# The Weaknesses of Backward Forward Sweep Load Flow Method for Electric Distribution Systems by Cheng and Shirmohammadi

Carol Cheng and Dariush Shirmohammadi proposed in their paper (IEEE Transactions on Power Systems, Vol. 10, No. 2, May 1995) a robust three phase power flow algorithm for radial and weakly meshed electric distribution system. This power flow method is composed of three (3) basic steps that are performed iteratively until a specified convergence index has been satisfied in all busses. The 3 steps are:

1. Solving the current injection in all busses using the formula, I=conjugate(S/V)

2. Solving the line currents or branch currents by summing up all the injected currents that will flow on a particular branch all the way to the root node.

3. Backward propagation of the new bus voltages from the root node up to the terminal load busses. This can be done by subtracting the voltage drop in the line from the “from bus” to solve the “to bus” voltages.

The above steps are executed iteratively until the power mismatch has converged. For typical test feeders of around 150 busses, the solution can converge in less that 4 iterations for a relatively low power mismatch. In addition to fast convergence, the algorithm can be also implemented such that it will only utilize a relatively small amount of memory thereby further increasing the computing speed of the load flow. Most of power engineers and power engineering students find this algorithm as very helpful for problems where speed of loadflow computation is a great concern like the load flow simulation of electric distribution systems with several tens of thousands of busses. I actually use this loadflow method in my undergraduate project about optimal capacitor placement. A commercial power flow software, Synergy by Stoner, also uses this method. I further analyze the quality of the algorithm when we use this method in electric distribution systems loss segregation where we are to segregate technical losses of an electric distribution system with several tens of thousands of nodes/busses. The load flow simulation of a distribution system with around 16000 busses usually takes, more or less, 2 minutes with an average of 8 iterations, 0.00001 power mismatch and 24 hourly levels (1 loadflow simulation per hour). Although I am convence with the performance of the algorithm in terms of speed, I notice some weaknesses of this methods in terms of the accuracy of the solution.

1. The solution does not converge if the voltage drop in a branch became very large. Although a large voltage drop happens only if the line current from a bus current injection is very large due to a large load, it is not reasonable and my not be possible for actual system. It can be because of the error in gathering informations for the input data. This is how the scenario happens; due to large voltage drop, the receiving end voltage may be small enough such that the computed injected current will be sufficiently large to further increase the line current thereby further increasing the voltage drop along the line. This process will continue until the receiving end voltage became negative and totally diverge to the actual solution.

2. Although I have no sound explanation, but base from my experience, the solution converge very slow if the loads of the large electric distribution system is composed of mixed combinations of very large and very small ones. Or in other words, there is a very big difference between large and small loads.

I`m not through with the study and analysis of the said load flow method and I am hoping to further learn more about it. The user can be safeguarded from errors of the solution due to scenario number 1 by incorporating error or warning flags in programming.