QUESTION $1[18$ Marks$]$

Design a one$-$line diagram of a power system with one source $($generator$)$ at bus

$1$ and two step up transformers $($T$1$ and T$2)$ connected to bus $2$ through parallel

transmission lines $($line $1$ and line $2)$ and two step down transformers $($T$3$ and

T$4).$ T$1$ and T$3$ at transmission Line $1$ and T$2$ and T$4$ at Transmission Line $2.$

Two loads $($motor and normal load$)$ are connected to bus $2.$ Motor is directly

connected at Bus $2,$ while the normal is connected to bus $2$ through transmission

Line $3$ and transformer T$5.$ Select a common base of $100$ MVA and $21\mathrm{.}5$ kV on

the generator side. The manufacturer's data for each component is given as

follows:

$($a$)$ Identify the per$-$unit values of the network in each section and classify the

impedance diagram $($per$-$phase, per$-$unit equivalent circuit$)$ of the system

by indicating the obtained per$-$unit impedance of each component.

$($b$)$ If the motor in bus $2$ operates at full load with $0\mathrm{.}8$ power factor lagging at

a terminal voltage of $21\mathrm{.}5$ kV $,$ investigate the value of total current flowing

out of the generator.

$[6$ Marks$]$ electrical power system