| Fault type | Connection at fault point | |------------|---------------------------| | Single line-to-ground (SLG) | Z1, Z2, Z0 in series | | Line-to-line (L-L) | Z1, Z2 in parallel | | Double line-to-ground (DLG) | Z1 in series with (Z2∥Z0) |
Fault clears at angle ( \delta_c ). System stable if area ( A_1 ) (accelerating) = area ( A_2 ) (decelerating). power system analysis lecture notes ppt
[ I_a1 = \fracV_fZ_1 + Z_2 + Z_0 + 3Z_f ] [ I_f = 3I_a1 ] | Fault type | Connection at fault point
[ C = \frac2\pi \epsilon_0\ln(D/r) \ \textF/m ] fault current | ( I_f = V_th /
| Concept | Formula | |---------|---------| | Base impedance | ( Z_base = V_base^2 / S_base ) | | Y-bus element | ( Y_ik = -y_ik ) (off-diag) | | Newton-Raphson | ( \beginbmatrix \Delta P \ \Delta Q \endbmatrix = J \beginbmatrix \Delta \delta \ \Delta |V| \endbmatrix ) | | Sym. fault current | ( I_f = V_th / (Z_th+Z_f) ) | | SLG fault | ( I_f = 3V_f / (Z_1+Z_2+Z_0) ) | | Swing equation | ( (2H/\omega_s) d^2\delta/dt^2 = P_m - P_e ) |
| 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.
[ I_f = \fracV_thZ_th + Z_f ] where ( Z_th ) includes generators (using subtransient reactance ( X_d'' )).