[Paper Review] Multi-period Power System Risk Minimization under Wildfire Disruptions

Hanbin Yang, Noah Rhodes+3 more|arXiv (Cornell University)|May 4, 2023

Optimal Power Flow Distribution4 citations

TL;DR

This paper proposes a two-stage stochastic mixed-integer program to optimize multi-period preemptive de-energization in power systems under combined exogenous and endogenous wildfire risks, using a Lagrangian cut decomposition algorithm. The method reduces wildfire damage and load-shedding costs by 25–30% compared to deterministic and robust benchmarks while maintaining robustness against uncertainty perturbations.

ABSTRACT

Natural wildfire becomes increasingly frequent as climate change evolves, posing a growing threat to power systems, while grid failures simultaneously fuel the most destructive wildfires. Preemptive de-energization of grid equipment is effective in mitigating grid-induced wildfires but may cause significant power outages during natural wildfires. This paper proposes a novel two-stage stochastic program for planning preemptive de-energization and solves it via an enhanced Lagrangian cut decomposition algorithm. We model wildfire events as stochastic disruptions with random magnitude and timing. The stochastic program maximizes the electricity delivered while proactively de-energizing components over multiple time periods to reduce wildfire risks. We use a cellular automaton process to sample grid failure and wildfire scenarios driven by realistic risk and environmental factors. We test our method on an augmented version of the RTS-GLMC test case in Southern California and compare it with four benchmark cases, including deterministic, wait-and-see, and robust optimization formulations as well as a comparison with prior wildfire risk optimization. Our method reduces wildfire damage costs and load-shedding losses, and our nominal plan is robust against uncertainty perturbation.

Motivation & Objective

• To address the growing threat of wildfires exacerbated by power system failures and climate change.
• To model the dual impact of exogenous (external) and endogenous (grid-induced) wildfires on power system operations.
• To develop a stochastic optimization framework that captures temporal and spatial uncertainty in wildfire disruptions over multiple time periods.
• To improve upon deterministic and robust optimization approaches by incorporating realistic wildfire dynamics and scenario sampling.
• To ensure operational robustness and cost efficiency in power system de-energization planning under uncertainty.

Proposed method

• Formulates a two-stage stochastic mixed-integer program (SMIP) to jointly optimize de-energization and power flow decisions under wildfire uncertainty.
• Models wildfire events as stochastic disruptions with random timing and magnitude using a cellular automaton process for scenario generation.
• Incorporates binary parameters to represent component damage from both exogenous and endogenous wildfires in each time period.
• Uses a Lagrangian cut decomposition algorithm to efficiently solve large-scale SMIP instances by exploiting binary variable structure and generating valid cuts.
• Employs progressive hedging and scenario decomposition to handle the complexity of multi-period, multi-scenario optimization.
• Validates the model on an augmented RTS-GLM test case in Southern California with realistic weather and vegetation data.

Figure 4 : Illustration of the RTS-GMLC system.

Experimental results

Research questions

• RQ1 How does the inclusion of both exogenous and endogenous wildfire risks affect optimal de-energization decisions in power systems?
• RQ2 Can a two-stage stochastic program outperform deterministic and robust optimization models in minimizing total wildfire and load-shedding costs?
• RQ3 How does the proposed Lagrangian cut decomposition algorithm improve computational efficiency for large-scale SMIP problems with binary variables?
• RQ4 What is the trade-off between minimizing wildfire damage and minimizing load-shedding under mixed wildfire scenarios?
• RQ5 How robust is the nominal plan under out-of-sample scenarios with varying wildfire types and intensities?

Key findings

• The nominal plan optimized under mixed exogenous and endogenous wildfire scenarios (X*) achieved a balance between minimizing load-shedding and damage costs, outperforming plans optimized under only one wildfire type.
• X* reduced total expected cost by 25–30% compared to deterministic and robust optimization benchmarks, with a total cost of $4,792.8 under mixed scenarios.
• The X^exo plan (only exogenous wildfires) incurred high load-shedding costs ($3,380.4) when endogenous fires were present, indicating poor robustness.
• The X^end plan (only endogenous wildfires) was overly conservative, de-energizing 31 transmission lines in period 16 and incurring high load-shedding costs ($3,147.0) even under non-disruptive conditions.
• The X* plan achieved a total cost of $3,612.7 under mixed scenarios, with 1,678.2 MW of load-shedding and 1,333.6 damage cost, demonstrating effective risk trade-offs.
• The decomposition algorithm successfully solved large-scale instances with 500 scenarios, showing computational efficiency and scalability for real-world deployment.

Figure 5 : Confidence intervals (bar) and point estimates (circle) of the lower and upper bounds for solutions with different sample sizes. The shaded area indicates the range of extreme values (maximum and minimum).