Homework # $4$

ENEE $350$:

Name

Due Date: $12/16/2024$

A $3-$phase, $20$kVA,$208V,4-$pole star$-$connected synchronous generator has a synchronous reactance of $x_s=1\mathrm{.}5$ per phase. The resistance of the stator winding is negligible. The machine is connected to a $3-$phase $208$ V infinite bus. Neglect rotational losses.

a$)$ The field current and the mechanical input power are adjusted so that the synchronous machine delivers $10$ kW at $0\mathrm{.}8$ lagging power factor. Determine the excitation voltage $E{f}_f$ and the power angle $.$

b$)$ The mechanical input power is kept constant but the field current is adjusted to make the power factor unity. Determine the percent change in the field current with respect to its value in part $($a$).$

A $3-$phase, $2300V,60Hz,12-$pole, Y$-$connected synchronous motor has $4\mathrm{.}5$ per phase synchronous reactance and negligible stator winding resistance. The motor is connected to an infinite bus and draws $250$ A at $0\mathrm{.}8$ power factor lagging. Neglect rotational losses.

a$)$ Determine the output power.

b$)$ Determine the power to which the motor can be loaded slowly without losing synchronism. Determine the torque, stator current, and supply power factor for this condition.

A $1$MVA,$3-$phase, $2300V,60Hz,10-$pole, Y$-$connected cylindrical rotor synchronous motor is connected to an infinite bus. The synchronous reactance is $7\mathrm{.}3.$ All losses may be neglected. The synchronous motor delivers $760$ kW and the motor operates at $0\mathrm{.}85$ power factor leading.

a$)$ Determine the excitation voltage Ef$.$

b$)$ Determine the maximum power and torque the motor can deliver for the excitation current of part $($a$).$

c$)$ The power output is kept constant at $760$ kW and the field current is decreased. By what factor can the field current of part $($a$)$ be reduced before synchronism is lost?

A $3-$phase, $190kW,2300V,60Hz,$ Y$-$connected non$-$salient rotor synchronous motor has a synchronous reactance of $11$ per phase. When it draws $165\mathrm{.}8$ kW the power angle is $15$ electrical degrees. Neglect ohmic losses.

a$)$ Determine the excitation voltage per phase $E_f.$

b$)$ Determine the supply line current $I_a.$

c$)$ Determine the supply power factor,

d$)$ If the mechanical load is thrown off and all losses become negligible,

Determine the new line current and supply power factor.

Draw the phasor diagram.

By what percent should the field current If be changed to minimize the line current?