In this paper, a sudden growth of reactive power demand at a load bus accompanied with the single branch (power transformer or transmission line) outage contingency is studied to determine the critical line at which the weak bus is diagnosed with help of Fast Voltage Stability Index (FVSI). The importance of this work is due to the fact that the power system which is operating under normal mode may be threatened as it may face a sudden increase demand contingency, which may lead to cascading outages, and/or violations of bus voltage which may lead to voltage collapse. This diagnosis of the weak bus is useful to determine the optimum location for shunt compensation required to improve

This paper dealt with possible type of contingencies which occurred in several power systems in the world which related to maloperation of a protection system for a line or a transformer and their consequences related to overloading another branches and hence, lead to cascading outages. To minimize the fault level and prevent the cascading outages and hence , prevent partial (brownout) or complete (blackout) collapse of the system an earthing (grounding) transformer is used on both sides of the faulted line .This suggested solution to able the system to be a secure system against maloperation of a protective system.This paper offers the simulation results of the IEEE 14 Bus system which represented in MATLAB at off line security analysis.