Bridging Circuits and Fields: Foundational Questions in Power Theory

Description

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. Cover Title Page Copyright Page Acknowledgements Preface Table of Contents 1. Introduction 1. The Subject Matter: Why Does it Matter? 1.1 Author’s Motivation 1.2 Reader’s Motivation 1.3 What is Electrical Power? 2. Foundational Issues Related to the Concept of Electrical Power 2.1 Ontological Point of View 2.2 Epistemological Point of View 3. Contributions of This Monograph to Power Theory 3.1 Reappraisal and Reformulation of Steinmetz’s Symbolic Method 3.2 Reappraisal of Janet’s Heuristic Expression S = VI * 3.3 Demonstration of the Mathematical Isomorphism between Steinmetz’s Power Expression and Poynting’s Expression for Energy Flow 3.4 Reactive Power is as much Power as Active Power 3.5 Apparent Power does have Physical Meaning 3.6 Criticism of the Interpretation of Double-frequency Terms 3.7 Validity of the Instantaneous Power Concept 3.8 Physical Interpretation of Voltage and Current as Inseparable Entities 3.9 Issues Related to Load Flow and State Estimation 4. Research Methodology 5. Literature and References 6. Style 7. Structure 2. Power Theory in Electrical Circuits 1. Introduction 2. A Critical Assessment of the Existing Power Paradigm 2.1 Steinmetz’s Assumptions Underpinning His Symbolic Method: A Critical Review 2.2 Steinmetz’s Symbolic Method: A Disguised Geometric Algebra 2.3 Rigorization of Janet’s Expression 3. Conclusion 3. Is the Poynting Theorem the Keystone of a Conceptual Bridge between Classical Electromagnetic Theory and Classical Circuit Theory? 1. Introduction 2. Theoretical Debates on the Relevance of the Poynting Theorem for Circuit Theory 2.1 Proponents of the Poynting Theorem as Bridge between Classical Electromagnetic and Circuit Theories 2.2 Opponents’ View: The Poynting Theorem is not the Bridge between Classical Electromagnetic and Circuit Theories 3. Empirical Measurement of the Poynting Vector 4. Conclusion 4. Electromagnetic Power 1. Introduction 2. Ontology of Electromagnetic Power Theory 3. Epistemology of the Electromagnetic Power Theory 4. The Main Characteristics of the Electromagnetic Power Theory 5. Geometric Algebra in Electrical Engineering and Power Theory 5.1 Pre-history of Geometric Algebra in Mathematics 5.2 The History of Geometric Algebra in Electrical Engineering 5.3 Applications of Geometric Algebra in Power Theory 5.4 Conclusions from Literature on Geometric Algebra in Power Theory Appendix 5. Epistemology of Power Theory 1. Introduction 2. Mathematical Guises and Disguises of an Elusive Physical Concept: Electrical Power 2.1 Electrical Magnitudes Expressed as Real-valued Functions of Time; Power Equations as Partial Differential Equations: Bedell and Crehore 2.2 Electrical Magnitudes Expressed as Complex-valued and/or Vector-valued Functions: Steinmetz and Janet 2.3 Electrical Magnitudes Expressed as Hypercomplexvalued Functions: Macfarlane and Kennelly 2.4 Heaviside Operational Calculus and the Steinmetz Symbolic Method: Two Types of Mathematical Transformations in Circuit Theory 2.5 The A-C Kalkül: Mathis and Marten 2.6 A Conjecture: Electromagnetic Power as Spacetime Density of Electromagnetic Force in Circuits 3. Power Theory at the Mesoscopic and Subatomic Levels 3.1 Electrons, Positrons, and Photons 4. Power Theory – A Gauge Theory 4.1 Power Theory and the Physics of Condensed Matter 4.2 Power Theory and Quantum Metrology 5. Conclusion 6. Epilogue as Prologue 1. Can We Unify the Concepts of Power in Circuits and Energy-momentum in Electromagnetic Fields? 2. Is the Current Power Paradigm Still Valid? 3. Conclusion 4. Hypothesis of a Quantum Electromagnetic Power Theory is Consistent with Quantum Electrodynamics and with the Theory of Restraint Relativity 5. Power Engineering Theory and Practice: Quo Vadis? Bibliography Index