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Distributed Model-Free Turbine Repositioning for Wake Overlap Minimization in Floating Offshore Wind Farms

Zekai Chen, Ryozo Nagamune

arXiv:2610.08646v1eess.SYcs.SYmath.DS

TL;DR

Wake effects reduce downstream turbine power capture and contribute to floating wind farms’ high energy cost, while prior centralized model-based approaches face practical limitations. The paper uses model-free distributed online optimization informed by local wake-dynamics estimates. In simulations, the proposed method achieved slightly higher steady-state power than the FOWFSim-based baseline and reduced computation time by more than 3000-fold.

  • Problem

    Wake effects reduce downstream turbine power capture and increase structural loads, while centralized control and simplified steady-state wake models limit practical handling of uncertainty and wind-farm scaling.

    Source: §I · p. 1

  • Method

    A model-free distributed online optimization method uses local sensing and physics-informed wake-dynamics knowledge to derive turbine yaw angles without explicit wake models.

    Source: §I · p. 1, §V · p. 6

  • Results

    At steady state, proposed distributed output reached 8.499 MW versus FOWFSim-based 8.488 MW, while computation fell from 0.2313 s to 0.0746 ms per iteration, a more than 3000-fold reduction.

    Source: 2) Power Production · p. 5, 6) Computation Time · p. 5

  • Takeaways & Limitations

    Simulation results indicate that the proposed method mitigates wake effects while remaining efficient enough for real-time operation.

    Source: 6) Computation Time · p. 6

Abstract

from arXiv · show

This paper presents a model-free method for turbine repositioning control in floating offshore wind farms. The method uses a distributed online optimization framework to mitigate the wake effect. Conventional approaches rely on centralized, model-based control architectures, which suffer from poor practical feasibility. To overcome this limitation and address nonconvexity and inaccessible gradient information, we incorporate physics-informed knowledge of wake dynamics into the control system design. We demonstrate the effectiveness of the proposed method by comparing it with a centralized, model-based baseline in mid-fidelity simulations. Results indicate that the proposed method achieves slightly better performance while significantly reducing computational cost.

I. INTRODUCTION

Wake effects reduce downstream turbine performance and contribute to the high cost of floating offshore wind farms. The paper proposes distributed, model-free turbine repositioning, addressing limitations of centralized model-based approaches.

I. INTRODUCTION

  • Upstream turbines create slower, more turbulent wake regions that reduce downstream power capture and increase structural loads.Wake effects can cause annual wind-farm revenue losses of 20% to 30%.Source: §I · p. 1
  • Nacelle yaw repositions floating turbines to reduce overlap between incoming wakes and rotor disks.This turbine-repositioning strategy uses floating turbines’ additional degrees of freedom to mitigate wakes.Source: §I · p. 1
  • Prior approaches use simplified, low-fidelity steady-state wake models and centralized control, limiting handling of uncertainty and scaling with wind-farm size.The paper identifies these constraints as obstacles to practical deployment.Source: §I · p. 1
  • The proposed model-free distributed method uses local sensing and wake-dynamics knowledge to derive yaw angles without explicit wake models.The paper also describes the framework as computationally efficient and validates it in FAST.Farm.Source: §I · p. 1

A. Wind Farm Setup

  • The wind-farm setup considers an array of N floating offshore wind turbines, with a two-turbine example illustrated in Figure 1.The setup section introduces the turbine and yaw-angle notation.Source: A. Wind Farm Setup · pp. 1–2, Figure 1 · p. 2

B. Assumptions on Wind Farms

The assumptions specify stable baseline turbine control, a greedy freestream turbine, local sensing, and neighbor communication. These conditions support the distributed control structure.

B. Assumptions on Wind Farms

  • Each turbine has a baseline controller that regulates stability and power output; changing its yaw angle is assumed not to induce instability.The baseline-controller assumption is attributed to.Source: B. Assumptions on Wind Farms · p. 2
  • The freestream turbine FOWT1 operates greedily and pursues the best attainable performance under the given wind condition.Its measurement M1,t is broadcast as a performance reference for downstream turbines.Source: B. Assumptions on Wind Farms · p. 2
  • Sensors on each turbine are assumed to measure blade load Mn,t and yaw angle γn,t at every time step.Source: B. Assumptions on Wind Farms · p. 2
  • Each turbine communicates with its immediate upstream neighbor by exchanging blade load and yaw angle, while M1,t is broadcast to all turbines.The local controller uses the broadcast measurement, the neighbor’s yaw, and its own measurement to determine yaw.Source: B. Assumptions on Wind Farms · p. 2

C. Wake Overlap Minimization Problem Formulation

The formulation minimizes aggregate local costs tied to wake overlap, with each downstream turbine’s cost depending on its own yaw and its upstream neighbor’s yaw. The distributed online process respects yaw constraints.

