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Deducing Mathematically

A 50 Hz, 4-po...

Question

A 50 Hz, 4-pole turbo generator rated 100 MVA, 11 kV has an inertia constant of 10 MJ/MVA. If the mechanical input is suddenly raised to 90 MW for an electrical load of 60 MW. Neglect mechanical and electrical losses. Then the rotor acceleration is ______electrical degrees /sec $^{2}$ .
270

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Solution

The correct option is A 270
The rating of the machine, $G = 100 M V A$

Inertia constant, $H = 10 M J / M V A$

Accelerating power, $P_{a} = 90 M W - 60 M W = 30 M W$

Angular momentum, $M = \frac{G H}{180 f} = \frac{100 \times 10}{180 \times 50} = \frac{1}{9} M J - s / e l e c t r i c a l d e g r e e$

Acceleration, $α = \frac{P_{a}}{M} = \frac{30}{1 / 9} = 270 e l e c . d e g r e e / s^{2}$

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