1. Clarke Transformation (3s2s)
Implements the following equations:
I
α
I
β
=
=
I
a
2(
I
b
+
I
a
3/)
This transformation converts balanced three phase quantities into balanced two phase
quadrature quantities as shown in figure below:
βI
αI
αI
βI
The instantaneous input and the output quantities are defined by the following equations:
sin
sin(
sin(
t
ω
t
πω
t
πω
)3/2
)3/2
+
−
sin
sin(
t
ω
t
πω
+
)2/
I
I
I
a
b
c
=
=
=
I
I
I
I
α
I
β
=
=
I
I
2. Park Transformation (2s2r)
Implements the following equations:
I
I
d
q
I
=
α
I
−=
α
I
cos
θ
+
sin
θ
+
sin
θ
cos
θ
β
I
β
This transformation converts vectors in 2-phase orthogonal stationary system into the
rotating reference frame as shown in figure below:
βI
β
αI
q
βI
qI
d
dI
αI
βI
αI
α
3.
β
Inverse Park Transformation (2r2s)
Implements the following equations:
I
α
I
−
θ
θ
+
cos
sin
sin
cos
θ
θ
=
=
I
I
I
I
d
d
q
q
This transformation projects vectors in orthogonal rotating reference frame into two phase
orthogonal stationary frame.
q
β
βI
qI
qI
dI
qI
dI
dIαI
d
α
4. Space Vector Modulation