Conceptual Framework For Determining The Treewidth of Distribution Grids

While distribution grids are often operated radially, they are typically designed to be more redundant, so that each load has multiple connections to the main grid. For complex networks like these, the notion of treewidth can be used to quantify their complexity. In this paper, we propose a new conceptual framework and derive an exact formula for computing treewidth with the help of our constructs. We argue that our framework effectively captures complexities in the structure of distribution grids and has a potential to simplify the calculation of treewidth. After analysing our findings, we hypothesise that the treewidth of distribution grids will typically be low implying that some difficult power system problems can be solved on them in parameterised polynomial time with dynamic programming. We demonstrate this with an example problem of dividing a distribution grid into tree-like operational subgraphs around the primary substations so that no voltage violations occur.