MATLAB Program Based on Newton-Raphson Algorithm for Power Flow Calculation

This article presents a MATLAB program based on the Newton-Raphson algorithm, designed for power flow calculation in electrical networks with known admittance matrix, PQ nodes, PV nodes, and slack bus (UA). The implementation involves solving nonlinear power flow equations through iterative matrix operations. Below are explanations of key program variables and their computational significance:

- U: Bus voltages at all nodes (complex voltage values calculated through iterative updates)

- S: Injected power at all nodes (calculated using power flow equations S = V × conj(I))

- S_net: Total network losses (sum of all line losses computed from bus voltages and admittance matrix)

- PQ_P: Calculated active power injection at PQ nodes (updated during each Newton-Raphson iteration)

- PQ_Q: Calculated reactive power injection at PQ nodes (iteratively corrected until convergence)

- delt_PQ_P: Active power correction values at PQ nodes (power mismatches used in Jacobian matrix formulation)

- delt_PQ_Q: Reactive power correction values at PQ nodes (residuals driving the convergence process)

- delt_UA_P: Active power correction values at slack bus (balances system power requirements)

- delt_U_2: Voltage squared correction values at slack bus (maintains voltage magnitude constraints)

- delt_PQV: Calculated PQU^2 correction values (handles voltage-dependent power corrections)

- J: Jacobian matrix (key computational component containing partial derivatives of power equations with respect to voltage variables)

- e: Real part of voltage (rectangular coordinate component updated during iterations)

- f: Imaginary part of voltage (rectangular coordinate component solved simultaneously)

- delt_ef: Corrections for real and imaginary voltage parts (core variables in Newton-Raphson voltage updates)

The algorithm implementation involves constructing the Jacobian matrix, solving linear systems for corrections, and updating voltages until power mismatches fall below tolerance thresholds. This information should help you understand the program's working principles and implementation approach. Please contact us if you have any questions or require further clarification.