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AIM:
To find the critical clearing angle and critical clearing time using mat lab
ALGORITHM
1. Get the values of terminal voltage and generator voltage.
2. Get the value of power in per unit.
3. Get reactance during pre fault, fault and post fault conditions.
4. Calculate Pmax1 , Pmax2 ,Pmax3.
5. Calculate the critical clearing angle using the formula.
Pm
Cos deler = --------------(Delmax-DeIO)+cos(Delmax)
Pmax
THEORY :
Stability :
Stability problem is concerned with the behavior 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 synchronizing torque.
(ii) Rotor oscillations of increasing magnitude due to lack of sufficient damping torque.
FORMULA:
Reactive power Qe = sin(cos-1(p.f))
Voltage behind transient condition
Voltage of infinite bus
Where,
Angular separation between E1 and EB
Prefault Operation:
During Fault Condition:
Pe = 0
Find out X from the equivalent circuit during fault condition
Post fault Condition:
Find out X from the equivalent circuit during post fault condition
Critical Clearing Angle:
Critical Clearing Time:
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.
PROBLEM:
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:
Thus the program for finding critical clearing angle and critical clearing time is written using MATLAB and outputs are obtained.