branch-and-Bound 354
10.2.3 Limiting the Maximum Number of Computations 356
10.2.4 Computationally Efficient MPDTC Algorithm 357
10.3 Performance...
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Nachrichtentechnik |
| Genre: | Importe, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | Gebunden |
| ISBN-13: | 9781119010906 |
| ISBN-10: | 111901090X |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Geyer, Tobias |
| Hersteller: | Wiley |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 251 x 174 x 35 mm |
| Von/Mit: | Tobias Geyer |
| Erscheinungsdatum: | 14.11.2016 |
| Gewicht: | 0,999 kg |
Tobias Geyer joined ABB's Corporate Research Center as a deputy group leader and principal scientist in 2012. In this role, he is building up a dedicated research team focusing on Model predictive control (MPC) for power electronic systems. After obtaining his PhD at ETH Zurich, he spent three years in GE's Corporate Research Center in Munich as a project leader for high-power electronics and drives. He subsequently worked at the intersection of academia and industrial research, fully funded by ABB and part of an ABB research team, whilst being employed by the University of Auckland as a Research Fellow. During this time, his focus was on the development of a new generation of drive control schemes that is intended to replace ABB's currently used schemes in their medium-voltage drive portfolio. Tobias Geyer has been working on MPC for power electronics since 2002, and was one of the first researchers who began working in this field. During the past 12 years he has written approximately 100 peer-reviewed journal and conference publications and patent applications. He is also an Associate Editor of Transactions on Power Electronics and Transactions on Industry Applications.
Preface xvii
Acknowledgments xix
List of Abbreviations xxi
About the Companion Website xxvii
Part I Introduction
1 Introduction 3
1.1 Industrial Power Electronics 3
1.1.1 Medium-Voltage, Variable-Speed Drives 3
1.1.2 Market Trends 5
1.1.3 Technology Trends 6
1.2 Control and Modulation Schemes 7
1.2.1 Requirements 7
1.2.2 State-of-the-Art Schemes 8
1.2.3 Challenges 9
1.3 Model Predictive Control 11
1.3.1 Control Problem 11
1.3.2 Control Principle 12
1.3.3 Advantages and Challenges 16
1.4 Research Vision and Motivation 19
1.5 Main Results 19
1.6 Summary of this Book 21
1.7 Prerequisites 25
References 26
2 Industrial Power Electronics 29
2.1 Preliminaries 29
2.1.1 Three-Phase Systems 29
2.1.2 Per Unit System 31
2.1.3 Stationary Reference Frame 33
2.1.4 Rotating Reference Frame 36
2.1.5 Space Vectors 40
2.2 Induction Machines 42
2.2.1 Machine Model in Space Vector Notation 42
2.2.2 Machine Model in Matrix Notation 44
2.2.3 Machine Model in the Per Unit System 45
2.2.4 Machine Model in State-Space Representation 48
2.2.5 Harmonic Model of the Machine 50
2.3 Power Semiconductor Devices 51
2.3.1 Integrated-Gate-Commutated Thyristors 51
2.3.2 Power Diodes 53
2.4 Multilevel Voltage Source Inverters 54
2.4.1 NPC Inverter 54
2.4.2 Five-Level ANPC Inverter 62
2.5 Case Studies 68
2.5.1 NPC Inverter Drive System 68
2.5.2 NPC Inverter Drive System with Snubber Restrictions 70
2.5.3 Five-Level ANPC Inverter Drive System 71
2.5.4 Grid-Connected NPC Converter System 72
References 75
3 Classic Control and Modulation Schemes 77
3.1 Requirements of Control and Modulation Schemes 77
3.1.1 Requirements Relating to the Electrical Machine 77
3.1.2 Requirements Relating to the Grid 80
3.1.3 Requirements Relating to the Converter 83
3.1.4 Summary 83
