# Power System Stability

Power System Stability is the ability of a power system network to regain its equilibrium state even after being subjected to a disturbance. The main objective one must understand in power transmission is that the maximum amount of real power is aimed to be transferred to the load. Achieving this is practically not possible due to frequent load variation (either increase or decrease), but with various methods and analysis operating the system in the most stable region can be implemented and that is where this area of study comes into the picture.

Understanding the type of instability introduced into the system, the network is brought back to its equilibrium operating condition to achieve maximum power transfer. Let us first understand the main parameters that need to be taken into account to ensure a stable network.

We know the equation to determine the real power transferred in a transmission line:

Pe =
EV sin𝛿

X

Where,
Pe = Magnitude of real power transferred
E = Excitation voltage
V = Terminal Voltage
𝛿 = Load angle/ Power angle (the angle between the Excitation voltage phasor and the terminal voltage phasor)
X = The total reactance

Therefore the relation can be plotted as follows:

This is defined as the power angle curve.

If we notice, as the load angle increases the power transferred also increases and reaches the maximum at 90°. But, when it further increases the power transferred decreases significantly.

Thus, the load angle should be maintained in such a way that the power should not be decreased.

A change in load results in a number of issues:
1. Change in frequency
3. Change in rotational characteristics (especially speed of the machine)

Thus, a variation in load makes the system lose its synchronism and that is brought back with the help of Load Frequency Control.

The system stability can be classified depending on the type of disturbances it incurs in the system. They may be classified into:

2. Transient Stability
3. Dynamic Stability

The ability of the machine (synchronous machine) to deliver maximum real power to the loads by maintaining equilibrium even when it experiences a small and gradual variation of load. Small load variations may occur when the frequency of oscillations made by the rotor is less than the natural frequency of the system (basically the change in rotational characteristics of the synchronous machines may fall under this category).

## Transient Stability

Transient Stability is the ability of the machine to deliver maximum real power to loads when it experiences a sudden and large variation of load. This type of variation of the load is due to the occurrence of three-phase fault that lasts for a few cycles. The types of three-phase faults may be:

CASE 1: WHEN IT OCCURS NEAR TO THE BUSBAR
CASE 2: WHEN IT OCCURS MIDWAY BETWEEN THE SENDING AND RECEIVING END
CASE 3: WHEN IT OCCURS ON THE BUSBAR

## Dynamic Stability

The ability of the system to remain stable against smaller disturbances that do not last more than a few seconds. These smaller disturbances may occur due to random small variations in load or power generation levels. If these disturbances are cleared in few seconds, the system is said to be dyanamically stable.

### Assumptions

There are a few assumptions taken and need to be kept in mind while analyzing the stability of a power system network.

1. Effect of the shunt capacitance is neglected
2. The resistance is neglected
3. Mechanical input to the alternator is assumed to be constant (angular velocity is constant, running at synchronous speed)
4. Effect of damper winding is neglected

Author: Vaishnav Chathayil is pursuing his B.Tech. in Electrical and Electronics engineering at National Institute of Technology, Calicut.