Milano Power System Modelling and Scripting

1. Auflage 2010
ISBN: 978-3-642-13669-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 558 Seiten

Reihe: Power Systems

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.

Autoren/Hrsg.

Milano, Federico

Inhaltsverzeichnis

1;Title Page;1
2;Preface;6
3;Contents;11
4;List of Figures;19
5;List of Tables;26
6;List of Examples;30
7;List of Scripts;33
8;Notation;34
9;Part I Introduction;39
9.1;Power System Modelling;40
9.1.1;Background;40
9.1.2;Motivations;41
9.1.3;Modelling Physical Systems;42
9.1.4;Hybrid Dynamical Model;48
9.2;Power System Architecture;55
9.2.1;Structure of Software Projects;55
9.2.2;Classes and Procedures;57
9.2.3;Modularity;59
9.2.4;Architecture of a Power System Software Tool;63
9.3;Power System Scripting;67
9.3.1;Open and Closed Programming;67
9.3.2;Scripting;69
9.3.3;Scripting Languages for Computational Science;71
9.3.4;Suitable Computer Languages;72
9.3.5;Python Scripting Language;75
10;Part II Power System Analysis;95
10.1;Power Flow Analysis;96
10.1.1;Background;96
10.1.2;Taxonomy of Power Flow Problems;101
10.1.3;Classical Power Flow Equations;102
10.1.4;Power Flow Solvers;105
10.1.4.1;Jacobi and Gauss-Seidel's Method;105
10.1.4.2;Newton's Method;109
10.1.4.3;Power Flow Jacobian Matrix;112
10.1.4.4;Robust Newton's Method;117
10.1.4.5;Iwamoto's Method;119
10.1.4.6;Inexact and Dishonest Newton's Methods;120
10.1.4.7;Fast Decoupled Power Flow;121
10.1.4.8;DC Power Flow;127
10.1.4.9;Single and Distributed Slack Bus Models;130
10.1.5;A General Framework for Power Flow Solvers;131
10.1.5.1;Stability of the Continuous Newton's Method;132
10.1.6;Summary;135
10.2;Continuation Power Flow Analysis;137
10.2.1;Background;137
10.2.2;System Model;141
10.2.3;Direct Methods;142
10.2.3.1;Saddle-Node Bifurcation;143
10.2.3.2;Limit-Induced Bifurcation;145
10.2.3.3;Nonlinear Programming;147
10.2.4;Homotopy Methods;148
10.2.4.1;Continuation Power Flow;151
10.2.4.2;Predictor Step;151
10.2.4.3;Corrector Step;155
10.2.4.4;Continuous Newton's Method and Homotopy;160
10.2.4.5;N-1 Contingency Analysis;161
10.2.5;Summary;163
10.3;Optimal Power Flow Analysis;165
10.3.1;Background;165
10.3.2;Optimal Power Flow Model;167
10.3.3;Nonlinear Programming Solvers;173
10.3.3.1;Generalized Reduced Gradient Method;174
10.3.3.2;Interior Point Method;176
10.3.4;Summary of IPM Parameters;187
10.4;Eigenvalue Analysis;188
10.4.1;Background;188
10.4.2;Small Signal Stability Analysis;192
10.4.2.1;Bifurcation Points;194
10.4.2.2;Participation Factors;198
10.4.2.3;Analysis in the Z-Domain;202
10.4.3;Computing the Eigenvalues;203
10.4.3.1;Power Method;203
10.4.3.2;Inverse Iteration;205
10.4.3.3;Rayleigh's Iteration;205
10.4.4;Power Flow Modal Analysis;206
10.4.4.1;Singular Value Decomposition;207
10.4.5;Summary;210
10.5;Time Domain Analysis;212
10.5.1;Background;212
10.5.2;Power System Model;219
10.5.2.1;Current-Injection Model;220
10.5.2.2;Power-Injection Model;222
10.5.3;Numerical Integration Methods;225
10.5.3.1;Explicit Methods;225
10.5.3.2;Implicit Methods;228
10.5.4;Numerical Integration Routine;231
10.5.4.1;Step Length;233
10.5.4.2;Disturbances;235
10.5.4.3;Stop Criterion;237
10.5.5;Electro-magnetic Transients;244
10.5.6;Quasi-static Analysis;246
10.5.7;Summary;250
11;Part III Device Models;252
11.1;Device Generalities;253
11.1.1;General Device Model;253
11.1.1.1;Initialization of Device Internal Variables;255
