Power Systems: Load Flow, Fault Levels, Stability and Economic Operation
Power Systems in the PGCIL Field Engineer/DT paper tests load flow, per-unit analysis, fault levels, stability, economic dispatch and frequency/voltage control - the analysis that sits behind transmission system operation.
Load flow and per unit
Remember the three bus types: the slack (swing) bus fixes voltage magnitude and angle and absorbs the mismatch; PV (generator) buses hold |V| and inject scheduled P; PQ buses fix P and Q. The Y-bus is sparse and symmetric - its diagonal is the sum of admittances incident on a bus, and off-diagonals are the negatives of branch admittances. Per-unit conversion uses S_base (three-phase) and V_base (line-to-line), giving Z_base = V²_base/S_base.
Faults and stability
Symmetrical fault current in per unit is V_th/Z_th, and fault level is S_base/|Z_pu|. Line-to-ground faults are the most frequent; three-phase faults are generally the most severe. The swing equation (2H/ωs)(d²δ/dt²) = P_m − P_e underpins the equal-area criterion and the critical clearing angle.
Economic operation
For thermal units the optimum is equal incremental cost, dC₁/dP₁ = dC₂/dP₂ = λ, modified by loss penalty factors when transmission losses are included.
Worked example
A 132 kV bus has a Thevenin reactance of j0.2 pu on a 100 MVA base. Fault level = 100/0.2 = 500 MVA, so fault current = 500 MVA/(√3 × 132 kV) ≈ 2.19 kA. Note the line-to-line voltage is used with √3, never the phase voltage.
Traps
Using phase instead of line voltage in per-unit formulas, forgetting that the slack bus supplies system losses, and assuming X/R is negligible when estimating DC offset or breaker duty.