Models and Methods

Optimization Models

DCOTS (DC Optimal Transmission Switching)

• Uses linearized DC power flow approximation
• Decision variables: voltage angles, generation, power flows, load shedding, line switching
• Optional: line hardening decisions (y variables)
• Computationally efficient for large-scale problems
• Ignores reactive power and voltage magnitude constraints

LACOTS (Linear AC Optimal Transmission Switching)

• Uses linearized AC power flow
• Includes reactive power and voltage magnitude variables
• Optional: line hardening decisions (y variables)
• More accurate representation of AC power systems
• Can warm-start from DCOTS solution for faster convergence (includes z and y values)

DCOPF / LACOPF (Pure Power Flow — no wildfire switching)

• Same DC / linearized-AC formulations as DCOTS / LACOTS, but with all wildfire-risk machinery disabled: no binary z switching variables, no risk threshold, no auto-loaded wildfire data
• Lines are never de-energized to mitigate risk — useful as a no-action baseline or for studies that shouldn't be biased by wildfire considerations
• Investment options (battery, solar, hardening) still apply and are co-optimized as usual
• Allowed objectives: "loadshed" and "cost" only ("wildfire" and "tradeoff" require risk data)
• Use solve_opf(opt_parameters) for DCOPF/LACOPF. Legacy solve_ots calls with OPF models still work with a warning.
• LACOPF can warm-start from DCOPF (:warm_start => "auto")

Nonlinear AC Verification / Recovery

• verify_ac(ac_parameters, planning_results) builds package-owned JuMP nonlinear AC models using polar AC power-flow equations
• :mode => "ACPF" performs strict replay feasibility: fixed topology, fixed allocation, and saved dispatch where available
• :mode => "ACOPF" performs AC redispatch/recovery with active/reactive load shedding, while keeping planning decisions fixed
• Planning outputs are treated as fixed data: :z / :switched_off_lines, :allocated_load, solar capacity :s, and battery capacity :x
• AC models do not create planning variables such as z, y, x, s, or a; they only create continuous operational AC variables
• Diagnostics are enabled by default and classify solver failures, voltage limit violations, thermal overloads, angle-limit violations, AC recovery load shedding, reactive generator limit binding, and islanding
• PowerIO is used for MATPOWER parsing; reference dictionaries and AC equations are package-owned

Solution Methods

Optimal Method (default)

• Solves a Mixed-Integer Programming (MIP) problem for line switching decisions
• Binary z[d,l] variables for each risky line switching decision
• If a threshold or threshold_pct is provided, adds a linear risk constraint: energized risk ≤ threshold × total_risk (hardening is credited toward the threshold)
• If no threshold is provided and the objective includes wildfire risk (e.g., "wildfire", "tradeoff"), risk minimization is handled in the objective
• If hardening is enabled, binary y[l] variables are always added regardless of switching method
• Pros: Globally optimal switching decisions, optimality guarantees
• Cons: Slower solve times (seconds to minutes for large systems)

Thresholded Method

• Fast heuristic that pre-determines switching decisions before solving
• Sorts risky lines by wildfire risk and de-energizes the riskiest ones to meet the specified threshold (threshold or threshold_pct required)
• Switching variables are fixed scalars; the remaining problem is solved as an LP (or MIP if hardening is enabled)
• If hardening is enabled, binary y[l] variables are still solved optimally within the LP/MIP
• Pros: 2-10x faster solve times for large-scale studies
• Cons: Switching decisions are suboptimal; threshold parameter is required
• Use cases: Large-scale studies, Monte Carlo analysis, initial screening

Objective Functions

Line Hardening

The package supports transmission line hardening as a wildfire risk mitigation strategy alongside operational switching decisions. The hardening decision represents a permanent physical intervention — vegetation management, covered conductors, or undergrounding — that reduces a line's wildfire risk contribution by a user-defined effectiveness factor. The default cost parameter ($7M/mile) reflects undergrounding; adjust :hardening_cost_per_mile to model other methods.

Key Concepts:

• Decision variable y[l]: Binary variable indicating whether line l is hardened (1) or not (0)
• Risk mitigation: Hardened lines have their wildfire risk reduced by an effectiveness factor (default: 100%)
• Energization enforcement: Hardened lines must remain energized (cannot be switched off)
• Cost-based optimization: Balances hardening cost against operational benefits

Budget Handling:

• Non-cost objectives (loadshed, wildfire, tradeoff): Budget is required (default: $1B if not specified)
• Cost objective: Budget is optional (default: unlimited). Hardening cost appears in objective function.

Thresholded Method with Hardening: When using the thresholded method with hardening enabled, switching and hardening decisions are decoupled:

• Switching decisions (z) are pre-computed by sorting lines by risk and de-energizing the riskiest ones to meet the threshold
• Hardening decisions (y) remain binary optimization variables solved optimally by the LP/MIP solver
• Hardenable lines that were thresholded off use y[l] as their effective energization variable in power flow constraints — a hardened line is re-energized with zero wildfire risk contribution
• The shared infrastructure budget is enforced as a linear constraint over the binary y variables (and any battery/solar variables)

Objective Modifications:

• loadshed: Adds small penalty for not hardening: + 0.01 * Σ(1-y[l])
• wildfire: Risk from hardened lines is reduced: risk[l] * (1 - effectiveness * y[l])
• cost: Adds hardening cost: + Σ(cost_per_mile * length[l] * y[l])
• tradeoff: Uses modified risk calculation from wildfire objective