Ebook: Power System Modelling and Scripting

Electric power systems are experiencing significant changes at the worldwide scale in order to become cleaner, smarter, and more reliable. This edited book examines a wide range of topics related to these changes, which are primarily caused by the introduction of information technologies, renewable energy penetration, digitalized equipment, new operational strategies, and so forth. The emphasis will be put on the modeling and control of smart grid systems. The book addresses research topics such as high efficiency transformers, wind turbines and generators, fuel cells, or high speed turbines and generators.

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Power system modelling and scripting is a quite general and ambitious title. Of course, to embrace all existing aspects of power system modelling would lead to an encyclopedia and would be likely an impossible task. Thus, the book focuses on a subset of power system models based on the following assumptions: (i) devices are modelled as a set of nonlinear differential algebraic equations, (ii) all alternate-current devices are operating in three-phase balanced fundamental frequency, and (iii) the time frame of the dynamics of interest ranges from tenths to tens of seconds. These assumptions basically restrict the analysis to transient stability phenomena and generator controls. The modelling step is not self-sufficient. Mathematical models have to be translated into computer programming code in order to be analyzed, understood and “experienced”. It is an object of the book to provide a general framework for a power system analysis software tool and hints for filling up this framework with versatile programming code. This book is for all students and researchers that are looking for a quick reference on power system models or need some guidelines for starting the challenging adventure of writing their own code. Table of Contents Cover Power System Modelling and Scripting ISBN 9783642136689 e-ISBN 9783642136696 Preface Contents List of Figures List of Tables List of Examples List of Scripts Notation General Notation Rules Frequent Symbols Device Model Notation Bases for Per Unit Values Part I Introduction Chapter 1 Power System Modelling 1.1 Background 1.2 Motivations 1.3 Modelling Physical Systems 1.4 Hybrid Dynamical Model Chapter 2 Power System Architecture 2.1 Structure of Software Projects 2.2 Classes and Procedures 2.3 Modularity 2.4 Architecture of a Power System Software Tool Chapter 3 Power System Scripting 3.1 Open and Closed Programming 3.2 Scripting 3.3 Scripting Languages for Computational Science 3.4 Computer Languages Suitable for Power System Analysis 3.5 Python Scripting Language Part II Power System Analysis Chapter 4 Power Flow Analysis 4.1 Background 4.2 Taxonomy of Power Flow Problems 4.3 Classical Power Flow Equations 4.4 Power Flow Solvers o 4.4.1 Jacobi and Gauss-Seidel's Method o 4.4.2 Newton's Method o 4.4.3 Power Flow Jacobian Matrix o 4.4.4 Robust Newton's Method o 4.4.5 Iwamoto's Method o 4.4.6 Inexact and Dishonest Newton's Methods o 4.4.7 Fast Decoupled Power Flow o 4.4.8 DC Power Flow o 4.4.9 Single and Distributed Slack Bus Models 4.5 A General Framework for Power Flow Solvers o 4.5.1 Stability of the Continuous Newton's Method 4.6 Summary Chapter 5 Continuation Power Flow Analysis 5.1 Background 5.2 System Model 5.3 Direct Methods o 5.3.1 Saddle-Node Bifurcation o 5.3.2 Limit-Induced Bifurcation o 5.3.3 Nonlinear Programming 5.4 Homotopy Methods o 5.4.1 Continuation Power Flow o 5.4.2 Predictor