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A Bayesian Hierarchical Model for Generating Synthetic Unbalanced Power Distribution Grids

Henrique O. Caetano, Rahul K. Gupta, Marco Aiello, Carlos Dias Maciel

TL;DR

This work tackles the scarcity of real power distribution data by introducing a Bayesian Hierarchical Model to generate unbalanced three-phase distribution systems from a given topology and aggregated node demand. By learning from real networks, the framework captures phase-type probabilities and per-phase demand distributions, enabling fast sampling of realistic synthetic grids and transferring learned patterns across systems. Key contributions include the probabilistic specification of 3-phase presence, phase allocation via Dirichlet distributions, a truncated normal model for per-phase demand, a phase-consistency filter, and demonstrated transfer learning on European 906 and IEEE 123 systems with MAPE below $8\%$, while maintaining feasible voltage profiles. This approach offers a privacy-preserving, scalable tool for planning and operational analysis of modern, unbalanced power grids.

Abstract

The real-world data of power networks is often inaccessible due to privacy and security concerns, highlighting the need for tools to generate realistic synthetic network data. Existing methods leverage geographic tools like OpenStreetMap with heuristic rules to model system topology and typically focus on single-phase, balanced systems, limiting their applicability to real-world distribution systems, which are usually unbalanced. This work proposes a Bayesian Hierarchical Model (BHM) to generate unbalanced three-phase distribution systems learning from existing networks. The scheme takes as input the base topology and aggregated demand per node and outputs a three-phase unbalanced system. The proposed scheme achieves a Mean Absolute Percentage Error (MAPE) of less than $8\%$ across all phases, with computation times of 20.4 seconds for model training and 3.1 seconds per sample generation. The tool is applied to learn from publicly available SMART-DS dataset and applied to generate European 906 and IEEE-123 systems. We demonstrate the transfer learning capability of the proposed tool by leveraging a model trained on an observed system to generate a synthetic network for an unobserved system. Specifically, the tool is trained using the publicly available SMART-DS dataset and subsequently applied to generate synthetic networks for the European 906-bus system and the IEEE 123-bus system. This tool allows researchers to simulate realistic unbalanced three-phase power data with high accuracy and speed, enhancing planning and operational analysis for modern power grids.

A Bayesian Hierarchical Model for Generating Synthetic Unbalanced Power Distribution Grids

TL;DR

This work tackles the scarcity of real power distribution data by introducing a Bayesian Hierarchical Model to generate unbalanced three-phase distribution systems from a given topology and aggregated node demand. By learning from real networks, the framework captures phase-type probabilities and per-phase demand distributions, enabling fast sampling of realistic synthetic grids and transferring learned patterns across systems. Key contributions include the probabilistic specification of 3-phase presence, phase allocation via Dirichlet distributions, a truncated normal model for per-phase demand, a phase-consistency filter, and demonstrated transfer learning on European 906 and IEEE 123 systems with MAPE below , while maintaining feasible voltage profiles. This approach offers a privacy-preserving, scalable tool for planning and operational analysis of modern, unbalanced power grids.

Abstract

The real-world data of power networks is often inaccessible due to privacy and security concerns, highlighting the need for tools to generate realistic synthetic network data. Existing methods leverage geographic tools like OpenStreetMap with heuristic rules to model system topology and typically focus on single-phase, balanced systems, limiting their applicability to real-world distribution systems, which are usually unbalanced. This work proposes a Bayesian Hierarchical Model (BHM) to generate unbalanced three-phase distribution systems learning from existing networks. The scheme takes as input the base topology and aggregated demand per node and outputs a three-phase unbalanced system. The proposed scheme achieves a Mean Absolute Percentage Error (MAPE) of less than across all phases, with computation times of 20.4 seconds for model training and 3.1 seconds per sample generation. The tool is applied to learn from publicly available SMART-DS dataset and applied to generate European 906 and IEEE-123 systems. We demonstrate the transfer learning capability of the proposed tool by leveraging a model trained on an observed system to generate a synthetic network for an unobserved system. Specifically, the tool is trained using the publicly available SMART-DS dataset and subsequently applied to generate synthetic networks for the European 906-bus system and the IEEE 123-bus system. This tool allows researchers to simulate realistic unbalanced three-phase power data with high accuracy and speed, enhancing planning and operational analysis for modern power grids.
Paper Structure (12 sections, 5 equations, 7 figures, 2 tables, 3 algorithms)

This paper contains 12 sections, 5 equations, 7 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Synthetic Network Generation Framework
  3. Estimating Probabilities from the Real data
  4. Bayesian Hierarchical Model
  5. Creating the Synthetic Power System
  6. Filtering samples for phase consistency
  7. Results and Discussion
  8. Fitting Real-world Data to the BHM
  9. Creating synthetic power systems from user input
  10. Using transfer learning to create synthetic power systems
  11. Validation of Phase Consistency Algorithm
  12. Conclusions

Figures (7)

  • Figure 1: Flowchart of the proposed methodology.
  • Figure 2: Histogram showing the distribution of the percentage of active power allocated to each phase for 3-phase loads, derived from collected data.
  • Figure 3: Probability of a load being 3-phase ($p_{3\Phi(d)}$) as a function of the normalized distance $d$, derived from the SMART-DS dataset.
  • Figure 4: Comparison between user input (red line) and BHM model-generated samples (blue bars) for active power distribution across all loads and three network phases, presented for both balanced (upper) and unbalanced (lower) scenarios.
  • Figure 5: Assessment of the proposed approach's transfer learning capability. The histograms depict the active power distribution for the same power system.
  • ...and 2 more figures