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GATE 2014 EE (EE1) – Question 52

Power Systems · Economic Load Dispatch (with and without considering transmission losses) · 2 marks · Multiple choice

Two plants have fuel costs $C_1=0.05P_{g1}^2+AP_{g1}+B$ and $C_2=0.10P_{g2}^2+3AP_{g2}+2B$, with constants A,B. They optimally share 1000 MW at incremental cost ₹100/MWh. Find P₁:P₂ load-sharing ratio.

  1. 1:4
  2. 2:3
  3. 3:2
  4. 4:1

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Show answer and explanation

Correct answer: (D) 4:1

Explanation

Equal incremental costs give0.1Pg1+A=100and0.2Pg2+3A=100. Thus Pg1=1000−10Aand Pg2=500−15A. Their sum1000implies A=20, giving Pg1=800MWand Pg2=200MW. Therefore **P1:P2=4:1,D**. Constant cost terms do not affect marginal dispatch.