11.1.2;Devices as Classes;258
11.1.2.1;Base Device Class;260
11.1.2.2;Methods of the Base Class;268
11.1.2.3;Specific Device Methods;273
11.2;Power Flow Devices;279
11.2.1;Topological Elements;279
11.2.1.1;Bus;279
11.2.1.2;Areas, Zones, Regions and Systems;281
11.2.2;Static Generators;282
11.2.2.1;PV Generator;282
11.2.2.2;Constant Voltage Phasor Generator;286
11.2.2.3;PQ Generator;288
11.2.3;Static Loads;289
11.2.3.1;PQ Load;289
11.2.3.2;Constant Power Factor Load;291
11.2.3.3;Shunt Admittance;292
11.2.3.4;Switched Shunt Admittances;292
11.3;Transmission Devices;294
11.3.1;Transmission Line;294
11.3.1.1;Line Sections;296
11.3.1.2;Tie Line;298
11.3.1.3;Distributed Transmission Line Models;299
11.3.1.4;Effect of Frequency Variation;301
11.3.1.5;Coupling Device and Zero-Impedance Line;302
11.3.2;Transformer;303
11.3.2.1;Two-Winding Transformer;303
11.3.2.2;Under Load Tap Changer;306
11.3.2.3;Phase Shifting Transformer;309
11.3.2.4;Three-Winding Transformer;310
11.3.3;Vectorial Implementation;313
11.3.3.1;Incidence Matrix;315
11.3.3.2;Jacobian and Hessian Matrices;316
11.3.3.3;Network Connectivity;318
11.4;OPF Devices;321
11.4.1;Network Constraints;321
11.4.1.1;Bus Voltage Limits;321
11.4.1.2;Transmission Line limits;321
11.4.2;Generator Constraints;322
11.4.2.1;Capability Curve;322
11.4.2.2;Supply Offer;323
11.4.2.3;Reactive Power Payment Function;326
11.4.2.4;Generator Power Reserve;328
11.4.2.5;Generator Power R329
11.4.3;Load Constraints;331
11.4.3.1;Demand Bid;331
11.4.3.2;Demand Daily Profile;332
11.4.3.3;Demand Power R333
11.5;Faults and Protections;335
11.5.1;Fault;335
11.5.2;Breaker;336
11.5.3;Relay;337
11.5.4;Phasor Measurement Unit;339
11.5.5;Bus Frequency Estimation;341
11.6;Loads;343
11.6.1;Voltage Dependent Load;343
11.6.2;ZIP Load;345
11.6.3;Frequency Dependent Load;346
11.6.4;Voltage Dependent Load with Dynamic Tap Changer;347
11.6.5;Exponential Recovery Load;350
11.6.6;Thermostatically Controlled Load;351
11.6.7;Jimma's Load;352
11.6.8;Mixed Load;353
11.7;Alternate-Current Machines;355
11.7.1;Synchronous Machine;355
11.7.1.1;Synchronous Machine Parameters;356
11.7.1.2;Initialization;357
11.7.1.3;Common Equations;358
11.7.1.4;Stator Electrical Equations;359
11.7.1.5;Magnetic Equations;359
11.7.1.6;Simplified Magnetic Equations;362
11.7.1.7;Synchronous Machine Model Taxonomy;366
11.7.1.8;Saturation;369
11.7.1.9;Center of Inertia;372
11.7.1.10;Dynamic Shaft;373
11.7.1.11;Sub-synchronous Resonance;375
11.7.2;Induction Machine;378
11.7.2.1;Initialization;378
11.7.2.2;Torque Model;379
11.7.2.3;Electromechanical Model;379
11.7.2.4;Detailed Single-Cage Model;380
11.7.2.5;Detailed Double-Cage Model;381
11.8;Synchronous Machine Regulators;384
11.8.1;Turbine Governor;384
11.8.1.1;Turbine Governor Type I;387
11.8.1.2;Turbine Governor Type II;388
11.8.2;Automatic Voltage Regulator;390
11.8.2.1;Automatic Voltage Regulator Type I;392
11.8.2.2;Automatic Voltage Regulator Type II;393
11.8.2.3;Automatic Voltage Regulator Type III;395
11.8.3;Power System Stabilizer;398
11.8.3.1;Simplified Power System Stabilizer Model;400
11.8.3.2;Power System Stabilizer Type I;400
11.8.3.3;Power System Stabilizer Type II;400
11.8.3.4;Power System Stabilizer Type III;402
11.8.4;Over-Excitation Limiter;402
11.8.5;Under-Excitation Limiter;405
11.9;Direct-Current Devices;407
11.9.1;Direct-Current Nodes;407
11.9.2;Common Interface Equations for Direct-Current Devices;407
11.9.3;Ideal Generators;409
