Analysis of Synchronous Machines

Winding Distribution in an Ideal Machine Introduction The Winding Function Calculation of the Winding Function Multipole Winding Configurations Inductances of an Ideal Doubly Cylindrical Machine Calculation of Winding Inductances Mutual Inductance Calculation-An Example Winding Functions for Multiple Circuits Analysis of a Shorted Coil-An Example General Case for C Circuits Winding Function Modifications for Salient-Pole Machines Leakage Inductances of Synchronous Machines Practical Winding Design Reference Frame Theory Introduction Rotating Reference Frames Transformation of Three-Phase Circuit Variables to a Rotating Reference Frame Stationary Three-Phase r-L Circuits Observed in a d-q-n Reference Frame Matrix Approach to the d-q-n Transformation The d-q-n Transformation Applied to a Simple Three-Phase Cylindrical Inductor Winding Functions in a d-q-n Reference Frame Direct Computation of d-q-n Inductances of a Cylindrical Three-Phase Inductor The d-q Equations of a Synchronous Machine Introduction Physical Description Synchronous Machine Equations in the Phase Variable or as-, bs-, cs- Reference Frame Transformation of the Stator Voltage Equations to a Rotating Reference Frame Transformation of Stator Flux Linkages to a Rotating Reference Frame Winding Functions of the Three-Phase Stator Windings in a d-q-n Reference Frame Winding Functions of the Rotor Windings Calculation of Stator Magnetizing Inductances Mutual Inductances between Stator and Rotor Circuits d-q Transformation of the Rotor Flux Linkage Equation Power Input Torque Equation Summary of Synchronous Machine Equations Expressed in Physical Units Turns Ratio Transformation of the Flux Linkage Equations System Equations in Physical Units Using Hybrid Flux Linkages Synchronous Machine Equations in Per Unit Form Steady-State Behavior of Synchronous Machines Introduction d-q Axes Orientation Steady-State Form of Park's Equations Steady-State Torque Equation Steady-State Power Equation Steady-State Reactive Power Graphical Interpretation of the Steady-State Equations Steady-State Vector Diagram Vector Interpretation of Power and Torque Phasor Form of the Steady-State Equations Equivalent Circuits of a Synchronous Machine Solutions of the Phasor Equations Solution of the Steady-State Synchronous Machine Equations Using MathCAD Open-Circuit and Short-Circuit Characteristics Saturation Modeling of Synchronous Machines Under Load Construction of the Phasor Diagram for a Saturated Round-Rotor Machine Calculation of the Phasor Diagram for a Saturated Salient-Pole Synchronous Machine Zero Power Factor Characteristic and the Potier Triangle Other Reactance Measurements Steady-State Operating Characteristics Calculation of Pulsating and Average Torque during Starting of Synchronous Motors Transient Analysis of Synchronous Machines Introduction Theorem of Constant Flux Linkages Behavior of Stator Flux Linkages on Short-Circuit Three-Phase Short-Circuit, No Damper Circuits, Resistances Neglected Three-Phase Short-Circuit from Open Circuit, Resistances and Damper Windings Neglected Short-Circuit from Loaded Condition, Stator Resistance and Damper Winding Neglected Three-Phase Short-Circuit from Open Circuit, Effect of Resistances Included, No Dampers Extension of the Theory to Machines with Damper Windings Short-Circuit of a Loaded Generator, Dampers Included Vector Diagrams for Sudden Voltage Changes Effect of Exciter Response Transient Solutions Utilizing Modal Analysis Comparison of Modal Analysis Solution with Conventional Methods Unsymmetrical Short-Circuits Power System Transient Stability Introduction Assumptions Torque Angle Curves Mechanical Acceleration Equation in Per Unit Equal Area Criterion for Transient Stability Transient Stability Analysis Transient Stability of a Two Machine System Multi-Machine Transient Stability Analysis Types of Faults and Effect on Stability Step-by-Step Solution Methods Including Saturation Machine Model Including Saturation Summary-Step-by-Step Method for Calculating Synchronous Machine Transients Excitation Systems and Dynamic Stability Introduction Generator Response to System Disturbances Sources of System Damping Excitation System Hardware Implementations IEEE Type 1 Excitation System Excitation Design Principles Effect of the Excitation System on Dynamic Stability Naturally Commutated Synchronous Motor Drives Introduction Load Commutated Inverter (LCI) Synchronous Motor Drives Principle of Inverter Operation Fundamental Component Representation Control Considerations Starting Considerations Detailed Steady-State Analysis Time Step Solution Sample Calculations Torque Capability Curves Constant Speed Performance Comparison of State Space and Phasor Diagram Solutions Extension of d-q Theory to Unbalanced Operation Introduction Source Voltage Formulation System Equations to Be Solved System Formulation with Non-Sinusoidal Stator Voltages Solution for Currents Solution for Electromagnetic Torque Example Solutions Linearization of the Synchronous Machine Equations Introduction Park's Equations in Physical Units Linearization Process Transfer Functions of a Synchronous Machine Solution of the State Space and Measurement Equations Design of a Terminal Voltage Controller Design of a Classical Regulator Computer Simulation of Synchronous Machines Introduction Simulation Equations MATLAB (R) Simulation of Park's Equations Steady-State Check of Simulation Simulation of the Equations of Transformation Simulation Study Consideration of Saturation Effects Air Gap Saturation Field Saturation Approximate Models of Synchronous Machines Appendix 1: Identities Useful in AC Machine Analysis Appendix 2: Time Domain Solution of the State Equation Appendix 3: Three-Phase Fault Appendix 4: TrafunSM Appendix 5: SMHB Synchronous Machine Harmonic Balance