Power System Stability

The first electric PS was a dc system built by Edison in 1882.
The subsequent PS that were constructed in the late 19th century were all dc systems.
However despite the initial popularity of dc systems by the turn of the 20th century ac systems started to outnumber them.
The ac systems were though to be superior as ac machines were cheaper than their dc counterparts and more importantly ac voltages are easily transformable from one level to other using transformers.
The early stability problems of ac systems were experienced in 1920 when insufficient damping caused spontaneous oscillations or hunting.
These problems were solved using generator damper winding and the use of turbine-type prime movers.

The stability of a system refers to the ability of a system to return back to its steady state when subjected to a disturbance.
Conversely, instability means a condition denoting loss of synchronism or falling out of step
Power is generated by synchronous generators that operate in synchronism with the rest of the system.
A generator is synchronized with a bus when both of them have same frequency, voltage and phase sequence.
We can thus define the power system stability as the ability of the power system to return to steady state without losing synchronism.

Stability -refers to stable operation of the synchronous machines connected to a PS when they are subjected to sudden disturbances.
Hence, stability is the ability of PS to return to stable operation when it is subjected to a disturbance.
Instability - refers to loss of synchronism (or falling out of step) of synchronous machines in the PS.
The stability studies are classified into three types depending upon the nature of the disturbance:
- Transient Stability
- Dynamic Stability
- Steady state Stability

The study of steady state stability is concerned with the determination of upper limit of loading synchronous machines before loosing synchronism.
In PS, small disturbances will continuously occur due to variation in load, changes in the speed of prime mover, fault in certain parts of the system etc.
These small disturbances may excite the system into a state of natural oscillations.
In dynamically stable systems the amplitude of oscillations will be small and they die out quickly.
In dynamically unstable systems the amplitude of oscillation is very large and they exist for a long time.
This type of unstable behaviour may create serious problems in PS operation (i.e. may lead to unnecessary frequent load shedding).

Large disturbances may occur in PS due to switching heavy loads, switching long TL, major faults, etc.
The sudden large disturbances are characterized by large changes in the speed of the rotor of SM, large change in power angle and fast change in power transfer.
These characteristics may lead to loss of synchronism.
This type of instability is called transient instability.
The aim of transient stability is to determine whether the system will remain in synchronism or not following a sudden or major disturbances, such as transmission line fault, sudden heavy loads, tripping of generating units or switching lines with heavy loads.

SM has a maximum limit of power transfer when remains in synchronism. When the power transfer exceeds the limit it cannot stay in synchronism.
SM connected to an infinite bus is basically a spring-inertia oscillatory system. The inertia is due to the mechanical part (rotor) and the spring action is due to the synchronous tie with infinite bus.
If \(\delta\) is the angular displacement of the rotor is electrical radians then the power transfer is proportional to \(\sin\delta\). Hence the mathematical equation governing the system dynamics is non-liner.

The dc-offset currents and harmonic components are neglected. The currents and voltages are assumed to have fundamental component alone.
The symmetrical components are used for the representation of unbalanced faults.
The machine speed variations will not affect the generated voltage.

studies are restricted to small and gradual changes in the system operating conditions.
we basically concentrate on restricting the bus voltages close to their nominal values.
We also ensure that phase angles between two buses are not too large and check for the overloading of the power equipment and transmission lines.
These checks are usually done using power flow studies.

involves the study of the power system following a major disturbance.
Following a large disturbance the synchronous alternator the machine power (load) angle changes due to sudden acceleration of the rotor shaft.
The objective of the transient stability study is to ascertain whether the load angle returns to a steady value following the clearance of the disturbance.

The ability of a power system to maintain stability under continuous small disturbances is investigated under the name of Dynamic Stability (also known as small-signal stability).
These small disturbances occur due random fluctuations in loads and generation levels.
In an interconnected power system, these random variations can lead catastrophic failure as this may force the rotor angle to increase steadily.

\(\checkmark\) In this chapter we shall discuss the transient stability aspect of a power system.