An analysis method for an electrical power system whereby the plurality of buses are grouped into agents, family lines of agents and families of agents based on the reactive reserves depleted when the buses are loaded. Contingencies are then applied to the electrical power system. The reactive reserves are monitored, and an exhaustion factor is determined for one or more family lines in one or more families. A boundary case solution is used to assess where, why, and how the contingency causes voltage instability, voltage collapse and/or local blackout. Based on this information, the design of voltage rescheduling, active rescheduling, unit commitment, load shedding, etc., is determined that can be used as preventive, corrective or emergency controls in applications such as system design and planning, operation planning, reactive and voltage management, real time control and Special Protection System Control. Based on this information, solutions can then be applied to the power system.