CLARKE & PARK TRANSFORMS ON THE TMS320C2xx

Clarke & Park Transforms

on the TMS320C2xx

Application Report

Literature Number: BPRA048

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Table of Contents

1.

Overview .......................................................................................... 5

2.

Clarke and Park transforms in the Field Orientated Control (FOC)5

3.

Mathematical consideration. ............................................................ 6

3.1 Mathematical Clarke transform....................................................... 6

3.2 Mathematical Park transform.......................................................... 7

3.3 Mathematical Inverse Park and Clarke transforms. ....................... 7

3.4 Transforms summary........................................................................ 8

4.

Clarke and Park implementation on the C2xx ................................. 9

4.1 Conventions...................................................................................... 9

4.1.1

4.1.2

Fully C-compatible functions .....................................................................9

Assembly compatible functions ..................................................................9

4.2 Functions ........................................................................................ 10

4.2.1

4.2.2

4.2.3

4.2.4

Park assembly compatible........................................................................10

Inverse Park assembly compatible...........................................................10

Park C compatible....................................................................................12

Inverse Park C compatible.......................................................................12

4.3 Processor utilization (maximum)................................................... 13

4.3.1

4.3.2

4.3.3

Park ..........................................................................................................13

Inverse Park .............................................................................................13

Park + Inverse Park.................................................................................13

4.4 Memory utilization ......................................................................... 14

4.4.1

4.4.2

4.4.3

5.

Park ..........................................................................................................14

Inverse Park .............................................................................................14

Park + Inverse Park.................................................................................15

Annexe............................................................................................ 16

5.1 Main assembly example to call Park and inverse Park function

without cos/sin calculation in inverse Park................................... 16

5.2 Main assembly example to call Park and inverse Park function

with cos/sin calculation in inverse Park........................................ 18

5.3 Clarke_Park function for assembly main ...................................... 20

5.4 Inverse Park function without cos/sin calculation for assembly

main ................................................................................................ 23

5.5 Inverse Park function with cos/sin calculation for assembly

main ................................................................................................ 26

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5.6 Main C example to call Park and inverse Park function without

cos/sin calculation in inverse Park................................................ 29

5.7 Main C example to call Park and inverse Park function with

cos/sin calculation in inverse Park................................................ 30

5.8 Clarke_Park function fully C compatible without cos/sin

parameters return........................................................................... 31

5.9 Clarke_Park function fully C compatible with cos/sin

parameters return........................................................................... 35

5.10 Inverse Park function fully C compatible with cos/sin

calculation...................................................................................... 39

5.11 Inverse Park function fully C compatible without cos/sin

calculation...................................................................................... 43

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1. Overview

Clarke and Park transforms are used in high performance drive architectures

(vector control) related to permanent magnet synchronous and asynchronous

machines. In this paper, the user will find functions to easily implement Clarke

and Park transforms to his application.

Through the use of the Clarke transform, the real (Ids) and imaginary (Iqs)

currents can be identified. The Park transform can be used to realize the

transformation of the Ids and the Iqs currents from the stationary to the moving

reference frame and control the spatial relationship between the stator vector

current and rotor flux vector.

2. Clarke and Park transforms in the Field Orientated

Control (FOC)

The FOC consists of controlling the components of the motor stator currents,

represented by a vector, in a rotating reference frame d,q aligned with the rotor

flux. The vector control system requires the dynamic model equations of the

induction motor and returns the instantaneous currents and voltages in order to

calculate and control the variables.

The electric torque of an AC induction motor can be described by the

interaction between the rotor currents and the flux wave resulting from the

stator currents induction. Since the rotor currents cannot be measured with cage

motors, this current is replaced by an equivalent quantity described in a rotating

system coordinates called d,q following the rotor flux.

The Clarke transform uses three-phase currents ia, ib and ic to calculate currents

in the two-phase orthogonal stator axis: i¦Á and i¦Â. These two currents in the fixed

coordinate stator phase are transformed to the isd and isq currents components in

the d,q frame with the Park transform. These currents isd, isq and the

instantaneous flux angle ¦Ñ , calculated by the motor flux model, are used to

calculate the electric torque of an AC induction motor.

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