# 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

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.
(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.