a$)$ A $440$V distribution board from which the cable is fed has a fault level of $5$MVA. Calculate the size of:

$($i$)$ XLPE copper cable for $1$ second fault clearance time $(3$ marks$)$

$($ii$)$ PVC copper cable for $1$ second fault clearance time $(3$ marks$)$

$$

b$)$ Verify that the two $($XLPE and PVC copper cable$)$ sizes $($in mm$2)$ selected in question a$)$ can supply a $3$ phase, $400$ volt, $75$ kW motor over a distance of $50$m when the cable is directly buried in the ground. The motor has a power factor of $0\mathrm{.}85$ lagging and will be started with a star$-$delta starter $($assume $3$ times starting current$).$ The voltage drop should not exceed $5\%.$ Ignore all derating factors as it is assumed cable is installed under standard conditions with no derating. $(9$ marks$)$

$$

Show all calculations.$$

$$

Tip:

ISC $=($AxK$)/$t

Where:

K$=115$ for PVC$/$copper cables of $1000$ V rating

K$=143$ for XLPE$/$copper cables of $1000$ V rating

and where:

the conductor cross sectional area in mm

the duration of the fault in seconds

A $=$ the conductor cross sectional area in mm

t $=$ the duration of the fault in seconds

$$

Use data sheets below for XLPE and PVC cables

$$

$$

$$