Transient Stability is the ability of a power system to return to its normal state after a major disturbance, such as a fault or a disconnection or connection of a large load.
When there is a disturbance in the system, there are oscillations. These oscillations are called swings. Transient stability analysis is concerned with the response of the power system to such oscillations. A power system with proper response will bring the system back to steady state operations within a short period of time.
Steady State Stability
Steady State Stability is the ability of a power system to respond to slow or gradual changes in its operating parameters. When a number of power sources and loads are connected to a system, there will be gradual shifting of loads from one generator to another. These oscillations, if not properly controlled, can develop into large oscillations which can cause bigger disturbances.