**AIM:**

To become familiar with various aspects of the transient and small signal stability analysis

of Single-Machine-Infinite Bus (SMIB) system.

**PROGRAM REQUIRED:**

MATLAB 5.3

**THEORY:**

**Stability:**Stability problem is concerned with the behaviour of power system when it is subjected

to disturbance and is classified into small signal stability problem if the disturbances are small and

transient stability problem when the disturbances are large.

**Transient stability:**When a power system is under steady state, the load plus transmission loss

equals to the generation in the system. The generating units run a synchronous speed and system

frequency, voltage, current and power flows are steady. When a large disturbance such as three

phase fault, loss of load, loss of generation etc., occurs the

power balance is upset and the

generating units rotors experience either acceleration or deceleration. The system may come back

to a steady state condition maintaining synchronism or it may break into subsystems or one or

more machines may pull out of synchronism. In the former case the system is said to be stable and

in the later case it is said to be unstable.

**Small signal stability:**When a power system is under steady state, normal operating condition,

the system may be subjected to small disturbances such as variation in load and generation,

change in field voltage, change in mechanical toque etc., The nature of system response to small

disturbance depends on the operating conditions, the transmission system strength, types of

controllers etc. Instability that may result from small disturbance may be of two forms,

(i) Steady increase in rotor angle due to lack of synchronising torque.

(ii) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.

**FORMULA:**

**PROCEDURE:**

1. Enter the command window of the MATLAB.

2. Create a new M – file by selecting File - New – M – File

3. Type and save the program.

4. Execute the program by either pressing Tools – Run

5. View the results.

**EXERCISE:**

1. A 60Hz synchronous generator having inertia constant H = 5 MJ/MVA and a direct axis

transient reactance Xd

1 = 0.3 per unit is connected to an infinite bus through a purely

reactive circuit as shown in figure. Reactances are marked on the diagram on a common

system base. The generator is delivering real power Pe = 0.8 per unit and Q = 0.074

per unit to the infinite bus at a voltage of V = 1 per unit.

a) A temporary three-phase fault occurs at the sending end of the line at point F.When

the fault is cleared, both lines are intact. Determine the critical clearing angle and

the critical fault clearing time.

b) Verify the result using MATLAB program.

**PROGRAM:**

Pm = 0.8; E = 1.17; V = 1.0;

X1 = 0.65; X2 = inf; X3 = 0.65;

eacfault(Pm, E, V, X1, X2, X3)

For b)

Pm = 0.8; E = 1.17; V = 1.0;

X1 = 0.65; X2 = 1.8; X3 = 0.8;

eacfault(Pm, E, V, X1, X2, X3)

**RESULT:**

Finally,became familiar with various aspects of the transient and small signal stability analysis

of Single-Machine-Infinite Bus (SMIB) system.

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