The PPT explains the Swing Equation (rotor dynamics in power systems) and the Equal Area Criterion (graphical method for transient stability). It includes the derivation, physical meaning, a power–angle curve diagram with accelerating and decelerating areas, applications, and key references.

1. P O W E R S Y S T E M S T A B I L I T Y
P R E P A R E D B Y
P U J A G U R A V
Swing Equation and Equal Area
Criterion

2. Introduction
 Stability in power systems is the ability to maintain
synchronism after disturbances
 Swing equation describes rotor dynamics
 Equal area criterion used for transient stability
analysis

3. Derivation of Swing Equation
 Basic power balance:
 Pm - Pe = (2H/ωs) * d²δ/dt²
Where:
Pm = Mechanical input power
Pe = Electrical output power
H = Inertia constant
δ = Rotor angle

4. Physical Significance
 Explains acceleration or deceleration of generator
rotor
 Increase in δ → energy stored in rotor changes
 Determines stability under faults

5. Equal Area Criterion (Concept)
 Graphical method to assess transient stability
 Condition: Area of accelerating power = Area of
decelerating power

6. Equal Area Criterion (Derivation)
 Condition for stability:
 ∫ from δ0 to δc (Pm - Pe) dδ = ∫ from δc to δmax (Pe
- Pm) dδ
Where:
δ0 = Initial rotor angle
δc = Critical clearing angle

7. Diagram – Swing Curve

8. Applications
 Determining critical clearing angle
 Stability assessment for faults in transmission lines
 Helps in designing protection schemes

9. Summary
 Swing equation = fundamental of rotor stability
 Equal area criterion = graphical stability tool
 Widely used in transient stability studies

10. References
 Power System Stability and Control – P. Kundur
 Modern Power System Analysis – I.J. Nagrath & D.P.
Kothari