Power Systems: Swing Equation, Equal Area Criterion & Fault Analysis
Power generation and transmission engineering questions asked in PSU interviews including NTPC, PowerGrid, NPCIL, and state electricity boards.
In-Depth Interview Questions & Model Solutions
Q1Derive and explain the physical significance of the Swing Equation in synchronous generators.
The Swing Equation governs the electromechanical rotor dynamics: `M * (d²δ / dt²) = Pa = Pm - Pe`, where M is the angular momentum, δ is the rotor load angle, Pm is mechanical power input, and Pe is electrical power output (`Pe = (Ev*V / X) * sin δ`). If a fault occurs on the transmission line, Pe drops sharply while Pm remains constant, creating accelerating power `Pa > 0`, which increases rotor angle δ. If fault clearing time exceeds the Critical Clearing Time (CCT), the system loses synchronism.
- M = (G * H) / (π * f) where H is the inertia constant in MJ/MVA.
- Equal Area Criterion states accelerating area A1 must equal decelerating area A2 for stability.
- Critical Clearing Angle (δcr) determines the maximum permissible breaker tripping delay.
Q2Explain the working of Differential Protection on power transformers and how Magnetizing Inrush is prevented.
Differential protection (Merz-Price scheme) operates on Kirchhoff’s Current Law: under normal operation, current entering equals current leaving (secondary CT currents balance in the relay operating coil). During internal fault, a spill current flows through the operating coil, tripping the circuit breaker. To prevent false tripping during transformer energization due to high Magnetizing Inrush Current (rich in 2nd harmonics), relays use Harmonic Restraint (tripping is blocked if 2nd harmonic exceeds ~15% of fundamental).
- Percentage biased differential relay uses restraining coils to handle CT saturation.
- 2nd harmonic restraint blocks false inrush tripping.
- 5th harmonic restraint blocks over-excitation tripping.
Technical Panel Interview Strategy Tips
- For NTPC and PowerGrid boards, know the typical transmission voltages in India (400 kV, 765 kV AC, and ±800 kV HVDC).