Step o 5.4.3 Corrector Step o 5.4.4 Continuous Newton's Method and Homotopy o 5.4.5 N-1 Contingency Analysis 5.5 Summary Chapter 6 Optimal Power Flow Analysis 6.1 Background 6.2 Optimal Power Flow Model 6.3 Nonlinear Programming Solvers o 6.3.1 Generalized Reduced Gradient Method o 6.3.2 Interior Point Method 6.4 Summary of IPM Parameters Chapter 7 Eigenvalue Analysis 7.1 Background 7.2 Small Signal Stability Analysis o 7.2.1 Bifurcation Points o 7.2.2 Participation Factors o 7.2.3 Analysis in the Z-Domain 7.3 Computing the Eigenvalues o 7.3.1 Power Method o 7.3.2 Inverse Iteration o 7.3.3 Rayleigh's Iteration 7.4 Power Flow Modal Analysis o 7.4.1 Singular Value Decomposition 7.5 Summary Chapter 8 Time Domain Analysis 8.1 Background 8.2 Power System Model o 8.2.1 Current-Injection Model o 8.2.2 Power-Injection Model 8.3 Numerical Integration Methods o 8.3.1 Explicit Methods o 8.3.2 Implicit Methods 8.4 Numerical Integration Routine o 8.4.1 Step Length o 8.4.2 Disturbances o 8.4.3 Stop Criterion 8.5 Electro-magnetic Transients 8.6 Quasi-static Analysis 8.7 Summary Part III Device Models Chapter 9 Device Generalities 9.1 General Device Model o 9.1.1 Initialization of Device Internal Variables 9.2 Devices as Classes o 9.2.1 Base Device Class o 9.2.2 Methods of the Base Class o 9.2.3 Speci.c Device Methods Chapter 10 Power Flow Devices 10.1 Topological Elements o 10.1.1 Bus o 10.1.2 Areas, Zones, Regions and Systems 10.2 Static Generators o 10.2.1 PV Generator o 10.2.2 Constant Voltage Phasor Generator o 10.2.3 PQ Generator 10.3 Static Loads o 10.3.1 PQ Load o 10.3.2 Constant Power Factor Load o 10.3.3 Shunt Admittance o 10.3.4 Switched Shunt Admittances Chapter 11 Transmission Devices 11.1 Transmission Line o 11.1.1 Line Sections o 11.1.2 Tie Line o 11.1.3 Distributed Transmission Line Models o 11.1.4 E.ect of Frequency Variation o 11.1.5 Coupling Device and Zero-Impedance Line 11.2 Transformer o 11.2.1 Two-Winding Transformer o 11.2.2 Under Load Tap Changer o 11.2.3 Phase Shifting Transformer o 11.2.4 Three-Winding Transformer 11.3 Vectorial Implementation o 11.3.1 Incidence Matrix o 11.3.2 Jacobian and Hessian Matrices o 11.3.3 Network Connectivity Chapter 12 OPF Devices 12.1 Network Constraints o 12.1.1 Bus Voltage Limits o 12.1.2 Transmission Line limits 12.2 Generator Constraints o 12.2.1 Capability Curve o 12.2.2 Supply Offer o 12.2.3 Reactive Power Payment Function o 12.2.4 Generator Power Reserve o 12.2.5 Generator Power Ramp 12.3 Load Constraints o 12.3.1 Demand Bid o 12.3.2 Demand Daily Pro.le o 12.3.3 Demand Power Ramp Chapter 13 Faults and Protections 13.1 Fault 13.2 Breaker 13.3 Relay 13.4 Phasor Measurement Unit 13.5 Bus Frequency Estimation Chapter 14 Loads 14.1 Voltage Dependent Load 14.2 ZIP Load 14.3 Frequency Dependent Load 14.4 Voltage Dependent Load with Dynamic Tap Changer 14.5 Exponential Recovery Load 14.6 Thermostatically Controlled Load 14.7 Jimma's Load 14.8 Mixed Load Chapter 15 Alternate-Current Machines 15.1 Synchronous Machine o 15.1.1 Synchronous Machine Parameters o 15.1.2 Initialization o 15.1.3 Common Equations o 15.1.4 Stator Electrical Equations o 15.1.5 Magnetic Equations o 15.1.6 Simpli.ed Magnetic Equations o 15.1.7 Synchronous Machine Model Taxonomy o 15.1.8 Saturation o 15.1.9 Center of Inertia o 15.1.10 Dynamic Shaft o 15.1.11 Sub-synchronous Resonance 15.2 Induction Machine o 15.2.1 Initialization o 15.2.2 Torque Model o 15.2.3 Electromechanical Model o 15.2.4 Detailed Single-Cage Model o 15.2.5 Detailed Double-Cage Model Chapter 16 Synchronous Machine Regulators 16.1 Turbine