The block Park transforms abc variables (u) into dqo variables (y) with arbitrary angular orientation
y = P*uP 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]