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Analysis of radial distribution systems with embedded series Flexible AC Transmission System (FACTS) devices is facilitated by a formulation of power flow equations with bus voltage magnitudes and line flows as independent variables. Since control variables such as the line and bus reactive powers figure directly in the formulation, handling the control action of FACTS devices in distribution systems is direct and easily implemented. Using the Breadth-First-Search (BFS), the bus incidence matrix of a radial distribution system is first rendered strictly upper diagonal, leading to reduced computational effort. All the common FACTS device models under steady-state conditions are easily incorporated in the new framework by a simple process of "variable swapping." Using IEEE standard systems, the line flow-based (LFB) formulation is shown to provide easy implementation with multiple series and shunt FACTS devices in the system and enable direct evaluation of the FACTS device ratings.