Transforms¶

Park Transform¶

abc to dq¶

T_p = 2.0/3.0*[[ cos(theta), cos(theta-2.0/3.0*pi), cos(theta+2.0/3.0*pi)],
               [-sin(theta),-sin(theta-2.0/3.0*pi),-sin(theta+2.0/3.0*pi)]];

dq to abc¶

T_p_inv = [[            cos(theta),            -sin(theta)],
           [ cos(theta-2.0/3.0*pi), -sin(theta-2.0/3.0*pi)],
           [ cos(theta+2.0/3.0*pi), -sin(theta+2.0/3.0*pi)]];

abc to dqz¶

T_p = 2.0/3.0*[[ cos(theta), cos(theta-2.0/3.0*pi), cos(theta+2.0/3.0*pi)],
               [-sin(theta),-sin(theta-2.0/3.0*pi),-sin(theta+2.0/3.0*pi)],
               [        0.5,                   0.5,                   0.5]];

dqz to abc¶

T_p_inv = [[            cos(theta),            -sin(theta), 1.0],
           [ cos(theta-2.0/3.0*pi), -sin(theta-2.0/3.0*pi), 1.0],
           [ cos(theta+2.0/3.0*pi), -sin(theta+2.0/3.0*pi), 1.0]];

Transforms Power Invariant Forms¶

Park Transform¶

abc to dq¶

T_p = sqrt(2.0/3.0)*[[ cos(theta), cos(theta-2.0/3.0*pi), cos(theta+2.0/3.0*pi)],
                     [-sin(theta),-sin(theta-2.0/3.0*pi),-sin(theta+2.0/3.0*pi)]];

dq to abc¶

T_p_inv = T_p.';

abc to dqz¶

T_p = sqrt(2.0/3.0)*[[   cos(theta), cos(theta-2.0/3.0*pi), cos(theta+2.0/3.0*pi)],
                     [  -sin(theta),-sin(theta-2.0/3.0*pi),-sin(theta+2.0/3.0*pi)],
                     [sqrt(2.0)/2.0,         sqrt(2.0)/2.0,         sqrt(2.0)/2.0]];

dqz to abc¶

T_p_inv = T_p.';