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Reference frame theory

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Reference frame theory

1. 1. UNIT- II Reference frame theory 16 November 2012 1PRB/Dept.of EEE/SCE
2. 2. INTRODUCTION Generally, the machine model can be described by differential equations with time varying mutual inductances, For example ( for a synchronous machine) (for a induction machine) but such a model tends to be very complex under dynamic analysis due to the following reasons (1) electric circuit in relative motion (2) electric circuits with varying magnetic reluctance So that, Several change of variables are used to reduce the complexity of these differential equations. 16 November 2012 2PRB/Dept.of EEE/SCE
3. 3. TRANSFORMATION The process of replacing one set of variables by another related set of variables is called transformation. In the study of power systems and electrical machine analysis, mathematical transformations are often used to decouple variables, to facilitate the solution of difficult equations with time-varying coefficients, or to refer all variables to a common reference frame. Evolution of transformation technique R. H. Park - Transformation – 1920 ( for a synchronous machine) He transformed a change of variables (voltages ,currents and flux linkages) associated with the stator windings of a synchronous machine to a variables associated with fictious windings rotating with the rotor at synchronous speed. (The stator variables are transformed to a synchronously rotating reference frame fixed in the rotor) 16 November 2012 3PRB/Dept.of EEE/SCE
4. 4. H. C. Stanley - Transformation – 1930 (for a induction machine) He transformed a change of variables associated with the rotor windings(rotor variables) of a induction machine to a variables associated with fictious stationary windings (stationary reference frame) fixed in the stator G. Kron - Transformation (for a induction machine) He transformed a change of variables associated with both stator and rotor windings of a symmetrical induction machine to a variable associated with reference frame rotating in synchronism with the rotating magnetic field. This reference frame is commonly referred to as the synchronously rotating reference frame. D. S . Brereton -Transformation ( for a induction machine) He proposed a change of variables associated with the stator windings of a induction machine to a variables associated with the reference frame fixed in the rotor. 16 November 2012 4PRB/Dept.of EEE/SCE
5. 5. Krause and Thomas- Transformation (after 1965) Both were shown that time varying inductances can be eliminated by referring the stator and rotor variables to a common reference frame which may rotate at any speed. This common reference frame is also called arbitrary reference frame. E. Clarke - Transformation He transformed a change of variables associated with the stationary circuits to a variables associated with stationary reference frame. The stationary two-phase variables of Clarke’s transformation are denoted as α and β. (Both are orthogonal). 16 November 2012 5PRB/Dept.of EEE/SCE
6. 6. Advantages of reference frame transformation 1. The number of voltage equations are reduced. 2. The time – varying voltage equations become time – invariant ones. 3. Performance of power systems and electric machines can be analyzed without complexities in the voltage equations. 4. Transformations make it possible for control algorithms to be implemented on the DSP 5. With aid of this technique , many of the basic concepts and interpretations of this general transformations are concisely established. 16 November 2012 6PRB/Dept.of EEE/SCE
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