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Introduction to Power Quality |
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1 | (54) |
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Definition of Power Quality |
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1 | (1) |
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Causes of Disturbances in Power Systems |
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1 | (2) |
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Classification of Power Quality Issues |
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3 | (10) |
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4 | (1) |
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Short-Duration Voltage Variations |
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4 | (3) |
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Long-Duration Voltage Variations |
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7 | (1) |
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8 | (1) |
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8 | (4) |
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Voltage Fluctuation and Flicker |
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12 | (1) |
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Power-Frequency Variations |
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12 | (1) |
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Formulations and Measures Used for Power Quality |
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13 | (16) |
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13 | (5) |
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The Average Value of a Nonsinusoidal Waveform |
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18 | (1) |
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The rms Value of a Nonsinusoidal Waveform |
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18 | (1) |
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19 | (1) |
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19 | (1) |
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19 | (1) |
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Lowest Order Harmonic (LOH) |
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19 | (1) |
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Total Harmonic Distortion (THD) |
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19 | (1) |
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Total Interharmonic Distortion (TIHD) |
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20 | (1) |
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Total Subharmonic Distortion (TSHD) |
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20 | (1) |
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Total Demand Distortion (TDD) |
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20 | (1) |
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Telephone Influence Factor (TIF) |
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20 | (1) |
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20 | (1) |
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21 | (1) |
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Telephone Form Factor (TFF) |
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21 | (1) |
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22 | (1) |
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22 | (1) |
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Application Example 1.1: Calculation of Input/Output Currents and Voltages of a Three-Phase Thyristor Rectifier |
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23 | (1) |
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Application Example 1.2: Calculation of Input/Output Currents and Voltages of a Three-Phase Rectifier with One Self-Commutated Electronic Switch |
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24 | (1) |
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Application Example 1.3: Calculation of Input Currents of a Brushless DC Motor in Full-on Mode (Three-Phase Permanent-Magnet Motor Fed by a Six-Step Inverter) |
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25 | (1) |
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Application Example 1.4: Calculation of the Efficiency of a Polymer Electrolyte Membrane (PEM) Fuel Cell Used as Energy Source for a Variable-Speed Drive |
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26 | (1) |
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Application Example 1.5: Calculation of the Currents of a Wind Power Plant PWM Inverter Feeding Power into the Power System |
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26 | (3) |
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Effects of Poor Power Quality on Power System Devices |
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29 | (1) |
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Standards and Guidelines Referring to Power Quality |
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29 | (5) |
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IEC 61000 Series of Standards for Power Quality |
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30 | (2) |
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32 | (2) |
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Harmonic Modeling Philosophies |
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34 | (2) |
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35 | (1) |
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Harmonic-Domain Simulation |
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35 | (1) |
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Iterative Simulation Techniques |
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35 | (1) |
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Modeling Harmonic Sources |
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36 | (1) |
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Power Quality Improvement Techniques |
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36 | (6) |
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High Power Quality Equipment Design |
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36 | (1) |
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36 | (1) |
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Dedicated Line or Transformer |
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37 | (1) |
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Application Example 1.6: Interharmonic Reduction by Dedicated Transformer |
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37 | (1) |
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Optimal Placement and Sizing of Capacitor Banks |
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38 | (2) |
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Derating of Power System Devices |
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40 | (1) |
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Harmonic Filters, APLCs, and UPQCs |
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40 | (1) |
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Application Example 1.7: Hand Calculation of Harmonics Produced by Twelve-Pulse Converters |
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41 | (1) |
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Application Example 1.8: Filter Design to Meet IEEE-519 Requirements |
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41 | (1) |
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Application Example 1.9: Several Users on a Single Distribution Feeder |
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41 | (1) |
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42 | (2) |
