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Strategic Electric Distribution Network Sensing via Spectral Bandits

Samuel Talkington, Rahul Gupta, Richard Asiamah, Paprapee Buason, Daniel K. Molzahn

TL;DR

An online bandwidth-constrained sensor sampling algorithm that takes advantage of the graphical structure inherent in the power flow equations and promotes a sampling policy that strategically accounts for electrical distance is proposed.

Abstract

Despite their wide-scale deployment and ability to make accurate high-frequency voltage measurements, communication network limitations have largely precluded the use of smart meters for real-time monitoring purposes in electric distribution systems. Although smart meter communication networks have limited bandwidth available per meter, they also have the ability to dedicate higher bandwidth to varying subsets of meters. Using this capability to enable real-time monitoring from smart meters, this paper proposes an online bandwidth-constrained sensor sampling algorithm that takes advantage of the graphical structure inherent in the power flow equations. The key idea is to use a spectral bandit framework where the estimated parameters are the graph Fourier transform coefficients of the nodal voltages. The structure provided by this framework promotes a sampling policy that strategically accounts for electrical distance. Maxima of sub-Gaussian random variables model the policy rewards, which relaxes distributional assumptions common in prior work. The scheme is implemented on a synthetic electrical network to dynamically identify meters exposing violations of voltage magnitude limits, illustrating the effectiveness of the proposed method.

Strategic Electric Distribution Network Sensing via Spectral Bandits

TL;DR

An online bandwidth-constrained sensor sampling algorithm that takes advantage of the graphical structure inherent in the power flow equations and promotes a sampling policy that strategically accounts for electrical distance is proposed.

Abstract

Despite their wide-scale deployment and ability to make accurate high-frequency voltage measurements, communication network limitations have largely precluded the use of smart meters for real-time monitoring purposes in electric distribution systems. Although smart meter communication networks have limited bandwidth available per meter, they also have the ability to dedicate higher bandwidth to varying subsets of meters. Using this capability to enable real-time monitoring from smart meters, this paper proposes an online bandwidth-constrained sensor sampling algorithm that takes advantage of the graphical structure inherent in the power flow equations. The key idea is to use a spectral bandit framework where the estimated parameters are the graph Fourier transform coefficients of the nodal voltages. The structure provided by this framework promotes a sampling policy that strategically accounts for electrical distance. Maxima of sub-Gaussian random variables model the policy rewards, which relaxes distributional assumptions common in prior work. The scheme is implemented on a synthetic electrical network to dynamically identify meters exposing violations of voltage magnitude limits, illustrating the effectiveness of the proposed method.

Paper Structure

This paper contains 23 sections, 7 theorems, 33 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Proposed Framework and Contributions
  4. Notation
  5. Problem setting
  6. Power flow model for distribution systems
  7. Review of the LinDistFlow approximation
  8. Action set and reward formulation
  9. Stochastic LinDistFlow model
  10. Concentration of nodal voltage perturbations
  11. Condition for positive semi-definite Laplacian
  12. Confidence ellipsoid, sampling policy, and regret
  13. Sensor Sampling Algorithm
  14. Optimism principle
  15. Spectral UCB
  16. ...and 8 more sections

Key Result

Lemma 1

Given Assumption assum:known-phase, there exists a Laplacian matrix $L = (R + X \mathbf{I} \kappa)^{-1}$ and orthonormal eigenbasis $W$ such that $L := W \Lambda W^\mathsf{T}$, $\Lambda := \operatorname{diag}(\lambda_1,\dots,\lambda_n)$, and the LinDistFlow model is then $v = v^{\bullet} \mathds{1}

Figures (3)

  • Figure 1: Illustration of the problem: Given an aggregate bandwidth limit across nodes, adaptively design sampling a policy $\mathcal{S}\subseteq \mathcal{N}$ to expose violations of voltage magnitude limits.
  • Figure 2: Performance with unity power factor at all nodes. The plots show regret relative to the LinDistFlow and AC optimal sampling vs. time with spectral (left) and $\ell_2$ (right) regularization.
  • Figure 3: Performance with random, non-unity power factors. The plots show regret relative to the LinDistFlow and AC optimal sampling vs. time with spectral (left) and $\ell_2$ (right) regularization.

Theorems & Definitions (14)

  • Lemma 1
  • Lemma 2
  • Definition 1
  • Lemma 3
  • Theorem 1
  • Lemma 4
  • proof
  • Theorem 2
  • proof
  • proof
  • ...and 4 more