We wish to use a 40 hp, 1760 r/min, 440 V, 3-phase squirrel-cage induction motor as an asynchronous generator. The rated current of the motor is 41 A, and the full-load power factor is 84%.

Question

a. Calculate the capacitance required per phase if the capacitors are connected in delta.
b. At what speed should the driving engine run to generate a frequency of 60 Hz?

Accepted Answer

a. The apparent power drawn by the machine when it operates as a motor is

[latex]\begin{aligned}S &=\sqrt{3} E I \&=1.73 imes 440 imes 41 \&=31.2 kVA\end{aligned}[/latex]

The corresponding active power absorbed is

[latex]\begin{aligned}P &=S \cos heta \&=31.2 imes 0.84 \&=26.2 kW\end{aligned}[/latex]

The corresponding reactive power absorbed is

[latex]\begin{aligned}Q &=\sqrt{S^{2}-P^{2}} \&=\sqrt{31.2^{2}-26.2^{2}} \&=17 kvar\end{aligned}[/latex]

When the machine operates as an asynchronous generator, the capacitor bank must supply at least 17 ÷ 3 = 5.7 kvar per phase. The voltage per phase is 440 V because the capacitors are connected in delta. Consequently, the capacitive current per phase is

[latex]\begin{aligned}I_{ c } &=Q / E=5700 / 440 \&=13 A\end{aligned}[/latex]

The capacitive reactance per phase is

[latex]\begin{aligned}X_{ c } &=E / I=440 / 13 \&=34 \Omega\end{aligned}[/latex]

The capacitance per phase must be at least

[latex]\begin{aligned}C &=1 / 2 \pi f X_{ c } \&=1 /(2 \pi imes 60 imes 34) \&=78 \mu F\end{aligned}[/latex]

Fig. 15 shows how the generating system is connected. Note that if the load also absorbs reactive power, the capacitor bank must be increased to provide it.

b. The driving engine must turn at slightly more than synchronous speed. Typically, the slip should be equal to the full-load slip when the machine operates as a motor. Consequently,

[latex]\begin{aligned} ext { slip } &=1800-1760 \&=40 r / min\end{aligned}[/latex]

The engine should therefore run at an approximate speed of

[latex]\begin{aligned}n &=1800+40 \&=1840 r / min\end{aligned}[/latex]

Question 14.6: We wish to use a 40 hp, 1760 r/min, 440 V, 3-phase squirrel-...

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