Engineering Electrical Machines and Power Electronics - 3 phase, 6 pole induction motor

[VinnyCee]

Homework Statement

A three phase, 6-pole, \Delta connected induction motor is rated 208V, 60Hz. It has R_R\,=\,5.2\,\Omega, R_S\,=\,2.2\,\Omega, X_m\,=\,220\,\Omega, X_{lr}\,=\,7.5\,\Omega, X_{ls}\,=\,2.3\,\Omega.

Calculate the starting torque and both phase and line currents when the motor is started in \Delta and Y.

Homework Equations

Various equations from the notes about induction machines and multiple pole pairs.

I_{S,\,Y}\,=\,\frac{\frac{V_{rated}}{\sqrt{3}}}{(R_S\,+\,j\,X_{ls})+(j\,X_m\,||\,R_R\,+\,j\,X_{lr})}

T_Y\,=\,3\,\cdot\,\frac{P_{gap}}{\omega_s}\,\cdot\,\frac{p}{2}

I_{R,\,Y}\,=\,I_{S,\,Y}\,\cdot\,\frac{j\,X_m}{R_R\,+\,j\,X_{lr}\,+\,j\,X_m}

P_{gap}\,=\,|I_{R,\,Y}|\,\cdot\,R_R

The Attempt at a Solution

I_{S,\,Y}\,=\,\frac{\frac{208}{\sqrt{3}}}{(2.2\,+\,j\,2.3)+(j\,220\,||\,5.2\,+\,j\,7.5)}\,=\,10\,\angle\,-53.8^{\circ}

In Y, the line current is same as phase current above, right?

I get the torque in Y as T_Y\,=\,11.68\,Nm.

Does that look right?

 

[VinnyCee]

This is correct. The solutions also state...

I_{ph,\,Y}\,=\,|I_{S,\,Y}|\,=\,10\,A

I_{l,\,Y}\,=\,I_{ph,\,Y}\,=\,10\,A

And for \Delta:

T_{\Delta}\,=\,3\,\cdot\,T_Y\,=\,35\,A

I_{ph,\,\Delta}\,=\,\frac{208}{120}\,\cdot\,10\,=\,17.34\,A

I_{l,\,\Delta}\,=\,\sqrt{3}\,\cdot\,I_{ph,\,\Delta}\,=\,30\,A