Optimal SVI-Weighted PSPS Decisions with Decision-Dependent Outage Uncertainty

TL;DR

The paper tackles PSPS planning under wildfire risk by introducing a two-stage distributionally robust optimization framework where outage probabilities depend on de-energization decisions. It leverages distribution shaping and Kantorovich-Rubinstein duality to transform a challenging decision-dependent stochastic problem into a tractable MILP, enabling day-ahead unit commitment with line de-energization while guarding against uncertainty in wildfire outages. The approach integrates both ignition probability and downstream impact (acres burned and SVIs) and demonstrates its merit on the IEEE RTS 24-bus system, showing how higher robustness levels can reduce out-of-sample costs at the expense of increased commitment costs. The study also explores evaluation metrics like REVPI and reveals that weighting lines by wildfire impact metrics can improve the cost-risk trade-off, with limitations tied to the choice of ambiguity set and forecast quality for future work.

Abstract

Public Safety Power Shutoffs (PSPS) are a pre-emptive strategy to mitigate the wildfires caused by power system malfunction. System operators implement PSPS to balance wildfire mitigation efforts through de-energization of transmission lines against the risk of widespread blackouts modeled with load shedding. Existing approaches do not incorporate decision-dependent wildfire-driven failure probabilities, as modeling outage scenario probabilities requires incorporating high-order polynomial terms in the objective. This paper uses distribution shaping to develop an efficient MILP problem representation of the distributionally robust PSPS problem. Building upon the author's prior work, the wildfire risk of operating a transmission line is a function of the probability of a wildfire-driven outage and its subsequent expected impact in acres burned. A day-ahead unit commitment and line de-energization PSPS framework is used to assess the trade-off between total cost and wildfire risk at different levels of distributional robustness, parameterized by a level of distributional dissimilarity $κ$. We perform simulations on the IEEE RTS 24-bus test system.

Figures (7)

• Figure 1: IEEE RTS 24-bus system schematic with each transmission line and bus highlighted to depict its WLFP (a), SVI SVI (b), and expected acres burned from a Pyregence forecast on January 27, 2025 (c). The geographic layout is from RTSGMLC.
• Figure 2: Five scenarios for the RTS derived from the tree reduction based on WLFP and load data from 2020. Box plots of the bus WLFP for each scenario are also shown.
• Figure 3: Total cost per scenario for the IEEE 24-bus system over a 24-hour horizon under different first-stage strategies ($\kappa=0$, $0.25$, $0.99$, and Wait & See).
• Figure 4: Outage scenario probabilities for the IEEE 24-bus system over a 24-hour horizon under different first-stage DR optimization strategies ($\kappa=0$, $0.25$, $0.99$). Scenarios with $z^{-}_{\ell}=0$ have zero probability ($\pi_{s}=0$ for $\xi_{\ell,s}=1$).
• Figure 5: PSPS (a) generation, (b) load shedding, (c) total costs (excluding VoLL), and (d) VoLL costs for the IEEE RTS 24-bus system optimized over 24 hours (e.g. the case when at most 2 lines are active Fig. \ref{['fig:ScenarioCostBreakdownDROIEEE1424h']} (b)). Left bars are risk-neutral ($\kappa=0$), and right bars are risk-averse ($\kappa=0.99$) results.