Governor o 16.1.1 Turbine Governor Type I o 16.1.2 Turbine Governor Type II 16.2 Automatic Voltage Regulator o 16.2.1 Automatic Voltage Regulator Type I o 16.2.2 Automatic Voltage Regulator Type II o 16.2.3 Automatic Voltage Regulator Type III 16.3 Power System Stabilizer o 16.3.1 Simpli.ed Power System Stabilizer Model o 16.3.2 Power System Stabilizer Type I o 16.3.3 Power System Stabilizer Type II o 16.3.4 Power System Stabilizer Type III 16.4 Over-Excitation Limiter 16.5 Under-Excitation Limiter Chapter 17 Direct-Current Devices 17.1 Direct-Current Nodes 17.2 Common Interface Equations for Direct-Current Devices 17.3 Ideal Generators 17.4 Basic RLC Models 17.5 Direct-Current Machines 17.6 Other Direct-Current Devices o 17.6.1 Solid Oxide Fuel Cell o 17.6.2 Solar Photovoltaic Cell o 17.6.3 Battery Energy System Chapter 18 AC/DC Devices 18.1 High-Voltage Direct-Current Transmission System o 18.1.1 Per Unit System for DC Quantities o 18.1.2 Recti.er Model o 18.1.3 Inverter Model o 18.1.4 HVDC Control 18.2 Voltage Source Converter o 18.2.1 Simpli.ed Dynamic VSC Model o 18.2.2 Power Flow VSC Model Chapter 19 FACTS Devices 19.1 Static Var Compensator o 19.1.1 SVC Type I o 19.1.2 SVC Type II o 19.1.3 SVC Initialization 19.2 Thyristor Controlled Series Compensator o 19.2.1 TCSC Initialization 19.3 Static Synchronous Compensator o 19.3.1 Detailed Model o 19.3.2 Simpli.ed Dynamic Model o 19.3.3 Power Flow Model o 19.3.4 STATCOM Initialization 19.4 Static Synchronous Series Compensator o 19.4.1 Detailed Model o 19.4.2 Simpli.ed Dynamic Model o 19.4.3 Power Flow Model o 19.4.4 SSSC Initialization 19.5 Uni ed Power Flow Controller o 19.5.1 Detailed Model o 19.5.2 Simpli.ed Dynamic Model o 19.5.3 Power Flow Model o 19.5.4 UPFC Initialization Chapter 20 Wind Power Devices 20.1 Wind Speed Models o 20.1.1 Weibull's Distribution o 20.1.2 Composite Wind Speed Model o 20.1.3 Mexican Hat Wavelet Model 20.2 Wind Turbines o 20.2.1 Single Machine and Aggregate Models o 20.2.2 Wind Turbine Initialization o 20.2.3 Turbine Model o 20.2.4 Dynamic Shaft o 20.2.5 Non-Controlled Speed Wind Turbine o 20.2.6 Doubly-Fed Asynchronous Generator o 20.2.7 Direct-Drive Synchronous Generator Part IV Spare Material and Concluding Remarks Chapter 21 Data Formats 21.1 Data Format Taxonomy o 21.1.1 Data Organization and Structures o 21.1.2 Kind of Supported Data o 21.1.3 Number of Files o 21.1.4 Default Values, Prototypes and Data Manipulation 21.2 Canonical Model 21.3 Common Information Model 21.4 Consistent Data Schemes Chapter 22 Visualization Matters 22.1 Graphical Interface vs. Command Line Approach 22.2 Result Visualization o 22.2.1 Standard Two-Dimensional Plots o 22.2.2 Temperature Maps o 22.2.3 Three-Dimensional Plots o 22.2.4 Geographic Information System Chapter 23 Challenges of Scripting for Power System Education 23.1 Concepts and De nitions o 23.1.1 Proprietary Software o 23.1.2 Open Source Software o 23.1.3 Free Software o 23.1.4 Free Open Source Software 23.2 Education-Oriented FOSS o 23.2.1 Pedagogical Issues o 23.2.2 Failure of FOSS for Power System Analysis Part V Appendices Appendix A Python Libraries A.1 CVXOPT A.2 NumPy A.3 Matplotlib Appendix B System Classes B.1 System Properties and Settings Appendix C Control Diagrams C.1 Representation of Basic Functions C.2 Hard Limits Appendix D IEEE 14-Bus System Data D.1 Common Data D.2 Static Data D.3 Market Data D.4 Dynamic Data D.5 FACTS Data D.6 Wind Turbine Data Appendix E Software Packages and Links E.1 Software Packages Used in the Book E.2 Links related to Power System Analysis References Index