- Asked 3/22
- 2078 Bhadra · 5 marks
Load sharing among three generators
Short answer
Each unit's stiffness K = P_r/(R f0): G1 500, G2 125, G3 133.33 MW/Hz. With ∆f = +1 Hz, G1 loses 500 MW (to 0 MW), G2 loses 125 MW (to 125 MW), G3 loses 133.33 MW (to 66.67 MW). Total load = 191.67 MW.
Three generators of 500MW, 2% drop, 250MW, 4% drop and 200MW, 3% drop are supplying to a common load. When each generator is fully loaded, they operate at common frequency of 49Hz. Calculate the system load shared by each unit when frequency increased to 50Hz.
All three units are fully loaded at 49 Hz. As frequency rises to 50 Hz, each moves up its droop line and sheds load equal to its stiffness times the rise ( Hz).
| Unit | Rating (MW) | Droop | (MW/Hz) | Reduction (MW) | Load at 50 Hz (MW) |
|---|---|---|---|---|---|
| G1 | 500 | 2 % | 500/(0.02×50) = 500 | 500 | 0 |
| G2 | 250 | 4 % | 250/(0.04×50) = 125 | 125 | 125 |
| G3 | 200 | 3 % | 200/(0.03×50) = 133.33 | 133.33 | 66.67 |
| Total | 950 | – | 758.33 | 758.33 | 191.67 |
Answer: At 50 Hz, G1 = 0 MW (it reaches its no-load point, Hz), G2 = 125 MW, G3 = 66.67 MW; total system load ≈ 191.67 MW.
✓ Answer checked by Claude Opus 5.5 (high effort)
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