External wake effects

As offshore wind clusters and government-led planned sites continue to expand, the issue of external wake interactions among adjacent wind farms is becoming increasingly significant [12–14]. In general, a wake refers to a flow phenomenon characterized by velocity deficit and enhanced turbulence that forms downstream of a wind turbine as it extracts kinetic energy from the wind [15]. The wake released from upstream turbines can negatively influence the performance of downstream turbines, leading to reduced power generation efficiency [16].

This phenomenon occurs not only within a single wind farm (internal wakes) but also between neighbouring farms within cluster zones, where its impact is amplified as farm sizes increase and spatial layouts become denser. Wake effects typically manifest as diminished wind velocity, increased turbulence intensity, and subsequent energy losses, all of which ultimately reduce the annual energy production (AEP) and financial performance of downstream assets [17–20]. Therefore, quantifying external wake effects and identifying optimal inter-farm spacing are essential for developers, policymakers, and regulators during the design and planning stages of offshore wind clusters.

Policy and spatial planning frameworks for inter-farm spacing in offshore wind clusters

Inter-farm spacing serves as a key spatial design parameter for large-scale offshore wind developments organized through clustered or government-planned siting schemes. Adequate spacing between neighbouring wind farms helps minimize generation losses due to external wakes, ensures long-term energy efficiency, and reduces the risk of conflicts among project developers. Inadequate spacing can lead to wake-induced efficiency decline, economic loss, and even legal disputes between adjacent projects [21–23].

To mitigate such risks, many countries have established policies or engineering-based guidelines governing inter-farm spacing. In the United Kingdom, for instance, the Round 4 Offshore Wind Leasing guidelines specify a minimum distance of 7.5 km between new projects and at least 5 km from existing adjacent projects [8]. These regulations aim to minimize wake-induced energy losses and ensure safe marine navigational corridors. “Taiwan’s Offshore Wind Power Development Rules” legally mandate a minimum spacing of 1.2 km between offshore wind farms.

In contrast, countries such as Germany, the Netherlands, and Denmark have not set fixed numerical criteria for inter-farm spacing. Instead, spacing and layouts are determined within the context of Marine Spatial Planning (MSP) processes, which consider navigational safety, environmental preservation, and other competing ocean uses in an integrated manner.

Currently, Korea lacks explicit legal criteria concerning the minimum spacing between offshore wind farms to mitigate external wake effects. The Offshore Traffic Safety Assessment Guidelines prescribe separation distances based primarily on navigational safety defined as six times the length of the largest passing vessel plus 500 m and 0.3 nautical miles [24]. These criteria prioritize maritime safety rather than energy production efficiency or wake loss mitigation.

Considering the nation’s transition toward government-led planned sites and large-scale cluster-type developments, there is an urgent need to establish a formal regulatory framework for inter-farm spacing. Incorporating international policy best practices and scientific research findings into Korean spatial planning policies would help prevent energy yield and revenue losses due to external wakes. Moreover, such institutionalization would promote sustainable industry growth and facilitate equitable coordination among offshore wind developers in the long term.

Study area

According to data from the Electricity Regulatory Commission of the MOTIE as of September 2025, a total of 109 offshore wind projects in Korea have received energy business licenses (EBL), amounting to an aggregate authorized capacity of approximately 34.8 GW (excluding cancelled and relinquished permits) (Table 1). Over 60% of these projects are concentrated in Jeonnam Province, where 68 projects with a combined capacity of around 21.3 GW have been approved (Fig 1), establishing the region as the nation’s focal point for offshore wind development. Ulsan and Incheon are also advancing large-scale offshore wind clusters, with project pipelines totalling approximately 6.0 GW and 3.4 GW, respectively, indicating the nationwide proliferation of offshore wind cluster development.

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Table 1. Status of offshore wind projects which has secured offshore wind energy business licenses by region in South Korea as of September 2025.

https://doi.org/10.1371/journal.pone.0341955.t001

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Fig 1. The spatial distribution of offshore wind projects in South Korea which have secured energy business licenses, visualized using QGIS.

The blue square represents the Shinan offshore wind farm cluster. Coordinate system: EPSG 5181, WGS 84 / Pseudo-Mercator.

https://doi.org/10.1371/journal.pone.0341955.g001

Of particular note, Shinan County in Jeonnam was officially designated as a renewable energy cluster zone in April 2025 by MOTIE, encompassing ten cluster-type projects with a total capacity of 3,166 MW. Accordingly, this study selects the Shinan offshore wind cluster zone as a representative case to quantitatively analyse energy yield losses resulting from external wake interactions under large-scale clustered deployment scenarios.

