Power Definitions and the Physical Mechanism of Power Flow

Foreword xi

Preface xiii

1 Electric Energy Flow: Physical Mechanisms 1

1.1 Problems 16

1.2 References 18

2 Single-Phase Systems With Sinusoidal Waveforms 21

2.1 The Resistance 21

2.2 The Inductance 25

2.3 The Capacitance 27

2.4 The R - L - C Loads 29

2.5 The Apparent Power 30

2.6 The Concept of Power Factor and Power Factor Correction 34

2.7 Comments on Power Factor 38

2.8 Other Means of Reactive Power Control and Compensation 41

2.9 Series Compensation 44

2.10 Reactive Power Caused by Mechanical Components that Store Energy 45

2.11 Physical Interpretation of Instantaneous Powers by Means of Poynting Vector 48

2.12 Problems 57

2.13 References 60

3 Single-Phase Systems with Nonsinusoidal Waveforms 63

3.1 The Linear Resistance 63

3.2 The Linear Inductance 68

3.3 The Linear Capacitance 71

3.4 The Linear Series R . L . C Circuit 71

3.5 The Nonlinear Resistance 74

3.6 The Nonlinear Inductance 80

3.7 Nonlinear Load: The General Case 83

3.8 Problems 90

3.9 References 92

4 Apparent Power Resolution for Nonsinusoidal Single-Phase Systems 93

4.1 Constantin I. Budeanu’s Method 95

4.2 Stanislaw Fryze’s Method 99

4.3 Manfred Depenbrock’s Method 102

4.4 Leszek Czarnecki’s Method 106

4.5 The Author’s Method 110

4.6 Comparison Among the Methods 115

4.7 Power Factor Compensation 120

4.8 Comments on Skin Effect, Apparent Power, and Power Factor 128

4.9 The Additiveness Problem 131

4.10 Problems 135

4.11 References 137

5 Three-Phase Systems with Sinusoidal Waveforms 139

5.1 Background: The Balanced and Symmetrical System 140

5.2 The Three-Phase Unbalanced System 142

5.3 The Power Factor Dilemma 145

5.4 Powers and Symmetrical Components 149

5.4.1 How Symmetrical Components are Generated 149

5.4.2 Expressing the Powers by Means of Symmetrical Components 154

5.5 Effective Apparent Power Resolutions 158

5.5.1 FBD-Method 158

5.5.2 L. S. Czarnecki's Method 165

5.5.3 IEEE Std. 1459–2010 Method 167

5.5.4 Comparison Between The Two Major Engineering Schools of Thought 169

5.6 Problems 182

5.7 References 184

6 Three-Phase Nonsinusoidal and Unbalanced Conditions 185

6.1 The Vector Apparent Power Approach 185

6.2 The IEEE Std. 1459-2010's Approach 187

6.3 The DIN 40110’s Approach 192

6.3.1 The IEEE Std. 1459-2010 Approach 195

6.3.2 The DIN 40110 Approach 196

6.4 Observations and Suggestions 198

6.5 Problems 201

6.6 References 202

7 Power Definitions for Time-Varying Loads 205

7.1 Background: Basic Example 206

7.2 Single-Phase Sinusoidal Case 210

7.2.1 Analytical Expressions of Powers: Single-Phase Sinusoidal 213

7.3 Single-Phase Nonsinusoidal Case 214

7.4 Three-Phase Sinusoidal and Unbalanced Condition 216

7.5 Three-Phase Systems with Nonsinusoidal and Unbalanced Condition 220

7.6 Problems 225

7.7 References 227

8 Appendices 229

8.1 Appendix I: The Electrostatic Field Distribution in a Coaxial Cable 229

8.2 Appendix II: Poynting Vector due to Displacement Current 231

8.3 Appendix III: Electric Field Caused by a Time-Varying Magnetic Field 232

8.4 Appendix IV: The Electromagnetic Wave Along the Three-Phase Line 235

8.5 Appendix V: Equation (5.99) 242

8.6 Appendix VI: Maximum Active Power (Three-Phase, Four-Wire System) 243

8.7 Appendix VII: About the Ratio p = Rs/Rn 247

8.8 Appendix VIII: The Use of Varmeters in the Presence of Nonsinusoidal

and Asymmetrical Voltages and Currents 249

8.9 References 258

Index 259