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APPENDICES

Amplitude invariant RMS value invariant

1 √2

Power invariant

3 2

  • 0

and

1

0

A.3 Synchronous coordinate, dq transformation (Park)

We can now define a transformation of the previous space vector drop the time argument “(t)” for simplicity) with

(we now

where

. This transformation makes

similar to fixed complex phasor. This transformation

is called dq transformation and can be regarded as observing the space vector from a coordinate

system rotating with the frequency

(synchronous coordinate or dq coordinate). We denote the

space vector in synchronous coordinates as

Figure 0.1 : Relation between

  • frame and dqframe (rotating) [23]

Giving dc steady state quantity, the synchronous coordinates are very useful for analysis, implementation of control algorithm (controller design is easier on dc quantities).

We can write

and

.

Source : [4]

75

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