Two generating stations 1 and 2 have full-load …
Question:
Two generating stations 1 and 2 have full-load capacities of 200 and 100 MW, respectively, at a frequency of 50 Hz. The two stations are interconnected by an induction motor and synchronous generator set with a full-load capacity of 25 MW. The speed regulation of Station-1, Station-2, and induction motor and synchronous generator set are 4%, 3.5%, and 2.5%, respectively. The loads on respective bus bars are 750 and 50 MW, respectively. Find the load taken by the motor-generator set.
Answer:
To solve this problem, we need to calculate the load taken by the motor-generator set (MG set) based on the frequency and speed regulations of the generating stations and the load distribution.
Given Data:
- Station 1 Capacity: 200 MW
- Station 2 Capacity: 100 MW
- Motor-Generator Set Capacity: 25 MW
- Load on Station 1 Bus Bar: 750 MW
- Load on Station 2 Bus Bar: 50 MW
- Speed Regulation of Station 1: 4% (0.04)
- Speed Regulation of Station 2: 3.5% (0.035)
- Speed Regulation of Motor-Generator Set: 2.5% (0.025)
Step 1: Calculate the Effective Output of Each Station
The formula for effective output considering speed regulation is:
Pout = Prated × (1 + Speed Regulation × (Pload / Prated))
Step 2: Calculate the Outputs
For Station 1:
Pout1 = 200 × (1 + 0.04 × (750 / 200)) = 200 × (1 + 0.15) = 230 MW
For Station 2:
Pout2 = 100 × (1 + 0.035 × (50 / 100)) = 100 × (1 + 0.0175) = 101.75 MW
Step 3: Calculate Total Load and MG Set Load
Total output from the stations:
Ptotal = Pout1 + Pout2 = 230 + 101.75 = 331.75 MW
Step 4: Load on Motor-Generator Set
The total demand is 800 MW (750 MW + 50 MW). The load on the motor-generator set is:
PMG = Ptotal - (Pload1 + Pload2) = 800 - 331.75 = 468.25 MW
Conclusion:
The load taken by the motor-generator set is 468.25 MW.
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