.Spot.Base.Transforms.park

Information

The function park calculates the matrix P that transforms abc variables into dqo variables with arbitrary angular orientation theta.
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  ]

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

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

up users guide

Interface

function park
  extends Icons.Function;
  input SI.Angle theta "transformation angle";
  output Real[3, 3] P "Park transformation matrix";
end park;