Structural Validation of Synthetic Power Distribution Networks Using the Multiscale Flat Norm

2024-03-19

International Conference on Conceptual Structures

AI Summary

In digital twin applications for distribution networks, conventional structural similarity metrics—such as subgraph isomorphism and graph edit distance—fail due to the absence of one-to-one node/edge correspondence between synthetic and physical networks. To address this, this paper introduces the multiscale flat norm—a geometric measure-theoretic metric—into power network structural validation for the first time. Our method integrates planar triangulation with linear programming optimization to automatically localize structural discrepancy regions (“patches”) and establishes theoretical stability bounds, thereby overcoming topological mismatch limitations in distance quantification. Experiments on a real U.S. county-scale distribution network demonstrate that, compared to the Hausdorff distance, our approach jointly captures topological and geometric discrepancies with higher fidelity, significantly enhancing the interpretability and reliability of digital twin quality assessment.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

We study the problem of comparing a pair of geometric networks that may not be similarly defined, i.e., when they do not have one-to-one correspondences between their nodes and edges. Our motivating application is to compare power distribution networks of a region. Due to the lack of openly available power network datasets, researchers synthesize realistic networks resembling their actual counterparts. But the synthetic digital twins may vary significantly from one another and from actual networks due to varying underlying assumptions and approaches. Hence the user wants to evaluate the quality of networks in terms of their structural similarity to actual power networks. But the lack of correspondence between the networks renders most standard approaches, e.g., subgraph isomorphism and edit distance, unsuitable. We propose an approach based on the multiscale flat norm, a notion of distance between objects defined in the field of geometric measure theory, to compute the distance between a pair of planar geometric networks. Using a triangulation of the domain containing the input networks, the flat norm distance between two networks at a given scale can be computed by solving a linear program. In addition, this computation automatically identifies the 2D regions (patches) that capture where the two networks are different. We demonstrate through 2D examples that the flat norm distance can capture the variations of inputs more accurately than the commonly used Hausdorff distance. As a notion of stability, we also derive upper bounds on the flat norm distance between a simple 1D curve and its perturbed version as a function of the radius of perturbation for a restricted class of perturbations. We demonstrate our approach on a set of actual power networks from a county in the USA.

Problem

• Comparing geometric networks without node-edge correspondences
• Evaluating structural similarity of synthetic power networks
• Computing distance using multiscale flat norm approach

Innovation

• Uses multiscale flat norm distance
• Solves linear program for triangulation
• Identifies 2D regions of differences