Power System Analysis and Design
Core concepts
This domain ties the rest together: per-unit, load flow, faults, stability, and protection. Choose base values and convert with Z_base = kV²/MVA, remembering that per-unit impedance changes when the base changes. Load flow solves for bus voltages and angles given P, Q, and |V| specifications; the slack bus absorbs mismatch, PV buses hold voltage, and PQ buses supply loads. Fault studies use symmetrical components - positive, negative, and zero sequence networks connected according to fault type - to find fault current, which sets breaker interrupting duty. Stability questions distinguish steady-state, transient, and voltage stability, and the swing equation ties rotor angle to accelerating power. Protection coordination requires time-current curves to overlap in the right order so the downstream device clears first.
Traps to expect
Forgetting to convert impedance to a new MVA base is the classic error. The zero-sequence network is often assumed present when a delta winding blocks it, or when a grounding transformer is actually needed. Also check whether line-to-ground or three-phase fault is larger - three-phase is often but not always the worst case. In per-unit, voltage is continuous through a transformer while actual volts change with the turns ratio.
Worked example
A 50 MVA, 138 kV base gives Z_base = 138²/50 ≈ 381 Ω. A line with 20 Ω of reactance is 20/381 ≈ 0.0525 pu. Changing the base to 100 MVA gives 0.0525 × 100/50 = 0.105 pu - the same physical line, a different number.