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44 | (8) |
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52 | (2) |
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54 | (1) |
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Harmonic Models of Transformers |
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55 | (54) |
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Sinusoidal (Linear) Modeling of Transformers |
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55 | (1) |
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Harmonic Losses in Transformers |
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56 | (4) |
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56 | (1) |
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57 | (1) |
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Magnetic Iron-Core (Hysteresis and Eddy-Current) Losses |
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57 | (1) |
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Application Example 2.1: Relation between Voltages and Flux Linkages for 0° Phase Shift between Fundamental and Harmonic Voltages |
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57 | (2) |
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Application Example 2.2: Relation between Voltages and Flux Linkages for 180° Phase Shift between Fundamental and Harmonic Voltages |
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59 | (1) |
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59 | (1) |
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Indirect Loss Measurement |
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60 | (1) |
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60 | (1) |
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Application Example 2.3: Application of the Direct-Loss Measurement Technique to a Single-Phase Transformer |
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60 | (1) |
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Derating of Single-Phase Transformers |
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60 | (4) |
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Derating of Transformers Determined from Direct-Loss Measurements |
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61 | (1) |
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Derating of Transformers Determined from the K-Factor |
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62 | (1) |
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Derating of Transformers Determined from the FHL-Factor |
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63 | (1) |
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Application Example 2.4: Sensitivity of K- and FHL-Factors and Derating of 25 k VA Single-Phase Pole Transformer with Respect to the Number and Order of Harmonics |
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63 | (1) |
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Application Example 2.5: K- and FHL -Factors and Their Application to Derating of 25 k VA Single-Phase Pole Transformer Loaded by Variable-Speed Drives |
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64 | (1) |
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Nonlinear Harmonic Models of Transformers |
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64 | (11) |
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The General Harmonic Model of Transformers |
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65 | (1) |
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Nonlinear Harmonic Modeling of Transformer Magnetic Core |
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66 | (1) |
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Time-Domain Transformer Core Modeling by Multisegment Hysteresis Loop |
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66 | (1) |
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Frequency- and Time-Domain Transformer Core Modeling by Saturation Curve and Harmonic Core-Loss Resistances |
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66 | (1) |
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Time-Domain Transformer Coil Modeling by Saturation Curve and a Constant Core-Loss Resistance |
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67 | (1) |
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Frequency-Domain Transformer Coil Modeling by Harmonic Current Sources |
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67 | (1) |
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Frequency-Domain Transformer Coil Modeling by Describing Functions |
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68 | (2) |
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Time-Domain Simulation of Power Transformers |
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70 | (1) |
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70 | (2) |
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Transformer Steady-State Solution from the Time-Domain Simulation |
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72 | (1) |
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Frequency-Domain Simulation of Power Transformers |
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72 | (1) |
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Combined Frequency- and Time-Domain Simulation of Power Transformers |
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72 | (1) |
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Numerical (Finite-Difference, Finite-Element) Simulation of Power Transformers |
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73 | (2) |
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Ferroresonance of Power Transformers |
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75 | (6) |
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System Conditions Susceptible (Contributive, Conducive) to Ferroresonance |
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76 | (1) |
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Transformer Connections and Single-Phase (Pole) Switching at No Load |
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76 | (2) |
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Application Example 2.6: Susceptibility of Transformers to Ferroresonance |
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78 | (1) |
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Ways to Avoid Ferroresonance |
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78 | (1) |
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Application Example 2.7: Calculation of Ferroresonant Currents within Transformers |
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79 | (2) |
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Effects of Solar-Geomagnetic Disturbances on Power Systems and Transformers |
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81 | (3) |
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Application Example 2.8: Calculation of Magnetic Field Strength H |
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81 | (1) |
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Solar Origins of Geomagnetic Storms |
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81 | (1) |
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Sunspot Cycles and Geomagnetic-Disturbance Cycles |
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82 | (1) |
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Earth-Surface Potential (ESP) and Geomagnetically Induced Current (GIC) |
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82 | (1) |
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Power System Effects of GIC |
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82 | (1) |
