ECE 5041 Electric Machine Spring 2024, Homework 5: 10%
(initial) Submit one single pdf file to include all results.
(initial) Everything should be typed. No hand-written results will be accepted.
(initial) Submit all individual Matlab files. No zip files will be accepted.
A 3-phase IPM machine used on a hybrid electric vehicle has the following parameters:
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 analysis and calculation
1.1 (3’) Write down the current limit circle equation of an IPM machine in the id-iq plane.
1.2 (2’) Write down the torque equation of an IPM machine in the dq reference frame.
1.3 (3’) Write down the maximum torque per amp curve equation for an IPM machine.
1.4 (6’) What’s the maximum torque this IPM machine can produce? Hint: the intersection of the current limit circle and the maximum torque per amp curve will give the operating point for the maximum torque.
1.5 (8’) Use Matlab to generator one single plot to include the current limit circle, maximum torque per amp curve, and constant torque curves for 0 Nm, 20 Nm, 40 Nm, 60 Nm, 80 Nm, 100 Nm, 120 Nm, 140 Nm, 160 Nm, Tmax in the id-iq plane. Just do the 2nd quadrant.
1.6 (3’) Write the equation for the voltage limit ellipse of an IPM machine in the id-iq plane.
1.7 (7’) Use Matlab to generate one single plot to include the following curves in the 2nd quadrant of the id-iq plane:
1) (1’)Current limit circle
2) Voltage limit ellipse for 2000 rpm. Highlight the possible operating area for this speed.
3) Voltage limit ellipse for 4000 rpm. Highlight the possible operating area for this speed.
4) Voltage limit ellipse for 8000 rpm. Highlight the possible operating area for this speed.
1.8 (8’) This IPM machine is running at 3000 rpm and delivering 40 Nm using the minimum current. What id and iq values is this IPM machine operating at? What Vd and Vq values are needed to produce this operating point?
Hint: using the minimum current means that the operating point (id, iq) are on the maximum torque per amp curve.
Problem 2. (40’) IPM machine simulation using sinusoidal voltage excitation
2.1 (6’) Watch the Matlab tutorial video on building an interior PM machine simulation and buildup your own IPM machine model following the tutorial step by step.
https://buckeyemailosu-
my.sharepoint.com/:v:/g/personal/zhang_564_osu_edu/EZ6BxVhLfNhAnsBM8KX0iYsBhsqhDUP nqKsnBet6pkh_kw?e=mY8hui
Take a screenshot of your simulation model and include in the homework submission.
2.2 (6’) Read the Matlab help file of the three-phase voltage source block used in the simulation and answer the following questions.
https://www.mathworks.com/help/physmod/sps/powersys/ref/threephaseprogrammablevolta gesource.html
a) (3’) what are the three parameters for this block?
b) Use the three parameters of this block to write down the equations for three phases.
2.3 (8’) Assume the rotor angle output of the IPM machine always starts from 0. The rotor angle is defined as the angle between the north pole (or d-axis) and the phase A axis. Explain or show how you setup the three parameters for the three-phase voltage source to produce the Vd and Vq values obtained in problem 1.8.
2.4 (4’) Read the Matlab help file on “subplot” and understand how to use it.
https://www.mathworks.com/help/matlab/ref/subplot.html
TA will deduct these 2 points if the subplot format in problem 2.5 is not correct.
2.5 (12’) Apply the three-phase voltage source initial angle calculated from problem 2.3 to your Matlab simulation and run the simulation. Generate the following plots over two fundamental cycles using the data stored in “ToWorkspace”. No credits will be given to the scope screenshots.
a) subplot(411): the electrical angle of the rotor.
b) subplot(412): three phase currents in steady states.
c) subplot(413): three input phase voltages, Van, Vbn, Vcn.
d) subplot(414): output electromagnetic torque of the machine.
All the four subplots should use the same timeaxis. For example, if you select to plotdata from t1 to t2 for one subplot, you should use t1 to t2 for the other subplots.
2.6 (4’) What are the id and iq current values in the simulation? What are the Vd and Vq values in the simulation? Comment on if those values are consistent with your hand calculation results in problem 1.