Balancing Wildfire Risk and Power Outages through Optimized Power Shut-Offs

I. INTRODUCTION

• De-energization can eliminate ignition risk from a line, but widespread shut-offs disrupt electricity service and can affect customers’ health.At their October 2019 peak, shut-offs turned off power to almost a million customer accounts.Source: §I · p. 1
• The optimization framework aims to maintain as much load delivery as possible while minimizing wildfire risk, addressing a gap in operational models focused on actively preventing fires.The authors describe it as the first model for supporting public safety power shut-off decisions in this setting.Source: §I · p. 2
• The model weighs wildfire risk against delivered load using a DC power flow representation and a risk parameter α, and is evaluated against two benchmarks on an augmented RTS-GMLC case.The case study adds wildfire-risk data to the test system.Source: §I · p. 2

II. WILDFIRE RISK AND ELECTRIC GRIDS

• High winds can increase both power-line fault likelihood and fire spread, motivating proactive de-energization despite its disruption to service.The paper frames this as a short-term operational trade-off.Source: §II · p. 2

A. Modelling Risk of Wildfire Ignitions

• Wildfire risk combines ignition probability, the chance an ignition becomes a fire, fire size and intensity, and resulting damage.The likelihood of a fire and its consequences depend on local conditions such as vegetation, humidity, topology, and weather.Source: A. Modelling Risk of Wildfire Ignitions · p. 2

1) Traditional Wildfire Risk Assessment:

• Traditional assessments provide relative regional threat and damage information for long-term planning, but often account for ignition sources only implicitly.The authors argue these tools must be adapted to estimate ignition-risk reductions from grid infrastructure.Source: 1) Traditional Wildfire Risk Assessment · p. 3

2) Wildfire Risk of Electric Components:

• The component-risk model combines area risk Rj with a relative ignition factor κe,j, which operators can adjust using equipment and weather information.The model assumes high-voltage equipment is the dominant ignition source in its immediate area; κ = 1.0 is the baseline, while values above or below one indicate elevated or reduced ignition risk.Source: 2) Wildfire Risk of Electric Components · p. 3
• The risk model is local: it does not capture a fire spreading from one area to adjacent areas.The authors distinguish this from mitigation of fire spread, which they say utilities do not control in the same way as ignition prevention.Source: 2) Wildfire Risk of Electric Components · p. 3

3) Short-Term Mitigation of Wildfire Risk:

• De-energizing equipment reduces its modeled wildfire risk to zero, making the energized-or-de-energized choice a decision about accepted risk.The authors contrast this short-term option with inspections and vegetation management, which take time to plan and implement.Source: 3) Short-Term Mitigation of Wildfire… · pp. 3–4
• Generators, lines, and buses use binary energized-status variables, while load shedding is a continuous fraction of each modeled load.The load fraction also represents the corresponding distribution infrastructure that is de-energized.Source: 3) Short-Term Mitigation of Wildfire… · p. 4
• Total component wildfire risk is expressed in the risk map’s units, which may be approximate relative scales rather than detailed numerical measures.The authors connect this coarseness to the difficulty of assigning numerical values to fire’s economic and societal impacts.Source: 3) Short-Term Mitigation of Wildfire… · p. 4

B. Modelling Risk of Power Shut-Offs

• Load delivery is maximized without monetizing outage impacts, while weights allow hospitals and other essential services to be prioritized.The amount of load delivered is the service measure.Source: B. Modelling Risk of Power Shut-Offs · p. 4

C. Trading off Risk of Wildfires and Power Shut-Offs

• Parameter α trades off serving more load at low values against avoiding wildfire risk at high values.Solving across α yields a Pareto front of optimal load-delivery and wildfire-risk trade-offs for operators to choose from.Source: C. Trading off Risk of Wildfires and… · p. 4

III. OPTIMAL POWER SHUT-OFFS

• The optimization supports short-term operational decisions, from a few days ahead through real time, about which components to keep energized.Decision variables include component energization, generator output, line flows, and voltage angles.Source: §III · p. 4

1) Component interactions:

