📘 Equal Area Criterion (EAC) – Transient Stability
Equal Area Criterion is a graphical method used to determine stability of a single machine infinite bus system after a large disturbance (like fault).
🔹 1️⃣ Basic Idea
Swing equation:M d²Î´/dt² = Pm − Pe
Instead of solving differential equation directly, we use power-angle curve. Electrical power:Pe = (EV/X) sinδ
Mechanical power Pm is constant (horizontal line).🔹 2️⃣ What Happens During Fault?
Before fault: Pe = Pmax sinδ₀ Pm = Pe System stable at δ₀ During fault: Transfer reactance increases Pe reduces drastically So: Pm > Pe Rotor accelerates → δ increases After fault clearance: Pe restored But rotor already gained speed. Now: Pe > Pm Rotor decelerates.🔹 3️⃣ Equal Area Condition
For system to be stable: Accelerating Area = Decelerating AreaArea A1 = Area A2
Where: A1 = ∫(Pm − Pe_fault) dδ A2 = ∫(Pe_post − Pm) dδ If A1 = A2 → Stable If A1 > A2 → Unstable🔹 4️⃣ Graphical Understanding
Power vs δ curve: • Horizontal line = Pm • Sine curve = Pe Area between Pm and Pe during acceleration = A1 Area during deceleration = A2 Equal areas → rotor comes back to synchronism.🔹 5️⃣ Critical Clearing Angle
Maximum δ at which: A1 = A2 If fault cleared before this angle → Stable If cleared after → Unstable This angle = δ_critical🔹 6️⃣ Important Observations
- Used only for SMIB system
- Mechanical power assumed constant
- Fault type changes Pe curve
- Clearing time very important
🎯 GATE Focus
- Conceptual questions on stability
- Graph-based questions
- Critical clearing angle calculation
- Comparison of fault types
Equal Area = Energy Balance During Disturbance
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