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The fuel cost functions of two powr plants are
Plant P1 : C1 = 0.05 Pg²1 + APg1 + B
Plant P2 : C2 = 0.10 Pg²2 + APg2 + 2B
Where, Pg1 and Pg2 are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 1000 MW load at increamental fuel cost of 100 Rs/MWh, the ratio of load shared by plants P1 and P2 is
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- 1: 4
- 2: 3
- 3: 2
- 4: 1
Correct Option: D
C1 = Pg²1(0.05) APg1 + B
Pg1 + Pg2 = 1000
C2 = 0.1Pg²2 + 3APg2 + B (dc1/dPg2) = 100
Now dc1/dPg2 = 2Pg1 × (0.05) + A
= 2 × 0.05Pg1 + A = 100 ...(i)
| and | × 0.1 Pg2 + 3A | |
| dPg2 |
= 2 × 0.1Pg2 + 3A = 100 ...(ii)
Solving equation (i) and (ii) we get
Pg1 = 800 MW
Pg2 = 200 MW
| ∴ | = | ||
| Pg2 | 1 |
