.PowerSystems.Blocks.Transforms.Rotation_abc .PowerSystems.Blocks.Transforms.Rotation_abcThe block Rotation_abc rotates u by an arbitrary angle theta into y according to
y = R_abc*u
The matrix R_abc rotates abc variables around the {1,1,1}-axis in abc-space with arbitrary angle theta.
Using the definition
g_k = 1/3 + (2/3)*cos(theta - k*2*pi/3), k=0,1,2 (phases a, b, c)it takes the form
[g_0, g_2, g_1]
R_abc(theta) = [g_1, g_0, g_2]
[g_2, g_1, g_0]
and has the real eigenvector
{1, 1, 1}/sqrt(3)
in the abc reference-frame.
Coefficient matrices of the form (symmetrical systems)
[x, xm, xm]
X = [xm, x, xm]
[xm, xm, x ]
are invariant under transformations R_abc
The connection between R_abc and R_dq0 is the following
R_abc = P0'*R_dq0*P0.with P0 the orthogonal transform 'Transforms.P0'.