Power Systems
Power Systems covers transmission-line parameters, per-unit analysis, load flow, fault levels, stability, protection and economics. ESE Prelims often combines a per-unit base change with a fault or load-flow quantity.
Core rules
- Per-unit: Zpu=Zactual/Zbase, Zbase=Vbase^2/Sbase for single-phase; for three-phase use line-line V and three-phase S with sqrt(3) in current base.
- Short line: Vs=Vr+IZ; medium line: nominal-pi or nominal-T; long line: ABCD parameters with hyperbolic functions.
- Surge impedance Zc=sqrt(L/C); natural load or surge impedance loading SIL=V^2/Zc.
- Symmetrical fault: If(pu)=Epu/Xth(pu); Ibase=Sbase/(sqrt(3)Vbase).
- Stability: steady-state limit occurs at delta=90 degrees for a lossless round-rotor machine; equal-area criterion judges transient stability.
- Protection: overcurrent, distance, differential and directional relays are selected by zone and coordination.
Worked example
On a 100 MVA, 11 kV base, a generator has X=0.2 pu. Ibase=100x10^6/(sqrt(3)x11x10^3)=5.248 kA. A bolted three-phase fault gives If=5.248/0.2=26.24 kA. The reasoning is to keep voltage and MVA bases consistent and divide the per-unit EMF by the Thevenin reactance.
Traps
Mixing line-to-line and phase voltage bases; using kW where kVA belongs; forgetting sqrt(3) in three-phase current; and assuming fault current is set by load current rather than by source impedance. In stability, do not confuse the steady-state angular limit with transient first-swing stability.