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GATE 2021 EE – Question 20

Power Systems · Economic Load Dispatch (with and without considering transmission losses) · 1 mark · Multiple choice

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are

$$\frac{dF_1}{dP_1}=40+0.2P_1$$

$$\frac{dF_2}{dP_2}=32+0.4P_2$$

They need to deliver a combined load of 260 MW. Ignoring the network losses, for economic operation, the generations $P_1$ and $P_2$ (in MW) are

  1. $P_1=P_2=130$
  2. $P_1=160,\ P_2=100$
  3. $P_1=140,\ P_2=120$
  4. $P_1=120,\ P_2=140$

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Correct answer: (B) $P_1=160,\ P_2=100$

Explanation

For economic operation the incremental costs are equal: $40+0.2P_1=32+0.4P_2$ with $P_2=260-P_1$. So $40+0.2P_1=136-0.4P_1$, giving $0.6P_1=96$, $P_1=160$ MW and $P_2=100$ MW.