Admittance Matrix Concentration Inequalities for Understanding Uncertain Power Networks

2025-10-20

AI Summary

Characterizing the spectral properties of the admittance matrix and quantifying errors in linear power flow models under parameter uncertainties—such as line outages—in electric power networks remains challenging. Method: This paper integrates random matrix theory with probabilistic concentration inequalities to derive, for the first time, unified probabilistic error bounds for DC, LinDistFlow, and AC power flow approximations under stochastic topology variations. Line statuses are modeled as independent Bernoulli random variables; rigorous analysis establishes concentration of the admittance matrix eigenvalue distribution and yields explicit upper bounds on power flow solution deviations. Contribution/Results: The work reveals mechanistic insights into how stochastic perturbations affect the network’s spectral structure and steady-state response. It provides verifiable theoretical guarantees for stability analysis and robust control design in uncertain power systems, bridging a critical gap between stochastic modeling and deterministic power system analysis.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper presents probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach imports tools from probability theory, such as concentration inequalities for random matrices with independent entries. It yields error bounds for common approximations of the AC power flow equations under parameter uncertainty, including the DC and LinDistFlow approximations.

Problem

• Probabilistic bounds for uncertain power network parameters
• Concentration inequalities for random admittance matrix spectrum
• Error bounds for AC power flow approximations under uncertainty

Innovation

• Probabilistic bounds for admittance matrix spectrum
• Concentration inequalities for random matrices
• Error bounds for AC power flow approximations