- #1
VinnyCee
- 489
- 0
Homework Statement
A PMAC machine is connected in Y and has 4 poles. [tex]I_F\,=\,27\,A[/tex] and [tex]L_m\,=\,20\,mH[/tex].
a) It is to operate at a torque of 35 Nm and at a speed of 4000 RPM. Calculate the necessary stator current [tex]I_S[/tex] and voltage [tex]V_{S\,line-to-line}[/tex] so that the losses are minimal.
b) If the maximum line-to-line voltage is [tex]500\,\sqrt{3}\,V[/tex], what would the maximum speed the motor would reach without field weakening, [tex]\omega_1[/tex], for the same torque of 35 Nm?
c) For speed [tex]1.2\cdot\omega_1[/tex], voltage the same, [tex]500\,\sqrt{3}\,V[/tex], and torque of 35 NM, what would be the stator current and it's angle?
Homework Equations
For minimum losses, the stator current must be minimized.
[tex]T\,=\,3\,\frac{p}{2}\,L_M\,I_S\,I_F[/tex]
[tex]V_S\,=\,\omega_S\,L_M\,I_F[/tex]
[tex]\omega_S\,=\,\frac{p}{2}\,\cdot\,Speed\,in\,RPM\,\cdot\,\frac{2\,\pi}{60}[/tex]
The Attempt at a Solution
a) Using the first equation above...
[tex](35\,Nm)\,=\,3\,\frac{(4)}{2}\,\left(20\,mH\right)\,I_S\,\left(27\,A\right)[/tex]
[tex]I_S\,=\,10.8\,A[/tex]
To get [tex]V_S[/tex] I need to use the second equation above. And to get that I need [tex]\omega_S[/tex] using the third equation.
[tex]\omega_S\,=\,\frac{(4)}{2}\,\cdot\,\left(4000\,RPM\right)\,\cdot\,\frac{2\,\pi}{60}\,=\,837.8\,\frac{rad}{sec}[/tex]
[tex]V_S\,=\,\left(837.8\,\frac{rad}{sec}\right)\,\left(20\,mH\right)\,\left(27\,A\right)\,=\,452.4\,V[/tex]
Does that look right for part (a)? Also, how do I proceed for parts (b) and (c)?
Last edited: