[Paper Review] PaToPa: A Data-Driven Parameter and Topology Joint Estimation Framework in Distribution Grids

Jiafan Yu, Yang Weng+1 more|arXiv (Cornell University)|May 24, 2017

Sparse and Compressive Sensing Techniques27 references15 citations

TL;DR

PaToPa proposes a data-driven framework for joint estimation of line parameters and topology in distribution grids using an error-in-variables model within a maximum likelihood estimation framework. By transforming the NP-hard problem into a generalized low-rank approximation via variable reparameterization and noise decorrelation, and employing an iterative expectation-maximization-like algorithm, PaToPa achieves high accuracy in parameter and topology estimation even with noisy measurements, outperforming existing methods on IEEE test systems with real feeder data.

ABSTRACT

The increasing integration of distributed energy resources (DERs) calls for new planning and operational tools. However, such tools depend on system topology and line parameters, which may be missing or inaccurate in distribution grids. With abundant data, one idea is to use linear regression to find line parameters, based on which topology can be identified. Unfortunately, the linear regression method is accurate only if there is no noise in both the input measurements (e.g., voltage magnitude and phase angle) and output measurements (e.g., active and reactive power). For topology estimation, even with a small error in measurements, the regression-based method is incapable of finding the topology using non-zero line parameters with a proper metric. To model input and output measurement errors simultaneously, we propose the error-in-variables (EIV) model in a maximum likelihood estimation (MLE) framework for joint line parameter and topology estimation. While directly solving the problem is NP-hard, we successfully adapt the problem into a generalized low-rank approximation problem via variable transformation and noise decorrelation. For accurate topology estimation, we let it interact with parameter estimation in a fashion that is similar to expectation-maximization fashion in machine learning. The proposed PaToPa approach does not require a radial network setting and works for mesh networks. We demonstrate the superior performance in accuracy for our method on IEEE test cases with actual feeder data from South California Edison.

Motivation & Objective

• To address the critical challenge of inaccurate or missing topology and line parameters in distribution grids due to aging infrastructure and limited monitoring.
• To develop a joint estimation framework that simultaneously estimates line parameters and topology using abundant phasor and power measurements from AMI and µPMU deployments.
• To overcome the limitations of regression-based methods that fail under measurement noise by modeling both input (voltage) and output (power) measurement errors.
• To enable accurate estimation in both radial and meshed distribution networks, not restricted to radial topology assumptions.
• To provide a robust, data-driven solution for operational planning and monitoring in distribution grids with high distributed energy resource (DER) penetration.

Proposed method

• Formulates the joint estimation problem as an error-in-variables (EIV) model within a maximum likelihood estimation (MLE) framework to account for noise in both input (voltage) and output (power) measurements.
• Transforms the non-convex, NP-hard optimization problem into a generalized low-rank approximation (GLRA) problem through variable reparameterization and noise decorrelation.
• Introduces two relaxation strategies: identity matrix and diagonal matrix relaxation of the measurement covariance matrix to balance computational tractability and estimation accuracy.
• Employs an iterative algorithm inspired by expectation-maximization: alternating between parameter estimation (using QR decomposition and matrix updates) and topology inference via connected/disconnected bus identification.
• Uses QR decomposition of the admittance matrix A to decompose the solution space and derive update rules for the dual variables c and d, representing the direction of parameter deviation.
• Applies iterative refinement via alternating optimization of c, d, σ, and the diagonal matrices D_c and D_d, ensuring convergence to a local minimum with strong empirical performance.

Experimental results

Research questions

• RQ1 Can a data-driven framework jointly estimate line parameters and topology in distribution grids with high accuracy despite noisy voltage and power measurements?
• RQ2 How can measurement errors in both input (voltage) and output (power) variables be properly modeled to improve estimation robustness compared to standard regression?
• RQ3 What mathematical reformulation enables the NP-hard joint estimation problem to be approximated as a generalized low-rank matrix approximation problem?
• RQ4 How does the iterative interaction between parameter estimation and topology inference enhance overall accuracy, especially in the presence of small measurement errors?
• RQ5 To what extent does the proposed method outperform existing regression-based or single-line estimation techniques on real-world and IEEE test feeder data?

Key findings

• PaToPa achieves superior accuracy in joint parameter and topology estimation compared to traditional regression-based methods, especially under noisy conditions where regression fails to detect topology.
• The method successfully identifies the correct topology even when measurement errors cause almost all off-diagonal elements of the estimated admittance matrix to be non-zero in standard regression.
• The diagonal matrix relaxation strategy significantly improves estimation accuracy over identity matrix relaxation by preserving heterogeneity in measurement noise levels.
• On IEEE test cases using real feeder data from South California Edison, PaToPa demonstrates robust performance across various noise levels and network configurations, including meshed networks.
• The iterative algorithm converges reliably and maintains high accuracy, with numerical results showing strong robustness across diverse test cases.
• The framework is applicable to both radial and meshed distribution networks, extending beyond the limitations of prior methods restricted to radial topologies.