A 50-kW, 250 V, 1200 rpm dc shunt motor when tested on no-load at 250 V draw an armature current of 13.2 A, while its speed is 1215 rpm. Upon conducting other tests it is found that Ra = 0.06 Ω and Rf = 50 Ω while Vb (brush voltage drop) = 2 V. Calculate the motor efficiency at a shaft load of 50

Question

A 50-kW, 250 V, 1200 rpm dc shunt motor when tested on no-load at 250 V draw an armature current of 13.2 A, while its speed is 1215 rpm. Upon conducting other tests it is found that [latex] R_{a} = 0.06 \Omega [/latex] and R_{f} = 50 \Omega [/latex] while [latex] V_{b}[/latex] (brush voltage drop) = 2 V.

Calculate the motor efficiency at a shaft load of 50 kW at rated voltage with a speed of 1195 rpm. Assume that the stray load loss is 1% of the output.

What would be the load for the motor to have maximum efficiency and what would be its value?

Accepted Answer

No-load test

Armature input [latex] =250 imes 13.2 [/latex] =3300 W

[latex] P_{r o t}=P_{i 0}+P_{f w}=3300-0.06 imes(13.2)^{2}-2 imes 13.2 [/latex]

= 3263 W

As speed varies very little from no-load to full-load [latex] P_{r o t} [/latex] almost remains constant.

On-load

[latex] P_{ ext {out }}=50 kW [/latex] (at shaft)

Let the armature current be [latex] I_{a}[/latex]. We write the power balance equation.

[latex] 250 I_{a}-0.06 I_{a}^{2}-2 I_{a}-3263-\underbrace{0.01 imes 50 imes 10^{3}}_{P_{s t}}=50 imes 10^{3} [/latex]

Or [latex] 0.06 I_{a}^{2}-248 I_{a}+53763=0 [/latex]

Solving we get

[latex] I_{a} [/latex] = 229.6 A

[latex] P_{ ext {in }}=250 imes 229.6+\frac{(250)^{2}}{50}=[/latex]58650 W

[latex] \eta=\frac{50000}{58650} imes 100=85.25 \% [/latex]

We shall assume that [latex] P_{st}[/latex] remains mainly constant in the range of load, we are investigating. Then

[latex] \eta=\frac{250 I_{a}-0.06 I_{a}^{2}-2 I_{a}-3763\left(P_{ ext {out }}+P_{s t} ight)}{250 I_{a}+250 imes 5} [/latex]

For maximum efficiency [latex] \frac{d \eta}{d I_{a}}=0 [/latex]

Solving we get [latex] I_{a}=284 A [/latex]

Substituting this value of [latex] I_{a} [/latex] in expression, we get

[latex] \eta_{\max }=86.36 \% [/latex]

Question 7.58: A 50-kW, 250 V, 1200 rpm dc shunt motor when tested on no-lo...

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