1
GATE EE 2014 Set 1
+2
-0.6
The fuel cost functions of two power plants are
Plant $${P_1}:\,{C_1} = 0.05\,Pg_1^2 + AP{g_1} + B$$
Plant $${P_2}:\,{C_2} = 0.10\,Pg_2^2 + 3AP{g_2} + 2B$$
Where, $$P{g_1}$$ and $$P{g_2}$$ are the generator powers of two plants and $$A$$ and $$B$$ are the constants. If the two plants optimally share $$1000$$ $$MW$$ load at incremental fuel cost of $$100$$ $$Rs/MWh,$$ the ratio of load shared by plants $${P_1}$$ and $${P_2}$$ is
A
$$1:4$$
B
$$2:3$$
C
$$3:2$$
D
$$4:1$$
2
GATE EE 2011
+2
-0.6
A load center of 120 MW derives power from two power stations connected by 220 kV transmission lines of 25 km and 75 km as shown in the figure below. The three generators G1,G2 and G3 are of 100 MW capacity each and have identical fuel cost characteristics. The minimum loss generation schedule for supplying the 120 MW load is
A
$$P1 = 80\,MW +$$ losses
$$P2 = 20\,MW$$
$$P3 = 20\,MW +$$ losses
B
$$P1 = 60\,MW$$
$$P2 = 30\,MW$$ $$+$$ losses
$$P3 = 30\,MW$$
C
$$P1 = 40\,MW$$
$$P2 = 40\,MW$$
$$P3 = 40\,MW +$$ losses
D
$$P1 = 30\,MW +$$ losses
$$P2 = 45\,MW$$
$$P3 = 45\,MW$$
3
GATE EE 2009
+2
-0.6
Three generators are feeding a load of $$100$$ $$MW$$. The details of the generators Rating, Efficiency and Regulation are shown below

In the event of increased load power demand, which of the following will happen?

A
All the generators will share equal power
B
Generator-$$3$$ will share more power compared to Generator-$$1$$
C
Generator-$$1$$ will share more power compared to Generator-$$2$$
D
Generator-2 will share more power compared to Generator-$$3$$
4
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
$${P_{G1}} = 0\,MW;\,\,{P_{G2}} = 250\,MW$$
EXAM MAP
Medical
NEET