importance of studying voltage stability of power system?

Answer 1

The purpose of a power system is to supply operating voltage and current to some particular devices, whatever they are.

To properly design those devices, or choose the appropriate ones, you must know the voltages normally produced by the power system, as well as the voltages which might be encountered during extreme situations.
that information provides you with wiring insulation specifications, and the ability to choose the correct components to build the devices. There is no point in wiring equipment, homes, and factories with wire that is insulated for 150 Volts on a 115 Volt power system if the system puts out 250 volts under light loads, and 115 volts under heavy load. Fires and short circuits will result. Capacitors will short out. Solid state devices will blow out, or short. Insulation in motor windings will fail and shorts will occur. Everything will be a mess.