A power system is operating close to its maximum roadability limit$,$ with a critical voltage of Vc $=0\mathrm{.}8$ p$.$u$.$ at one of its load buses. A disturbance increases the reactive power demand by $0\mathrm{.}3$ p$.$u$.,$ bringing the system closer to instability.

$1.$ Calculate the new load bus voltage assuming a simple linear relationship: where k $=0\mathrm{.}5$ p$.$u$.$

$2.$ Propose a load shedding strategy that reduces the reactive power demand by $0\mathrm{.}15$

p$.$u$.$ and calculate the new voltage.

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$3.$ Discuss why load shedding is an effective emergency measure to prevent voltage collapse.