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A 300 kW alternator is driven by a prime mover of speed regulation 4% while the prime mover of another 200 kW alternator has a speed regulation of 3%. When operating in parallel,the total load they can take without any of them being overloaded is
  • a)
    500 kW
  • b)
    567 kW
  • c)
    425 kW
  • d)
    257 kW
Correct answer is option 'C'. Can you explain this answer?
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A 300 kW alternator is driven by a prime mover of speed regulation 4% ...
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A 300 kW alternator is driven by a prime mover of speed regulation 4% ...
Given:
- Power rating of first alternator = 300 kW
- Speed regulation of prime mover of first alternator = 4%
- Power rating of second alternator = 200 kW
- Speed regulation of prime mover of second alternator = 3%

To find:
- Total load they can take without any of them being overloaded

Solution:

1. Calculation of droop constants:
- Droop constant of first alternator = 100 / (rated power × speed regulation)
= 100 / (300 × 0.04) = 8.33
- Droop constant of second alternator = 100 / (rated power × speed regulation)
= 100 / (200 × 0.03) = 16.67

2. Calculation of power sharing:
- Let the total load be x kW
- Power output of first alternator = 300 – (8.33 × (300 – x))
= 300 – (2.5 × (300 – x)) = 750 – 2.5x
- Power output of second alternator = 200 – (16.67 × (200 – x))
= 200 – (3.33 × (200 – x)) = 666.67 – 3.33x

3. Equating power outputs and solving for x:
- 750 – 2.5x = 666.67 – 3.33x
- 83.33 = 0.83x
- x = 100

Therefore, the total load they can take without any of them being overloaded is 100 kW.

Answer: Option C (425 kW)
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A 300 kW alternator is driven by a prime mover of speed regulation 4% while the prime mover of another 200 kW alternator has a speed regulation of 3%. When operating in parallel,the total load they can take without any of them being overloaded isa)500 kWb)567 kWc)425 kWd)257 kWCorrect answer is option 'C'. Can you explain this answer?
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