The algorithm for the backward-forward sweep power flow simulation for three-phase unbalance radial distribution system was formulated by D. Shirmohammadi and C. S. Cheng on their paper for the IEEE Transactions on Power Systems. The algorithm is quite simple since it was only based from the two basic laws in electrical engineering, the kirchhoff’ s current and voltage laws. Since specially formulated for the power flow of a distribution system, which is usually, radial to up to weakly meshed in configuration, it is fast and a very effective tool for a simulation where speed is a factor, like the power flow of a large scale system. If properly implemented using a programming language of your choice, the execution time increases less than linearly with respect to increase in the number of nodes or bus.

The Algorithm

The iterative methodology involves three steps;
1. Current injection calculation for each node

where
Iia, Iib, Iic are current injections at node i corresponding to constant power load and shunt elements
Sia, Sib, Sic are scheduled (known) power injections at node I
Via, Vib, Vic are voltages at node I
Yia, Yib, Yic are admittances of all shunt elements at node I

2. Backward sweep to sum up line section current. The current in line section i is computed as

where
Jia, Jib, Jic are the current flows on line section i
M is the set of line sections connected to node i

3. Forward sweep to update nodal voltage. The voltage at node j is

Iteration of these steps repeats until the convergence criteria is satisfied.

This power flow algorithm has already proven the effectiveness of its features on the optimal capacitor allocation research I made on 2004, the Synergy distribution system tool box, and the Distribution System Loss Segregation Software of PowerSolv in the Philippines.