1. UNIT V STABILITY ANALYSIS 9
Importance of stability analysis in power system planning and operation
- classification of power system stability
- angle and voltage stability
– Single Machine Infinite Bus (SMIB) system:
Development of swing equation
- equal area criterion
- determination of critical clearing angle and time
– solution of swing equation by modified Euler method and Runge-Kutta fourth order method.

2. STABILITY ANALYSIS
The stability of a system refers to the ability of a system to return back to its steady state when subjected to a disturbance.
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.
It is also define that the power system stability as the ability of the power system to return to steady state without losing synchronism

4. Steady State Stability
Steady State Stability studies are restricted to small and gradual changes in the system operating conditions.
In this 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

5. Transient Stability
Transient Stability 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.

6. Dynamic Stability
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 to 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.

7. Classification of power system stability

8. POWER SYSTEM STABILITY:
Ability to remains in operating equilibrium
ANGLE STABILITY:
Ability to maintain synchronism
Torque balance of synchronous machines (I/p turbine & o/p generator.
VOLTAGE STABILITY :
Ability to maintain steady acceptable volatge

9. Basic concept of ’synchronism’
In the normal equilibrium condition, all the synchronous generators run at a constant speed and the difference between the rotor angles of any two generators is constant.
Under any disturbance, the speed of the machines will deviate from the steady state values due to mismatch between mechanical and electrical powers (torque) and therefore, the difference of the rotor angles would also change.
If these rotor angle differences (between any pair of generators) attain steady state values after some finite time, then the synchronous generators are said to be in ’synchronism’.

10. Small signal instability
The disturbance occurring in the system is small.
Such kind of small disturbances always take place in the system due to random variations of the loads and the generation.
The change in the electrical torque of a synchronous generator can be resolved into two components, namely,
a) synchronizing torque (Ts) - which is proportional to the change in the rotor angle.
b) damping torque (Td), which is proportional to the change in the speed of the machine
Depending on the amounts of synchronizing and damping torques, small signal instability can manifest itself in two forms

11. Two forms
When there is insufficient amount of synchronizing torque, the rotor angle increases steadily.
On the other hand, for inadequate amount of damping torque, the rotor angle undergoes oscillations with increasing amplitude.
a) Stable state (where TS & TD are Positive)
b) Non-Oscillatory Instability (TS – Negative &
TD -Positive)
c) Oscillatory Instability (TS – Positive & TD - Neg)

13. Types of small signal instability

14. Transient instability
If the disturbance on the system is quite severe and sudden, the machine is unable to maintain synchronism under the impact of this disturbance.
In this case, there is a large excursion of the rotor angle (even if the generator is transiently stable).

15. In case 1, under the influence of the fault, the generator rotor angle increases to a maximum, subsequently decreases and settles to a steady state value following oscillations with decreasing magnitude.

16. In case 2, the rotor angle decreases after attaining a maximum value.
However, subsequently it undergoes oscillations with increasing amplitude. This type of instability is not caused by the lack of synchronizing torque; rather it occurs due to lack of sufficient damping torque in the
post fault system condition.

17. In case 3, the rotor angle monotonically keeps on increasing due to insufficient synchronizing torque till the protective relay trips it. This type of instability, in which the rotor angle never decreases, is termed as ’first swing instability’.