synchronously rotating frame machine model
The circuit shows the model of implementation of synchronously rotating frame. Here, the
input is the values of the voltages corresponding to the 3 phases of the system.Now our
aim is to get these values in the reference of the synchronously rotating frame. For this
purpose first we convert the values into a synchronously static frame and then we rotate
this frame to get the desired output. Vas, Vbs, Vcs are the voltages which are at 120
degree phase with each other.Also we define these values as Vas = Vm cos(Wet+phi)
and the remaining values at 120 degree phase more and less from this. Now we take our
d,q axes which are at 90 degrees. Also consider the angle between as and q is theta.Now
we can make the voltage values into components along the d,q system . Now we give the
system which already exists the property of rotation and let us take the angle of rotation
as theta_e.Now we name it as the de-qe system which is our target synchronously
rotating frame. Now again we can get the components of the voltages along the required
rotating axes. Also, here we have to take the rotor velocity Wr into consideration.For this
purpose we need to subtract this much magnitude from the rotation speed of the axes
which is We.Also here the values of Wr is not constant.So we get it from the equation of
torque of the rotor and give it as another input to the system.Here the stator is not rotating,
so it won’t give any problem. Now to get the complete matrix of relationship between input
and output we consider the currents which are in different branches of the circuit and
obtain the relation in the matrix form.