Optimizing Transmission Infrastructure Investments to Support Line De-energization for Mitigating Wildfire Ignition Risk

Abstract: Wildfires pose a growing risk to public safety in regions like the western United States, and, historically, electric power systems have ignited some of the most destructive wildfires. To reduce wildfire ignition risks, power system operators preemptively de-energize high-risk power lines during extreme wildfire conditions as part of "Public Safety Power Shutoff" (PSPS) events. While capable of substantially reducing acute wildfire risks, PSPS events can also result in significant amounts of load shedding as the partially de-energized system may not be able to supply all customer demands. In this work, we investigate the extent to which infrastructure investments can support system operations during PSPS events by enabling reduced load shedding and wildfire ignition risk. We consider the installation of grid-scale batteries, solar PV, and line hardening or maintenance measures (e.g., undergrounding or increased vegetation management). Optimally selecting the locations, types, and sizes of these infrastructure investments requires considering the line de-energizations associated with PSPS events. Accordingly, this paper proposes a multi-period optimization formulation that locates and sizes infrastructure investments while simultaneously choosing line de-energizations to minimize wildfire ignition risk and load shedding. This formulation is evaluated using two geolocated test cases along with realistic infrastructure investment parameters and actual wildfire risk data from the US Geological Survey. We evaluate the performance of investment choices by simulating de-energization decisions for the entire 2021 wildfire season with optimized infrastructure placements. With investment decisions varying significantly for different test cases, budgets, and operator priorities, the numerical results demonstrate the proposed formulation's value in tailoring investment choices to different settings.

• The paper presents a multi-period MILP formulation that jointly optimizes infrastructure investments and operational decisions during PSPS events.
• It integrates batteries, solar PV, and line hardening options to strategically balance load shedding reduction with wildfire risk mitigation.
• Simulations on RTS-GMLC and WECC systems demonstrate that multi-investment strategies significantly improve system resilience under wildfire conditions.

This paper (2203.10176) addresses the growing challenge of mitigating wildfire ignition risks associated with electric power systems, particularly in regions prone to wildfires like the western United States. Utilities employ Public Safety Power Shutoffs (PSPS) by preemptively de-energizing high-risk power lines during severe wildfire conditions. While effective at reducing acute ignition risk, PSPS events can lead to significant load shedding, impacting customers. The paper investigates how strategic infrastructure investments can support system operations during PSPS events, enabling reduced load shedding and wildfire risk.

The core problem tackled is how to optimally locate and size infrastructure investments, such as grid-scale batteries, solar photovoltaic (PV) generators, and line hardening/maintenance measures (like undergrounding or increased vegetation management), while simultaneously considering the operational decisions of which lines to de-energize during PSPS events.

The paper proposes a multi-period optimization formulation to address this challenge. Key aspects of the approach include:

