Introduction of Parker transformation matrix;
1. Mathematically, Parker transformation is just a coordinate transformation. From abc coordinate to dq0 coordinate, ua, ub, uc, ia, ib, ic, flux A, flux B and flux C are all converted to dq0 coordinate, and vice versa if necessary.
2. In the physical sense, park transform is equivalent to the projection of ia, ib and ic currents on the α and β axes to the D and Q axes, and the current on the stator to the direct axis and the quadrature axis.
3. For steady state, iq and id are just a constant after such equivalence. From the observer's point of view, our observation point has shifted from the stator to the rotor. We no longer care about the rotating magnetic field generated by the three windings of the stator, but about the rotating magnetic field generated by the equivalent direct axis and the quadrature axis.
The transformation form of Parker transformation matrix;
1, Parker transformation, which is a coordinate transformation, is no different from the coordinate transformation of complex numbers mentioned above. The only difference is that Parker transform is a linear transform.
2. The object of Parker transform is two-dimensional static coordinate system, and the operation process is to map the points in the static coordinate system to the rotating coordinate system one by one.
3. To put it bluntly, Parker transform is the mathematical expression of the same two-dimensional space vector in two different coordinate systems, but the selection of these two coordinate systems is special, one is a rectangular coordinate system that is perpendicular to each other and the other is a rectangular coordinate system that rotates at a constant speed.
This is understood from the mathematical level. Students with poor spatial imagination are not friendly enough. In this way, when establishing the differential equation of the electromagnetic relationship of the rotor circuit, its coefficient matrix becomes a constant matrix, rather than a coefficient matrix that changes with time and space, which greatly simplifies the differential equation for analyzing the electromagnetic relationship between the generator and the motor.