3.2 Structure of Control and Modulation Schemes 84
3.3 Carrier-Based Pulse Width Modulation 85
3.3.1 Single-Phase Carrier-Based Pulse Width Modulation 86
3.3.2 Three-Phase Carrier-Based Pulse Width Modulation 94
3.3.3 Summary and Properties 101
3.4 Optimized Pulse Patterns 103
3.4.1 Pulse Pattern and Harmonic Analysis 104
3.4.2 Optimization Problem for Three-Level Converters 107
3.4.3 Optimization Problem for Five-Level Converters 112
3.4.4 Summary and Properties 117
3.5 Performance Trade-Off for Pulse Width Modulation 117
3.5.1 Current TDD versus Switching Losses 118
3.5.2 Torque TDD versus Switching Losses 120
3.6 Control Schemes for Induction Machine Drives 121
3.6.1 Scalar Control 122
3.6.2 Field-Oriented Control 123
3.6.3 Direct Torque Control 130
Appendix 3.A: Harmonic Analysis of Single-Phase Optimized Pulse Patterns 139
Appendix 3.B: Mathematical Optimization 141
3.B.1 General Optimization Problems 142
3.B.2 Mixed-Integer Optimization Problems 142
3.B.3 Convex Optimization Problems 143
References 145
Part II Direct Model Predictive Control With Reference Tracking
4 Predictive Control with Short Horizons 153
4.1 Predictive Current Control of a Single-Phase RL Load 153
4.1.1 Control Problem 153
4.1.2 Prediction of Current Trajectories 154
4.1.3 Optimization Problem 156
4.1.4 Control Algorithm 156
4.1.5 Performance Evaluation 158
4.1.6 Prediction Horizons of more than 1 Step 161
4.1.7 Summary 163
4.2 Predictive Current Control of a Three-Phase Induction Machine 164
4.2.1 Case Study 164
4.2.2 Control Problem 165
4.2.3 Controller Model 166
4.2.4 Optimization Problem 167
4.2.5 Control Algorithm 168
4.2.6 Performance Evaluation 170
4.2.7 About the Choice of Norms 175
4.2.8 Delay Compensation 178
4.3 Predictive Torque Control of a Three-Phase Induction Machine 183
4.3.1 Case Study 183
4.3.2 Control Problem 184
4.3.3 Controller Model 184
4.3.4 Optimization Problem 185
4.3.5 Control Algorithm 186
4.3.6 Analysis of the Cost Function 187
4.3.7 Comparison of the Cost Functions for the Torque and Current Controllers 188
4.3.8 Performance Evaluation 191
4.4 Summary 193
References 194
5 Predictive Control with Long Horizons 195
5.1 Preliminaries 196
5.1.1 Case Study 196
5.1.2 Controller Model 197
5.1.3 Cost Function 197
5.1.4 Optimization Problem 198
5.1.5 Control Algorithm based on Exhaustive Search 200
5.2 Integer Quadratic Programming Formulation 201
5.2.1 Optimization Problem in Vector Form 201
5.2.2 Solution in Terms of the Unconstrained Minimum 202
5.2.3 Integer Quadratic Program 202
5.2.4 Direct MPC with a Prediction Horizon of 1 203
5.3 An Efficient Method for Solving the Optimization Problem 204
5.3.1 Preliminaries and Key Properties 205
5.3.2 Modified Sphere Decoding Algorithm 205
5.3.3 Illustrative Example with a Prediction Horizon of 1 207
5.3.4 Illustrative Example with a Prediction Horizon of 2 209
5.4 Computational Burden 211
5.4.1 Offline Computations 211
5.4.2 Online Preprocessing 211
5.4.3 Sphere Decoding 212
Appendix 5.A: State-Space Model 213
Appendix 5.B: Derivation of the Cost Function in Vector Form 214
References 216
6 Performance Evaluation of Predictive Control with Long Horizons 217
6.1 Performance Evaluation for the NPC Inverter Drive System 218
6.1.1 Framework for Performance Evaluation 218
6.1.2 Comparison at the Switching Frequency 250 Hz 220
6.1.3 Closed-Loop Cost 223
6.1.4 Relative Current TDD 225
6.1.5 Operation during Transients 231
6.2 Suboptimal MPC via Direct Rounding 232
6.3 Performance Evaluation for the NPC Inverter Drive System with an LC Filter 234
6.3.1 Case Study 235
