Stochastic Optimization of Distribution Networks: Application of Probabilistic Graphical Models in Electrical Grid Management

Abstract

In electricity grid management, optimizing distribution networks is a must for making sure that the grid is reliable, efficient, and resilient. Stochastic optimization methods have become very useful for dealing with the unknowns that come up in grid operations because of things like adding green energy, changing demand, and broken equipment. We present a new way to improve distribution networks when there is doubt in this study. It uses probabilistic graphical models (PGMs). Using PGMs lets us describe the complicated connections between loads, producers, and grid infrastructure, as well as the relationships between these parts of the distribution network. By recording these relationships, we can accurately show how unclear the grid is and make smart choices to make it work better. In particular, we use Bayesian networks (BNs) and Markov random fields (MRFs) to describe how the different factors in the network are likely to be related to each other. We show how well our method works by using it on a real-life delivery network problem. We look at a case study of a distribution network that has a lot of green energy sources and changing load levels. We use PGMs to build a statistical model of the distribution network by combining past data, weather forecasts, and real-time measures. Then, we create a stochastic optimization problem to find the best way to reduce the predicted operational cost while still meeting different operational restrictions, like voltage limits, power balance, and equipment limitations. We use advanced optimization algorithms, like stochastic gradient descent and genetic algorithms, to quickly solve the optimization problem that was given. We show that our method works and can be scaled up for handling distribution networks when there is doubt by doing a lot of computer tests and risk analyses. The suggested method can make delivery networks much more reliable, cost-effective, and resilient than traditional linear optimization methods, as shown by our results. Overall, this study shows that probabilistic graphical models can be a very useful tool for managing the electricity grid and finding the best ways to use distribution networks in the face of randomness. Including unknowns in the modeling process helps we make stronger and more dependable choices that will help current distribution systems work well.