Reference Frame Theory

PAUL C. KRAUSE, PHD, started PC Krause and Associates, Inc. in 1983. He was a Professor in the School of Electrical and Computer Engineering at Purdue University for 39 years and before that he taught at the University of Wisconsin as well as the University of Kansas. He is a Life Fellow of the IEEE and has authored or co-authored over 100 technical papers and three textbooks on electric machines. He was the recipient of the IEEE Nikola Tesla Award in 2010.

• About the Author xvPreface xvii1 A Brief History of Reference Frame Theory 1References 32 Tesla’s Rotating Magnetic Field 52.1 Introduction 52.2 Rotating Magnetic Field for Symmetrical Two-Phase Stator Windings 52.3 Rotating Magnetic Field for Symmetrical Three-Phase Stator Windings 112.4 Rotating Magnetic Field for Symmetrical Two-Phase Rotor Windings 132.5 Rotating Magnetic Field for Symmetrical Three-Phase Rotor Windings 152.6 Closing Comments 17References 173 Tesla’s Rotating Magnetic Field and Reference Frame Theory 193.1 Introduction 193.2 Transformation of Two-Phase Symmetrical Stator Variables to the Arbitrary Reference Frame 203.3 Transformation of Two-Phase Symmetrical Rotor Variables to the Arbitrary Reference Frame 243.4 Transformation of Three-Phase Stator and Rotor Variables to the Arbitrary Reference Frame 263.5 Balanced Steady-State Stator Variables Viewed from Any Reference Frame 313.6 Closing Comments 35References 354 Equivalent Circuits for the Symmetrical Machine 374.1 Introduction 374.2 Flux-Linkage Equations for a Magnetically Linear Two-Phase Symmetrical Machine 374.3 Flux-Linkage Equations in the Arbitrary Reference Frame 394.4 Torque Expression in Arbitrary Reference Frame 414.5 Instantaneous and Steady-State Phasors 424.6 Flux-Linkage Equations for a Magnetically Linear Three-Phase Symmetrical Machine and Equivalent Circuit 454.7 Closing Comments 49References 505 Synchronous Machines 515.1 Introduction 515.2 Synchronous Machine 515.3 Equivalent Circuit For Three-Phase Synchronous Generator 535.4 Closing Comment 57Reference 576 Brushless dc Drive with Field Orientation 596.1 Introduction 596.2 The Permanent-Magnet ac Machine 596.3 Instantaneous and Steady-State Phasors 626.4 Field Orientation of a Brushless dc Drive 656.5 Torque Control of a Brushless dc Drive 756.6 Closing Comments 78References 797 Field Orientation of Induction Machine Drives 817.1 Introduction 817.2 Field Orientation of a Symmetrical Machine 817.3 Torque Control of Field-Orientated Symmetrical Machine 867.4 Closing Comments 89References 898 Additional Applications of Reference Frame Theory 918.1 Introduction 918.2 Neglecting Stator Transients 918.3 Symmetrical Components Derived by Reference Frame Theory 938.4 Multiple Reference Frames 978.5 Closing Comments 97References 97Index 99