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System Model for Calculation of GIC |
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83 | (1) |
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Mitigation Techniques for GIC |
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84 | (1) |
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Conclusions Regarding GIC |
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84 | (1) |
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84 | (5) |
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84 | (1) |
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Factors Influencing Choice of Grounded or Ungrounded System |
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84 | (3) |
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Application Example 2.9: Propagation of a Surge through a Distribution Feeder with an Insulator Flashover |
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87 | (1) |
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Application Example 2.10: Lightning Arrester Operation |
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87 | (1) |
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88 | (1) |
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88 | (1) |
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89 | (1) |
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Calculation of Magnetic Forces |
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89 | (1) |
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Measurement of Derating of Three-Phase Transformers |
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89 | (9) |
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90 | (1) |
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Three-Phase Transformers in Δ-Δ or Y-Y Ungrounded Connection |
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90 | (1) |
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Three-Phase Transformers in Δ-Y Connection |
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91 | (1) |
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Accuracy Requirements for Instruments |
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92 | (1) |
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Comparison of Directly Measured Losses with Results of No-Load and Short-Circuit Tests |
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93 | (1) |
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A 4.5 kVA Three-Phase Transformer Bank #1 Feeding Full-Wave Rectifier |
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94 | (1) |
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A 4.5 kVA Three-Phase Transformer Bank #2 Supplying Power to Six-Step Inverter |
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94 | (1) |
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A 15 kVA Three-Phase Transformer Supplying Power to Resonant Rectifier |
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95 | (1) |
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A 15 kVA Three-Phase Transformer Bank Absorbing Power from a PWM Inverter |
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96 | (1) |
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Discussion of Results and Conclusions |
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97 | (1) |
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97 | (1) |
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Comparison with Existing Techniques |
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98 | (1) |
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98 | (1) |
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98 | (6) |
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104 | (3) |
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107 | (2) |
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Modeling and Analysis of Induction Machines |
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109 | (46) |
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Complete Sinusoidal Equivalent Circuit of a Three-Phase Induction Machine |
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110 | (3) |
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Application Example 3.1: Steady-State Operation of Induction Motor at Undervoltage |
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112 | (1) |
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Application Example 3.2: Steady-State Operation of Induction Motor at Overvoltage |
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112 | (1) |
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Application Example 3.3: Steady-State Operation of Induction Motor at Undervoltage and Under-Frequency |
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113 | (1) |
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Magnetic Fields of Three-Phase Machines for the Calculation of Inductive Machine Parameters |
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113 | (5) |
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Steady-State Stability of A Three-Phase Induction Machine |
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118 | (2) |
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Application Example 3.4: Unstable and Stable Steady-State Operation of Induction Machines |
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118 | (1) |
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Application Example 3.5: Stable Steady-State Operation of Induction Machines |
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118 | (1) |
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Resolving Mismatch of Wind-Turbine and Variable-Speed Generator Torque-Speed Characteristics |
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118 | (2) |
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Spatial (Space) Harmonics of a Three-Phase Induction Machine |
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120 | (2) |
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Time Harmonics of A Three-Phase Induction Machine |
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122 | (1) |
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Fundamental and Harmonic Torques of an Induction Machine |
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123 | (4) |
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The Fundamental Slip of an Induction Machine |
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124 | (1) |
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The Harmonic Slip of an Induction Machine |
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124 | (1) |
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The Reflected Harmonic Slip of an Induction Machine |
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125 | (1) |
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Reflected Harmonic Slip of an Induction Machine in Terms of Fundamental Slip |
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126 | (1) |
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Reflected Harmonic Slip of an Induction Machine in Terms of Harmonic Slip |
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127 | (1) |
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Measurement Results for Three- and Single-Phase Induction Machines |
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127 | (5) |
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Measurement of Nonlinear Circuit Parameters of Single-Phase Induction Motors |
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128 | (2) |
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Measurement of Current and Voltage Harmonics |
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130 | (1) |
