Power Grids' Dynamic Enlargement Calculus Using Petri Nets

The robustness of power grids characterizes the behavior of grids in situations of serial failures and/or human errors. A coherent method of evaluating vulnerability is to quantify this attribute in terms of the scale-free graph theory. One way of increasing power grid robustness consists of adding new electric lines between the existing nodes. Once the target scale-free network is found, the real network must be enlarged to the graph of the target network. The choice of a reasonable solution is made difficult by the great number of topological solutions, because this number increases as the number of the network nodes becomes bigger. Thus, the first aim is to make an inventory of all these solutions. The second necessary step is to build correct algorithms able to find the nodes of the real grid which will be connected respecting economical criteria. In continuation of our previous research, our paper proposes a Petri net-based method of building all enlargement variants, starting from non-robust networks to the nearest free-scale, robust network. Starting from some distinctive characteristics of elementary enlargements introduced in our earlier works, this allows us to obtain a mathematically unique, robustness-oriented enlargement solution