A three-phase Δ-connected six-pole winding is installed in 36 slots on a stator. There are 150 turns of wire in each slot of the windings. All coils in each phase are connected in series. The flux per pole in the machine is 0.060 Wb, and the speed of rotation of the magnetic field is 1000 r/min.

(a) What is the frequency of the voltage produced in this winding?
(b) What are the resulting phase and terminal voltages of this stator?

Question

A three-phase Δ-connected six-pole winding is installed in 36 slots on a stator. There are 150 turns of wire in each slot of the windings. All coils in each phase are connected in series. The flux per pole in the machine is 0.060 Wb, and the speed of rotation of the magnetic field is 1000 r/min.

(a) What is the frequency of the voltage produced in this winding?
(b) What are the resulting phase and terminal voltages of this stator?

Accepted Answer

(a) The frequency of the voltage produced in this winding is

[latex]f_{s e}=\frac{n_{s m} P}{120}=\frac{(1000 \ r / min )(6 ext { poles })}{120}=50 \ Hz[/latex]

(b) There are 36 slots on this stator, with 150 turns of wire per slot. Since this is a six-pole machine, there are three sets of coils (in 12 slots) associated with each phase. The voltage in the coils in one pair of slots is

[latex]E_A=\sqrt{2} \pi N_C \phi f=\sqrt{2} \pi(150 \ t )(0.060 \ Wb )(50 \ Hz )=2000 \ V[/latex]

There are 12 slots associated with each phase, and the all of the coils in a slot are connected in series, so the total phase voltage is

[latex]V_\phi=12(2000 \ V )=24,000 \ V[/latex]

Since the machine is Δ -connected, [latex]V_L=V_\phi=24,000 \ V.[/latex]

Question 3.5: A three-phase Δ-connected six-pole winding is installed in 3...

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