**Documentation Home Page** ◇ **Courseware Home Page**

Pour la **documentation en FRANÇAIS**, utilisez l'outil de traduction de votre navigateur Chrome, Edge ou Safari. Voir un exemple.

# PMSM - Exercises

# Page Content

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*and_{d}*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.

- What do you observe in terms of current magnitudes in (a, b, c) and (α, β) reference frames?
- 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*and_{d}*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.

- What do you observe in terms of current magnitudes in (a, b, c) and (α, β) reference frames?

# 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)?

- Do the measured currents in (a, b, c) follow the reference currents?
- 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 ?

- Do the measured currents in (a, b, c) follow the reference currents?
- 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?

- Do the measured currents in (a, b, c) follow the reference currents?

## 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*and the integral gain

_{p}*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

**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 ?

- Do the measured currents in (a, b, c) follow the reference currents?
- 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?

- Do the measured currents in (a, b, c) follow the reference currents?
- 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?

- What do you observe in terms of current magnitudes, speed, and torque values?
- 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.

- Do the measured currents in (a, b, c) follow the reference currents?

# 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**.- Does the measured speed follow the reference speed?
- Does the measured torque follow the reference torque?
- Do the measured currents follow the reference currents?
- What are the values of armature voltage and current of the DC machine?
- Show the results to support your answers.

- Set the r
**eference 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.

OPAL-RT TECHNOLOGIES, Inc. | 1751, rue Richardson, bureau 1060 | Montréal, Québec Canada H3K 1G6 | opal-rt.com | +1 514-935-2323