Generating Power Stations


Question 1
The expressions of fuel cost of two thermal generating units as a function of the respective power generation \mathrm{P}_{\mathrm{G} 1} and \mathrm{P}_{\mathrm{G} 2} are given as

\mathrm{F}_{1}\left(\mathrm{P}_{\mathrm{G} 1}\right)=0.1 \mathrm{aP}_{\mathrm{G} 1}^{2}+40 \mathrm{P}_{\mathrm{G} 1}+120 \mathrm{Rs} /hour
0 \mathrm{MW} \leq \mathrm{P}_{\mathrm{G} 1} \leq 350 \mathrm{MW}

\mathrm{F}_{2}\left(\mathrm{P}_{\mathrm{G} 2}\right)=0.2 \mathrm{P}_{\mathrm{G} 2}^{2}+30 \mathrm{P}_{\mathrm{G} 2}+100 \mathrm{Rs} /hour
0 \mathrm{MW} \leq \mathrm{P}_{\mathrm{G} 2} \leq 300 \mathrm{MW}

where a is a constant. For a given value of a, optimal dispatch requires the total load of 290 \mathrm{MW} to be shared as \mathrm{P}_{\mathrm{G} 1}=175 \mathrm{MW} and \mathrm{P}_{\mathrm{G} 2} =115 \mathrm{MW}. With the load remaining unchanged, the value of a is increased by 10 \% and optimal dispatch is carried out. The changes in \mathrm{P}_{\mathrm{G} 1} and the total cost of generation, F\left(=F_{1}+F_{2}\right) in Rs/hour will be as follows.
A
\mathrm{P}_{\mathrm{G} 1} will decrease and \mathrm{F} will increase
B
Both \mathrm{P}_{\mathrm{G} 1} and \mathrm{F} will increase
C
P_{\mathrm{G1}} will increase and F will decrease
D
Both \mathrm{P}_{\mathrm{G} 1} and F will decrease
GATE EE 2023   Power Systems
Question 1 Explanation: 
\begin{aligned} & \mathrm{IC}_{1}=0.2 \mathrm{aP}_{\mathrm{a}_{1}}+40 \\ & \mathrm{IC}_{2}=0.4 \mathrm{P}_{\mathrm{a}_{2}}+30 \end{aligned}

For optimal dispatch,
\mathrm{IC}_{1}=\mathrm{IC}_{2}

0.2 \mathrm{aP}_{\mathrm{G}_{1}}+40=0.4 \mathrm{P}_{\mathrm{G}_{2}}+30

Given :
\begin{aligned} \mathrm{P}_{\mathrm{G}_{1}} & =175 \mathrm{MW} \text { and } \mathrm{P}_{\mathrm{G}_{2}}=115 \mathrm{MW} \\ \therefore 0.2 \mathrm{a} \times 175+40 & =0.4 \times 115+30 \\ \Rightarrow \quad \mathrm{a} & =1.0286 \end{aligned}

Economic scheduling,
\mathrm{P}_{\mathrm{G}_{1}}+\mathrm{P}_{\mathrm{G}_{2}}=290 \mathrm{MW}

Now, if a increases by 10 \%, \mathrm{P}_{\mathrm{G}_{1}} should be decreases and total cost of generation increases.
Question 2
Base load power plants are

P: wind farms.
Q: run-of-river plants.
R: nuclear power plants.
S: diesel power plants.
A
P, Q and S only
B
P, R and S only
C
P, Q and R only
D
Q and R only
GATE EE 2015-SET-1   Power Systems


Question 3
Out of the following plant categories

(i) Nuclear
(ii) Run-of-river
(iii) Pump Storage
(iv) Diesel
The base load power plant are
A
(i) and (ii)
B
(ii) and (iii)
C
(i), (ii) and (iv)
D
(i), (iii) and (iv)
GATE EE 2009   Power Systems
Question 3 Explanation: 
Pumped storage plants and diesel stations supply power during peak loads.
NOTE: Base load-plant
(i) Low operating cost
(ii) Capability of working continuously long period.
Question 4
For harnessing low variable waterheads, the suitable hydraulic turbine with high percentage of reaction and runner adjustable vanes is
A
Kaplan
B
Francis
C
Pelton
D
Impeller
GATE EE 2004   Power Systems
Question 4 Explanation: 
Kaplan is used for run-of-river and poundage stations with heads of upto 70 m (low head). This type has an axial-flow rotor with variable-pitch blades.
Question 5
In the thermal power plants, the pressure in the working fluid cycle is developed by
A
condenser
B
super heater
C
feed water pump
D
turbine
GATE EE 2004   Power Systems
Question 5 Explanation: 
NOTE:
Condenser : The function of condenser are
(i) To provide vaccum at outlet of steam turbine.
(ii) To condense the steam ams pass on the condensate to boiler feed.
Super heater is a device used to convert saturated steam or wet steam into dry steam used for power generation process.


There are 5 questions to complete.