In this simulation Field Orientated Control, FOC, of an Induction motor is implemented on PSIM.

There are several important aspects of the simulation:

The power stage, which is characterized by the red traces which includes:

- The DC voltage source

- The 3-phase inverter
- The induction motor model
- The mechanical constant torque load

The control stage, which is characterized by the green traces. There are several main aspects of the control circuit:

- The initial
**abc-dqo**transformation from the current sensors for the motor - The slip calculation
- The generation of theta used by the
**abc-dqo**and**dq0-abc**transformations - The PI controllers for
**Id, Iq** - The PI controller for speed

The control algorithm has been implemented in the s-domain with analog control blocks.

**Theta and Electrical Speed Calculation**

The slip is calculated by commanded **Iq/Id** multiplied by the inverted rotor time constant:

This is then added to the conversion of the sensed shaft speed converted to the magnetic revolutions per second with the RPM to MRS block.

To get MRS, we convert **rpm **to **rad/s** and multiply by the pole pairs, which is 3 for this case:

Integrating the addition of these will give theta which is used by the **dq** transformation blocks. In our simulation theta is being allowed to accumulate and if this was to be implemented with a DSP a resetting integral (0 to 2π), would be needed to prevent memory overflow.

The motor has a very light load in the simulation as a result, the slip, the difference between electrical and mechanical speed, is minimal. At 100 N*m torque load the slip will be ~2%.

**DQ Reference Transformation**

In this simulation the **abc-dqo** transformation from the feedback sensors is assuming that the **q-axis** is lagging the **d-axis**, a flag can be toggled in the transformation block to have the **q-axis** lead the **d-axis**.

**Speed Control**

** **

The speed of the motor is controlled by controlling **Iq**. The motor is working in the 1st quadrant with a positive torque and a positive speed. So, a positive speed gives a positive value of **Iq**; however, **Iq** from the motor feedback has a negative value in the 1st quadrant so gain block P14, resolves this sign issue.