A 500 MW, 21 kV, 50 Hz three phase two pole alternator has 0.8 lagging p.f. with moment of inertia of 27.5×10 3 kgm -2 . The inertia constant H will be _______ MJ/MVA.

To calculate the inertia constant ( H ) for the alternator, we can use the formula:

[

H = frac{J cdot omega_s}{S_{base}}

]

Where:

– ( J ) is the moment of inertia in kg·m²

– ( omega_s ) is the synchronous angular speed in rad/s

– ( S_{base} ) is the base apparent power in MVA

Given:

– Moment of inertia, ( J = 27.5 times 10^3 , text{kgm}^2 )

– The rated power of the alternator, ( P = 500 , text{MW} ) which is ( 500 , text{MVA} ) because it’s a three-phase system.

– The synchronous speed ( omega_s ) for a 50 Hz system is given by:

[

omega_s = 2 pi f = 2 pi times 50 approx 314.16 , text{rad/s}

]

Now, substituting the values into the formula:

[

H = frac{27.5 times 10^3 cdot 314.16}{500 times 10^6}

]

Calculating this:

[

H approx frac{27.5 times 10^3 cdot 314.16}{500