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An isolated sync. generator is rated at 50MW which is also the maximum continous power limit of its prime mover. It is equipped with a speed governor with 5% drop.Initially the generator is feeding 3 loads of 4MW each at 50Hz.One of these load is program to trip permanently if the freq fall below 48Hz. If an additional load of 3.5MW is connected than the frequency will settled to.?
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An isolated sync. generator is rated at 50MW which is also the maximum...
Solution:

Introduction:
In this problem, we need to find out the settled frequency when an additional load of 3.5MW is connected to the isolated sync. generator.

Given Data:
Rated Power of Sync. Generator = 50MW
Maximum Continous Power Limit of Prime Mover = 50MW
Speed Governor Drop = 5%
Load 1 = 4MW
Load 2 = 4MW
Load 3 = 4MW
Additional Load = 3.5MW
Tripping Frequency = 48Hz

Calculations:

Step 1: Total Load on Generator
Total Load = Load 1 + Load 2 + Load 3 + Additional Load
Total Load = 4MW + 4MW + 4MW + 3.5MW
Total Load = 15.5MW

Step 2: Determine the Power Output of Generator
Power Output of Generator = Total Load / Power Factor
Assuming Power Factor = 0.8 (Typical Value), then
Power Output of Generator = 15.5MW / 0.8
Power Output of Generator = 19.375MW

Step 3: Determine the Governor Set Point
Governor Set Point = Rated Speed x (1 - Speed Governor Drop)
Assuming Rated Speed = 3000 rpm (For 50Hz), then
Governor Set Point = 3000 rpm x (1 - 0.05)
Governor Set Point = 2850 rpm

Step 4: Determine the New Speed of Generator
New Speed of Generator = Power Output of Generator / Governor Set Point
New Speed of Generator = 19.375MW / 2850 rpm
New Speed of Generator = 6.798 Hz/rpm

Step 5: Determine the New Frequency of Generator
New Frequency of Generator = Rated Frequency - Change in Speed
New Frequency of Generator = 50Hz - (New Speed of Generator x 60)
New Frequency of Generator = 50Hz - (6.798 Hz/rpm x 60 rpm)
New Frequency of Generator = 50Hz - 407.88 Hz
New Frequency of Generator = 49.592Hz

Step 6: Check Whether the Frequency is Above the Tripping Frequency
New Frequency of Generator > Tripping Frequency
49.592Hz > 48Hz

Conclusion:
Therefore, when an additional load of 3.5MW is connected to the isolated sync. generator, the frequency will settle at 49.592Hz which is above the tripping frequency of 48Hz.
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An isolated sync. generator is rated at 50MW which is also the maximum continous power limit of its prime mover. It is equipped with a speed governor with 5% drop.Initially the generator is feeding 3 loads of 4MW each at 50Hz.One of these load is program to trip permanently if the freq fall below 48Hz. If an additional load of 3.5MW is connected than the frequency will settled to.?
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