A 200 MVA and 1000 MVA synchronous machine has H1 = 2 MJ/MVA and H2 =

1.	A 200 MVA and 1000 MVA synchronous machine has H1 = 2 MJ/MVA and H2 = 4 MJ/MVA respectively which are operating in parallel. Calculate the equivalent H constant for both relative to a 10 MVA base.1. 44 MJ/MVA2. 440 MJ/MVA3. 444 MJ/MVA4. 4400 MJ/MVA
Answer» Correct Answer - Option 2 : 440 MJ/MVA Concept: The KVA is inversely proportional to the inertia constant. \(S \propto \frac{1}{H}\) \(\Rightarrow \frac{{{S_{new}}}}{{{S_{old}}}} = \frac{{{H_{old}}}}{{{H_{new}}}}\) Calculation: Given that, S1 = 200 MVA, H1 = 2 MJ/MVA S2 = 1000 MVA, H2 = 4 MJ/MVA Common base = 10 MVA. We know that \(S \propto \frac{1}{H}\) \(\Rightarrow \frac{{{S_{new}}}}{{{S_{old}}}} = \frac{{{H_{old}}}}{{{H_{new}}}}\) For generator 1: \({H_{new}} = \frac{{200}}{{10}} \times 2 = 40\;MJ/MVA\) For generator 2: \({H_{new}} = \frac{{1000}}{{10}} \times 4 = 400\;MJ/MVA\) Equivalent inertia constant (H) = 400 + 40 = 440 MJ/MVA

A 200 MVA and 1000 MVA synchronous machine has H1 = 2 MJ/MVA and H2 = 4 MJ/MVA respectively which are operating in parallel. Calculate the equivalent H constant for both relative to a 10 MVA base.1. 44 MJ/MVA2. 440 MJ/MVA3. 444 MJ/MVA4. 4400 MJ/MVA

Answer» Correct Answer - Option 2 : 440 MJ/MVA

Concept:

The KVA is inversely proportional to the inertia constant.

\(S \propto \frac{1}{H}\)

\(\Rightarrow \frac{{{S_{new}}}}{{{S_{old}}}} = \frac{{{H_{old}}}}{{{H_{new}}}}\)

Calculation:

Given that,

S1 = 200 MVA, H1 = 2 MJ/MVA

S2 = 1000 MVA, H2 = 4 MJ/MVA

Common base = 10 MVA.

We know that \(S \propto \frac{1}{H}\)

\(\Rightarrow \frac{{{S_{new}}}}{{{S_{old}}}} = \frac{{{H_{old}}}}{{{H_{new}}}}\)

For generator 1:

\({H_{new}} = \frac{{200}}{{10}} \times 2 = 40\;MJ/MVA\)

For generator 2:

\({H_{new}} = \frac{{1000}}{{10}} \times 4 = 400\;MJ/MVA\)

Equivalent inertia constant (H) = 400 + 40 = 440 MJ/MVA

Discussion

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