# Clarke-Park transform for a 3 phase induction motor current

I am facing some problems in performing clarke-park transform for an induction motor(4 pole stator, squirrel cage IM). The motor is run with three sine wave inputs, 120 degrees phase shifted with each other. I am measuring the rotor position from the encoder and using twice of this value as theta for the park transform(position in radians). But since the rotor speed is slightly less than the synchronous speed, the transform is displaying a sinusoidal waveform. The frequency of Id-q sine wave increases with increase in the input frequency. For 10Hz input sine wave I am getting 0.01Hz sine Id-Iq values. I also tried by integrating the speed(rad/s) to get theta, but the result was the same.

Instead of using the rotor position value, if I use a constant of 2*pift for theta, I get a proper constant dq values. But when I would be performing control, I wont have the frequency data available with me and it would be difficult to get a constant dq values. I had used the same formulas for the PM synchronous motors and it gave constant Id, Iq values.

Could you please suggest any way of solving this problem. Thanks

It looks like you are trying to work in open loop. But usually these transforms are used in conjunction with some kind of PID controller to keep the Id and Iq close to constant values (Id is kept near 0, Iq is the torque generating current). This way any deviation of the required values will be compensated by the controller. This technique is known as Field Oriented Control (FOC) or Vector Control:

simulate this circuit – Schematic created using CircuitLab

Update:
Actually the gamma part is redundant here since the phase currents are summing up to zero.

• I will be doing control as the next step but thought that Idq values must be constant in order to use them. I will try by applying the PI loops to both the currents and check if they follow a reference – gabbar Apr 30 '15 at 22:50

As you have stated when this approach has been applied to a PM synchronous motor the expected results are obtained.

This is because, as the name implies, the electrical frequency & the rotor frequency are proportional to the polecount - Synchronous machines only generate torque at sync speed.

Unfortunately with Induction machines the rotor frequency is proportional to the pole count AND slip - Induction machines only generate torque at any speed BUT sync speed -> rotor $\omega$ is less than electrical $\omega$

The use of rotor angle as an input to the park&clark therefore will not work in the same way with induction machines. What is required is a slip frequency calculation block to infer the electrical angle, the angle which can be used in the C&P transforms

• could you please suggest some material that could help me in calculating the slip frequency. – gabbar Apr 30 '15 at 23:10