Enhanced Newton-Raphson Method for Solving Three-Phase Unbalanced Distribution Networks

<p>To better address challenges in three-phase unbalanced distribution networks, we propose an enhanced version of the Newton-Raphson method. This improved algorithm incorporates adaptive Jacobian matrix formulations and phase-specific power flow equations to handle diverse node configurations effectively. The implementation requires developing specialized voltage update functions that account for phase imbalances and implementing convergence criteria that monitor both magnitude and angle differences across all three phases.</p> <p>We recommend modifying the method's core algorithm to include phase-dependent admittance matrices and implementing symmetric component transformations for handling unbalanced conditions. The enhanced approach should feature automatic initialization routines that estimate initial voltage values based on network topology and load characteristics. Key functions would include a three-phase power mismatch calculator and a decoupled solution approach for improved computational efficiency.</p> <p>These algorithmic improvements enable better adaptation to various distribution network models and facilitate practical validation through simulation frameworks. The implementation should incorporate tolerance settings for unbalanced conditions and include diagnostic outputs for convergence behavior analysis. Such enhancements contribute to deeper understanding of three-phase unbalanced network challenges and provide valuable references for future research in distribution system analysis.</p>