Coordinate Transformation of SVPWM Control Algorithm

We should note that the components of α and β in the stationary coordinate system obtained after Clarke transformation are still sinusoidal signals, neither step signals nor ramp signals.

The main control method at present is based on PI controller. However, PI controller can only achieve the tracking of DC signal without steady-state error. When it tracks the sine wave signal, unstable steady-state error will inevitably occur. In order to achieve the control of α and β axis components without steady-state error, there are two main directions:

One is to design a controller that can handle sinusoidal signals without steady-state errors (obviously requires more research depth and is more difficult);

The second is to convert the sine wave signal into a DC signal so that the PI controller can continue to be used (with reduced difficulty);

Obviously, our predecessors were already familiar with the parameter tuning method of PI controller. Therefore, using the second method to convert a new problem into a solved problem can greatly simplify the design problem. Robert H. Park then proposed the park transformation.

As shown in the figure above, the amplitude of the projection Vα, Vβ of the synthetic vector Vδ in the α, β coordinate system is a sine transformation. Design the d, q coordinate system, when it rotates at the same angular velocity as Vδ, the amplitude of the projection Vd, Vq on the d, q axis is constant, that is, relative to the selected vector, Vd, Vq is a DC quantity, so the PI control strategy can be used for design.

The specific matrix algorithm is as follows;

Build a matlab model based on the formula, set the electromagnetic angle of vector rotation θ=0.25s/2pi, and simulate the waveform as follows;

In summary, the coordinate transformation of SVPWM is introduced above. I think the essence of vector control is the separate control of active and reactive power. And coordinate transformation is the method to achieve decoupling. Vector control is "magnetic field oriented control", which means that the direction of the magnetic field is oriented on a coordinate axis D (artificially defined), and the direction of the torque is exactly perpendicular to the magnetic field, so it is just oriented to the Q axis (artificially defined as perpendicular to the D axis). If the current of the motor is also decoupled on the DQ coordinate axis, the torque and magnetic field can be decoupled and controlled separately.