Equal area criteria for transient stability analysis.

Simulation of transient stability using equal area criterion, calculating critical clearing angle & time for fault conditions.

Question 1) A 50Hz, 500 MVA, 40kV generator (with transformer) is connected to a 400kV infinite bus bar through an interconnector. The generator has H=205 MJ/MVA, voltage behind transient reactance of 450 kV and is loaded 320 MW. The transfer reactance between generator and bus-bar under various conditions are: Pre-fault: 0.5 pu During fault: 1.5 pu Post fault: 0.75 pu .Calculate the critical clearing angle & critical clearing time. Also detect for clearing angle 40, 50 & 70 is system is stable or not.

Answer: Solution for Problem Statement

Output:

In MATLAB, the problem of calculating the critical clearing angle and critical clearing time for transient stability is solved using the Equal Area Criterion. The Power-Angle Curve is plotted to visualize the system's stability under pre-fault, fault, and post-fault conditions.

The system's stability is evaluated for the following clearing angles using the Power-Angle Curve obtained from MATLAB simulation and analytical calculations:

1. Clearing Angle 40°: ✅ Stable.
2. Clearing Angle 50°: ✅ Stable.
3. Clearing Angle 70°: ❌ Unstable.

Stable Condition:

• Critical Clearing Angle > Clearing Angle (δc)
• Area A1 (accelerating) = Area A2 (decelerating)
• System regains synchronism after fault clearance.

Unstable Condition:

• Clearing Angle (δc) > Critical Clearing Angle (67.17°)
• Area A1 > Area A2
• System loses synchronism and remains unstable.

How to Use This MATLAB Simulation for Transient Stability Analysis

1. Download or Open the File with MATLAB.
2. Make sure to save the file in your preferred directory or MATLAB workspace.
3. Run the Program/Script.
4. Enter the Input Data: Enter the values as per the given numerical problem statement.

As per Above Problem Statement:

• Enter internal voltage of machine: 400
• Enter infinite bus voltage: 450
• Enter reactance before fault : 0.5
• Enter reactance during fault : 1.5
• Enter reactance after fault : 0.75
• Enter mechanical power input : 320
• Enter Inertia Constant H (MJ/MVA) : 205
• Enter the clearing angle δ_cl (in degrees) for stability check: 70

Output