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Online Planning of Power Flows for Power Systems Against Bushfires Using Spatial Context

Jianyu Xu, Qiuzhuang Sun, Yang Yang, Huadong Mo, Daoyi Dong

TL;DR

This work tackles online planning of power flows under the risk of bushfires by integrating a Moore-based stochastic fire-spread model with a DC-OPF framework in a spatial-contextual online learning setting. A contextual online learning algorithm is developed that treats in-situ fire locations as spatial context and adaptively tracks non-stationary fire dynamics via adaptive change-point detection, while solving a sequence of LPs to minimize expected operational costs. Key contributions include a Moore-based spread model with containment, a provable sublinear regret bound for the online planner, validation on NSW bushfire data, and demonstration on IEEE 11- and 57-bus networks showing superior performance over benchmarks. The approach enables real-time, data-driven, resilient power-system operation under dynamic bushfire threats and offers a foundation for extensions to more complex fire models and AC OPF.

Abstract

The 2019-20 Australia bushfire incurred numerous economic losses and significantly affected the operations of power systems. A power station or transmission line can be significantly affected due to bushfires, leading to an increase in operational costs. We study a fundamental but challenging problem of planning the optimal power flow (OPF) for power systems subject to bushfires. Considering the stochastic nature of bushfire spread, we develop a model to capture such dynamics based on Moore's neighborhood model. Under a periodic inspection scheme that reveals the in-situ bushfire status, we propose an online optimization modeling framework that sequentially plans the power flows in the electricity network. Our framework assumes that the spread of bushfires is non-stationary over time, and the spread and containment probabilities are unknown. To meet these challenges, we develop a contextual online learning algorithm that treats the in-situ geographical information of the bushfire as a 'spatial context'. The online learning algorithm learns the unknown probabilities sequentially based on the observed data and then makes the OPF decision accordingly. The sequential OPF decisions aim to minimize the regret function, which is defined as the cumulative loss against the clairvoyant strategy that knows the true model parameters. We provide a theoretical guarantee of our algorithm by deriving a bound on the regret function, which outperforms the regret bound achieved by other benchmark algorithms. Our model assumptions are verified by the real bushfire data from NSW, Australia, and we apply our model to two power systems to illustrate its applicability.

Online Planning of Power Flows for Power Systems Against Bushfires Using Spatial Context

TL;DR

This work tackles online planning of power flows under the risk of bushfires by integrating a Moore-based stochastic fire-spread model with a DC-OPF framework in a spatial-contextual online learning setting. A contextual online learning algorithm is developed that treats in-situ fire locations as spatial context and adaptively tracks non-stationary fire dynamics via adaptive change-point detection, while solving a sequence of LPs to minimize expected operational costs. Key contributions include a Moore-based spread model with containment, a provable sublinear regret bound for the online planner, validation on NSW bushfire data, and demonstration on IEEE 11- and 57-bus networks showing superior performance over benchmarks. The approach enables real-time, data-driven, resilient power-system operation under dynamic bushfire threats and offers a foundation for extensions to more complex fire models and AC OPF.

Abstract

The 2019-20 Australia bushfire incurred numerous economic losses and significantly affected the operations of power systems. A power station or transmission line can be significantly affected due to bushfires, leading to an increase in operational costs. We study a fundamental but challenging problem of planning the optimal power flow (OPF) for power systems subject to bushfires. Considering the stochastic nature of bushfire spread, we develop a model to capture such dynamics based on Moore's neighborhood model. Under a periodic inspection scheme that reveals the in-situ bushfire status, we propose an online optimization modeling framework that sequentially plans the power flows in the electricity network. Our framework assumes that the spread of bushfires is non-stationary over time, and the spread and containment probabilities are unknown. To meet these challenges, we develop a contextual online learning algorithm that treats the in-situ geographical information of the bushfire as a 'spatial context'. The online learning algorithm learns the unknown probabilities sequentially based on the observed data and then makes the OPF decision accordingly. The sequential OPF decisions aim to minimize the regret function, which is defined as the cumulative loss against the clairvoyant strategy that knows the true model parameters. We provide a theoretical guarantee of our algorithm by deriving a bound on the regret function, which outperforms the regret bound achieved by other benchmark algorithms. Our model assumptions are verified by the real bushfire data from NSW, Australia, and we apply our model to two power systems to illustrate its applicability.
Paper Structure (18 sections, 3 theorems, 63 equations, 10 figures, 3 tables, 1 algorithm)

This paper contains 18 sections, 3 theorems, 63 equations, 10 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Electricity network operational problem
  4. Bushfire spread model
  5. Operational management against bushfire
  6. Online Optimization Algorithm
  7. Estimation of model parameters
  8. Online learning algorithm
  9. Real Data on Bushfire Spread
  10. Simulation Study
  11. Case Study 1: IEEE 11 Bus System
  12. Case Study 2: IEEE 57 Bus System
  13. Conclusions
  14. Technical Proofs
  15. Proof of Proposition \ref{['proposition lp optimal']}
  16. ...and 3 more sections

Key Result

Proposition 1

Given $(p^{+}_{h,t-1},p^{-}_{h,t-1})_{h=1}^H$ and conditional on $\mathcal{B}_{t-1}$, Problem eq:power_flow can be reformulated as the following LP: where $\{\mathcal{H}(i,\mathcal{S}')\}_{i\in\mathcal{S},\mathcal{S}'\in\mathcal{P}(\mathcal{S}(i))}$ are auxiliary decision variables to linearize the $\{|\beta(i,j)|\}_{(i,j)\in\mathcal{E}}$, $\mathcal{S}(i)$ is the set of nodes in $\mathcal{S}$ tha

Figures (10)

  • Figure 1: The $1$-neighbors to $3$-neighbors of a node.
  • Figure 2: An example of the spread of bushfires.
  • Figure 3: The spread of bushfires at different times in two randomly selected days. The time $t$ here refers to the elapsed time since the start of the 48-hour observation horizon.
  • Figure 4: The MLEs $\Hat{p}^{+}_{t}$ and $\Hat{p}^{-}_{t}$ within $24$ hours for two geographical regions. Red curves indicate the mean of $\hat{p}_t^+$ or $\hat{p}_t^-$ during each specified time interval.
  • Figure 5: The Q-Q plots for the estimation biases $\Hat{p}^{+}_{t}-{p}^{+}_{t}$ and $\Hat{p}^{-}_{t}-{p}^{-}_{t}$ within the $24$-hour observation window for two randomly selected regions.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Theorem 1
  • Theorem 2