Solves load flow for radial distribution feeders with spot and distributed loads across 3 to 6 feeder nodes. Employs the robust iterative Backward/Forward Sweep (BFS) method to calculate node voltages, branch current flows, line section I²R losses, and total feeder technical efficiency.
Governing Formulas & Standards
Standards Basis: IEEE Std 141 / Distribution Automation Guidelines
I_{\text{branch}, k} = \sum I_{\text{downstream}}, \quad V_{k+1} \approx V_k - \frac{P_k R_k + Q_k X_k}{V_k}, \quad P_{\text{loss}} = 3 \cdot I^2 \cdot R
Iterates backward to aggregate branch currents from loads, then sweeps forward from the substation to calculate exact node voltage drops and technical line losses.
Worked Engineering Example: Load Flow on 4-Node 11 kV Industrial Feeder (7.8 km Total Length)
- Backward Current Sweep: Sum branch currents from Node 4 back to substation → Head-end Current = 74.8 A
- Forward Voltage Sweep: Compute cumulative voltage drop from substation to Node 4 → Tail-end Voltage = 10.42 kV (0.947 pu)
- Compute Total Technical Losses: Sum 3·I²·R across all 4 line sections → 38.6 kW (2.88% of input power)
Final Solution: Tail Voltage: 0.947 pu (5.3% Drop) | Total Losses: 38.6 kW | Feeder Efficiency: 97.1%
Frequently Asked Questions
- Why is Backward/Forward Sweep preferred over Newton-Raphson for radial feeders?
- Radial feeders have high R/X ratios and a tree structure. BFS exploits the radial topology directly without building or inverting a large Jacobian matrix, ensuring fast execution and 100% numerical convergence.
Interactive calculation engine and real-time CAD solver available online at https://amithvijayan.in/tools/radial-feeder-load-flow.