• Generators, loads, and lines can be energized only when their connected buses are energized.The model enforces these component-to-bus relationships through constraints.Source: 1) Component interactions · p. 4

2) Generators:

• Generator constraints set output to zero when a generator is off and otherwise enforce its minimum and maximum generation limits.Source: 2) Generators · p. 4

3) Power flow representation and transmission limits:

• The DC power-flow constraints enforce line-flow limits when energized, zero flow when de-energized, and nodal balance accounting for shed load.For an energized line, its flow follows the standard DC power-flow constraint and stays within its thermal limit.Source: 3) Power flow representation and… · pp. 4–5

4) Optimal Power Shut-Off Problem:

• The full OPS formulation is a mixed-integer linear program with integer variables for system components.Source: 4) Optimal Power Shut-Off Problem · p. 5

IV. BENCHMARK METHODS

• Both benchmark heuristics first shut off components using wildfire-risk thresholds, then maximize load served with those components unavailable.The benchmarks differ in how the risk threshold is applied.Source: §IV · p. 5

A. Step 1: Component shut-off

• The area heuristic shuts off all components in an area above its total-risk threshold, whereas the transmission heuristic deactivates lines exceeding an individual-risk threshold.Neither heuristic directly shuts down loads, generators, or buses except when they must be disconnected.Source: A. Step 1: Component shut-off · p. 5

B. Step 2: Maximize Load Delivery

• The maximum-load-delivery formulation accommodates islands and further component disabling when outages make ordinary optimal power flow infeasible.It can disable isolated generators or shed additional load when needed.Source: B. Step 2: Maximize Load Delivery · p. 5
• After load delivery is solved, post-processing disables network islands with no attached load.Source: B. Step 2: Maximize Load Delivery · p. 5
• The heuristics choose shut-offs solely by wildfire risk and then maximize load, whereas OPS jointly considers risk reduction and load shed.The separate load-maximization problem does not consider wildfire risk and may leave energized components that are unnecessary for serving load.Source: B. Step 2: Maximize Load Delivery · p. 5

A. Implementation

• The OPS and maximum-load-delivery problems are mixed-integer linear programs, solved in under 0.5 seconds and 0.05 seconds, respectively.The implementation uses Julia v1.4 and Gurobi v8.1 on a 12-thread Intel CPU with 16 GB of memory.Source: A. Implementation · p. 6

B. System model with wildfire risk

• The test case starts from the 73-bus RTS-GMLC system, omits its HVDC line, and places the network across Southern California, Nevada, and western Arizona.Its artificial risk map is inspired by a Southern California map from October 2019.Source: B. System model with wildfire risk · p. 6
• The model assigns risk values of 0.0, 1.0, 2.0, and 4.0 to low-, medium-, high-, and extreme-risk zones, respectively.These zone values are associated with components and their assumed fault probabilities.Source: B. System model with wildfire risk · p. 6
• Generators, buses, and loads use an assumed ignition probability of 1; load risk weights are also set to 1.The text notes that load size alone may not capture differences in ignition probability between urban and rural distribution systems.Source: B. System model with wildfire risk · p. 6
• Transmission-line ignition risk varies with voltage and length: each 10 km segment is assigned a risk zone, with κ=1.0 for 230 kV lines and κ=2.0 for 138 kV lines.The lower-voltage lines are assumed to have higher ignition probability relative to the higher-voltage lines.Source: B. System model with wildfire risk · p. 6

VI. CASE STUDY: NUMERICAL RESULTS

• OPS is evaluated across α values from 0 to 1 in 0.01 steps to produce a Pareto curve, while the transmission heuristic is swept across Rmax thresholds.The study also compares the area heuristic's single operating point and standard operation with all components energized.Source: §VI · pp. 6–7

