Adoption of Park’s Transformation for Inverter Fed Drive

Abstract

Park's transformation in the context of ac machine is applied to obtain quadrature voltages for the 3-phase balanced voltages. In the case of a inverter fed drive, one can adopt Park's transformation to directly derive the quadrature voltages in terms simplified functions of switching parameters. This is the main result of the paper which can be applied to model based and predictive control of electrical machines. Simulation results are used to compare the new dq voltage modelling response to conventional directquadrature (dq) axes modelling response in direct torque control -space vector modulation scheme. The proposed model is compact, decreases the computation complexity and time. The model is useful especially in model based control implemented in real time, in terms of a simplified set of switching parameters. Keyword:Direct Corresponding Author:Jayarama Pradeep, Department of Electrical and Electronics Engineering, Sathyabama University, Jeppiaar Nagar, Old Mamallapuram Road, Chennai-600 119. Email: jaya_7pradeep@yahoo.co.in INTRODUCTIONIn three-phase machines usually the behavior and performance are described and analyzed by their voltage and current equations. The coefficients of the differential equations which describes the dynamic behavior of the machines are time varying [1], [2] (except when the rotor is stationary). The mathematical modelling of such a system tends to be complex as the flux linkages, induced voltages, and currents change continuously as the system is in relative motion. For such a complex electrical machine analysis, mathematical transformations [3]-[6] are often used to separate or decouple the variables and to solve equations involving time varying quantities by referring all variables to a common reference frame either stationary or rotating. Among the various methods available for transformation, the well known [8], [9] are: Clarke Transformation and Park Transformation By proper selection of the reference frame, it is possible to simplify considerably the complexity of the mathematical machine model. While these transformations were initially developed for the analysis and simulation of ac machines, they are now extremely useful tools in the digital control of such machines. As digital control techniques are extended to the control of the currents, torque and flux of such machines, the need for compact, accurate machine models is obvious.Generally while modelling a drive, the 3-φ voltages V a , V b , V c are generated through a switching model of the inverter. Using Parks transformation, quadrature voltages V d , V q are then obtained from V a , V b , V c . In this paper, we present a new approach to obtain V d , V q voltages directly in terms of a simplified form of switching parameters of the inverter. This result is made possible by combining the switching equations and the Parks transformation and using some regularity found in the coefficients involved. This methodology which gives V d , V q directly in terms of a simplified set of switching parameters will be useful in ...

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“…Nevertheless, the variables of current in (z 1 , z 2 ) and (o 1 , o 2 ) do not participate effectively in the conversion of electromechanical which generates losses of stator. The conversion matrix should be used to illustrate the immobile (α, β) plane in the revolving plane (d, q) which is presented as follows [30]:…”