Motor Control Problems

With reference to the power electronics block diagrams and rectifier formulas in Lecture $24,$ complete the following problems.

MC$.1-$ An Inverter$-$fed synchronous motor with rectifier$-$fed field supply

A $3-$phase synchronous motor is used to run a large pump. The machine ratings are $50$ kVA and $480$ VAC $.$ The field winding draws $5\mathrm{.}0$ A when supplied with $400$ VDC$.$ A field current of $2\mathrm{.}5$ A results in unity power factor at rated conditions.

The motor is driven by a $3-$phase rectifier and inverter combination. The $3-$phase, diode rectifier is connected directly to the $\backslash (\backslash$mathbf$\{480\}\backslash )$ VAC power grid $($infinite bus$).$ The rectifier output connects to a DC link capacitor and to the input of a voltage source inverter $($VSI$).$ The rotor field for the synchronous motor is supplied by a smaller rectifier. In this case, it's a phase$-$controlled, $3-$phase rectifier connected directly to the $480$ VAC power grid.

a$)$ Draw the system diagram, showing the motor, both rectifiers, the inverter, and the connections to the power grid. Use appropriate symbols for each of the $3$ power converter modules and label the components in the diagram.

b$)$ What is the nominal voltage on the DC link capacitor? $($Use the DC voltage equation for a $3-$phase rectifier.$)$

c$)$ When the motor is operating at rated power and the field current is $4\mathrm{.}0$ A $,$ is the motor operating at leading or lagging power factor? You can't calculate $\backslash (\backslash$mathbf$\{$E$\}\_\{\backslash$text $\{$af $\}\}\backslash )$ because you don't know $\backslash ($ X$\_\{$s$\}\backslash ).$ However, if you sketch the V$-$curves for a synchronous motor, you can tell by the field current where it is operating. Use this to justify and explain your answer.

d$)$ What is the required rectifier phase angle that will result in a field winding current of $4\mathrm{.}0$ A $?$

MC$.2-$ An Inverter$-$fed synchronous motor with chopper$-$fed field supply

Use the same synchronous motor as problem MC$.1$ and use the same rectifier$-$inverter combination for the stator power supply. But now use a chopper connected to the DC link to provide power for the rotor field winding.

a$)$ Draw the system diagram for this configuration.

b$)$ What is the required duty cycle D for the chopper to deliver $4\mathrm{.}0$ A to the field winding?