A. Pareto Front

• At equal load delivery, OPS consistently achieves lower wildfire risk; the area heuristic has both higher risk and more load shed than the other methods.The comparison covers OPS, the transmission heuristic, and the area heuristic.Source: Figure 2 · p. 7, A. Pareto Front · p. 7
• At α=0.25, OPS reaches very low but non-zero risk while serving approximately 75% of system load.As α decreases further, delivered load falls slowly before dropping to zero at α=1.0, when all equipment is turned off.Source: A. Pareto Front · p. 7
• For the transmission heuristic, lowering Rmax from 70 to 20 keeps load delivery relatively high while reducing wildfire risk to less than half its original value.Below Rmax=20, both wildfire risk and delivered load decrease.Source: A. Pareto Front · p. 7
• At α=1.0, OPS turns off the entire system, eliminating risk but serving no load.The transmission heuristic likewise serves no load when Rmax=0.Source: A. Pareto Front · p. 7

B. Operation Schemes

• The selected medium-risk settings are α=0.01 for OPS and Rmax=18.9 for the transmission heuristic; the low-risk settings are α=0.15 and Rmax=0.0021, respectively.The area heuristic uses a regional threshold of Rmax=30.0.Source: B. Operation Schemes · p. 7

1) Medium-Risk Operation Schemes:

• The medium-risk OPS topology sheds only 10 MW and forms a near-radial, tree-like network, while the transmission heuristic disables western lines and isolates some loads.OPS disables more components in lower-risk zones to preserve near-full load delivery, but removes redundancy.Source: 1) Medium-Risk Operation Schemes · p. 8, Figure 3 · p. 8
• The medium-risk OPS solution is no longer N-1 secure because it removes redundancy to reduce wildfire risk.The text describes the resulting reliability impact as preferable to an intentional blackout.Source: 1) Medium-Risk Operation Schemes · p. 8
• Both medium-risk methods cut wildfire risk by 50%: OPS served 8540 MW (10 MW shed), versus TH's 8220 MW (330 MW shed), from 8550 MW under standard operation.The two scenarios have similar wildfire risk, while OPS serves more load.Source: 1) Medium-Risk Operation Schemes · pp. 7–8, Table I · p. 8

2) Low-Risk Operation Schemes:

• Relative to the medium-risk case, low-risk solutions reduce wildfire risk by an order of magnitude, but deliver much less load.Source: 2) Low-Risk Operation Schemes · p. 8

C. Optimal Power Shut-Off Solutions

• Transmission lines contribute 57% of total risk in medium-risk solutions and 20% in low-risk solutions.Source: Table II · p. 9, C. Optimal Power Shut-Off Solutions · p. 9

2) Low-Risk Operation Schemes:

• At comparable risk levels, the optimal power shut-off reduces load shed by 25% relative to the transmission heuristic.Source: 2) Low-Risk Operation Schemes · p. 9
• Both low-risk approaches shut down almost all components in the high-risk western region and island some grid regions, while the optimized strategy favors components with lower load-delivery impact.Source: 2) Low-Risk Operation Schemes · p. 9
• The low-risk islanding result assumes generators can operate stably in separate islands and the grid can later be resynchronized.Source: 2) Low-Risk Operation Schemes · p. 9

3) The value of a targeted approach:

• The area heuristic uses a regional threshold, the transmission heuristic considers individual line risk, and the optimization also accounts for components’ impact on serving load.Source: 3) The value of a targeted approach · p. 9

C. Optimal Power Shut-Off Solutions

• The shut-off threshold depends on both line risk and transferred power, allowing high-risk lines to remain energized when they carry significant power.Source: C. Optimal Power Shut-Off Solutions · p. 9

• The optimal power shut-off problem serves more load at lower wildfire-risk values than the threshold-based heuristic.Source: §VII · p. 9
• Highly loaded lines remain energized at higher wildfire-risk values, while less-loaded lines are shut off at lower risk values.Source: §VII · p. 9
• The minimum-risk network topology is tree-like and sometimes splits the system into islands.Source: §VII · p. 9
• Future work calls for more detailed, current-weather wildfire-risk models and multi-period optimization, while retaining a fixed topology because lines require inspection before re-energization.Source: §VII · pp. 9–10
• The optimized topology is not N-1 secure, so additional faults can significantly affect reliability and expected load delivery; future work also needs more detailed distribution-grid modeling.Source: §VII · p. 10
• The real-time model could be extended to longer-term planning, including distributed-generation construction and identifying critical lines for wildfire mitigation.Source: §VII · p. 10