Formal Reliability Analysis of an Integrated Power Generation System Using Theorem Proving

In recent years, alongside conventional generators, the renewable energy-based power systems consisting of wind and solar farms, and the batteries with large capacities, termed as energy storage systems (ESS), have been increasingly installed and operated for electric power generation. The uncertainties in the generated power, due to the variability of wind speed or solar radiation and the improper charging and discharging of the batteries, greatly affects the proper operation as well as the reliability of these power systems. Due to their huge cost and safety-critical nature, the reliability analysis using traditional simulation tools, which are mainly based on Monte Carlo approach, may not be an appropriate choice. In this article, we propose to use higher order logic theorem proving to conduct an accurate reliability analysis of the power systems consisting of conventional generators, the renewable energy sources, and the ESS. For this purpose, we formally verify the generic convolution properties for n-discrete random variables and also formalize the properties of Binomial random variables in the context of power system. For illustration purposes, we present the reliability analysis of IEEE 118-bus test system consisting of 11 conventional generators, 1 wind/solar farm of 5 identical units, and 4 identical ESS batteries.