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E-raamat: Analysis of Electrical Circuits with Variable Load Regime Parameters: Projective Geometry Method

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  • Sari: Power Systems
  • Ilmumisaeg: 06-Feb-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319284514
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Analysis of Electrical Circuits with Variable Load Regime Parameters: Projective Geometry MethodSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Power Systems
  • Ilmumisaeg: 06-Feb-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319284514
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This book introduces electric circuits with variableloads and voltage regulators. It allows to define invariant relationships forvarious parameters of regime and circuit sections and to prove the conceptscharacterizing these circuits. The book presents the fundamentals of electriccircuits and develops circuit theorems. Generalized equivalent circuitsare introduced. Projective geometry is used for the interpretation of changesof operating regime parameters. Expressions of normalized regime parameters andtheir changes are presented. Convenient formulas for the calculation ofcurrents are given. Parallel voltage sources and the cascade connection ofmulti-port networks are described. The two-value voltage regulationcharacteristics of loads with limited power of voltage source is considered.This second edition is extended and contains additional chapters on circuits withnon-linear regulation curves, circuits with non-linear load characteristics,concepts of power-source and

power-load elements with two-valuedcharacteristics, quasi-resonant voltage converters with self-limitation ofcurrent as well as the similarity of characteristics of converters andelectronic devices.This book is useful to engineers, researchers andgraduate students who are interested in the basic electric circuit theory andthe regulation and monitoring of power supply systems.

Introduction.- Part I: Electrical Circuits with One Load- Projective Coordinates ofa Straight Line Point.- Operating Regimesof an Active Two-Pole. Display of Projective Geometry.- Generalized EquivalentCircuit of an Active Two-Pole with a Variable element.- Two-Port Circuits.- Parallelingof Limited Capacity Voltage Sources.- Part II : Multi-port Circuits - Projective Coordinates of a Point on the Planeand Space.- Operating Regimes of an Active Multi-port.- Recalculation of Load Currentsof Active Multi-ports.- Passive Multi-PortCircuits.- GeneralizedEquivalent Circuit of a Multi-port.- Part III: Circuits with Non-LinearRegulation Curves.- Regulation of Load Voltages.- Stabilization of LoadVoltages.- Pulse-Width Modulation Regulators.- Part IV: Circuits withNon-Linear Load Characteristics.- Power-Source and Power-Load Elements.- Quasi-ResonantVoltage Converter with Self-Limitation of the Load Current. Similarity of LoadCharacteristics of Some Electronic Devices.- Concl

usions.
1 Introduction 1(28)
1.1 Typical Structure and Equivalent Circuits of Power Supply Systems. Features of Circuits with Variable Operating Regime Parameters
1(2)
1.2 Disadvantages of the Well-Known Calculation Methods of Regime Parameters in the Relative Form for Active Two-Poles
3(8)
1.2.1 Volt—Ampere Characteristics of an Active Two-Pole
3(1)
1.2.2 Regime Parameters in the Relative Form
4(3)
1.2.3 Regime Change in the Relative Form
7(2)
1.2.4 Active Two-Port with Changeable Resistance
9(1)
1.2.5 Scales of Regime Parameters for Cascaded Two-Ports
9(2)
1.3 Analysis of the Traditional Approach to Normalizing of Regime Parameters for the Voltage Linear Stabilization
11(3)
1.4 Active Two-Port
14(3)
1.4.1 Volt Characteristics of an Active Two-Port
14(1)
1.4.2 Traditional Recalculation of the Load Currents
14(3)
1.5 Nonlinear Characteristics
17(4)
1.5.1 Efficiency of Two-Ports with Different Losses
17(3)
1.5.2 Characteristic Regimes of Solar Cells
20(1)
1.5.3 Quasi-resonant Voltage Converter
20(1)
1.5.4 Power-Source and Power-Load Elements
21(1)
1.6 Regulated Voltage Converters
21(4)
1.6.1 Voltage Regulator with a Limited Capacity Voltage Source
21(2)
1.6.2 Buck Converter
23(1)
1.6.3 Boost Converter
24(1)
References
25(4)
Part I Electrical Circuits with one Load. Projective Coordinates of a Straight Line Point
2 Operating Regimes of an Active Two-Pole. Display of Projective Geometry
29(26)
