Introduction to Transients in Electrical Circuits: Analytical and Digital Solution Using an EMTP-based Software
- Length: 711 pages
- Edition: 1
- Language: English
- Publisher: Springer
- Publication Date: 2021-09-17
- ISBN-10: 303068248X
- ISBN-13: 9783030682484
- Sales Rank: #9073827 (See Top 100 Books)
This book integrates analytical and digital solutions through Alternative Transients Program (ATP) software, recognized for its use all over the world in academia and in the electric power industry, utilizing a didactic approach appropriate for graduate students and industry professionals alike.
This book presents an approach to solving singular-function differential equations representing the transient and steady-state dynamics of a circuit in a structured manner, and without the need for physical reasoning to set initial conditions to zero plus (0+). It also provides, for each problem presented, the exact analytical solution as well as the corresponding digital solution through a computer program based on the Electromagnetics Transients Program (EMTP).
Of interest to undergraduate and graduate students, as well as industry practitioners, this book fills the gap between classic works in the field of electrical circuits and more advanced works in the field of transients in electrical power systems, facilitating a full understanding of digital and analytical modeling and solution of transients in basic circuits.
Preface Contents List of Figures List of Tables 1 Introduction to Fundamental Concepts in Electric Circuit Analysis 1.1 Introduction 1.2 Preliminary Concepts 1.3 Electrical Quantities 1.4 Power and Energy 1.5 Circuit Elements 1.6 Kirchhoff’s Laws 1.7 Analytical and Digital Circuit Solution 1.8 Conclusions and Motivations for Electromagnetic Transients Studies References 2 Singular Functions 2.1 Single Step Function 2.2 Unitary Impulse Function 2.3 The Family of Singular Functions 2.4 Causal Functions 2.5 Derivative of an Ordinary Sectionally Continuous Function 2.6 Decomposition of a Function into Singular Functions 2.7 The Distribution Concept 2.8 The Unitary Impulse Function as Distribution 2.9 Initial Condition at t = 0+ 2.10 Initial Decomposition of Functions in Steps 2.11 Decomposition of Functions into Impulses 2.12 Convolution Integral 2.13 Properties of the Convolution Integral 2.14 Proposed Problems 2.15 Conclusions References 3 Differential Equations 3.1 Introduction 3.2 Ordinary Differential Equations 3.2.1 Solution of the Homogeneous Differential Equation 3.2.2 Considerations on Algebraic Equations 3.2.3 Solution of the Non-homogeneous Differential Equation 3.3 Differential Equations with Singular and Causal Forcing Functions 3.3.1 Step Type Forcing Function {\varvec U}_{ - 1} \left( {\varvec t} \right) 3.3.2 Forcing Function Type Impulse {\varvec U}_{0} \left( {\varvec t} \right) 3.3.3 Systematic Method for Calculating Initial Conditions at {\varvec t} = 0_{ {\,+\,} } 3.4 Conclusions References 4 Digital Solution of Transients in Basic Electrical Circuits 4.1 Introduction 4.2 Basic Algorithm for Computational Solution of EMTP-Based Programs 4.3 Solution of Differential Equations via Digital Integration 4.4 Digital Computational Model of the Elements with Concentrated Parameters 4.4.1 Resistance {\varvec R} 4.4.2 Inductance {\varvec L} 4.4.3 Capacitance {\varvec C} 4.5 Numerical Oscillations in EMTP Due to the Trapezoidal Integration Method 4.6 Conclusions References 5 Transients in First Order Circuits 5.1 Introduction 5.2 Continuity Theorem 5.3 Response to Impulse and Response to Step 5.4 Sequential Switching 5.5 Magnetically Coupled Circuits 5.6 DuHamel Integrals 5.7 Proposed Problems 5.8 Conclusions References 6 Transients in Circuits of Any Order 6.1 Introduction 6.2 Circuits Initially Deenergized 6.3 Thévenin and Norton Equivalents for Initially Energized Capacitances and Inductances 6.4 Circuits Initially Energized 6.5 Switching Transients 6.6 Proposed Problems 6.7 Conclusions References 7 Switching Transients Using Injection of Sources 7.1 Introduction 7.2 Method of Voltage Source Injection 7.3 Current Source Injection Method 7.4 Displacement of Current Source Method 7.5 Proposed Problems 7.6 Conclusions References Appendix A Processing in the ATP Appendix B Main Relations Involving Singular Functions Appendix C Laplace Transform Properties Appendix D Laplace Transform Pairs Appendix E Heaviside Expansion Theorem
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