The GATE Grind

GATE 2023 EE – Question 21

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

The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G1}$ and $P_{G2}$ are given as

$F_1(P_{G1})=0.1aP_{G1}^2+40P_{G1}+120$ Rs/hour, $0\le P_{G1}\le350$ MW

$F_2(P_{G2})=0.2P_{G2}^2+30P_{G2}+100$ Rs/hour, $0\le P_{G2}\le300$ MW

where $a$ is a constant. For a given value of $a$, optimal dispatch requires the total load of 290 MW to be shared as $P_{G1}=175$ MW and $P_{G2}=115$ MW. With the load remaining unchanged, the value of $a$ is increased by 10% and optimal dispatch is carried out. The changes in $P_{G1}$ and the total cost of generation, $F(=F_1+F_2)$ in Rs/hour will be as follows

  1. $P_{G1}$ will decrease and $F$ will increase
  2. Both $P_{G1}$ and $F$ will increase
  3. $P_{G1}$ will increase and $F$ will decrease
  4. Both $P_{G1}$ and $F$ will decrease

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Show answer and explanation

Correct answer: (A) $P_{G1}$ will decrease and $F$ will increase

Explanation

Equal incremental cost at the original dispatch: $0.2a(175)+40=0.4(115)+30=76$, so $a=36/35=1.0286$. With $a'=1.1a=1.1314$: $0.2263P_{G1}+40=0.4(290-P_{G1})+30$ gives $P_{G1}=169.3$ MW, which is lower. The total cost: before $\approx16465$ Rs/h, after ($P_{G1}=169.3$, $P_{G2}=120.7$) $\approx16770$ Rs/h, which is higher.