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APPENDICES

# APPENDICES

• A.

Three phase system – Coordinate transformations

• A.

1 Voltage and current definition

First of all, we can define the voltage and current of a three phase system :

3

3

(positive sequence here)

3

3

## For any three phase system composed of positive and negative sequence we have

If the system present an asymmetry, a zero sequence appears and is define as the mean value

3

A good thing is that there will never be any zero sequence in the currents, provided that there is no neutral connection.

# A.2 Equivalent two phase system,

transformation (Clarke)

A three phase system can be described with only two components imaginary respectively). Furthermore, we call a space vector the quantity

and

(real and

2 3

where

is a scaling constant. The transformation from ABC to

(Clarke transformation)

depending on the scaling constant

is :

74

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