As an introduction, we need to know about **power state stability**. It is really the capability of the system to return to its steady state condition after subjected to certain disturbances. We can now consider a synchronous generator to understand the power system stability. The generator is in synchronism with the other system connected to it. The bus connected to it and the generator will have same phase sequence, voltage and the frequency. So, we can say that the power system stability here is the capability of the power system to come back to its steady condition without affecting synchronism when subjected to any disturbances. This system stability is classified into – Transient Stability, Dynamic Stability and ** Steady State Stability**.

**Transient Stability:** Study of power system which are subjected to sudden major disturbances.**Dynamic Stability:** Study of power system which are subjected to small continuous disturbances.

## Steady State Stability

It is the study which implies small and gradual variations or changes in the working state of the system. The purpose is to determine the higher limit of loading in the machine before going to lose the synchronism. The load is increased slowly.

The highest power which can be transferred to the receiving end of the system without affecting the synchronism is termed as Steady State Stability limit.

The Swings equation is known by

P_{m} → Mechanical power

P_{e} → Electrical power

δ → Load angle

H → Inertia constant

ω_{s} → Synchronous speed

Consider the above system (figure above) which is operating on steady state power transfer of

Assume the power is increased by a small amount say Δ P_{e}. As a result, the rotor angle becomes

from δ_{0}.

p → frequency of oscillation.

The characteristic equation is used to determine the system stability due to small changes.

## Conditions for System Stability

Without loss of stability, the Maximum power transfer is given by

Assume, the condition when the system is in operation with lower than the steady state stability limit. Then, it may oscillate continuously for a lengthy time if the damping is very low. The oscillation which persists is a hazard to system security. The |V_{t}| should be kept constant for each load by adjusting the excitation. This is to maintain the **steady state stability** limit.

- A system can never be operated higher than its steady state stability limit but it can operate beyond the transient stability limit.
- By reducing the X (reactance) or by raising the |E| or by increasing the |V|, the improvement of steady state stability limit of the system is possible.
- Two systems to improve the stability limit are quick excitation voltage and higher excitation voltage.
- To reduce the X in the transmission line which is having high reactance, we can employ parallel line.