C. Wake Overlap Minimization Problem Formulation

  • Each turbine’s local cost is nonincreasing as its wake overlap decreases and depends on its own yaw and the yaw of its immediate upstream neighbor.The cost is constructed from onboard measurements in Section III-C.1.Source: C. Wake Overlap Minimization Problem… · p. 2
  • At each time step, turbines minimize local costs in a distributed online process, sharing yaw information and the freestream measurement.This process is framed as multi-agent coordination-based distributed online optimization.Source: C. Wake Overlap Minimization Problem… · pp. 2–3
  • The formulation fixes FOWT1 at the greedy yaw angle and bounds each turbine’s yaw magnitude by γmax to reduce fatigue from excessive yawing.The greedy yaw angle tracks the incoming wind direction.Source: C. Wake Overlap Minimization Problem… · p. 3

III. DISTRIBUTED MODEL-FREE CONTROL DESIGN

The distributed controller follows a perceive-then-control design: each turbine estimates local wake conditions and uses that information, together with upstream data, to choose its next yaw angle.

A. Design Overview

  • Each turbine’s controller estimates wake conditions, then selects its next yaw angle using that estimate and data from its upstream neighbor.The perception subsystem estimates wake overlap and asymmetric wake distribution; the control subsystem uses these estimates and upstream data to reposition the turbine.Source: A. Design Overview · p. 3

B. Perception Subsystem: Wake Dynamics Estimation

  • The Multi-Blade Coordinate transform maps blade-root loads into collective, tilt, and yaw moments in the rotor-disk frame.The authors use onboard blade-root measurements and apply the transform to obtain a stationary representation of rotor-disk load.Source: B. Perception Subsystem: Wake Dynamics… · p. 3
  • Collective moment indicates wake-overlap extent, while yaw moment indicates lateral wake asymmetry; together, they provide the two features needed to estimate local wake dynamics.The load signals reveal rotor-disk distribution because out-of-plane bending moment is positively correlated with wind speed.Source: B. Perception Subsystem: Wake Dynamics… · p. 3
  • The perception analysis uses a FAST.Farm simulation of two NREL 5 MW turbines spaced 5D apart under steady 10 m/s hub-height wind, with the downstream turbine tested at different lateral offsets.Figure 5 shows cases at ∆y2/D = {±0.5, 0}.Source: B. Perception Subsystem: Wake Dynamics… · p. 3, Figure 5 · p. 4

1) Indicator of Wake Overlap Extent:

Collective moment serves as an indicator of wake-overlap extent.

1) Indicator of Wake Overlap Extent:

  • As FOWT2 moves farther out of the wake, M_col2 increases toward the freestream value M_col1, regardless of whether it is left or right of FOWT1.The trend links increasing collective moment with decreasing wake overlap.Source: 1) Indicator of Wake Overlap Extent · p. 4

2) Indicator of Lateral Wake Asymmetry:

The yaw-moment sign indicates which lateral side FOWT2 occupies relative to FOWT1, reflecting wake asymmetry across the rotor disk.

2) Indicator of Lateral Wake Asymmetry:

C. Control Subsystem

The control subsystem defines a local cost from collective-moment deficit and derives each turbine’s next yaw angle by minimizing that cost.

1) Cost Function Design:

  • The cost f_n,t is the normalized deficit of M_col,n,t relative to FOWT1’s M_col, using FOWT1 as the best-attainable reference under the wind condition.Source: 1) Cost Function Design · p. 4
  • Minimizing f_n,t moves each turbine toward FOWT1’s performance, and the cost decreases as that turbine’s wake overlap decreases.Source: 1) Cost Function Design · p. 4
  • Excessive yawing is penalized because it reduces M_col,n,t and therefore increases the cost.Source: 1) Cost Function Design · p. 4

2) Control Algorithm:

The controller combines a PI-derived yaw increment with a wake-informed yaw direction to reposition each turbine. The direction rule uses local wake information while avoiding a turn that conflicts with the upstream turbine.