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Measurement of Flux-Density Harmonics in Stator Teeth and Yokes (Back Iron) |
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130 | (2) |
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Application Example 3.6: Measurement of Harmonics within Yoke (Back Iron) and Tooth Flux Densities of Single-Phase Induction Machines |
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132 | (1) |
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Inter- and Subharmonic Torques of Three-Phase Induction Machines |
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132 | (2) |
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Subharmonic Torques in a Voltage-Source-Fed Induction Motor |
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132 | (1) |
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Subharmonic Torques in a Current-Source-Fed Induction Motor |
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133 | (1) |
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Application Example 3.7: Computation of Forward-Rotating SubharmonicTorque in Voltage-Source-Fed Induction Motor |
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134 | (1) |
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Application Example 3.8: Rationale for Limiting Harmonic Torques in an Induction Machine |
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134 | (1) |
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Application Example 3.9: Compulation of Forward-Rotating Subharmonic Torque in Current-Source-Fed Induction Motor |
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134 | (1) |
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Interaction of Space and Time Harmonics of Three-Phase Induction Machines |
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134 | (1) |
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Application Example 3.10: Computation of Rotating MMF with Time and Space Harmonics |
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134 | (1) |
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Application Example 3.11: Computation of Rotating MMF with Even Space Harmonics |
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135 | (1) |
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Application Example 3.12: Computation of Rotating MMF with Noninteger Space Harmonics |
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135 | (1) |
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Conclusions Concerning Induction Machine Harmonics |
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135 | (1) |
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Voltage-Stress Winding Failures of AC Motors FED by Variable-Frequency, Voltage- and Current-Source PWM Inverters |
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136 | (5) |
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Application Example 3.13: Calculation of Winding Stress Due to PWM Voltage-Source Inverters |
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137 | (2) |
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Application Example 3.14: Calculation of Winding Stress Due to PWM Current-Source Inverters |
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139 | (2) |
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Nonlinear Harmonic Models of Three-Phase Induction Machines |
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141 | (2) |
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Conventional Harmonic Model of an Induction Motor |
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141 | (1) |
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Modified Conventional Harmonic Model of an Induction Motor |
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141 | (1) |
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Simplified Conventional Harmonic Model of an Induction Motor |
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142 | (1) |
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Spectral-Based Harmonic Model of an Induction Machine with Time and Space Harmonics |
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142 | (1) |
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Static and Dynamic Rotor Eccentricity of Three-Phase Induction Machines |
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143 | (1) |
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Operation of Three-Phase Machines Within a Single-Phase Power System |
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144 | (1) |
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Classification of Three-Phase Induction Machines |
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144 | (1) |
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145 | (1) |
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145 | (5) |
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150 | (3) |
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153 | (2) |
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Modeling and Analysis of Synchronous Machines |
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155 | (54) |
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Sinusoidal State-Space Modeling of a Synchronous Machine in the Time Domain |
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156 | (2) |
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Electrical Equations of a Synchronous Machine |
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156 | (1) |
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Mechanical Equations of a Synchronous Machine |
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157 | (1) |
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Magnetic Saturation of a Synchronous Machine |
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158 | (1) |
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Sinusoidal Model of a Synchronous Machine in dqO Coordinates |
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158 | (1) |
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Steady-State, Transient, and Subtransient Operation |
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158 | (19) |
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Definition of Transient and Subtransient Reactances as a Function of Leakage and Mutual Reactances |
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160 | (4) |
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Phasor Diagrams for Round-Rotor Synchronous Machines |
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164 | (1) |
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Consumer (Motor) Reference Frame |
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164 | (1) |
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Generator Reference Frame |
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164 | (1) |
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Similarities between Synchronous Machines and Pulse-Width-Modulated (PWM) Current-Controlled, Voltage-Source Inverters |
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165 | (1) |
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Phasor Diagram of a Salient-Pole Synchronous Machine |
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165 | (2) |
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Application Example 4.1: Steady-State Analysis of a Nonsalient-Pole (Round-Rotor) Synchronous Machine |
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167 | (1) |
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Application Example 4.2: Calculation of the Synchronous Reactance Xs of a Cylindrical-Rotor (Round-Rotor, Nonsalient-Pole) Synchronous Machine |
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167 | (2) |
