# MATLAB Program for Transient and Small Signal Stability Analysis – Single Machine Infinite Bus System | EE1404 – Power System Simulation Laboratory

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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