2) Control Algorithm:

  • A simple proportional-integral (PI) controller with Kp = 0.8 and Ki = 0.0125 is used to determine un,t+1 in the incremental PI form.The passage also states that un,t is determined using M col.Source: 2) Control Algorithm · p. 4
  • The yaw direction uses wake asymmetry and the upstream turbine’s yaw to steer toward less-waked regions without a conflicting turn into its wake.When the upstream turbine is effectively stationary, the direction is determined from the local wake-asymmetry signal; otherwise it opposes the upstream yaw direction.Source: 2) Control Algorithm · p. 4
  • The direction signal sets the repositioning side, while the PI output sets the increment size; together they determine the next yaw change.The perception subsystem provides wake-overlap extent and asymmetric wake distribution over the rotor disk.Source: 2) Control Algorithm · p. 4

IV. CASE STUDY

The case study tests the method in FAST.Farm on a three-turbine floating array and evaluates wake overlap, farm power, and static regret against a fixed-yaw benchmark.

A. Simulation Setup

  • The proof-of-concept case uses a 1 × 3 array of NREL 5 MW semi-submersible turbines, spaced 5D apart with no lateral offset.The simulations use a steady 10 m/s hub-height wind, a 30° maximum yaw angle, and 970 m mooring lines.Source: A. Simulation Setup · p. 4
  • Simulations run for 3000 s in FAST.Farm, with signals sampled at 10 Hz on a 24-core laptop with 32 GB of RAM.A self-developed interface was used to run the simulations.Source: A. Simulation Setup · p. 4

B. Performance Metrics

  • Static regret compares online cumulative cost with the minimum cost attainable by a fixed yaw vector over the full horizon.The fixed-yaw optimum is approximated using yaw angles from the model-based optimization baseline; sublinear regret is the stated criterion for good online performance.Source: B. Performance Metrics · p. 5

C. Simulation Results

In the case study, the proposed method reaches power comparable to the model-based baseline while reducing wake-related cost; its regret remains below the considered sublinear bounds.

1) Total Cost:

  • Farm-level cost converges after about 1000 s to a value comparable to the model-based case, indicating wake mitigation despite a slower response.Figure 7(a) shows the time evolution of farm-level cost.Source: 1) Total Cost · p. 5, Figure 7 · p. 5

2) Power Production:

  • 8.499 MW for the proposed method and 8.488 MW for FOWFSim-based control compare with the greedy baseline’s 5.693 MW in steady-state farm power.The corresponding increases over greedy are 49.3% and 49.1%, respectively.Source: 2) Power Production · p. 5, Figure 7 · p. 5
  • The proposed yaw actions converge more slowly than FOWFSim-based actions, while FOWT2 and FOWT3 reach yaw values of comparable magnitude.The reported yaw outcomes are consistent with balancing wake-overlap reduction against excessive yawing.Source: 3) Yaw Actuation · p. 5, Figure 7 · p. 5

4) Static Regret:

  • Static regret remains below all considered sublinear reference bounds, supporting the proposed method’s online-optimization performance.Figure 7(d) compares static regret with the reference functions.Source: 4) Static Regret · p. 5, Figure 7 · p. 5

5) Steady-State Wake Field:

The wake-field comparison shows both controlled cases reducing downstream wake overlap relative to greedy operation. The conclusion reports lower computational effort and slightly better power for the proposed method, while identifying further operating conditions for future work.

5) Steady-State Wake Field:

  • Both controlled cases steer downstream turbines toward higher-wind regions and reduce wake overlap compared with greedy operation.Figure 8 compares the steady-state wake fields from FAST.Farm for the three cases.Source: 5) Steady-State Wake Field · p. 5, Figure 8 · p. 6

6) Computation Time:

  • The proposed method requires 0.0746 ms per iteration versus 0.2313 s for FOWFSim-based control, a reduction of more than 3000-fold.The comparison measures time from acquiring measurements to sending the next yaw angle; the paper attributes the reduction to distributed formulation and local logic that avoids gradient computation.Source: 6) Computation Time · pp. 5–6

V. CONCLUSION

  • The conclusion reports slightly better power output with substantially lower computational effort; nonarray layouts and time-varying winds remain future-work settings.The proposed method estimates wake dynamics from onboard blade-load signals and designs its cost function to indicate wake overlap.Source: §V · p. 6
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