Power system stability
Power system stability is concerned with the ability of the generators to run in synchronism and to supply the loads at acceptable frequency, rotor angle and voltage ranges in case of normal (load variations) and abnormal disturbances (faults, generator tripping) that may occur in power systems.
The stability of power system is the ability of a system to remain in a state of equilibrium under normal operating condition and return to an acceptable equilibrium state when subjected to a disturbance.
Equilibrium or Normal state: Synchronous generators operate in synchronism with the rest of the system.
1. A generator is synchronized with a bus when both of them have same frequency, voltage and phase sequence.
2. Rotor angle of all generators w.r.t. synchronously rotating reference axis should remain constant.
The stability problem is concerned with the behavior of the synchronous machines after a disturbance.
Types of Stability
Rotor angle stability
Rotor angle stability refers to the ability of the synchronous machines of an interconnected power system to remain in synchronism after being subjected to a disturbance. Instability results in some generators accelerating (decelerating) and losing synchronism with other generators. Rotor angle stability depends on the ability of each synchronous machine to maintain equilibrium between electromagnetic torque and mechanical torque.
Under steady state, there is equilibrium between the input mechanical torque and output electromagnetic torque of each generator, and its speed remains a constant.
T_{e} = T_{S} or T_{m}
Under a disturbance, this equilibrium is upset and the generators accelerate/ decelerate according to the mechanics of a rotating body.
T_{a} = T_{m} – T_{e} for synchronous generator.
Steady state stabilities & its limits
The power system is steady-state stable for a particular steady-state operating condition if, following a small and slow disturbance, it returns to essentially the same steady-state operating condition. Ex.:- Small load and/or generation variations.
Disturbances are considered to be sufficiently small such that the linearization of system equations is permissible for purposes of analysis. The time frame of interest is of the order of 10 to 20 seconds following a disturbance
Steady state stability limit: The upper limit of machine’s loading without loss of synchronism when the disturbance is small & increased gradually at a slow rate.
Transisent Stability
The power system is transiently stable for a particular steady-state operating condition if, following a large disturbance, it returns to a significantly different but acceptable steady-state operating condition is attained. Ex. - Different types of transmission line short circuits, bus or transformer faults, loss of generation, loss of a large load.
Transient stability studies are needed to ensure that the system can withstand the transient condition following a major disturbance. Disturbances are large so that the linearization of system equations is not permissible for purposes of analysis. The time frame of interest is of the order of 3 to 5 seconds following a disturbance.
Transient stability limit: The upper limit of machine’s loading without loss of synchronism when a sudden and large disturbance occurred.