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E-raamat: Bridging Circuits and Fields: Foundational Questions in Power Theory

(University of Cape Town, South Africa)
  • Formaat: 174 pages
  • Ilmumisaeg: 29-Nov-2021
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351779777
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Bridging Circuits and Fields: Foundational Questions in Power TheorySuurem pilt
  • Formaat: 174 pages
  • Ilmumisaeg: 29-Nov-2021
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351779777
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Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.
Acknowledgements iii
Preface v
1 Introduction
1(9)
1 The Subject Matter: Why Does it Matter?
1(3)
1.1 Author's Motivation
1(1)
1.2 Reader's Motivation
2(1)
1.3 What is Electrical Power?
3(1)
2 Foundational Issues Related to the Concept of Electrical Power
4(1)
2.1 Ontological Point of View
4(1)
2.2 Epistemological Point of View
4(1)
3 Contributions of This Monograph to Power Theory
5(2)
3.1 Reappraisal and Reformulation of Steinmetz's Symbolic Method
5(1)
3.2 Reappraisal of Janet's Heuristic Expression S = VI*
5(1)
3.3 Demonstration of the Mathematical Isomorphism between Steinmetz's Power Expression and Poynting's Expression for Energy Flow
5(1)
3.4 Reactive Power is as much Power as Active Power
6(1)
3.5 Apparent Power does have Physical Meaning
6(1)
3.6 Criticism of the Interpretation of Double-frequency Terms
7(1)
3.7 Validity of the Instantaneous Power Concept
7(1)
3.8 Physical Interpretation of Voltage and Current as Inseparable Entities
7(1)
3.9 Issues Related to Load Flow and State Estimation
7(1)
4 Research Methodology
7(1)
5 Literature and References
8(1)
6 Style
9(1)
7 Structure
9(1)
2 Power Theory in Electrical Circuits
10(12)
1 Introduction
10(1)
2 A Critical Assessment of the Existing Power Paradigm
11(9)
2.1 Steinmetz's Assumptions Underpinning His Symbolic Method: A Critical Review
11(4)
2.2 Steinmetz's Symbolic Method: A Disguised Geometric Algebra
15(3)
2.3 Rigorization of Janet's Expression
18(2)
3 Conclusion
20(2)
3 Is the Poynting Theorem the Keystone of a Conceptual Bridge between Classical Electromagnetic Theory and Classical Circuit Theory?
22(16)
1 Introduction
22(1)
2 Theoretical Debates on the Relevance of the Poynting Theorem for Circuit Theory
23(12)
2.1 Proponents of the Poynting Theorem as Bridge between Classical Electromagnetic and Circuit Theories
23(5)
2.2 Opponents' View: The Poynting Theorem is not the Bridge between Classical Electromagnetic and Circuit Theories
28(7)
3 Empirical Measurement of the Poynting Vector
35(1)
4 Conclusion
35(3)
4 Electromagnetic Power
38(22)
1 Introduction
38(1)
2 Ontology of Electromagnetic Power Theory
38(1)
3 Epistemology of the Electromagnetic Power Theory
39(1)
4 The Main Characteristics of the Electromagnetic Power Theory
40(1)
5 Geometric Algebra in Electrical Engineering and Power Theory
41(19)
5.1 Pre-history of Geometric Algebra in Mathematics
41(4)
5.2 The History of Geometric Algebra in Electrical Engineering
45(1)
5.3 Applications of Geometric Algebra in Power Theory
46(5)
5.4 Conclusions from Literature on Geometric Algebra in Power Theory
51(5)
Appendix
56(4)
5 Epistemology of Power Theory
60(26)
1 Introduction
60(1)
2 Mathematical Guises and Disguises of an Elusive Physical Concept: Electrical Power
60(12)
2.1 Electrical Magnitudes Expressed as Real-valued Functions of Time; Power Equations as Partial Differential Equations: Bedell and Crehore
61(1)
2.2 Electrical Magnitudes Expressed as Complex-valued and/or Vector-valued Functions: Steinmetz and Janet
61(1)
2.3 Electrical Magnitudes Expressed as Hypercomplex-valued Functions: Macfarlane and Kennelly
62(1)
2.4 Heaviside Operational Calculus and the Steinmetz Symbolic Method: Two Types of Mathematical Transformations in Circuit Theory
63(5)
2.5 The A-C Kalkul: Mathis and Marten
68(1)
2.6 A Conjecture: Electromagnetic Power as Spacetime Density of Electromagnetic Force in Circuits
69(3)
3 Power Theory at the Mesoscopic and Subatomic Levels
72(7)
3.1 Electrons, Positrons, and Photons
74(5)
4 Power Theory - A Gauge Theory
79(5)
4.1 Power Theory and the Physics of Condensed Matter
82(1)
4.2 Power Theory and Quantum Metrology
83(1)
5 Conclusion
84(2)
6 Epilogue as Prologue
86(7)
1 Can We Unify the Concepts of Power in Circuits and Energy-momentum in Electromagnetic Fields?
86(1)
2 Is the Current Power Paradigm Still Valid?
87(2)
3 Conclusion
89(2)
4 Hypothesis of a Quantum Electromagnetic Power Theory is Consistent with Quantum Electrodynamics and with the Theory of Restraint Relativity
91(1)
5 Power Engineering Theory and Practice: Quo Vadis?
92(1)
Bibliography 93(70)
Index 163
Alexander I. Petroianu is a specialist in power system analysis, operation, and control. Educated in Russia and Romania, he has broad experience in the power industry as dispatcher and head of the software department at the National Control Center in Romania, head of software development group at Brown-Boveri/ABB Germany, consultant to Eskom, the national power utility of South Africa, and technical manager (transmission) of the South African Power System Studies Institute. He is professor emeritus of Electrical Engineering, University of Cape Town, adjunct professor at the University of Calgary (Canada), a Life Fellow of the IEEE, and member of VDE, SAIEE, CIGRÉ, and IFAC. His recent research has focused on geometrical interpretation of the power transmission phenomenon. This book reflects his investigation into the mathematical and physical aspects of power theory.
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