๐ Power Systems – Mega Revision Formula Sheet (Page 20)
Final rapid revision formulas for GATE + PSU.
๐น Per Unit System
Base Current: I_base = S_base / (√3 V_base) Base Impedance: Z_base = V_base² / S_base Per Unit Value: PU = Actual / Base๐น Fault Analysis
3-Phase Fault Current: I_f = V / Z_total SLG Fault Current: I_f = 3V / (Z1 + Z2 + Z0) Fault MVA: MVA_fault = √3 V I If impedance reduces by x%, fault current increases by 1/(1-x)๐น Transmission Lines
Surge Impedance: Z_s = √(L/C) SIL = V² / Z_s Short line → Ignore capacitance Medium line → Nominal ฯ Long line → Hyperbolic equations๐น Stability
Power Equation (SMIB): P = (EV/X) sinฮด Maximum Power: P_max = EV / X Swing Equation: M d²ฮด/dt² = P_m - P_e Maximum power at ฮด = 90°๐น Economic Dispatch
Incremental Cost: dC/dP = ฮป With Losses: (dC/dP) × Penalty Factor = ฮป Penalty Factor: 1 / (1 - ∂P_L/∂P_i)๐น Load Flow
Gauss-Seidel → Linear convergence Newton-Raphson → Quadratic convergence Slack Bus → V & angle fixed PV Bus → P & V fixed PQ Bus → P & Q specified๐น HVDC
Power = V × I Advantages:- No reactive power flow
- No stability limit
- Lower losses for long distance
๐น Protection
Distance Relay → Measures impedance Zone 1 → 80% line Differential Relay → Based on KCL PSM = Fault Current / Relay Setting๐น Load Factors
Load Factor = Average Load / Peak Load Diversity Factor = Sum of Individual Max / System MaxPage 20 – Mega Revision Formula Sheet Completed
๐ฅ Power Systems Complete Master Module (20 Pages) Achieved ๐ฅ
.png)
No comments:
Post a Comment