6.3.2 Controller Model 237
6.3.3 Optimization Problem 237
6.3.4 Steady-State Operation 239
6.3.5 Operation during Transients 243
6.4 Summary and Discussion 245
6.4.1 Performance at Steady-State Operating Conditions 245
6.4.2 Performance during Transients 246
6.4.3 Cost Function 246
6.4.4 Control Objectives 247
6.4.5 Computational Complexity 247
Appendix 6.A: State-Space Model 248
Appendix 6.B: Computation of the Output Reference Vector 248
6.B.1 Step 1: Stator Frequency 248
6.B.2 Step 2: Inverter Voltage 249
6.B.3 Step 3: Output Reference Vector 250
References 251
Part III Direct Model Predictive Control With Bounds
7 Model Predictive Direct Torque Control 255
7.1 Introduction 255
7.2 Preliminaries 257
7.2.1 Case Study 257
7.2.2 Control Problem 259
7.2.3 Controller Model 259
7.2.4 Switching Effort 262
7.3 Control Problem Formulation 263
7.3.1 Naive Optimization Problem 263
7.3.2 Constraints 264
7.3.3 Cost Function 265
7.4 Model Predictive Direct Torque Control 266
7.4.1 Definitions 267
7.4.2 Simplified Optimization Problem 268
7.4.3 Concept of the Switching Horizon 268
7.4.4 Search Tree 274
7.4.5 MPDTC Algorithm with Full Enumeration 275
7.5 Extension Methods 277
7.5.1 Analysis of the State and Output Trajectories 278
7.5.2 Linear Extrapolation 279
7.5.3 Quadratic Extrapolation 280
7.5.4 Quadratic Interpolation 282
7.6 Summary and Discussion 284
Appendix 7.A: Controller Model of the NPC Inverter Drive System 286
References 287
8 Performance Evaluation of Model Predictive Direct Torque Control 289
8.1 Performance Evaluation for the NPC Inverter Drive System 289
8.1.1 Simulation Setup 290
8.1.2 Steady-State Operation 290
8.1.3 Operation during Transients 298
8.2 Performance Evaluation for the ANPC Inverter Drive System 300
8.2.1 Controller Model 301
8.2.2 Modified MPDTC Algorithm 303
8.2.3 Simulation Setup 304
8.2.4 Steady-State Operation 305
8.2.5 Operation during Transients 312
8.3 Summary and Discussion 314
Appendix 8.A: Controller Model of the ANPC Inverter Drive System 315
References 316
9 Analysis and Feasibility of Model Predictive Direct Torque Control 318
9.1 Target Set 319
9.2 The State-Feedback Control Law 320
9.2.1 Preliminaries 321
9.2.2 Control Law for a Given Rotor Flux Vector 322
9.2.3 Control Law along an Edge of the Target Set 331
9.3 Analysis of the Deadlock Phenomena 331
9.3.1 Root Cause Analysis of Deadlocks 332
9.3.2 Location of Deadlocks 335
9.4 Deadlock Resolution 337
9.5 Deadlock Avoidance 340
9.5.1 Deadlock Avoidance Strategies 340
9.5.2 Performance Evaluation 343
9.6 Summary and Discussion 347
9.6.1 Derivation and Analysis of the State-Feedback Control Law 347
9.6.2 Deadlock Analysis, Resolution, and Avoidance 347
References 348
10 Computationally Efficient Model Predictive Direct Torque Control 350
10.1 Preliminaries 351
10.2 MPDTC with Branch-and-Bound 352
10.2.1 Principle and Concept 352
10.2.2 Properties of Branch-and-Bound 354
10.2.3 Limiting the Maximum Number of Computations 356
10.2.4 Computationally Efficient MPDTC Algorithm 357
10.3 Performance...
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Nachrichtentechnik |
| Genre: | Importe, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | Gebunden |
| ISBN-13: | 9781119010906 |
| ISBN-10: | 111901090X |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Geyer, Tobias |
| Hersteller: | Wiley |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 251 x 174 x 35 mm |
| Von/Mit: | Tobias Geyer |
| Erscheinungsdatum: | 14.11.2016 |
| Gewicht: | 0,999 kg |
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