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Application Example 4.3: dqO Modeling of a Salient-Pole Synchronous Machine |
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169 | (1) |
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Application Example 4.4: Calculation of the Amortisseur (Damper Winding) Bar Losses of a Synchronous Machine during a Balanced Three-Phase Short-Circuit, Line-to-Line Short-Circuit, Out-of-Phase Synchronization, and Unbalanced Load Based on the Natural abc Reference System |
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169 | (1) |
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Application Example 4.5: Measured Voltage Ripple of a 30 kVA Permanent-Magnet Synchronous Machine, Designed for a Direct-Drive Wind-Power Plant |
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170 | (1) |
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Application Example 4.6: Calculation of Synchronous Reactances Xd and Xq from Measured Data Based on Phasor Diagram |
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170 | (1) |
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Application Example 4.7: Design of a Low-Speed 20 kW Permanent-Magnet Generator for a Wind-Power Plant |
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171 | (1) |
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Application Example 4.8: Design of a 10 kW Wind-Power Plant Based on a Synchronous Machine |
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172 | (2) |
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Synchronous Machines Supplying Nonlinear Loads |
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174 | (1) |
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Switched-Reluctance Machine |
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175 | (1) |
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Some Design Guidelines for Synchronous Machines |
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175 | (1) |
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175 | (1) |
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Recommended Current Densities |
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175 | (1) |
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Relation between Induced Ephase and Terminal Vphas Voltages |
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175 | (1) |
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Iron-Core Stacking Factor and Copper-Fill Factor |
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175 | (1) |
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Winding Forces during Normal Operation and Faults |
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175 | (2) |
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177 | (1) |
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Harmonic Modeling of a Synchronous Machine |
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177 | (17) |
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Model of a Synchronous Machine as Applied to Harmonic Power Flow |
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178 | (1) |
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Definition of Positive-Negative-, and Zero-Sequence Impedances/Reactances |
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179 | (1) |
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Relations between Positive-, Negative-, and Zero-Sequence Reactances and Synchronous, Transient, and Subtransient Reactances |
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180 | (1) |
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Synchronous Machine Harmonic Model Based on Transient Inductances |
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180 | (2) |
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Application Example 4.9: Measured Current Spectrum of a Synchronous Machine |
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182 | (1) |
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Synchronous Machine Model with Harmonic Parameters |
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182 | (1) |
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Application Example 4.10: Harmonic Modeling of a 24-Bus Power System with Asymmetry in Transmission Lines |
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183 | (1) |
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Application Example 4.11: Harmonic Modeling of a 24-Bus Power System with a Nonlinear Static VAr Compensator (SVC) |
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184 | (1) |
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Synchronous Machine Harmonic Model with Imbalance and Saturation Effects |
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184 | (2) |
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Synchronous Machine Harmonic Model Based on dqO Coordinates |
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186 | (1) |
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Synchronous Machine Harmonic Model Based on abc Coordinates |
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187 | (1) |
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Computation of Synchronous Machine Injected Harmonic Currents [ Inl(h)] |
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188 | (2) |
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Application Example 4.12: Effect of Frequency Conversion on Synchronous Machine Negative-Sequence Impedance |
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190 | (1) |
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Application Example 4.13: Effect of Imbalance on Power Quality of Synchronous Machines |
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190 | (1) |
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Application Example 4.14: Effect of Delta Connection on Power Quality of Synchronous Machines |
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191 | (1) |
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Application Example 4.15: Effect of Saturation on Power Quality of Synchronous Machines |
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191 | (1) |
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Application Example 4.16: Impact of Nonlinear Loads on Power Quality of Synchronous Machines |
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192 | (1) |
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Static- and Dynamic-Rotor Eccentricities Generating Current and Voltage Harmonics |
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192 | (2) |
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Shaft Flux and Bearing Currents |
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194 | (1) |
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194 | (1) |
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194 | (1) |
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195 | (9) |
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204 | (3) |
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207 | (2) |
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Interaction of Harmonics with Capacitors |
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209 | (18) |
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Application of Capacitors to Power-Factor Correction |
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209 | (4) |
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Definition of Displacement Power Factor |
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210 | (1) |
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Total Power Factor in the Presence of Harmonics |
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211 | (1) |
