A small squirrel-cage induction motor has a starting current of six times the full-load current and a full-load slip of 0.05. Find in pu of full-load values, the current (line) and starting torque with the following methods of starting ((a) to (d)). (a) direct switching. (b) stator-resistance

Question

A small squirrel-cage induction motor has a starting current of six times the full-load current and a full-load slip of 0.05. Find in pu of full-load values, the current (line) and starting torque with the following methods of starting ((a) to (d)).

(a) direct switching.

(b) stator-resistance starting with motor current limited to 2 pu,

(c) autotransformer starting with motor current limited to 2 pu, and

(d) star-delta starting.

(e) what autotransformer ratio would give 1 pu starting torque?

Accepted Answer

(a) Direct switching

[latex] I_{s}=6 pu[/latex]

[latex] T_{s}=(6)^{2} imes 0.05=1.8[/latex]

(b) Stator-resistance starting

[latex] I_{s}=2 pu[/latex] (limited to)

[latex] T_{s}=(2)^{2} imes 0.05=0.2 pu[/latex] (Eq. (9.60)

[latex] \frac{T_{s}}{T_{f l}}=\left(\frac{I_{s}}{I_{f l}} ight)^{2} s_{f l}[/latex] (9.60)

(c) Autotransformer starting

x = 2/6 = 1/3

[latex] I_{s}( ext { motor })=2 pu[/latex]

[latex] I_{s}( ext { line })=\frac{1}{3} imes 2 pu =0.67 pu[/latex]

[latex] T_{s}=(2)^{2} imes 0.05=0.2 pu[/latex] (Eq. (9.60))

(d) Star-delta starting

[latex] I_{s}=\frac{1}{3} imes 6=2 pu[/latex] (Eq. (9.68)

[latex] \frac{I_{s}( ext { star })}{I_{s}( ext { delta })}=\frac{1}{3}[/latex] (9.68)

[latex] T_{s}=\frac{1}{3} imes(6)^{2} imes 0.05=0.6 pu[/latex] (Eq. (9.69)

[latex] \frac{T_{s}(\operatorname{star})}{T_{f l}}=\frac{1}{3}\left(\frac{I_{S C}}{I_{f l}} ight)^{2} s_{f l}[/latex] (9.69)

(e) Autotransformer starting

[latex] T_{s}=x^{2}(6)^{2} imes 0.05=1.0 pu[/latex] (Eq. (9.64))

[latex] \frac{T_{s}}{T_{f l}}=x^{2}\left(\frac{I_{S C}}{I_{f l}} ight)^{2} s_{f l} [/latex] (9.64)

[latex] x=0.745(\approx 75 \% ext { tap })[/latex]

Question 9.12: A small squirrel-cage induction motor has a starting current...

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