Simulator 16 User Guide - PowerWorld

Augmenting Path Max Flow Min Cut Algorithm
The augmenting path max flow – min cut algorithm is used to identify the minimum number of
branches that need to be opened or removed from the system in order to isolate the Facility (power
system device) from an External region.
The algorithm is an application of the Max Flow - Min Cut theorem, which states that the maximum
flow that can be transferred from a set of source nodes to a set of sink nodes across a graph equals
the capacity of the minimum cut. The facility analysis in Simulator finds a min cut, although this cut
may not be unique.
The application consists of three stages:
1. Convert the electric network to a graph structure
In this stage, each branch of the system is converted to an undirected arc with graph flow capacity
equal to one. Thus, only one unit of graph flow can be sent through a branch. The Facility buses
and the External buses are converted to Facility and External supernodes, respectively. This
effectively reduces the problem to finding the min cut between these two supernodes. The number
of nodes and capacities of the Facility and the External region are also computed during this stage.
2. Find the Max Flow using the Augmenting Path Algorithm
This is an iterative process. At each step, the algorithm finds a new augmenting path from the
Facility to the External region and augments the graph flow along this path in one unit.
Consequently, the branches in the path won’t be available for flow augmentation in the next step.
Each new path is determined using a shortest path routine. The algorithm stops when no
augmenting path from the Facility to the External region can be found. The number of units
transferred from the Facility to the External region (path augmentations) reaches the number of
branches in a certain cut. Note that the number of branches in the min cut can not exceed the
capacity of either the Facility or the External region.
3. Determine the branches in the min cut
The identification of the branches that constitute the min cut consists in tracking down labels in
the buses and branches used during each path augmentation.
©2011 PowerWorld Corporation
938