Forward-Backward Sweep Power Flow Calculation Program for 33-Node Distribution Networks

Power flow calculation represents a fundamental component in power system analysis, particularly for radial networks like distribution systems. The forward-backward sweep method has emerged as a classical solution due to its computational efficiency and suitability for radial topologies. This article demonstrates the algorithm's implementation logic and key considerations using a 33-node distribution network as a case study.

Algorithm Core Concept The forward-backward sweep method solves steady-state power flow through alternating voltage-power iterations: Forward sweep: Starting from the root node (substation), the program calculates branch currents progressively along feeders using Kirchhoff's Current Law (KCL) to aggregate downstream load currents, while accounting for losses from line impedances. Code implementation typically involves topological sorting to ensure sequential processing from root to leaf nodes. Backward sweep: From terminal nodes back to the root, node voltages are updated according to Ohm's Law, with line losses dynamically corrected using power and voltage values from the current iteration. The algorithm structure naturally handles radial network characteristics without matrix inversion.

33-Node Model Characteristics This program targets a standard 33-node radial distribution network topology with distinctive features: Single power supply point with clear branch hierarchy High R/X ratio lines requiring explicit active-reactive power coupling handling Convergence criteria typically set as voltage deviation thresholds between iterations (e.g., 1e-5 p.u.) The implementation uses node-branch adjacency matrices for efficient network traversal and data structure.

Loss Calculation Implementation The program achieves accurate loss modeling through these computational steps: During each iteration, three-phase active losses are calculated using current branch current magnitudes and line resistances Losses are equivalenced as virtual loads added to downstream node power Relaxation factors are incorporated to mitigate oscillation issues and improve convergence speed Key functions include loss allocation algorithms and adaptive step-size control for numerical stability.

Engineering Significance This program can be directly applied to distribution network planning, reactive power optimization, and fault analysis scenarios. Its convergence performance and computational efficiency validate the practicality of forward-backward sweep methods for medium-small scale distribution networks. Future extensions could incorporate distributed generation integration or three-phase unbalanced operating conditions through modified current injection models.