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Application Example 5.1: Computation of Displacement Power Factor (DPF) and Total Power Factor (TPF) |
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212 | (1) |
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Benefits of Power-Factor Correction |
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212 | (1) |
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Application of Capacitors to Reactive Power Compensation |
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213 | (1) |
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Application of Capacitors to Harmonic Filtering |
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214 | (1) |
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Application Example 5.2: Design of a Tuned Harmonic Filter |
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214 | (1) |
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Power Quality Problems Associated With Capacitors |
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214 | (3) |
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Transients Associated with Capacitor Switching |
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214 | (1) |
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215 | (1) |
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Application Example 5.3: Harmonic Resonance in a Distorted Industrial Power System with Nonlinear Loads |
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216 | (1) |
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Application Example 5.4: Parallel Resonance Caused by Capacitors |
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217 | (1) |
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Application Example 5.5: Series Resonance Caused by Capacitors |
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217 | (1) |
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Application Example 5.6: Protecting Capacitors by Virtual Harmonic Resistors |
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217 | (1) |
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Frequency and Capacitance Scanning |
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217 | (1) |
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Application Example 5.7: Frequency and Capacitance Scanning |
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218 | (1) |
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Harmonic Constraints for Capacitors |
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218 | (3) |
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Harmonic Voltage Constraint for Capacitors |
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219 | (1) |
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Harmonic Current Constraint for Capacitors |
|
|
219 | (1) |
|
Harmonic Reactive-Power Constraint for Capacitors |
|
|
219 | (1) |
|
Permissible Operating Region for Capacitors in the Presence of Harmonics |
|
|
220 | (1) |
|
Application Example 5.8: Harmonic Limits for Capacitors when Used in a Three-Phase System |
|
|
220 | (1) |
|
Equivalent Circuits of Capacitors |
|
|
221 | (1) |
|
Application Example 5.9: Harmonic Losses of Capacitors |
|
|
222 | (1) |
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|
222 | (1) |
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|
223 | (3) |
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226 | (1) |
|
Lifetime Reduction of Transformers and Induction Machines |
|
|
227 | (34) |
|
Rationale for Relying on the Worst-Case Conditions |
|
|
228 | (1) |
|
Elevated Temperature Rise Due to Voltage Harmonics |
|
|
228 | (1) |
|
Weighted-Harmonic Factors |
|
|
228 | (8) |
|
Weighted-Harmcnic Factor for Single-Phase Transformers |
|
|
229 | (1) |
|
Measured Temperature Increases of Transformers |
|
|
230 | (1) |
|
Single-Phase Transformers |
|
|
230 | (1) |
|
|
|
231 | (1) |
|
Weighted-Harmonic Factor for Three-Phase Induction Machines |
|
|
231 | (3) |
|
Calculated Harmonic Losses and Measured Temperature Increases of Induction Machines |
|
|
234 | (1) |
|
Single-Phase Induction Motors |
|
|
234 | (1) |
|
Three-Phase Induction Motors |
|
|
235 | (1) |
|
Exponents of Weighted-Harmonic Factors |
|
|
236 | (2) |
|
Additional Losses or Temperature Rises Versus Weighted-Harmonic Factors |
|
|
238 | (2) |
|
Application Example 6.1: Temperature Rise of a Single-Phase Transformer Due to Single Harmonic Voltage |
|
|
239 | (1) |
|
Application Example 6.2: Temperature Rise of a Single-Phase Induction Motor Due to Single Harmonic Voltage |
|
|
239 | (1) |
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|
240 | (1) |
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240 | (1) |
|
Decrease of Lifetime Due to an Additional Temperature Rise |
|
|
241 | (1) |
|
Application Example 6.3: Aging of a Single-Phase Induction Motor with E = 0.74 eV Due to a Single Harmonic Voltage |
|
|
241 | (1) |
|
Application Example 6.4: Aging of a Single-Phase Induction Motor with E = 0.51 eV Due to a Single Harmonic Voltage |
|
|
241 | (1) |
|
Reduction of Lifetime of Components With Activation Energy E = 1.1 EV Due to Harmonics of the Terminal Voltage Within Residential or Commercial Utility Systems |
|
|
242 | (1) |
|
Possible Limits for Harmonic Voltages |
|
|
242 | (2) |
|
Application Example 6.5: Estimation of Lifetime Reduction for Given Single-Phase and Three-Phase Voltage Spectra with High Harmonic Penetration with Activation Energy E= 1.1 eV |
|
|
243 | (1) |
|
Application Example 6.6: Estimation of Lifetime Reduction for Given Single-Phase and Three-Phase Voltage Spectra with Moderate Harmonic Penetration with Activation Energy E = 1.1 eV |
|
|
243 | (1) |
|
Probabilistic and Time-Varying Nature of Harmonics |
|
|
244 | (1) |
|
|
|
244 | (1) |
|
Temperature as A Function of Time |
|
|
244 | (1) |
|
Application Example 6.7: Temperature Increase of Rotating Machine with a Step Load |
|
|
245 | (1) |
|
Various Operating Modes of Rotating Machines |
|
|
245 | (7) |
|
|
|
246 | (1) |
|
|
|
246 | (1) |
|
Steady State with Short-Term Operation |
|
|
247 | (1) |
|
|
|
247 | (1) |
|
Steady State with Intermittent Operation |
|
|
247 | (1) |
|
Application Example 6.8: Steady State with Superimposed Periodic Intermittent Operation with Irregular Load Steps |
|
|
248 | (1) |
|
Reduction of Vibrations and Torque Pulsations in Electric Machines |
|
|
249 | (1) |
|
Application Example 6.9: Reduction of Harmonic Torques of a Piston-Compressor Drive with Synchronous Motor as Prime Mover |
|
|
249 | (1) |
|
Calculation of Steady-State Temperature Rise ΔT of Electric Apparatus Based on Thermal Networks |
|
|
250 | (2) |
|
Application Example 6.10: Temperature-Rise Equations for a Totally Enclosed Fan-Cooled 100 hp Motor |
|
|
252 | (1) |
|
Application Example 6.11: Temperature-Rise Equations for a Drip-Proof 5 hp Motor |
|
|
252 | (1) |
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|
252 | (1) |
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|
|
253 | (5) |
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|
258 | (3) |
|
Power System Modeling under Nonsinusoidal Operating Conditions |
|
|
261 | (40) |
|
Overview of A Modern Power System |
|
|
261 | (2) |
|
|
|
263 | (7) |
|
|
|
263 | (1) |
|
Application Example 7.1: A Simple Power System Configuration |
|
|
263 | (2) |
|
Application Example 7.2: Construction of Bus Admittance Matrix |
|
|
265 | (1) |
|
Application Example 7.3: Building of Nonsingular Bus Admittance Matrix |
|
|
266 | (1) |
|
Application Example 7.4: Building of Singular Bus Admittance Matrix |
|
|
266 | (1) |
|
|
|
267 | (1) |
|
Application Example 7.5: Matrix Multiplication |
|
|
267 | (1) |
|
Application Example 7.6: Triangular Factorization |
|
|
267 | (2) |
|
|
|
269 | (1) |
|
Application Example 7.7: Jacobian Matrices |
|
|
269 | (1) |
|
|
|
270 | (7) |