2.1 Volt—Ampere Characteristics of an Active Two-Pole. Affine and Projective Transformations of Regime Parameters
29(13)
2.1.1 Affine Transformations
29(8)
2.1.2 Projective Transformations
37(5)
2.2 Volt—Ampere Characteristics of an Active Two-Pole with a Variable Element
42(5)
2.2.1 Thevenin Equivalent Circuit with the Variable Internal Resistance
42(2)
2.2.2 Norton Equivalent Circuit with the Variable Internal Conductivity
44(3)
2.3 Regime Symmetry for a Load-Power
47(7)
2.3.1 Symmetry of Consumption and Return of Power
48(2)
2.3.2 Symmetry Relatively to the Maximum Power Point
50(2)
2.3.3 Two Systems of Characteristic Points
52(2)
References
54(1)
3 Generalized Equivalent Circuit of an Active Two-Pole with a Variable Element
55(42)
3.1 Introduction
55(1)
3.2 Circuit with a Series Variable Resistance
56(14)
3.2.1 Disadvantage of the Known Equivalent Circuit
56(1)
3.2.2 Generalized Equivalent Circuit
57(3)
3.2.3 Relative Operative Regimes. Recalculation of the Load Current
60(5)
3.2.4 Example
65(5)
3.3 Circuit with a Shunt Variable Conductivity
70(12)
3.3.1 Disadvantage of the Known Equivalent Circuit
70(1)
3.3.2 Generalized Equivalent Circuit
71(3)
3.3.3 Relative Operative Regimes. Recalculation of the Load Current
74(4)
3.3.4 Example
78(4)
3.4 General Case of an Active Two-Pole with a Variable Conductivity
82(9)
3.4.1 Known Equivalent Generator
83(1)
3.4.2 Generalized Equivalent Circuit
84(3)
3.4.3 Example of a Circuit. Recalculation of the Load Current
87(4)
3.5 Stabilization of the Load Current
91(3)
References
94(3)
4 Two-Port Circuits
97(44)
4.1 Input-Output Conformity of Two-Ports as Affine Transformations
97(5)
4.1.1 Conformity of a Two-Port
97(2)
4.1.2 Conformity of Cascaded Two-Ports
99(3)
4.2 Input-Output Conformity of Two-Ports as Projective Transformations
102(14)
4.2.1 Conformity of a Two-Port
102(4)
4.2.2 Versions of Conformities, Invariants, and Cross Ratios
106(3)
4.2.3 Conformity of Cascaded Two-Ports
109(7)
4.3 Use of Invariant Properties for the Transfer of Measuring Signals
116(4)
4.3.1 Transfer of Signals over an Unstable Two-Port
116(3)
4.3.2 Conductivity Measurement by an Unstable Two-Port
119(1)
4.4 Deviation from the Maximum Efficiency of a Two-Port
120(6)
4.4.1 Regime Symmetry for the Input Terminals
121(2)
4.4.2 Regime Symmetry for the Output or Load
123(3)
4.5 Effectiveness of Modular Connections
126(5)
4.5.1 Complementary Knowledge About a Two-Port
126(1)
4.5.2 Parallel Connection of Two Converters
127(3)
4.5.3 Connection of Two-Ports with the Interaction
130(1)
4.6 Effectiveness Indices of a Two-Port with Variable Losses
131(7)
4.6.1 Problems of Energy Indices
131(1)
4.6.2 Influence of Losses on the Load Power
131(4)
4.6.3 Influence of Losses on the Efficiency
135(3)
References
138(3)
5 Paralleling of Limited Capacity Voltage Sources
141(26)
5.1 Introduction
141(1)
5.2 Initial Relationships
141(2)
5.3 Influence of the Load Value on the Current Distribution
143(10)
5.3.1 Analysis of Paralleling Voltage Sources
143(2)
5.3.2 Introduction of Two Concepts
145(3)
5.3.3 Comparison of a Loading Regime of Different Circuits
148(5)
5.4 Influence of the Equalizing Resistance on the Current Distribution
153(9)
5.4.1 Analysis of Paralleling Voltage Sources
153(1)
5.4.2 Introduction of Two Concepts
154(3)
5.4.3 Comparison of a Loading Regime of Different Circuits
157(5)
References
162(5)
Part II Multi-port Circuits. Projective Coordinates of a Point on the Plane and Space
6 Operating Regimes of an Active Multi-port
167(40)
6.1 Active Two-Port. Affine and Projective Coordinates on the Plane
167(16)
6.1.1 Affine Coordinates
167(6)
6.1.2 Particular Case of a Two-Port. Introduction of the Projective Plane
173(2)
6.1.3 General Case of a Two-Port. Projective Coordinates
175(8)
6.2 Projective Coordinates in Space
183(15)
6.2.1 Particular Case of a Multi-port
183(7)
6.2.2 General Case of a Multi-port. The Balanced Networks
190(8)
6.3 Projective Coordinates of an Active Two-Port with Stabilization of Load Voltages
198(7)
References
205(2)
7 Recalculation of Load Currents of Active Multi-ports
207(30)
7.1 Recalculation of Currents for the Case of Load Changes
207(6)
7.1.1 Active Two-Port
207(3)
7.1.2 Active Three-Port
210(3)
7.2 Recalculation of Currents for the Case of Changes of Circuit Parameters
213(11)
7.2.1 Change of Lateral Conductivity
213(6)
7.2.2 Change of Longitudinal Conductivity
219(5)
7.3 Comparison of Regimes and Parameters of Active Two-Ports
224(4)
