We present an overview of the applications of graph theory in power system modeling, dynamics, coherency, and control. We first study synchronization of generator dynamics using both nonlinear and small-signal representations of classical structure-preserving models of power systems in light of their network structure and the weights associated with the nodes and edges of the network graph. We ...

During major power system disturbances, when multiple component outages occur in rapid succession, it becomes crucial to quickly identify the transmission interconnections that have limited transfer capability. Understanding impact of an outage on these critical (called saturated cut-sets) is important for enhancing situational awareness and taking correct actions. This paper proposes a new gra...

The power graphPG of a finite group G is the graph with the vertex set G, where two distinct vertices are adjacent if one is a power of the other. We first show that PG has a transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups of G (under usual inclusion) to characterize the structure ofPG. Finally, a closed formula fo...

Satellite power system is a complex, highly interconnected hybrid system that exhibit nonlinear and mode switching behaviors. Directed factor graph is an inference model for fault diagnosis using probabilistic reasoning techniques. A novel approach for constructing the directed factor graph structure based on hybrid bond graph model is proposed. The system components status and their fault symp...

Rule-based graph programming is a deep and rich topic. We present an approach to exploiting the power of graph programming as a representation and as an execution medium in an evolutionary algorithm (EGGP). We demonstrate this power in comparison with Cartesian Genetic Programming (CGP), showing that it is significantly more efficient in terms of fitness evaluations on some classic benchmark pr...

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...