Hierarchical Graph Modeling for Multi-Scale Optimization of Power Systems

Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an implementation in the $\mathtt{J}\mathtt{u}\mathtt{l}\mathtt{i}\mathtt{a}$ package $\mathtt{P}\mathtt{l}\mathtt{a}\mathtt{s}\mathtt{m}\mathtt{o}\mathtt{.}\mathtt{j}\mathtt{l}$. We apply this framework to a tri-level hierarchical framework arising in wholesale market operations that involves day-ahead unit commitment, short-term unit commitment, and economic dispatch. We show that graph abstractions facilitate the construction, visualization, and solution of these complex problems.