|
Fundamental Bus Admittance Matrix |
|
|
271 | (1) |
|
Newton-Raphson Power Flow Formulation |
|
|
271 | (3) |
|
Fundamental Jacobian Entry Formulas |
|
|
274 | (2) |
|
Newton-Raphson Power Flow Algorithm |
|
|
276 | (1) |
|
Application Example 7.8: Computation of Fundamental Admittance Matrix |
|
|
276 | (1) |
|
Application Example 7.9: Evaluation of Fundamental Mismatch Vector |
|
|
277 | (1) |
|
Application Example 7.10: Evaluation of Fundamental Jacobian Matrix |
|
|
277 | (1) |
|
Application Example 7.11: Calculation of the Inverse of Jacobian Matrix |
|
|
277 | (1) |
|
Application Example 7.12: Inversion of a 3 x 3 Matrix |
|
|
277 | (1) |
|
Application Example 7.13: Computation of the Correction Voltage Vector |
|
|
277 | (1) |
|
Newton-Based Harmonic Power Flow |
|
|
277 | (10) |
|
Harmonic Bus Admittance Matrix and Power Definitions |
|
|
278 | (1) |
|
Modeling of Nonlinear and Linear Loads at Harmonic Frequencies |
|
|
279 | (1) |
|
The Harmonic Power Flow Algorithm (Assembly of Equations) |
|
|
279 | (2) |
|
Formulation of the Newton-Raphson Approach for Harmonic Power Flow |
|
|
281 | (3) |
|
Harmonic Jacobian Entry Formulas Related to Line Currents |
|
|
284 | (1) |
|
Newton-Based Harmonic Power Flow Algorithm |
|
|
285 | (1) |
|
Application Example 7.14: Computation of Harmonic Admittance Matrix |
|
|
286 | (1) |
|
Application Example 7.15: Computation of Nonlinear Load Harmonic Currents |
|
|
286 | (1) |
|
Application Example 7.16: Evaluation of Harmonic Mismatch Vector |
|
|
286 | (1) |
|
Application Example 7.17: Evaluation of Fundamental and Harmonic Jacobian Submatrices |
|
|
287 | (1) |
|
Application Example 7.18: Computation of the Correction Bus Vector and Convergence of Harmonic Power Flow |
|
|
287 | (1) |
|
Classification of Harmonic Power Flow Techniques |
|
|
287 | (6) |
|
Decoupled Harmonic Power Flow |
|
|
287 | (2) |
|
|
|
289 | (1) |
|
Modified Fast Decoupled Harmonic Power Flow |
|
|
290 | (1) |
|
Fuzzy Harmonic Power Flow |
|
|
290 | (1) |
|
Probabilistic Harmonic Power Flow |
|
|
290 | (2) |
|
Modular Harmonic Power Flow |
|
|
292 | (1) |
|
Application Example 7.19: Accuracy of Decoupled Harmonic Power Flow |
|
|
293 | (1) |
|
|
|
293 | (1) |
|
|
|
294 | (5) |
|
|
|
299 | (2) |
|
Impact of Poor Power Quality on Reliability, Relaying, and Security |
|
|
301 | (58) |
|
|
|
301 | (2) |
|
Application Example 8.1: Calculation of Reliability Indices |
|
|
302 | (1) |
|
Degradation of Reliability and Security Due to Poor Power Quality |
|
|
303 | (13) |
|
Single-Time and Nonperiodic Events |
|
|
303 | (1) |
|
Harmonics and Interharmonics Affecting Overcurrent and Under-Frequency Relay Operation |
|
|
304 | (1) |
|
|
|
305 | (1) |
|
Electromagnetic Field (EMF) Generation and Corona Effects in Transmission Lines |
|
|
305 | (1) |
|
|
|
305 | (1) |
|
Application Example 8.2: Lateral Profile of Electric Field at Ground Level below a Three-Phase Transmission Line |
|
|
305 | (1) |
|
Application Example 8.3: Lateral Profile of Magnetic Field at Ground Level under a Three-Phase Transmission Line |
|
|
306 | (1) |
|
|
|
306 | (1) |
|
Factors Reducing the Effects of EMFs |
|
|
307 | (1) |
|
Factors Influencing Generation of Corona |
|
|
308 | (1) |
|
Application Example 8.4: Onset of Corona in a Transmission Line |
|
|
308 | (1) |
|
Negative Effects of EMFs and Corona |
|
|
308 | (2) |
|
Solutions for the Minimization of EMFs, Corona, and Other Environmental Concerns in Newly Designed Transmission Lines |
|
|
310 | (2) |
|
|
|
312 | (1) |
|
No-Cost/Low-Cost EMF Mitigation Hearings of PUC of California |
|
|
312 | (1) |
|
|
|
313 | (1) |
|
Distributed-, Cogeneration, and Frequency/Voltage Control |
|
|
314 | (1) |
|
Application Example 8.5: Frequency Control of an Interconnected Power System Broken into Two Areas: The First One with a 300 MW Coal-Fired Plant and the Other One with a 5 MW Wind-Power Plant |
|
|
314 | (1) |
|
Application Example 8.6: Frequency Control of an Interconnected Power System Broken into Two Areas: The First One with a 5 MW Wind-Power Plant and the Other One with a 5 MW Photovoltaic Plant |
|
|
315 | (1) |
|
Tools for Detecting Poor Power Quality |
|
|
316 | (10) |
|
|
|
316 | (1) |
|
Application Example 8.7: Detection of Harmonic Power Flow Direction at Point of Common Coupling (PCC) |
|
|
317 | (1) |
|
|
|
318 | (1) |
|
Review of Existing Methods |
|
|
318 | (1) |
|
|
|
319 | (4) |
|
Accuracy Requirements for Instruments |
|
|
323 | (1) |
|
Application Example 8.8: Conventional Approach PLOSS = Pin - Pout |
|
|
323 | (1) |
|
Application Example 8.9: New Approach pcu = i'2(v1 - v'2) and Pfe = v1(i1-i'2) |
|
|
323 | (1) |
|
Application Example 8.10: Back-to-Back Approach of Two Transformers Simulated with CTs and PTs |
|
|
324 | (1) |
|
Application Example 8.11: Three-Phase Transformer with DC Bias Current |
|
|
324 | (1) |
|
Discussion of Results and Conclusions |
|
|
325 | (1) |
|
|
|
326 | (1) |
|
SCADA and National Instrument Labview Software |
|
|
326 | (1) |
|
Tools for Improving Reliability and Security |
|
|
326 | (10) |
|
Fast Interrupting Switches and Fault-Current Limiters |
|
|
327 | (1) |
|
Application Example 8.12: Insertion of a Fault Current Limiter (FCL) in the Power System |
|
|
328 | (1) |
|
Intentional Islanding, Interconnected, Redundant, and Self-Healing Power Systems |
|
|
329 | (1) |
|
|
|
330 | (1) |
|
|
|
331 | (3) |
|
Voltage Regulation, Ride-Through Capabilities of Load Components: CBEMA, ITIC Tolerance Curves, and SEMI F47 Standard |
|
|
334 | (1) |
|
Application Example 8.13: Ride-Through Capability of Computers and Semiconductor Manufacturing Equipment |
|
|
335 | (1) |
|
Backup, Emergency, or Standby Power Systems (Diesel-Generator Set, Batteries, Flywheels, Fuel Cells, Supercapacitors) |
|
|
335 | (1) |
|
Automatic Disconnect of Distributed Generators in Case of Failure of Central Power Station(s) |
|
|
336 | (1) |
|
Load Shedding and Load Management |
|
|
336 | (1) |
|
|
|
336 | (1) |
|
Matching the Operation of Intermittent Renewable Power Plants With Energy Storage |
|
|
336 | (2) |
|
Application Example 8.14: Design of a Hydro Pumped-Storage Facility Supplied by Energy from a Wind Farm |
|
|
336 | (1) |
|
Application Example 8.15: Peak-Power Tracker for Photovoltaic Power Plants |
|
|
337 | (1) |
|
|
|
338 | (1) |
|
|
|
339 | (12) |
|
|
|
351 | (7) |
|
|
|
358 | (1) |
|
The Roles of Filters in Power Systems |
|
|
359 | (38) |
|
|
|
359 | (2) |
|
Classification of Filters Employed in Power Systems |
|
|
361 | (1) |
|
Passive Filters as Used in Power Systems |
|
|
362 | (13) |
|
|
|
363 | (1) |
|
Common Types of Passive Filters for Power Quality Improvement |
|
|
364 | (1) |
|
First-Order, High-Pass Filter |
|
|
365 | (1) |
|
First-Order Damped High-Pass Filter |
|
|
366 | (1) |
|
Second-Order Band-Pass Filter |
|
|
367 | (2) |
|
Second-Order Damped Band-Pass Filter |
|
|
369 | (1) |
|
|
|
370 | (1) |
|
Classification of Passive Power Filters |
|
|
370 | (1) |
|
Potentials and Limitations of Passive Power Filters |
|
|
371 | (2) |
|
Application Example 9.1: Hybrid Passive Filter Design to Improve the Power Quality of the IEEE 30-Bus Distribution System Serving Adjustable-Speed Drives |
|
|
373 | (2) |
|
|
|
375 | (3) |
|
Classification of Active Power Filters Based on Topology and Supply System |
|
|
375 | (1) |
|
Classification of Active Power Filters Based on Power Rating |
|
|
375 | (3) |
|
|
|
378 | (4) |
|
Classification of Hybrid Filters |
|
|
378 | (4) |
|
Block Diagram of Active Filters |
|
|
382 | (1) |
|
|
|
383 | (9) |
|
Derivation of Reference Signal using Waveform Compensation |
|
|
385 | (1) |
|
Waveform Compensation using Time-Domain Filtering |
|
|
385 | (2) |
|
Waveform Compensation using Frequency-Domain Filtering |
|
|
387 | (1) |
|
Other Methods for Waveform Compensation |
|
