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Master of Science Thesis in Electric Power Engineering - page 17 / 114

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THREE PHASE CONTROLLED RECTIFIERS

RECTIFIER EQUATIONS Now, we need to apply the Park transformation (see APPENDIX A and [4] [12] ) which is

(2.14)

where

is a space vector (

). We get

(2.15)

(2.16)

And finally, with separation of Real and Imaginary part we obtain

(2.17)

(2.18)

3 2

(2.19)

INSTANTANEOUS POWER [4]

From the well known relation

for single phase rms value scaled phasors

and

(“*” indicates complex conjugate), we know that instantaneous power for three phase system will

be proportional to

(2.20)

2

1

3

√3

Note that the formula is independent of the coordinate system.

From the space vector definition we get (the time argument “(t)” is removed for simplicity)

2 3

And finally, the Real part gives us the active power

33

(2.21)

And with Imaginary part we obtain the reactive power

33

1 √3

(2.22)

8

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