33-Bus Power Flow Calculation Using Newton's Method in Rectangular Coordinates

This implementation performs 33-bus power flow calculation using Newton's method in rectangular coordinates. The computational process begins with collecting all essential power system parameters including generator outputs, transformer tap ratios, transmission line impedances, and load demands. A mathematical model of the power system is constructed using nodal admittance matrix formulation, where bus voltages are represented as complex quantities in rectangular form (real and imaginary components). The power flow equations are derived from the balance of active and reactive power at each bus, forming a system of nonlinear equations. The Newton-Raphson algorithm is implemented through iterative computation with the following key steps: initial flat voltage start (1.0∠0° per unit), Jacobian matrix formulation containing partial derivatives of power mismatches with respect to voltage components, and sequential solution of linear equations until convergence criteria are met. The Jacobian matrix structure efficiently handles the coupling between active power-voltage angle and reactive power-voltage magnitude relationships. Critical functions include: - Admittance matrix construction from branch parameters - Power mismatch calculation ΔP and ΔQ at each iteration - Jacobian matrix update with sensitivity coefficients - Linear equation solving using LU decomposition - Voltage correction and convergence checking The final analysis evaluates system stability through voltage profile examination, line flow limits verification, and reactive power adequacy assessment. Convergence tolerance is typically set at 0.0001 per unit for maximum power mismatch, ensuring computational accuracy for reliability assessment.