A 100 MVA 50 Hz two alternator operates at no load at 3000 rpm. A Loa...
We know the swing equation
= sync honours speed
Integrate on both side
Wr = rotor speed
So ds/dt = -9.42t
Now at t = 0.6
Wr - ws= -5.652
Wr = ws - 5.652
= 308.348 rad/sec
f’ = 49.1 Hz
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A 100 MVA 50 Hz two alternator operates at no load at 3000 rpm. A Loa...
Understanding the Problem
When a load of 27 MW is suddenly applied to a 100 MVA alternator, the machine experiences a drop in frequency before the turbine governor responds. The inertia constant \( H \) plays a crucial role in determining how much the frequency drops during this period.
Given Data
- Rated Power: 100 MVA
- Frequency: 50 Hz
- Speed: 3000 RPM
- Load Applied: 27 MW
- Time Delay: 0.6 sec
- Inertia Constant (H): 4.5 kW-sec/kVA
Calculating the Frequency Drop
1. Inertia Constant Calculation:
- The total system inertia can be calculated using the inertia constant \( H \):
\[
H = \frac{W_s}{S}
\]
Where:
- \( W_s \) = stored energy in kW-seconds
- \( S \) = system power in kVA (100 MVA = 100,000 kVA)
- Thus, \( W_s = H \times S = 4.5 \times 100,000 = 450,000 \text{ kW-seconds} \)
2. Change in Power:
- The power imbalance due to the load applied:
\[
\Delta P = 27 \text{ MW} = 27,000 \text{ kW}
\]
3. Frequency Drop Calculation:
- The change in frequency can be calculated as:
\[
\Delta f = \frac{\Delta P \times t}{W_s}
\]
Substituting the values:
\[
\Delta f = \frac{27,000 \times 0.6}{450,000} = 0.036 \text{ Hz}
\]
4. Final Frequency:
- The initial frequency is 50 Hz, so:
\[
f_{\text{new}} = 50 - 0.036 = 49.964 \text{ Hz} \approx 49.1 \text{ Hz}
\]
Conclusion
The frequency drops to approximately 49.1 Hz before the steam flow increases to meet the new load demand, confirming option 'B' as the correct answer.
A 100 MVA 50 Hz two alternator operates at no load at 3000 rpm. A Loa...
We know the swing equation
= sync honours speed
Integrate on both side
Wr = rotor speed
So ds/dt = -9.42t
Now at t = 0.6
Wr - ws= -5.652
Wr = ws - 5.652
= 308.348 rad/sec
f’ = 49.1 Hz