Strategic and Grid-Aware Maintenance Planning of Offshore Wind Farms

• Offshore O&M costs are amplified by larger turbines, specialized maintenance ships, and uncertain access under metocean conditions.Source: §I · p. 1, B. (Offshore) Wind farm maintenance · p. 2
• Large offshore wind outages can affect grid operations and reliability, motivating coordination between wind-farm maintenance and generator outage scheduling.Source: §I · p. 1
• The paper targets the understudied relationship between offshore wind maintenance planning, grid conditions, and electricity-market clearing.Source: §I · p. 1, B. (Offshore) Wind farm maintenance · p. 2
• Prior generator-maintenance studies examine operating cost, grid cost, or reliability under fixed maintenance requirements, with limited renewable-energy integration.Source: A. Generator maintenance planning · pp. 1–2
• Electricity-price-aware wind maintenance models account for opportunity cost or curtailment signals but generally do not model broader grid operations.Source: B. (Offshore) Wind farm maintenance · p. 2

Opportunities from current grid operations

• System operators’ maintenance-outage reporting requirements vary across operators and outage categories, although common structures emerge.Source: C. Opportunities from current grid… · pp. 2–3
• Wind farms are generally treated as variable or intermittent resources, with CAISO, NYISO, and PJM applying a 1 MW derate-reporting threshold.Source: C. Opportunities from current grid… · p. 2
• Short-notice preventive maintenance allows operators to use short-term forecasts of weather, metocean conditions, electricity prices, and grid conditions.Source: C. Opportunities from current grid… · p. 3
• Farm-level derate reporting lets operators assign turbine outages flexibly within derate windows.Source: C. Opportunities from current grid… · p. 3
• The paper formulates a bilevel model in which the wind operator anticipates the grid operator’s response to capacity derates needed for maintenance.Source: D. Objective and Contributions · p. 3, §II · p. 3
• The deterministic maintenance model schedules turbine outages over T timesteps while enforcing maintenance duration, timing, and parallel-work constraints.Source: A. Wind farm operator: Maintenance… · pp. 3–4
• The wind-farm objective combines power-sale revenue with fixed and variable maintenance costs, while availability depends on wind conditions.Source: A. Wind farm operator: Maintenance… · pp. 3–4

System operator: Economic dispatch

• The system operator computes cost-minimal generator injections and available wind production to meet demand at each timestep.Source: B. System operator: Economic dispatch · p. 4
• A potentially derated farm capacity and farm-wide availability factor determine the wind power available to economic dispatch.Source: B. System operator: Economic dispatch · p. 4
• Wind enters dispatch at zero marginal cost, while controllable-generator output is limited by installed capacity.Source: B. System operator: Economic dispatch · p. 4
• The dual variable λt of the energy-balance constraint sets the electricity price for a unit of power at time t.Source: B. System operator: Economic dispatch · p. 4

Grid-serving maintenance planning

• Grid-serving maintenance planning is defined as an alternative to profit-maximizing scheduling with fixed prices and fixed wind-farm capacity.Source: C. Grid-serving maintenance planning · p. 4
• The formulation imposes the economic-dispatch grid constraints together with the maintenance constraints from the wind-farm model.Source: C. Grid-serving maintenance planning · p. 4

• The formulation is bilevel, with the wind operator as leader and the system operator as follower.Source: 1) Model formulation · p. 4
• The wind operator chooses the optimal potentially derated farm capacity to submit to the system operator.Source: 1) Model formulation · p. 4
• The system operator then computes electricity prices and wind dispatch in response to the submitted capacity.Source: 1) Model formulation · p. 4
• The model assumes consistent wind-power availability across turbines and between the wind and system operators.Source: 1) Model formulation · p. 4
• The lower-level problem is reformulated using its first-order optimality conditions to obtain a tractable single-level equivalent.Source: 2) Solution approach · p. 4

• The derivation first addresses a bilinear term in the upper-level objective before applying these transformations.Source: 3) Resolving bilinear terms · p. 5
• Strong duality equalizes the primal and dual objectives of the lower-level dispatch problem.Source: 3) Resolving bilinear terms · p. 5
• The remaining bilinear terms are reformulated from complementary-slackness conditions using the Fortuny-Amat Big-M approach.Source: 3) Resolving bilinear terms · p. 5
• The reformulated model is a MILP containing wind-farm constraints, dispatch stationarity, and dispatch-feasibility constraints.Source: 3) Resolving bilinear terms · p. 5
• Dispatch variable domains are included among the reformulated constraints, with F used as the large Big-M scalar.Source: 3) Resolving bilinear terms · p. 5

• Metocean uncertainty affects both wind availability and whether turbine maintenance can be performed.Source: §III · p. 5
• The stochastic formulation extends the scenario-indexed dispatch structure while retaining the modeled uncertainty in environmental and operational conditions.Source: §III · p. 5, A. Grid operator under uncertainty · p. 5
• Wind availability is modeled with scenarios, while site access is a binomial variable indicating whether maintenance is possible.Source: §III · p. 5
• Site-access scenarios are conditional on wind-availability scenarios, with joint probabilities formed from marginal and conditional probabilities.Source: §III · p. 5
• For each realized wind-availability scenario, the grid operator computes cost-minimal dispatch without look-ahead or stochastic decisions.Source: A. Grid operator under uncertainty · p. 5

