1
GATE EE 2008
+2
-0.6
A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the system with cost curves $${C_1}$$ and $${C_2}$$ respectively defined as follows:
$${C_1}\left( {{P_{G1}}} \right) = {P_{G1}} + 0.055 \times P_{G1}^2$$
$${C_2}\left( {{P_{G2}}} \right) = 3{P_{G2}} + 0.03 \times P_{G2}^2$$
Where $${P_{G1}}$$ and $${P_{G2}}$$ are the MW injections from generator $${G_1}$$ and $${G_2}$$ respectively. Thus, the minimum cost dispatch will be
A
$${P_{G1}} = 250\,MW;\,\,{P_{G2}} = 0\,MW$$
B
$${P_{G1}} = 150\,MW;\,\,{P_{G2}} = 100\,MW$$
C
$${P_{G1}} = 100\,MW;\,\,{P_{G2}} = 150\,MW$$
D
$${P_{G1}} = 0\,MW;\,\,{P_{G2}} = 250\,MW$$
2
GATE EE 2005
+2
-0.6
A load centre is at an equidistant from the two thermal generating stations $${G_1}$$ and $${G_2}$$ as shown in figure. The fuel cost characteristics of the generating stations are given by
$${F_1} = a + b{P_1} + cP_1^2\,Rs/hour$$
$${F_2} = a + b{P_2} + 2cP_2^2\,Rs/hour$$

Where $${P_1}$$ and $${P_2}$$ are the generations in $$MW$$ of $${G_1}$$and $${G_2}$$, respectively. For most economic generation to meet $$300MW$$ of load $${P_1}$$ and $${P_2},$$ respectively, are

A
$$150, 150$$
B
$$100, 200$$
C
$$200, 100$$
D
$$175, 125$$
3
GATE EE 2003
+2
-0.6
Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are
$${\rm I}{C_1} = 20 + 0.3\,\,{P_1},\,{\rm I}{C_2} = 30 + 0.4\,\,{P_2},\,{\rm I}{C_3} = 30$$
Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are $$50$$ $$MW$$ and $$300$$ $$MW$$ respectively. If the plant is operating on economic load dispatch to supply the total power demand of $$700$$ $$MW$$, the power generated by each unit is
A
$${P_1} = 242.86MW;{P_2} = 157.14MW;$$ and $${P_3} = 300MW$$
B
$${P_1} = 157.14MW;{P_2} = 242.86MW;$$ and $${P_3} = 300MW$$
C
$${P_1} = 300.00MW;{P_2} = 300.00MW;$$ and $${P_3} = 100MW$$
D
$${P_1} = 242.86MW;{P_2} = 157.14MW;$$ and $${P_3} = 100MW$$
4
GATE EE 2000
+2
-0.6
The incremental cost characteristic of two generators delivering $$200$$ $$MW$$ are as follows $$\,\,\,{{d{F_1}} \over {d{P_1}}} = 20 + 0.1{P_1},\,\,{{d{F_2}} \over {d{P_2}}} = 16 + 0.2{P_2}$$
For economic operation, the generations $${P_1}$$ and $${P_2}$$ should be
A
$${P_1} = {P_2} = 100\,MW$$
B
$${P_1} = 80MW,\,\,{P_2} = 120\,MW$$
C
$${P_1} = 200MW,\,\,{P_2} = 0\,MW$$
D
$${P_1} = 120MW,\,\,{P_2} = 80\,MW$$
EXAM MAP
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