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8. Sinusoidal Steady-State in Three-Phase Circuits 
8.1
8.1 Three-Phase System versus Single-Phase System 
8.2
8.2 Three-Phase Sources and Three-Phase Power 
8.6
8.2.1 The Y-connected Source 
8.6
8.2.2 The 
D
-connected Source 
8.9
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Contents
 
 
xiii
8.3 Analysis of Balanced Three-Phase Circuits 
8.11
8.3.1 Equivalence Between a Y-connected Source and a 
D
-connected Source 8.11
8.3.2 Equivalence Between a Y-connected Load and a 
D
-connected Load 
8.12
8.3.3 The Single-Phase Equivalent Circuit for a Balanced Three-Phase Circuit 8.12
8.4 Analysis of Unbalanced Three-Phase Circuits 
8.17
8.4.1 Unbalanced Y–Y Circuit 
8.17
8.4.2 Circulating Current in Unbalanced Delta-connected Sources 
8.22
8.5 Symmetrical Components 
8.24
8.5.1 Three-Phase Circuits with Unbalanced Sources and Balanced Loads 
8.24
8.5.2 The Zero Sequence Component 
8.26
8.5.3 Active Power in Sequence Components 
8.27
8.5.4 Three-Phase Circuits with Balanced Sources and Unbalanced Loads 
8.28
8.6 Summary 
8.36
8.7 Problems 
8.37
9. Dynamic Circuits with Periodic Inputs – Analysis by Fourier Series 
9.1
9.1 Periodic Waveforms in Circuit Analysis 
9.2
9.1.1 The Sinusoidal Steady-State Frequency Response Function 
9.4
9.2 The Exponential Fourier Series 
9.7
9.3 Trigonometric Fourier Series 
9.9
9.4 Conditions for Existence of Fourier Series 
9.10
9.5 Waveform Symmetry and Fourier Series Coefficients 
9.11
9.6 Properties of Fourier Series and Some Examples 
9.15
9.7 Discrete magnitude and Phase Spectrum 
9.23
9.8 Rate of Decay of Harmonic Amplitude 
9.26
9.9 Analysis of Periodic Steady-State Using Fourier Series 
9.29
9.10 Normalised Power in a Periodic Waveform and Parseval’s Theorem 
9.38
9.11 Power and Power Factor in AC System with Distorted Waveforms 
9.43
9.12 Summary 
9.45
9.13 Problems 
9.47