7.4 Comparison of Regime of Active Two-Ports with Linear Stabilizations of Load Voltages
228(7)
References
235(2)
8 Passive Multi-port Circuits
237(38)
8.1 Input-Output Conformity of Four-Ports as an Affine Transformation
237(7)
8.2 Input-Output Conformity of Four-Ports as a Projective Transformation
244(16)
8.2.1 Output of a Four-Port
244(2)
8.2.2 Input of a Four-Port
246(5)
8.2.3 Recalculation of Currents at Load Changes
251(1)
8.2.4 Two Cascaded Four-Port Networks
252(2)
8.2.5 Examples of Calculation
254(6)
8.3 Transmission of Two Signals Over Three-Wire Line
260(3)
8.3.1 Transmission by Using of Cross-Ratio
260(2)
8.3.2 Transmission by Using of Affine Ratio
262(1)
8.4 Input-Output Conformity of a Balanced Six-Port
263(10)
References
273(2)
9 Generalized Equivalent Circuit of a Multi-port
275(14)
9.1 Generalized Equivalent of an Active Two-Port
275(7)
9.1.1 Disadvantages of Known Equivalent
275(1)
9.1.2 Introduction of the Formal Variant of a Generalized Equivalent
276(3)
9.1.3 Introduction of the Principal Variant of a Generalized Equivalent Circuit
279(3)
9.2 Generalized Equivalent of an Active Three-Port
282(4)
References
286(3)
Part III Circuits with Non-Linear Regulation Curves
10 Regulation of Load Voltages
289(24)
10.1 Base Model. Display of Conformal Geometry
289(6)
10.2 Using of Hyperbolic Geometry Model
295(10)
10.2.1 Case of One Load
296(3)
10.2.2 Case of Two Loads
299(6)
10.3 Example
305(7)
10.3.1 Case of One Load
306(2)
10.3.2 Case of Two Loads
308(4)
References
312(1)
11 Stabilization of Load Voltages
313(24)
11.1 Analysis of Load Voltage Stabilization Regimes
313(11)
11.1.1 Case of One Load
313(2)
11.1.2 Use of Hyperbolic Geometry
315(7)
11.1.3 Case of Two Loads
322(2)
11.2 Given Voltage for the First Variable Load and Voltage Regulation of the Second Given Load
324(10)
11.2.1 Use of Hyperbolic Geometry
328(2)
11.2.2 Regime Change for the First Given Load Resistance
330(3)
11.2.3 Example
333(1)
References
334(3)
12 Pulse-Width Modulation Regulators
337(24)
12.1 Introduction
337(1)
12.2 Regulation Characteristic of Boost Converter
337(11)
12.3 Regulation Characteristic of Buck—Boost Converter
348(9)
12.3.1 Buck—Boost Converter with an Idealized Choke
348(6)
12.3.2 Buck—Boost Converter with Losses of Choke
354(3)
References
357(4)
Part IV Circuits with Non-Linear Load Characteristics
13 Power-Source and Power-Load Elements
361(28)
13.1 Introduction
361(1)
13.2 Two-Valued Regime of a Regulated Converter. The Concept of a Power-Source and Power-Load Element
361(2)
13.3 Influence of Voltage Source Parameters and Power-Load Element onto a Power Supply Regime
363(11)
13.3.1 Ideal Voltage Source
363(1)
13.3.2 Voltage of a Power Supply with Limited Capacity
364(6)
13.3.3 Internal Resistance of a Voltage Source
370(2)
13.3.4 Power of a Power-Load Element
372(2)
13.4 Power-Load Element with Losses
374(7)
13.4.1 Series Loss Resistance
374(1)
13.4.2 Two-Port Loss Circuit
375(6)
13.5 Power Supply Line with Losses
381(7)
References
388(1)
14 Quasi-resonant Voltage Converter with Self-limitation of Load Current. Similarity of Load Characteristics of Some Electronic Devices
389(24)
14.1 Load Curve of an Active Two-Pole with Self-limitation of the Current
389(3)
14.2 Equivalent Generator of an Active Two-Pole with Self-limitation of Current
392(4)
14.3 Deviation from the Maximum Load Power Point
396(4)
14.4 Symmetrical Load Characteristic for the Full Area of the Load Voltage Variation
400(1)
14.5 Asymmetrical Load Characteristics
401(4)
14.6 Linearly Hyperbolic Approximation of a Solar Cell Characteristic
405(5)
14.6.1 Approximation Problem
405(1)
14.6.2 Formal Linearly Hyperbolic Approximation
405(5)
References
410(3)
Conclusions 413(2)
Index 415
A. Penin graduated from Radio Department Polytechnic Institute in 1974, Odessa, Ukraine. His engineering interest relates to power electronics. He worked (1980-2006) in the design office of solid-state electronics of the Academy of Sciences of Moldova. His speciality is the elaboration of power supply systems. From 2006 he has been working in the Institute of Electronic Engineering and Nanotechnologies of the Academy of Sciences of Moldova. He continues independent theoretical research in electric circuit theory with variable regimes. He is a senior research assistant, PhD (2011). The author has more than 60 publications, 40 patents of Moldova, one European patent, and one book.
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