Klos / Klos Mathematical Models of Electrical Network Systems

Theory and Applications - An Introduction
1. Auflage 2017
ISBN: 978-3-319-52178-7
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 412, 108 Seiten

Reihe: Lecture Notes in Electrical Engineering

This book is for all those who are looking for a non-conventional mathematical model of electrical network systems. It presents a modern approach using linear algebra and derives various commonly unknown quantities and interrelations of network analysis. It also explores some applications of algebraic network model of and solves some examples of previously unsolved network problems in planning and operation of network systems. Complex mathematical aspects are illustrated and described in a way that is understandable for non-mathematicians. Discussing interesting concepts and practically useful methods of network analysis, it is a valuable resource for lecturers, students, engineers

Autoren/Hrsg.

Klos, Andrzej

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Mathematical Model of Network System;11
4;1 Introduction;12
4.1;1.1 Network System;12
4.2;1.2 Modeling Network System;13
4.3;1.3 Solving Network System;14
4.4;1.4 Network Laws;15
5;2 Basic Notions;17
5.1;2.1 Network Graph Notions;17
5.2;2.2 Electrical Network Notions;17
6;3 Algebraic Model of Network Graph;20
6.1;3.1 Cut-Set and Loop-Set Vectors;20
6.2;3.2 Topology of Network;21
6.3;3.3 Topological Model of Loop-Sets;22
6.4;3.4 Topological Model of Cut-Sets;23
6.5;3.5 Orthogonality of Cut-Sets and Loop-Sets;25
6.6;3.6 Linear Space Model of Network Topology;26
6.7;3.7 Topological Transformation;27
6.8;3.8 Topological Matrix T;29
7;4 Algebraic Model of Network Currents;31
7.1;4.1 Matrix Model of Network Currents;31
7.2;4.2 Linear Space Model of Network Currents;32
7.3;4.3 Topological Transformation of Current Space;34
7.4;4.4 Current Relations Using Topological Matrix T;35
8;5 Algebraic Model of Network Voltages;37
8.1;5.1 Matrix Model of Network Voltages;37
8.2;5.2 Linear Space Model of Network Voltages;39
8.3;5.3 Topological Transformation of Voltage Space;40
8.4;5.4 Voltage Relations Using Topological Matrix T;41
9;6 Algebraic Model of Current–Voltage Vectors;43
9.1;6.1 Orthogonality of Current and Voltage Vectors;43
9.2;6.2 Current–Voltage Vector;44
9.3;6.3 Linear Space Model of Current–Voltage Vectors;45
9.4;6.4 Current–Voltage Vectors’ Relations Using Matrix T;46
9.5;6.5 Comment;47
10;7 Kirchhoff’s Laws Using Matrix T;49
10.1;7.1 Basic b-Dimensional Formulation;49
10.2;7.2 Pseudo-Unit Formulation;51
10.3;7.3 Current–Voltage Formulation;52
11;8 Current–Voltage Functional Relations;53
11.1;8.1 Branch Parameters;53
11.2;8.2 Ohm’s Law of Network System—Algebraic Model;56
11.3;8.3 Linear Space Model of Current–Voltage State Vectors in Network System;58
11.4;8.4 Formulation of Ohm’s Law Using Matrix T;61
11.5;8.5 Matrices of System Admittance and System Impedance;63
12;9 General Comments to Part I;65
12.1;9.1 Part II Application Examples;66
13;Application Examples;67
14;10 Applications of b-Dimensional Formulation of Kirchhoff’s Laws;68
14.1;10.1 Basic b-Dimensional Formulation;68
14.2;10.2 Pseudo-Unit Formulation;70
15;11 Network Solution Method Using Algebraic Network Model;74
15.1;11.1 Derivation of Method Using Matrix T;74
15.2;11.2 Classical Network Solution Methods;76
16;12 Method of Current and Voltage Sensitivity Analysis;78
16.1;12.1 Derivation of Method;78
16.2;12.2 Numerical Example;80
17;13 Method of Arbitrary Input Data;82
17.1;13.1 Description of Arbitrary Input Data;82
17.2;13.2 Derivation of Solution Equations;83
17.3;13.3 Solvability Analysis;85
17.4;13.4 Numerical Example;86
18;14 Logical Optimization Method of Network System;91
18.1;14.1 Example of Network System Matrices;91
18.2;14.2 Logical Analysis of Network System Equations;93
18.3;14.3 Application Possibilities;98
19;15 Current-Based Method of Load Flow Solution;100
19.1;15.1 Current State-Oriented Topology of Network;100
19.2;15.2 Current State Vector and Current Flow Method;101
19.3;15.3 Current-Based Load Flow Method;104
19.4;15.4 Verification of Method;105
19.5;15.5 Conclusions;107