Graphon-based Synthetic Power System Model and its Application in System Risk Analysis

The high confidentiality level of power system's data has motivated the ongoing research on the generation of synthetic power grids that mimic actual systems. The existing synthetic models rely on specific geographical and parametric assumptions, which leads to non-generalizable models that overfit the observed data. To fill up this research gap, this paper proposes the use of graphon, a non-parametric graph processing method, to generate graph samples of different sizes with similar topological and electrical characteristics as actual power systems. We first estimate the graphon based on realistic parameters of the observed actual power system. Then as an example of a use case, we sample multiple graphs from the graphon in order to provide a general assessment of the power system vulnerabilities.

I. Introduction and Motivation

The reliable and efficient operations of smart cities highly depend on improved monitoring and management of energy usage, increased efficiency, and enhanced power grid re-silience. When smart cities' critical infrastructures are optimized for safety and security, they can improve the quality of life for its citizens through enhanced public services and access to a sustainable environment. However, a fundamental limitation in research on power systems is the restricted access to the confidential data associated with actual power grids. For instance, in the U.S., power system's data related to the production, generation, transmission, and distribution of energy fall under the Critical Energy/Electricity Infrastructure Information (CEII), and therefore are not made available even for research purposes [1]. When partial power system data is made accessible, it often does so under a strong non-disclosure agreement. Therefore, any study done on actual power systems cannot be made public. Along this direction, some efforts were made to create synthetic power systems that mimic the characteristic features of actual power grids such as [2]–[4]. However, these developed models rely on several assumptions such as the geographical area, the region structure, the topological and electrical statistics, etc., with a limited number of test cases provided. Moreover, it is hard to assess how these synthetic models scale to massive power systems. Another limitation is that research is conducted on specific synthetic test cases, and therefore, the final results become dependent on the systems used in the study. To fill this research gap, this paper introduces graphons [5], a non-parametric graph processing method, to model and predict how power systems massively expand by taking the graphs to the limit, i.e., to an infinite number of vertices and edges. This graph theory concept allows to generate random power graphs that are consistent with the observed actual power graph. Since graphons treat power systems as graph objects, we will present a method to statistically equip graphs with electrical parameters. Therefore, statistically consistent power graphs of different sizes with topological and electrical information can be generated to assess power systems vulnerabilities.