7. A three-phase inverter and PM motor system is connected to a boost converter fed by a
$V_{Batt}$= 25 V battery. The machine has parameters $\Lambda_{PM}$ = 25 mWb, p = 8, and the boost
converter is limited to a voltage gain of G = 4 V/V.
In each problem below, you will compute the speed limit of the machine. There are three
items which affect the top speed: (i) the boost converter's gain, (ii) the generated EM torque,
and (iii) the inverter PWM method used. Ignore resistance ($R_s$), inductance ($L_s$), friction ($B_m$),
and inertia ($J_m$) terms in your calculations.
a. Assuming the boost converter is disabled (D = 0%), what is the maximum no-load
mechanical speed (in rad/s), $\omega_m$, that the machine can reach? Assume use of Sine PWM,
(G=1 V/V, $T_{EM}$ = 0, SPWM).
$\omega_{m,max}$ = rad/s
b. Find the maximum mechanical speed, now assuming that the boost converter works at its
full gain. In addition to the top speed, find the boost converter duty cycle, D. Assume
other conditions are the same (G = 4 V/V, $T_{EM}$ = 0, SPWM).
$D_{Boost}$ = %
$\omega_{m,max}$ = rad/s
