Categorical Databases for Mathematical Formalization of AC Optimal Power Flow

Abstract

It has been decades since category theory was applied to databases. In spite of their mathematical elegance, categorical models have traditionally had difficulty representing factual data, such as integers or strings. This paper proposes a categorical dataset for power system computational models, which is used for AC Optimal Power Flows (ACOPF). In addition, categorical databases incorporate factual data using multi-sorted algebraic theories (also known as Lawvere theories) based on the set-valued functor model. In the advanced metering infrastructure of power systems, this approach is capable of handling missing information efficiently. This methodology enables constraints and queries to employ operations on data, such as multiplicative and comparative processes, thereby facilitating the integration between conventional databases and programming languages like Julia and Python’s Pypower. The demonstration illustrates how all elements of the model, including schemas, instances, and functors, can modify the schema in ACOPF instances.