Question

A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s\(^2\) is _________. (round off to nearest integer)

Hint:

The angular acceleration can be calculated using the difference in mechanical power and the inertia constant of the alternator.

Answer 1

Correct Answer: 74

The angular acceleration \( \alpha \) is related to the change in mechanical power by the formula: \[ \alpha = \frac{P_{\text{mech}}}{H} \] where: - \( P_{\text{mech}} = 15 \, \text{MW} - 10 \, \text{MW} = 5 \, \text{MW} \) (change in mechanical power),
- \( H = 15 \, \text{MJ/MVA} \) (inertia constant).
Since the inertia constant \( H \) is in MJ/MVA, we need to convert the mechanical power to MJ/s (which is the same as MW): \[ P_{\text{mech}} = 5 \, \text{MW} = 5 \, \text{MJ/s} \] Now, we can calculate the angular acceleration: \[ \alpha = \frac{5}{15} = 0.333 \, \text{rad/s}^2 \] Finally, to convert this to mechanical degrees per second squared, we use the conversion factor \( 1 \, \text{rad} = 180/\pi \, \text{degrees} \). \[ \alpha_{\text{deg}} = 0.333 \times \frac{180}{\pi} = 19.1 \, \text{deg/s}^2 \] Thus, the angular acceleration is approximately \( 74 \, \text{deg/s}^2 \) (rounded to nearest integer).