[ I_a1 = \fracV_fZ_1 + Z_2 + Z_0 + 3Z_f ] [ I_f = 3I_a1 ]
Critical clearing angle ( \delta_c ) increases with higher inertia, faster fault clearing. 8. Conclusion & Summary Tables (PPT Final Module) Key formulas card:
neglected for overhead lines.
Base quantities: ( S_base ) (3-phase MVA), ( V_base ) (line-to-line kV).
[ C = \frac2\pi \epsilon_0\ln(D/r) \ \textF/m ] power system analysis lecture notes ppt
| Line type | R (Ω/km) | L (mH/km) | C (nF/km) | |-----------|----------|-----------|-----------| | Short (<80 km) | lumped | ignored | ignored | | Medium (80–240 km) | lumped | lumped | lumped (π model) | | Long (>240 km) | distributed parameters | | | 4. Load Flow Analysis (PPT Module 4) Goal: Determine voltage magnitude & angle at each bus for given loads/generations.
[ \textpu value = \frac\textActual value\textBase value ] [ I_a1 = \fracV_fZ_1 + Z_2 + Z_0
[ L = 2\times 10^-7 \ln \left( \fracDr' \right) \ \textH/m ] where ( r' = r \cdot e^-1/4 ) (geometric mean radius, GMR).