Question $5$

a$)$ Explain why in a power system with several generators, usually only some of the generators, but not all, participate in automatic generation control $($AGC$).$

$(5$ marks$)$

b$)$ Table Q$5$ shows the operating condition of a $\backslash (50-\backslash$mathrm$\{$Hz$\}\backslash )$ two$-$area power system. Area A and Area B are interconnected with a tie$-$line.

Table Q$5$ Operating Condition of the System

$\backslash$begin$\{$tabular$\}\{|$l$|$c$|$c$|\}$

$\backslash$hline $\backslash$multicolumn$\{1\}\{|$c$|\}\{$ Area $\}$ & A & B $\backslash \backslash$

$\backslash$hline Total output of coal$-$fired generators & $4000$ MW & $6000$ MW $\backslash \backslash$

$\backslash$hline Total output of a wind power station & $1000$ MW & $0$ MW $\backslash \backslash$

$\backslash$hline Total output of a nuclear power station & $10000$ MW & $33000$ MW $\backslash \backslash$

$\backslash$hline Load demand & $20000$ MW & $40000$ MW $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Load variation $\backslash (($D$)\backslash )$ for $\backslash (1\backslash \%\backslash )$ change in $\backslash \backslash$

system frequency

$\backslash$end$\{$tabular$\}$ & $\backslash (1\mathrm{.}5\backslash \%\backslash )$ & $\backslash (1\mathrm{.}5\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Speed regulation $\backslash (($R$)\backslash )$ of governor in all $\backslash \backslash$

power generators

$\backslash$end$\{$tabular$\}$ & $\backslash (4\backslash \%\backslash )$ & $\backslash (4\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Spinning reserve spread uniformly over $\backslash \backslash$

all coal$-$fired generators

$\backslash$end$\{$tabular$\}$ & $1000$ MW & $1000$ MW $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Frequency bias factor settings for $\backslash \backslash$

Automatic Generation Control

$\backslash$end$\{$tabular$\}$ & $\backslash (400\backslash$mathrm$\{$MW$\}/0\mathrm{.}1\backslash$mathrm$\{$~Hz$\}\backslash )$ & $\backslash (300\backslash$mathrm$\{$MW$\}/0\mathrm{.}1\backslash$mathrm$\{$~Hz$\}\backslash )\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$($i$)$ Without supplementary control from AGC, find the new steady$-$state frequency, generation and load of each area, and tie$-$line flow, if there is a loss of $1000$ MW load in Area B$.$

$(9$ marks$)$

$($ii$)$ With supplementary control from AGC, what would be the generation in Area A and B$,$ system frequency, and tie$-$line flow if there is a sudden loss of $1000$ MW load in Area B$?(3$ marks$)$

$($iii$)$ With supplementary control from AGC, what would be the generation in Area A and B$,$ system frequency, and tie$-$line flow if there is a sudden loss of $500$ MW generation carrying part of the spinning reserve in Area B$?$

$(3$ marks$)$

$($Total: $20$ marks$)$