Paul C. Krause - Reference Frame Theory

1 Cover

2 IEE Press Series on Power Engineering

3 Reference Frame Theory

4 Copyright

5 About the Author

6 Preface

7 1 A Brief History of Reference Frame Theory References

8 2 Tesla's Rotating Magnetic Field2.1 Introduction 2.2 Rotating Magnetic Field for Symmetrical Two‐Phase Stator Windings 2.3 Rotating Magnetic Field for Symmetrical Three‐Phase Stator Windings 2.4 Rotating Magnetic Field for Symmetrical Two‐Phase Rotor Windings 2.5 Rotating Magnetic Field for Symmetrical Three‐Phase Rotor Windings 2.6 Closing Comments References

9 3 Tesla's Rotating Magnetic Field and Reference Frame Theory3.1 Introduction 3.2 Transformation of Two‐Phase Symmetrical Stator Variables to the Arbitrary Reference Frame 3.3 Transformation of Two‐Phase Symmetrical Rotor Variables to the Arbitrary Reference Frame 3.4 Transformation of Three‐Phase Stator and Rotor Variables to the Arbitrary Reference Frame 3.5 Balanced Steady‐State Stator Variables Viewed from Any Reference Frame 3.6 Closing Comments References

10 4 Equivalent Circuits for the Symmetrical Machine4.1 Introduction 4.2 Flux‐Linkage Equations for a Magnetically Linear Two‐Phase Symmetrical Machine 4.3 Flux‐Linkage Equations in the Arbitrary Reference Frame 4.4 Torque Expression in Arbitrary Reference Frame 4.5 Instantaneous and Steady‐State Phasors 4.6 Flux‐Linkage Equations for a Magnetically Linear Three‐Phase Symmetrical Machine and Equivalent Circuit 4.7 Closing Comments References

11 5 Synchronous Machines5.1 Introduction 5.2 Synchronous Machine 5.3 Equivalent Circuit For Three‐Phase Synchronous Generator 5.4 Closing Comment Reference

12 6 Brushless dc Drive with Field Orientation6.1 Introduction 6.2 The Permanent‐Magnet ac Machine 6.3 Instantaneous and Steady‐State Phasors 6.4 Field Orientation of a Brushless dc Drive 6.5 Torque Control of a Brushless dc Drive 6.6 Closing Comments References

13 7 Field Orientation of Induction Machine Drives7.1 Introduction 7.2 Field Orientation of a Symmetrical Machine 7.3 Torque Control of Field‐Orientated Symmetrical Machine 7.4 Closing Comments References

14 8 Additional Applications of Reference Frame Theory8.1 Introduction 8.2 Neglecting Stator Transients 8.3 Symmetrical Components Derived by Reference Frame Theory 8.4 Multiple Reference Frames 8.5 Closing Comments References

15 Index

16 End User License Agreement

1 Chapter 7Table 7.2-1 Steady‐state voltage and torque equations for field orientation o...

1 Chapter 2Figure 2.2-1 Sinusoidally distributed stator winding. (a) Approximate sinuso...Figure 2.2-2 Closed paths of integration and the plot of .Figure 2.2-3 Plot of sinusoidal approximation of shown in Figure 2.2-2g.Figure 2.2-4 Elementary symmetrical, two‐pole two‐phase sinusoidally distrib...Figure 2.2-5 Symmetrical, two‐pole two‐phase sinusoidally distributed stator...Figure 2.2-6 Tesla's balanced steady‐state rotating magnetic field viewed ...Figure 2.3-1 Elementary two‐pole three‐phase sinusoidally distributed stator...Figure 2.4-1 Two‐phase rotating, identical, and sinusoidally distributed sym...Figure 2.5-1 Three‐phase rotating, identical, and sinusoidally distributed s...

2 Chapter 3Figure 3.2-1 Two‐pole two‐phase sinusoidally distributed fictitious windings...Figure 3.3-1 Two‐phase rotating, identical, and sinusoidally distributed win...Figure 3.3-2 The fictitious qr and dr windings.Figure 3.4-1 Elementary two‐pole three‐phase sinusoidally distributed stator...Figure 3.4-2 Elementary two‐pole three‐phase sinusoidally distributed rotor ...Figure 3.5-1 Direction of rotation of and the phase relation between and...

3 Chapter 4Figure 4.2-1 A two‐pole two‐phase symmetrical machine.Figure 4.3-1 Arbitrary reference frame equivalent circuits for a two‐phase, ...Figure 4.5-1 Equivalent circuit for a two‐phase symmetrical induction machin...Figure 4.5-2 Steady‐state torque–speed characteristics of a symmetrical indu...Figure 4.5-3 Equivalent circuit for steady‐state operation of a single‐fed s...Figure 4.5-4 Phasor diagram; motor action, s = 0.05.Figure 4.5-5 Phasor diagram; generator action, s = −0.05.Figure 4.6-1 A two‐pole three‐phase symmetrical machine.Figure 4.6-2 Arbitrary reference frame equivalent circuits for a three‐phase...

4 Chapter 5Figure 5.2-1 Salient‐rotor two‐pole three‐phase salient‐pole synchronous mac...Figure 5.3-1 Equivalent circuit for three‐phase synchronous machine in the r...Figure 5.3-2 Phasor diagram for generator operation.

5 Chapter 6Figure 6.2-1 Two‐pole two‐phase permanent‐magnet ac machine.Figure 6.2-2 (a) The and axis equivalent of a two‐phase permanent‐magnet ...Figure 6.3-1 Phasor diagram showing voltages, currents, and rotor and stator...Figure 6.3-2 Phasor diagram for and in phase.Figure 6.4-1 Inverter–machine drive. ( a ) Inverter configuration, ( b ) transis...Figure 6.4-2 Two‐pole three‐phase permanent‐magnet ac machine with sensors....Figure 6.4-3 The free‐acceleration torque–speed characteristics for a three‐...Figure 6.4-4 Phasor diagram for brushless dc drive operation at rad/s with...Figure 6.4-5 Torque–speed characteristics of a three‐phase machine for free ...Figure 6.4-6 Phasor diagram for brushless dc drive operation at with .Figure 6.4-7 Torque–speed characteristics for free acceleration with .Figure 6.4-8 Phasor diagram for brushless dc drive operation at with .Figure 6.5-1 Block diagram of constant‐torque control of a three‐phase perma...Figure 6.5-2 Phasor diagram for operating Point 1.Figure 6.5-3 Controlling .Figure 6.5-4 Phasor diagram for operating Point 2.