blockPark

Park-transform of input signal-vector

Information

The block Park transforms abc variables (u) into dqo variables (y) with arbitrary angular orientation

  y = P*u

P can be factorised into a constant, angle independent orthogonal matrix P0 and an angle-dependent rotation R

  P(theta) = R'(theta)*P0

Using the definition

  c_k = cos(theta - k*2*pi/3),  k=0,1,2 (phases a, b, c)
  s_k = sin(theta - k*2*pi/3),  k=0,1,2 (phases a, b, c)

it takes the form

                       [ c_0,  c_1, c_2]
  P(theta) = sqrt(2/3)*[-s_0, -s_1,-s_2]
                       [ w,    w,   w  ]

with

                        [ 1,      -1/2,       -1/2]
  P0 = P(0) = sqrt(2/3)*[ 0, sqrt(3)/2, -sqrt(3)/2]
                        [ w,         w,          w]

and

             [c_0, -s_0, 0]
  R(theta) = [s_0,  c_0, 0]
             [  0,  0,   1]

Parameters

Type	Name	Default	Description
Integer	nin (from MIMO)	1	dim of input signal-vector
Integer	nout (from MIMO)	1	dim of output signal-vector

Connectors

Type	Name	Description
Modelica.Blocks.Interfaces.RealInput[nin]	u (from MIMO)	input signal-vector
Modelica.Blocks.Interfaces.RealOutput[nout]	y (from MIMO)	output signal vector
Modelica.Blocks.Interfaces.RealInput	theta	transformation angle