They are
- Steady state stability
- Transient stability
- Dynamic stability
Steady state stability is the stability of the system to respond during minor disturbances during normal operations. The variation in the bus voltages and the phase angles are relatively small. Steady state stability is caused by switching small loads.
Transient stability, on the other hand, is the analysis of the response of the system to sudden and large variations in the system voltage and phase angles. This kind of variation is caused by a sudden fault or overload, caused by a tripping of a power source.
Power flow studies need to be conducted to study the response of a power system to steady state and transient faults.
Dynamic stability is the stability which is maintained against small variations. These variations can coalesce into large variations which can cause large fluctuations and tripping. Dynamic stability is ensured by the use of sophisticated control equipments.