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The incremental costs (in Rupees/M Wh) of operating two generating units are functions of their respective powers P1 and P2 in MW, and are given by
dC1 = 0.2P1 + 50; dC2 = 0.24P2 + 40; dP1 dP2
Where
20 MW ≤ P1 ≤ 150 MW
20 MW ≤ P2 ≤ 150 MW
For a certain load demand, P1 and P2 have been chosen such that dC1 /dP1 = 76 Rs/MWh and dC2/dP2 = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then P2 is __________.
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- 130
- 1360
- 1.036
- 136.36
Correct Option: D
= | = 76 = 0.2P1 + 50 | |
dP1 |
⇒ P1 = 130
and | = 68.8 = 0.24P2 + 40 | |
dP2 |
∴ P2 = 120
∴ P1 + P2 = 130 + 120 = 250
For minimization of total cost
= | |||
dp1 | dp2 |
∴ 0.2p1 + 50 = 0.24p2 + 40
∴ 0.2[250 – P2] + 50 = 0.24P2 + 40
∴ P2 = 136.36