Topic 2 Reference frame theory

# Topic 2 Reference frame theory - 2011 Edition...

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Topic 2 Reference Frame Theory ELE847 Advanced Electromechanical Systems 2011 Edition Bin Wu Professor Dept of Electrical & Computer Engineering Office: ENG328 Tel: (416) 979 5000 ext: 6484 Email: [email protected] Advanced Electromechanical Systems ELE847 2011 2 Main Topics 1. Introduction 2. Transformation in the stationary reference frame 3. Transformation between different reference frames 4. Transformation of 3 phase resistive circuits 5. Transformation of 3 phase inductive circuits 6. Transformation of other 3 phase circuits

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Advanced Electromechanical Systems ELE847 2011 3 What is a reference frame? Reference frame is a mathematical convention for the representation of physical variables (voltage, current, flux linkage, etc.) Purpose of developing reference frame The system variables can be transformed from one reference frame to another to simplify motor dynamic models simplify analysis, simulation and design of dynamic systems facilitate real time digital implementation of control schemes Most commonly used reference frames Stationary reference frame abc stationary reference frame dq stationary frame (it is known as αβ reference frame in literature) Rotating or arbitrary reference frames dq rotating reference frames Introduction Advanced Electromechanical Systems ELE847 2011 4 Three phase variable representation Consider the three phase currents i a , i b and i c , given by 0 5 10 15 20 25 30 -1 -0.5 0 0.5 1 Time [ms] Amplitude [Pu] i a i b i c ) sin( ˆ ) ( ) sin( ˆ ) ( ) sin( ˆ ) ( 3 4 3 2 π π ω ω ω = = = t i t i t i t i t i t i c b a Transformation in the Stationary Frame Note: The analysis is performed for current variables, but is applicable to any other types of variables (voltage, flux linkage, etc.)