ECE 5041 Electric Machine Spring 2024
Homework 6: 12%
Read and initial.
Submit one single pdf file to include all results. Submit all simulation files too.
SUBMIT ALL FILES INDIVIDUALLY. NO ZIP FILES WILL BE ACCEPTED.
All simulation plots need to use data stored in “ToWorkSpace”. No credits will be given to screenshots of scopes.
A 3-phase IPM machine used on a hybrid electric vehicle has the following parameters. You will use these machine parameters for your simulations in this homework.
Number of poles: 8
Peak value of maximum phase current Ipeak : 500 A
Peak value of maximum phase voltage V peak : 115 V
Phase winding dc resistance rs : 0.02 Ω
d-axis inductance Ld : 0.18 mH
q-axis inductance Lq : 0.25 mH
Flux linkage of permanent magnet λm : 0.05 V-s
Problem 1. (40’) IPM machine simulation using adc/ac power converter
1.1 (6’) Watch the Matlab tutorial video on using open-loop voltage control for an IPM machine driven by adc/ac converter and build your own IPM machine model following the tutorial.
Take a screenshot of your simulation model and include in the homework submission. Include the screenshots of subsystems too.
1.2 (7’) Set the dc bus voltage of the dc/ac converter to be 500 V. When sine-triangle PWM algorithm is used to generate the switching signals for three phases, the reference sinusoidal voltages are compared to a high frequency triangle carrier wave. Set the switching frequency to be 5 kHz,i.e., the frequency for the carrier triangle wave.
In your simulation, use p.u. values for both the reference voltage and carrier wave. The peak value for the triangle carrier wave is - 1 and +1 p.u. If mis used to represent the peak value of the reference voltage in p.u., the actual phase output voltage can be calculated using the following equation.
where miscalled modulation index, Vdc is the voltage of the dc bus. The range of modulation index is also between - 1 and +1 p.u.
Based on the above information, answer the following questions:
a) (3’) If modulation index is 0.5, what is the actual peak value of the output phase voltage?
b) (4’) If the desired actual peak value of the output phase voltage is 100 V, what should be the reference voltage value in p.u. for the simulation? What equation do you use to convert the desired actual output phase voltage to the reference voltage value in p.u.? (You will need to use this equation in your simulation)
1.3 (27’) Use the model you have built in 1.1 to make the machine run at 3000 rpm and produce
50 Nm. The operating point should be on the maximum torque per amp curve.
a) (3’) Comment on how to select the simulation step size for your simulation.
b) (3’) Calculate the requiredid and iq to produce 50 Nm at 3000 rpm.
c) (3’) Calculate the required Vd and Vq and apply these to your simulation.
(The Vd and Vq values I used in my simulation are for a different torque. You need to calculate what Vd and Vq are needed!)
d) (12’) Plot the following waveforms over two fundamental cycles when your simulation gets to steady state:
figure (1)
subplot(411) rotor electrical angle vs time
subplot(412) three-phase currents vs time
subplot(413) machined-axis and q-axis currents vs time
subplot(414) d-axis voltage reference,q-axis voltage reference, and 3-phase reference voltages vs time (actual value, not p.u.)
figure (2)
subplot(411) rotor electrical angle vs time
subplot(412) phase A reference voltage in p.u. and carrier wave vs time subplot(413) switching signal for top switch of phase A vs time
subplot(414) the actual d-axis voltage and q-axis voltage of the machine vs time
e) (3’) Explain why the three-phase currents and dq axis currents have ripples, which didn’t exist in the simulation in Homework 5.
f) (3’) Explain why the actual machined-axis and q-axis voltages are pulse voltages instead of dc voltages like what you saw in Homework 5.
Problem 2. (40’) IPM machine simulation using current feedback control
2.1 (6’) Watch the Matlab tutorial video on current closed-loop control of an IPM machine simulation and buildup your own simulation model following the tutorial. Set Kp to be 10 and Ki to be 5 for both current controllers. Set the speed to be 3000 rpm.
Take a screenshot of your simulation model and include in the homework submission. Include the screenshots of subsystems too.
2.2 (4’) Read the Matlab help file of the “Matlab Function” block used in the simulation and
answer the following questions. How do you declare inputs and outputs for a Matlab function?
2.3 (10’) Read the Matlab help file of the “stair generator” block and setup the d-axis and q-axis current commands following the requirements below.
d-axis current commands:
-20 A from 0 sec to 1 sec
- 100 A from 1 sec to 2 sec
-30 A from 2 sec to 3 sec
0 A from 3 sec to 4 sec
q-axis current commands:
-30 A from 0 sec to 1 sec
100 A from 1 sec to 2 sec
- 100 A from 2 sec to 3 sec
0 A from 3 sec to 4 sec
a) (5’) Plot the waveforms of d-axis and q-axis current commands vs time. subplot(211) d-axis current command vs time
subplot(212) q-axis current command vs time
b) (5’) Calculate the theoretical torque for the 4 time intervals above using the machine parameters and dq axis current commands.
2.4 Apply the dq axis current commands generated in 2.3 and run your simulation. Generate the following plots:
(7’) figure (1) over 4 seconds
subplot(411) d-axis current command and actual d-axis current vs time
subplot(412) q-axis current command and actual q-axis current vs time
subplot(413) machine torque
subplot(414) d-axis voltage command and q-axis voltage command
(3’) Comment on if the simulated torque is consistent with the calculate torque in 2.3(b).
(7’) figure (2) show 1 to 2 fundamental cycles before 2 sec and 1 to 2 fundamental cycles after 2 sec to show the current transient response
subplot(411) d-axis current command and actual d-axis current vs time
subplot(412) q-axis current command and actual q-axis current vs time
subplot(413) machine torque
subplot(414) d-axis voltage command and q-axis voltage command
(3’) Check the three-phase current waveforms in problem 1 and zoom in at the very beginning. How long does it take the system to get to steady state? Check the three-phase current waveforms in figure (2) above. How long does it take the system to get to the steady state when dq-axis currents have a step change? Does the current closed-loop control provide a better performance than the voltage open-loop control?