|
387 | (1) |
|
Derivation of Compensating Signals using Instantaneous Power Compensation |
|
|
388 | (1) |
|
Application Example 9.2: Instantaneous Power for Sinusoidal Supply Voltages and Distorted Load Currents |
|
|
389 | (1) |
|
Application Example 9.3: Instantaneous Power Consumed by a Resistive Load Subjected to Distorted Supply Voltages |
|
|
389 | (1) |
|
Application Example 9.4: Supply Current Distortion Caused by Active Filters with Instantaneous Power-Based Controllers |
|
|
390 | (1) |
|
Derivation of Compensating Signals using Impedance Synthesis |
|
|
390 | (1) |
|
|
|
390 | (1) |
|
Impedance-Based Compensation |
|
|
390 | (1) |
|
|
|
391 | (1) |
|
Generation of Compensation Signal using Reference-Following Techniques |
|
|
391 | (1) |
|
Application Example 9.5: Hybrid of Passive and Active Power Filters for Harmonic Mitigation of Six-Pulse and Twelve-Pulse Rectifier Loads |
|
|
392 | (1) |
|
|
|
392 | (3) |
|
|
|
395 | (2) |
|
Optimal Placement and Sizing of Shunt Capacitor Banks in the Presence of Harmonics |
|
|
397 | (46) |
|
Reactive Power Compensation |
|
|
398 | (2) |
|
Benefits of Reactive Power Compensation |
|
|
398 | (1) |
|
Drawbacks of Reactive Power Compensation |
|
|
399 | (1) |
|
Common Types Of Distribution Shunt Capacitor Banks |
|
|
400 | (2) |
|
Open-Rack Shunt Capacitor Bank |
|
|
400 | (1) |
|
Pole-Mounted Capacitor Bank |
|
|
401 | (1) |
|
|
|
401 | (1) |
|
Enclosed Fixed Capacitor Bank |
|
|
402 | (1) |
|
Enclosed Switched Capacitor Bank |
|
|
402 | (1) |
|
Classification Of Capacitor Allocation Techniques For Sinusoidal Operating Condition |
|
|
402 | (11) |
|
|
|
402 | (1) |
|
Numerical Programming Methods |
|
|
403 | (1) |
|
|
|
403 | (1) |
|
Artificial Intelligence-Based (AI-Based) Method |
|
|
404 | (1) |
|
|
|
404 | (3) |
|
|
|
407 | (1) |
|
|
|
407 | (1) |
|
Artificial Neural Networks |
|
|
407 | (1) |
|
|
|
408 | (2) |
|
|
|
410 | (1) |
|
|
|
410 | (1) |
|
|
|
411 | (1) |
|
Sequential Quadratic Programming |
|
|
411 | (1) |
|
Application Example 10.1: Fuzzy Capacitor Placement in an 11 kV, 34-Bus Distribution System with Lateral Branches under Sinusoidal Operating Conditions |
|
|
411 | (1) |
|
Application Example 10.2: Genetically Optimized Placement of Capacitor Banks in an 11 kV, 34-Bus Distribution System with Lateral Branches under Sinusoidal Operating Condition |
|
|
411 | (2) |
|
Optimal Placement And Sizing Of Shunt Capacitor Banks In The Presence Of Harmonics |
|
|
413 | (22) |
|
Reformulation of the Capacitor Allocation Problem to Account for Harmonic |
|
|
414 | (1) |
|
System Model at Fundamental and Harmonic Frequencies |
|
|
414 | (1) |
|
|
|
414 | (1) |
|
Objective Function (Cost Index) |
|
|
414 | (1) |
|
Application of Maximum Sensitivities Selection (MSS) for the Capacitor Allocation Problem |
|
|
415 | (1) |
|
Sensitivity Functions for MSS |
|
|
415 | (1) |
|
|
|
415 | (2) |
|
Convergence of the MSS Algorithm |
|
|
417 | (1) |
|
Application of Local Variation (LV) for the Capacitor Allocation Problem |
|
|
417 | (1) |
|
A Hybrid MSS-LV Algorithm for the Capacitor Allocation Problem |
|
|
417 | (1) |
|
Application Example 10.3: Optimal Placement and Sizing of Capacitor Banks in the Distorted 18-Bus IEEE Distribution System by MSS and MSS-LV Methods |
|
|
417 | (2) |
|
Fuzzy Approach for the Optimal Placement and Sizing of Capacitor Banks in the Presence of Harmonics |
|
|
419 | (2) |
|
Sensitivity of Objective Function and THD |
|
|
421 | (1) |
|
|
|
421 | (2) |
|
|
|
423 | (1) |
|
Application Example 10.4: Optimal Placement and Sizing of Capacitor Banks in the Distorted 18-Bus IEEE Distribution System by Fuzzy Expert System |
|
|
424 | (1) |
|
Optimal Placement, Replacement, and Sizing of Capacitor Banks in Distorted Distribution Networks by Genetic Algorithms |
|
|
425 | (1) |
|
|
|
425 | (1) |
|
|
|
426 | (2) |
|
Application Example 10.5: Optimal Placement and Sizing of Capacitor Banks in the 6-Bus IEEE Distorted System |
|
|
428 | (1) |
|
Application Example 10.6: Optimal Placement and Sizing of Capacitor Banks in the 18-Bus IEEE Distorted System |
|
|
429 | (1) |
|
Genetically Optimized Fuzzy Placement and Sizing of Capacitor Banks in Distorted Distribution Networks |
|
|
430 | (1) |
|
|
|
430 | (2) |
|
Application Example 10.7: Genetically Optimized Fuzzy Placement and Sizing of Capacitor Banks in the 18-Bus IEEE Distorted System |
|
|
432 | (1) |
|
Application Example 10.8: Genetically Optimized Fuzzy Placement and Sizing of Capacitor Banks in the 123-Bus IEEE System with 20 Nonlinear Loads |
|
|
433 | (2) |
|
|
|
435 | (4) |
|
|
|
439 | (4) |
|
Unified Power Quality Conditioner (UPQC) |
|
|
443 | (26) |
|
Compensation Devices at Fundamental and Harmonic Frequencies |
|
|
444 | (3) |
|
Conventional Compensation Devices |
|
|
444 | (1) |
|
Flexible AC Transmission Systems (FACTS) |
|
|
444 | (1) |
|
|
|
445 | (1) |
|
Active Power Line Conditioner (APLC) |
|
|
446 | (1) |
|
Remark Regarding Compensation Devices |
|
|
446 | (1) |
|
Unified Power Quality Conditioner (UPQC) |
|
|
447 | (3) |
|
|
|
447 | (1) |
|
|
|
448 | (1) |
|
Operation of the UPQC with Unbalanced and Distorted System Voltage and Load Current |
|
|
448 | (1) |
|
Operation of UPQC with Unbalanced System Voltages and Load Currents |
|
|
449 | (1) |
|
|
|
450 | (1) |
|
Pattern of Reference Signals |
|
|
451 | (1) |
|
UPQC Control Using the Park (DQ0) Transformation |
|
|
451 | (2) |
|
General Theory of the Park (dq0) Transformation |
|
|
451 | (1) |
|
Control of Series Converter Based on the dq0 Transformation |
|
|
452 | (1) |
|
Control of Shunt Converter Relying on the dq0 Transformation |
|
|
452 | (1) |
|
Control of DC Link Voltage using the dq0 Transformation |
|
|
453 | (1) |
|
UPQC Control Based on the Instantaneous Real and Imaginary Power Theory |
|
|
453 | (7) |
|
Theory of Instantaneous Real and Imaginary Power |
|
|
453 | (1) |
|
Application Example 11.1: The αβ0 Transformation for Three-Phase Sinusoidal System Supplying a Linear Load |
|
|
454 | (1) |
|
Application Example 11.2: The αβ0 Transformation for Three-Phase Sinusoidal System Supplying a Nonlinear Load |
|
|
455 | (1) |
|
Application Example 11.3: The αβ0 Transformation for Unbalanced Three-Phase, Four-Wire System Supplying a Linear Load |
|
|
455 | (1) |
|
UPQC Control System Based on Instantaneous Real and Imaginary Powers |
|
|
456 | (1) |
|
Phase-Lock Loop (PLL) Circuit |
|
|
456 | (1) |
|
Positive-Sequence Voltage Detector (PSVD) |
|
|
457 | (1) |
|
Control of Shunt Converter using Instantaneous Power Theory |
|
|
457 | (1) |
|
Control of DC Voltage using Instantaneous Power Theory |
|
|
458 | (1) |
|
Control of Series Converter using Instantaneous Power Theory |
|
|
459 | (1) |
|
|
|
460 | (6) |
|
Application Example 11.4: Dynamic Behavior of UPQC for Current Compensation |
|
|
462 | (1) |
|
Application Example 11.5: UPQC Compensation of Voltage Harmonics |
|
|
462 | (1) |
|
Application Example 11.6: UPQC Compensation of Voltage Imbalance |
|
|
462 | (1) |
|
Application Example 11.7: Dynamic Performance of UPQC for Sudden Voltage Variation |
|
|
462 | (1) |
|
Application Example 11.8: Damping of Harmonic Oscillations Using a UPQC |
|
|
462 | (2) |
|
Application Example 11.9: UPQC Compensation of Flicker |
|
|
464 | (2) |
|
|
|
466 | (2) |
|
|
|
468 | (1) |
| Appendix 1: Sampling Techniques |
|
469 | (4) |
| Appendix 2: Program List for Fourier Analysis |
|
473 | (6) |
| Appendix 3: Program List for Propagation of a Surge Through a Distribution Feeder With an Insulator Flashover |
|
479 | (2) |
| Appendix 4: Program List for Lightning Arrester Operation |
|
481 | (2) |
| Appendix 5: Equipment for Tests |
|
483 | (2) |
| Appendix 6: Measurement Error of Powers |
|
485 | (2) |
Appendix 7: Application Examples, Divided by
Chapter |
|
487 | (144) |
| Index |
|
631 | |
