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After completing the following series of exercises, the student will understand the control of a permanent magnet synchronous motor.
Real-time simulation results are shown in the laboratory panel.

Transformations

Open the model with the default settings.
Gradually apply a field voltage of 460 V for the DC machine.
Connect K1, as shown in figure 12.

Figure 12: PMSM Armature Connected to Three-phase Resistance

Gradually increase the armature voltage of the DC machine to 120 V.
Apply the Trigger.
Show the obtained waveforms from the simulation.
It should be noted that Clarke transformation is selected by default.
- What do you observe in terms of current magnitudes in (a, b, c) and (α, β) reference frames?
  Explain.
- What are the values of the currents I_d and I_q?
- What are the active powers in (a, b, c), (α, β), and (d, q) reference frames?
- What do you observe in terms of active powers’ values?
  Explain.
Switch the Transformation to Concordia, as shown in figure 13.

Figure 13: Selection of Concordia Transformation

200px Show the obtained waveforms from the simulation.
- What do you observe in terms of current magnitudes in (a, b, c) and (α, β) reference frames?
  Explain your observation.
- What are the values of the currents I_d and I_q?
  How do they differ from the values obtained when Clarke transformation was applied?
- What are the active powers in (a, b, c), (α, β), and (d, q) reference frames?
- What do you observe in terms of active powers’ values?
  Explain.

Self-Current Control

Hysteresis

Decrease the armature voltage of the DC machine to 0 V.
Deactivate the Trigger.
Disconnect K1, switch the Transformation to Clarke, and connect K2 (see figure 14).

Figure 14: Selection of Clarke Transformation with PMSM Connected to the Inverter

Go to “Current Control” tab and enter a hysteresis band value of 0.05 (see figure 15).

Figure 15: Self-Current Control with Hysteresis Controller

Apply a reference current of 5 A.
- Do the measured currents in (a, b, c) follow the reference currents?
  Show your results.
- Do the measured currents in (d, q) follow the reference currents?
  Show your results.
- What are the values of torque (Tem) and speed (N)?
Increase the reference current to 10 A.
- Do the measured currents in (a, b, c) follow the reference currents?
  Show your results.
- Do the measured currents in (d, q) follow the reference currents?
  Show your results.
- What are the values of torque and speed ?
Increase the reference current to 15 A.
- Do the measured currents in (a, b, c) follow the reference currents?
  Show your results.
- Do the measured currents in (d, q) follow the reference currents?
  Show your results.
- What are the values of torque and speed ?
- How does the increase in reference current impact the torque and speed of the PMSM?

PI Controller

- Decrease the reference current to 10 A, then 0 A.
- In the “Current Control” tab, switch the “Control” to PI as shown in figure 16.

Figure 16: Self-Current Control with PI Controller

Apply a reference current of 8 A.
Tune the gains Ki_self and Ti_self (see figure 17) of the PI controller so that the measured currents follow the reference currents in (a, b, c) and (d, q) reference frames.
- Explain how you proceed to set the values of the gains.
- Do the same gain’s values work if a reference current of 12 A is applied?
  Show your results.

Figure 17: Gains of the Self-Control PI Controller

Note

For the PI controller implemented in this laboratory, the gain K_i is defined as the ratio of the proportional gain K_p and the integral gain T_i.
K_i = K_p/T_i

Vector current control

Decrease the reference current to 6 A, then 0 A.
In the “Current Control” tab, switch the “Control” to Hysteresis and “Self/Vector Control” to Vector, as presented in figure 18.

Figure 18: Selection of Vector Current Control

Apply a reference current of 4 A.
- Do the measured currents in (a, b, c) follow the reference currents?
  Show your results.
- Do the measured currents in (d, q) follow the reference currents?
  Show your results.
- What are the values of torque and speed ?
Increase the reference current to 8 A.
- Do the measured currents in (a, b, c) follow the reference currents? Show your results.
- Do the measured currents in (d, q) follow the reference currents? Show your results.
- What are the values of torque and speed ?
Increase the reference current to 12 A.
- Do the measured currents in (a, b, c) follow the reference currents?
  Show your results.
- Do the measured currents in (d, q) follow the reference currents?
  Show your results.
- What are the values of torque and speed ?
- How does the increase in reference current impact the torque and speed of the PMSM?
With the reference at 12 A, decrease the load resistance of the DC machine to 15 ohms.
- What do you observe in terms of current magnitudes, speed, and torque values?
  Explain your observation.
- How does the decrease of resistance impact the armature voltage and current of the DC machine?
Increase the reference current to 15 A.
- Do the measured currents in (a, b, c) follow the reference currents?
  Show your results.
- Do the measured currents in (d, q) follow the reference currents?
  Show your results.
- Explain the importance of decreasing the load resistance when the reference current is approaching the maximum current () of the PMSM.

Speed control

Decrease the reference current to 10 A, then 5 A, and finally 0 A.
Increase the resistive load of the DC machine to 25 ohms.
Go to “Speed Control” tab and enable the Speed Control, as shown in figure 19.

Figure 19: Activation of the Speed Control

Set the reference speed as 250 rpm.
1. Does the measured speed follow the reference speed?
2. Does the measured torque follow the reference torque?
3. Do the measured currents follow the reference currents?
4. What are the values of armature voltage and current of the DC machine?
5. Show the results to support your answers.
Set the reference speed as 500 rpm.
- Repeat questions 1 to 5 above.
Set the reference speed as 750 rpm.
- Repeat questions 1 to 5 above.
Set the reference speed as 900 rpm.
- Repeat questions 1 to 5 above.
- How does the increase in reference speed impact the armature voltage and current of the DC machine?
  Explain.

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