1. Multi-Period DC Power Flow: The power system operation is modeled over multiple time periods (e.g., 24 hours) using the DC power flow approximation. This formulation considers generator limits, load shedding, power flow limits, voltage angle limits, and power balance constraints. Critically, the state of line energization ($z^\ell$) is fixed across all time periods within the planning horizon.
2. Infrastructure Investment Models:
   • Batteries: Modeled with energy storage limits, charge/discharge efficiencies, and rate limits. Variables include the number of batteries placed ($x^n$), charge/discharge rates ($p_{c,t}^n, p_{w,t}^n$), and a binary variable ($u_t^n$) to prevent simultaneous charging and discharging. Battery dynamics couple time periods through the state of charge.
   • Solar PV: Modeled with time-varying maximum potential output ($S_t^n$). Variables include the amount of solar PV installed ($a^n$) and the actual output ($p_{s,t}^n$), constrained by the installed capacity and potential output.
   • Line Hardening/Maintenance: Modeled as a binary decision ($y^\ell$) for candidate lines ($\mathcal{L}^{\text{harden}$). Hardening reduces the wildfire risk of a line by a factor $\beta$. A constraint ensures a line is not simultaneously hardened and de-energized.
3. Objective Function: The objective is to minimize a weighted sum of total load shedding and total wildfire risk over the considered time periods. A weighting parameter $\alpha \in [0, 1]$ allows prioritizing load shedding reduction ($\alpha=1$) or wildfire risk reduction ($\alpha=0$). The wildfire risk term is adjusted to account for risk reduction from hardened lines.
4. Budget Constraint: A total budget $B$ is imposed on the combined cost of battery, solar PV, and line hardening investments.
5. Infrastructure Investment Problem ($\text{Invest-Opt}$): This is formulated as a Mixed-Integer Linear Programming (MILP) problem that jointly optimizes investment variables ($x, a, y$) and operational variables ($p_g, \theta, f, p_{ls}, z, u, p_c, p_w, p_s$) to minimize the weighted objective subject to operational, physical, and budget constraints. Due to the computational complexity of optimizing over a full season, investment decisions are made based on a single, representative worst-case wildfire risk realization and peak demand profile.
6. Performance Evaluation ($\text{Seq-Opt}$): After determining optimal investment placements ($\hat{x}, \hat{a}, \hat{y}$) using the $\text{Invest-Opt}$ formulation, the paper evaluates the performance by simulating PSPS events over an entire historical wildfire season (2021). For each day exceeding a predefined wildfire risk threshold, a separate multi-period optimization problem ($\text{Seq-Opt}$) is solved. This problem fixes the investments and optimizes line de-energization and operational decisions to minimize a modified objective that balances current-day load shedding and wildfire risk while also incentivizing a high final battery state-of-charge for potential back-to-back PSPS days.

The approach is evaluated using two synthetic geolocated transmission networks: the 73-bus RTS-GMLC system and a 240-bus WECC system. Wildfire risk values are derived from USGS Wind-enhanced Fire Potential Index (WFPI) data. Realistic parameters for infrastructure costs (batteries, solar PV, undergrounding, covered conductors, vegetation management) and risk reduction factors ($\beta$) are used. The analysis considers various investment scenarios (single or multiple types), budgets ($100M to$1B), and prioritization weights ($\alpha$).

Key findings from the numerical results include:

• The optimal investment portfolio is sensitive to the budget, the type of line hardening/maintenance considered, and the operator's priority between reducing wildfire risk and load shedding ($\alpha$).
• When available as an option, line hardening, particularly undergrounding, often receives a significant portion of the budget, especially for lower values of $\alpha$ (prioritizing risk reduction). For larger networks or limited budgets, less expensive options like vegetation management may be preferred as they can be applied more widely.
• Batteries are predominantly installed for higher values of $\alpha$ (prioritizing load shedding reduction) as they provide local backup power during de-energization events. Solar PV also contributes to reducing load shedding.
• The need to consider optimal transmission switching (line de-energization) during investment planning is crucial. The optimization may choose to de-energize high-risk lines rather than hardening them, allocating the hardening budget to moderate-risk lines or other asset types.
• Multi-investment strategies generally provide better trade-off curves (simultaneously lower risk and load shedding) than single-investment strategies.
• The performance simulation over the 2021 season validates that the optimized investments improve system performance during PSPS events compared to no investment or de-energization only.

The paper acknowledges several limitations and areas for future research, including the use of the DC power flow approximation (motivating the need for AC models), the deterministic nature of the optimization (suggesting stochastic or robust optimization for uncertainties), the limited time horizon (pointing towards longer planning horizons), simplified generator models, lack of controlled islanding constraints, exclusion of contingencies (like N-1 security), single-stage planning (proposing multi-stage planning), valuation of investments' benefits under normal operating conditions, extending the analysis to distribution systems, and incorporating fairness considerations for localized impacts. A major challenge for all these extensions is the significant computational complexity, which requires further work on decomposition methods or improved heuristics.