B. Strategic wind farm maintenance under uncertainty

• Before uncertainty is realized, the wind operator chooses derated farm capacity and the maximum number of parallel maintenance slots.Source: B. Strategic wind farm maintenance… · p. 5
• Actual maintenance scheduling occurs after wind availability and site access are known.Source: B. Strategic wind farm maintenance… · p. 6
• The case study uses the RTS-GLMC system, including 73 conventional generators and three large-scale wind farms.Source: §IV · p. 6

A. Illustrative deterministic case

• Strategic maintenance deliberately reduces farm capacity during high wind availability to avoid low prices and increase profits.Source: §IV · p. 6
• Fixed-price and grid-serving approaches produce similar wind injections, prices, and effective farm capacities.Source: A. Illustrative deterministic case · p. 6
• Strategic maintenance schedules some work during high-wind, low-load periods, reducing injected wind power while selling the remaining power at a higher price.Source: A. Illustrative deterministic case · p. 7
• 1.45% and 1.20% are the average strategic profit increases relative to fixed-price and grid-serving planning, respectively.Source: A. Illustrative deterministic case · p. 7

• Relative profit gains are evaluated across farm sizes and per-turbine ratings using means and standard deviations.Each case assigns 20% of turbines to 20-hour, 10-hour, and 5-hour maintenance requirements.Source: Figure 3 · p. 7, B. Impact of farm and turbine size · p. 7
• Farm size is the main driver of strategic maintenance profit gains because larger farms have greater impact on system prices.Source: B. Impact of farm and turbine size · p. 7
• Smaller turbine ratings correlate with higher profit gains because they let operators distribute required farm derates more flexibly.Source: B. Impact of farm and turbine size · p. 7
• Profit gains relative to grid-serving maintenance are slightly lower than gains relative to fixed-price scheduling because grid-serving schedules avoid some very-low-price periods.Source: B. Impact of farm and turbine size · p. 7

• The stochastic model uses 10 realistic wind availability scenarios and estimates site-access probabilities from unsafe wind and wave conditions.For each wind scenario, five sets of access scenarios are sampled.Source: C. Maintenance planning under… · pp. 7–8
• Uncertainty spreads maintenance windows across scenarios, scheduling 3.46% more maintenance blocks on average and reducing profit by 1.76% versus the perfect-knowledge deterministic baseline.The stochastic problem solved to a 0.61% optimality gap in 23.2 minutes.Source: C. Maintenance planning under… · p. 8
• Forecast degradation is modeled through spread, which moves scenarios away from the ensemble mean, and lag, which shifts scenarios temporally relative to that mean.The degraded forecast is clipped to [0, 1] when needed, and lag is sampled from [−ℓ, ℓ].Source: C. Maintenance planning under… · p. 8
• Across forecast-quality cases, the stochastic model solved in 17.3 minutes on average with a 0.70% average optimality gap.Source: C. Maintenance planning under… · p. 8
• At lags up to six hours, additional maintenance windows more than double for each forecast-uncertainty level, while profit losses vary less monotonically.The profit impact is systematically higher for zero spread across the studied lag cases.Source: C. Maintenance planning under… · p. 8
• Profit losses are mainly driven by forecast spread: slight uncertainty can improve low-opportunity-cost scheduling, whereas high spread produces conservative capacity reductions and larger losses.Overall economic impacts are nonlinear and non-monotonic in forecast quality.Source: C. Maintenance planning under… · p. 9

Model and solution approach

• The models represent the wind-farm operator as choosing capacity derates before the system operator prices and dispatches generation.Both deterministic and stochastic formulations account for maintenance requirements; the stochastic version includes wind availability and site-access uncertainty.Source: §V · p. 9

Strategic maintenance planning

• Wind farms can schedule maintenance during low-price periods to reduce the opportunity cost of derating, while strategically avoiding very-low-price periods.The latter can involve scheduling some turbines during high-wind, low-demand periods.Source: §V · p. 9
• Strategic maintenance planning is partially aligned with a maintenance plan chosen by the system operator to serve grid objectives.This indicates overlap between profit-oriented and grid-serving maintenance decisions within the experiments.Source: §V · p. 9

Uncertainty

• Uncertainty in wind availability and site access reduces profit margins and requires additional maintenance intervals to ensure all requirements are fulfilled.Poorer forecast quality can make the plan increasingly conservative and increase profit losses relative to the deterministic benchmark.Source: §V · p. 9

Limitations

• Perfect information about the system operator’s behavior makes the reported additional profits an upper bound within the experiments.In practice, operators would need to predict grid signals and potentially robustify schedules against signal uncertainty.Source: §V · p. 9
• The study simplifies market clearing by assuming no grid congestion and examines only a single wind farm.The authors identify congestion and multiple strategic operators as directions for future model extensions.Source: §V · p. 9