Q$2.$ Shown in Fig. Q$2$ is part of the electrical schematic for a building, with relevant parameters of the supply circuit and transformer. The main LV switchboard is protected by a $1600$A MICB $($main incoming circuit breaker$).$ One $100$ m $-$long outgoing circuit is wired with one $\frac{3}{c}240m{m}^2$ PVC$/$SWA$/$PVC cable on tray, and is protected by a $630$A ACB $($air circuit breaker$).$ The switchboard impedance is assumed to be $0\mathrm{.}3$ mohm, and the earth fault loop impedance at the main LV switchboard is $20$ mohm. Both $1600$A and $630$A circuit breakers are controlled with IDMT relays for overcurrent and earth fault protection. Electronic relays with SI and EI curves are available for selection.

$($a$)$ Determine MAX and MIN fault currents at the remote end of the outgoing circuit.

$(6$ marks$)$

$($b$)$ Select relay types, and determine PS and TM of both overcurrent and earth$-$fault relays for MICB so that both the supply company's requirement $($Appendix Q$2)$ and the requirement of protection against indirect contact can be achieved.

$(13$ marks$)$

$($c$)$ Select relay types, and determine PS and TS of overcurrent relays for ACB if the discrimination between MICB and ACB is achieved under the $3-$phase fault at the remote end of the outgoing circuit. The grading time is assumed to be $0\mathrm{.}1$ sec $.$

$(6$ marks$)$

The time$-$current characteristic of relays is described by

$t=\frac{0\mathrm{.}14}{PS{M}^{0\mathrm{.}02}-1}TM$

$t=\frac{80}{PS{M}^2-1}TM$

The plug setting $($PS$)$ is in the range of $10\%-100\%$ with a step size of $10\%,$ and the time multiplier $($TM$)$ is in the range of $0\mathrm{.}1-1\mathrm{.}0$ with a step size of $0\mathrm{.}05.$

State all your assumptinns clearly