11.9.4;Basic RLC Models;410
11.9.5;Direct-Current Machines;412
11.9.6;Other Direct-Current Devices;415
11.9.6.1;Solid Oxide Fuel Cell;415
11.9.6.2;Solar Photovoltaic Cell;418
11.9.6.3;Battery Energy System;419
11.10;AC/DC Devices;423
11.10.1;High-Voltage Direct-Current Transmission System;423
11.10.1.1;Per Unit System for DC Quantities;424
11.10.1.2;Rectifier Model;424
11.10.1.3;Inverter Model;425
11.10.1.4;HVDC Control;426
11.10.2;Voltage Source Converter;428
11.10.2.1;Simplified Dynamic VSC Model;436
11.10.2.2;Power Flow VSC Model;437
11.11;FACTS Devices;441
11.11.1;Static Var Compensator;441
11.11.1.1;SVC Type I;441
11.11.1.2;SVC Type II;442
11.11.1.3;SVC Initialization;443
11.11.2;Thyristor Controlled Series Compensator;445
11.11.2.1;TCSC Initialization;447
11.11.3;Static Synchronous Compensator;447
11.11.3.1;Detailed Model;448
11.11.3.2;Simplified Dynamic Model;449
11.11.3.3;Power Flow Model;450
11.11.3.4;STATCOM Initialization;451
11.11.4;Static Synchronous Series Compensator;451
11.11.4.1;Detailed Model;452
11.11.4.2;Simplified Dynamic Model;454
11.11.4.3;Power Flow Model;455
11.11.4.4;SSSC Initialization;455
11.11.5;Unified Power Flow Controller;456
11.11.5.1;Detailed Model;456
11.11.5.2;Simplified Dynamic Model;459
11.11.5.3;Power Flow Model;461
11.11.5.4;UPFC Initialization;462
11.12;Wind Power Devices;463
11.12.1;Wind Speed Models;463
11.12.1.1;Weibull's Distribution;464
11.12.1.2;Composite Wind Speed Model;466
11.12.1.3;Mexican Hat Wavelet Model;467
11.12.2;Wind Turbines;468
11.12.2.1;Single Machine and Aggregate Models;469
11.12.2.2;Wind Turbine Initialization;471
11.12.2.3;Turbine Model;471
11.12.2.4;Dynamic Shaft;474
11.12.2.5;Non-Controlled Speed Wind Turbine;476
11.12.2.6;Doubly-Fed Asynchronous Generator;477
11.12.2.7;Direct-Drive Synchronous Generator;481
12;Part IV Spare Material and Concluding Remarks;485
12.1;Data Formats;486
12.1.1;Data Format Taxonomy;486
12.1.1.1;Data Organization and Structures;486
12.1.1.2;Kind of Supported Data;488
12.1.1.3;Number of Files;489
12.1.1.4;Default Values, Prototypes and Data Manipulation;489
12.1.2;Canonical Model;490
12.1.3;Common Information Model;491
12.1.4;Consistent Data Schemes;494
12.2;Visualization Matters;502
12.2.1;Graphical Interface vs. Command Line Approach;502
12.2.2;Result Visualization;505
12.2.2.1;Standard Two-Dimensional Plots;505
12.2.2.2;Temperature Maps;509
12.2.2.3;Three-Dimensional Plots;511
12.2.2.4;Geographic Information System;512
12.3;Challenges of Scripting for Power System Education;516
12.3.1;Concepts and Definitions;516
12.3.1.1;Proprietary Software;516
12.3.1.2;Open Source Software;517
12.3.1.3;Free Software;517
12.3.1.4;Free Open Source Software;518
12.3.2;Education-Oriented FOSS;518
12.3.2.1;Pedagogical Issues;518
12.3.2.2;Failure of FOSS for Power System Analysis;519
13;Part V Appendices;521
13.1;Python Libraries;522
13.1.1;CVXOPT;522
13.1.2;NumPy;530
13.1.3;Matplotlib;532
13.2;System Classes;535
13.2.1;System Properties and Settings;535
13.3;Control Diagrams;538
13.3.1;Representation of Basic Functions;538
13.3.2;Hard Limits;539
13.4;IEEE 14-Bus System Data;545
13.4.1;Common Data;545
13.4.2;Static Data;545
13.4.3;Market Data;545
13.4.4;Dynamic Data;546
13.4.5;FACTS Data;546
13.4.6;Wind Turbine Data;548
13.5;Software Packages and Links;551
13.5.1;Software Packages Used in the Book;551
13.5.2;Links related to Power System Analysis;552
14;References;553