Forward-Backward Sweep Algorithm: Modern Implementation for Power Flow Analysis

In modern power systems, radial distribution networks have become a widely adopted grid structure. To better understand the performance characteristics and operational behavior of this configuration, researchers continuously explore new computational methodologies. Among these, the forward-backward sweep algorithm stands out as a widely-used approach for efficiently solving three-phase power flow problems in radial distribution networks. The algorithm operates through two main phases: the forward sweep computes branch currents from end nodes toward the root using Kirchhoff's Current Law (KCL), while the backward sweep calculates node voltages from the root outward using Kirchhoff's Voltage Law (KVL) - typically implemented through iterative matrix operations or sparse matrix techniques. Key implementation aspects include: - Node numbering optimization using depth-first search for sequential processing - Handling of unbalanced three-phase loads through phase-specific impedance matrices - Convergence acceleration techniques like successive over-relaxation (SOR) factors - Parallel computation implementation for multiple feeder branches This algorithm not only significantly improves computational speed through its linear complexity O(n) relative to network size, but also enhances calculation accuracy by properly modeling phase imbalances and network topology constraints. These advantages make power system modeling and analysis more precise and reliable. Consequently, employing this algorithm provides superior support for power system design and operation, ultimately improving overall grid performance and reliability through features like voltage stability margin calculation and loss quantification.