Bayesian Model-based Generation of Synthetic Unbalanced Distribution Networks Incorporating Reliability Indices

TL;DR

A Bayesian Hierarchical Model (BHM) is proposed that generates phase-consistent unbalanced three-phase distribution systems, and incorporates reliability indices, and is applied to generate synthetic power distribution networks in Brazil.

Abstract

Real-world power distribution data are often inaccessible due to privacy and security concerns, highlighting the need for tools for generating realistic synthetic networks. Existing methods typically overlook critical reliability metrics such as the Customer Average Interruption Frequency Index (CAIFI) and the Customer Average Interruption Duration Index (CAIDI). Moreover, these methods often neglect phase consistency during the design stage, necessitating the use of a separate phase assignment algorithm. This work proposes a Bayesian Hierarchical Model (BHM) that generates phase-consistent unbalanced three-phase distribution systems, and incorporates reliability indices. The BHM learns the joint distribution of phase configuration, power demand, and reliability indices from a reference network, conditioning these attributes on topological features. We apply the proposed methodology to generate synthetic power distribution networks in Brazil, and validated it on known Brazilian networks. The results show that the BHM accurately reproduces the distributions of phase allocation, power demand, and reliability metrics on the training system. Furthermore, in out-of-sample validation on unseen data, the model generates phase-consistent networks and accurately predicts the reliability indices for the synthetic systems. The generated networks are also electrically feasible: three-phase power flows converge and voltages remain within typical operating limits, enabling studies of planning, reliability, and resilience.

Figures (8)

• Figure 1: Flowchart of the proposed two-part methodology for generating synthetic distribution networks.
• Figure 2: Phase allocation samples for the IEEE 123-bus system under four different prior probability scenarios. (a) Uninformative prior with all phases allowed. (b) Single-phase loads prohibited. (c) Two-phase loads prohibited. (d) Three-phase loads prohibited. In all cases, the resulting allocation is topologically consistent.
• Figure 3: Posterior predictive checks for the power demand. The figure compares the distribution (black line) and mean (blue cross) of real data with the simulated distribution (shaded areas) and mean (red circle) from the BHM .
• Figure 4: Posterior predictive checks for CAIFI model. It compares the distribution of real data (black dashed line) with the simulated distribution from the BHM (blue shaded area).
• Figure 5: Posterior predictive checks for CAIDI model. It compares the distribution of real data (black dashed line) with the simulated distribution from the BHM (blue shaded area).