Simulation of external wake effects on cluster zones

This study quantitatively evaluates energy yield losses caused by external wake effects within selected cluster-type offshore wind zones in Shinan County, Jeonnam Province. To achieve this, a hypothetical offshore wind project area was established adjacent to the Shinan cluster zone, and wind turbines were spatially arranged within both the cluster and the hypothetical project site. The turbine layout was based on the open-source 15 MW reference wind turbine model developed by the IEA [25–27], which was applied to both the cluster-type zones and the hypothetical project to closely replicate real-world development scenarios.

The installed capacity and number of turbines for each zone were determined according to local characteristics, using an average energy density criterion of approximately 5.0 MW/km² for the cluster-type zones. The hypothetical project was designed using a higher density criterion of roughly 9.0 MW/km², resulting in a total capacity of 390 MW to emphasize wake effects. Considering the prevailing wind direction in the southwest sea (northwest–north-northwest), the hypothetical project wind farm was positioned as far downstream as possible relative to the cluster, to conservatively assess maximum wake impacts. The design capacity for each of the ten cluster zones (Zones 1–10) was calculated using the energy density criterion (see Fig 2, Table 2).

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Table 2. Basic assumptions and wind farm layout design for each subarea (No. 1–10) and a hypothetical project site of the Shinan offshore wind farm cluster. The long-term wind speed at hub height (150 m) is extracted from the Vortex mesoscale modelled wind resource map.

https://doi.org/10.1371/journal.pone.0341955.t002

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Fig 2. Assumed arbitrarily located offshore wind project site (green shaded area) and the Shinan offshore wind cluster (red boundary zones of No. 1–10) for external wake simulation in this study.

Coordinate system: EPSG 5181, WGS 84 / Pseudo-Mercator.

https://doi.org/10.1371/journal.pone.0341955.g002

The overall analysis procedure is as follows (Fig 3):

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Fig 3. Analytical procedure for sensitivity analysis of annual economic loss due to external wakes in the Shinan offshore wind cluster zone, Southwest Korea.

https://doi.org/10.1371/journal.pone.0341955.g003

• A hypothetical offshore wind farm was placed within the Shinan cluster zone in Jeonnam.
• Both the cluster-type zones and the hypothetical farm were designed using the 15 MW reference wind turbine model.
• Three scenarios were constructed based on the completion and operational ratio of each cluster project area (30%, 60%, 100%).
• Four scenarios were established by varying the inter-farm spacing between project zones (no spacing, 1 km, 3 km, 5 km).
• Combining cluster operation ratios and inter-farm spacing, a total of 12 cases were used to perform sensitivity analyses of wake-induced energy yield losses.
• For each case, economic loss sensitivity analyses were also performed at various REC multipliers (2.0, 2.5, 3.5, 4.5 REC) based on the latest SMP + REC market conditions.

As a result, AEP losses and associated economic losses were estimated for each scenario. This allowed for a quantitative assessment of the business impacts of external wake effects and the formulation of relevant policy implications for offshore wind cluster development.

Wind resource input data

Vortex MAPS mesoscale modelling data was utilized as the primary wind resource input. Vortex MAPS, based on the Weather Research and Forecasting (WRF) [28] numerical weather model, is specifically designed for regional wind resource assessment and leverages reanalysis datasets such as ERA5 to generate long-term averages for wind speed, turbulence intensity, and vertical/horizontal profiles over periods exceeding 20 years with a horizontal resolution of 1 km [29]. For this analysis, Vortex MAPS provided long-term wind resource characteristics including mean wind speed, direction, temperature, and turbulence intensity for each candidate site. Most notably, Vortex MAPS serves as an alternative data source reflecting long-term climate characteristics, making it suitable for spatial distribution and vertical profile analysis during the early design stages of large offshore wind cluster developments.

Cluster operation ratios

Considering that individual sites within cluster zone 1–10 may not be completed and operated simultaneously, and recognizing that not all sites may progress as planned, the external wake loss sensitivity scenarios were established based on the operational ratio of the 10 cluster sites as follows:

• Scenario Base: No external wake losses present (only the hypothetical wind farm is operational)
• Scenario 1: 30% of cluster projects (3 sites, selected randomly) are completed
• Scenario 2: 60% of cluster projects (6 sites, selected randomly) are completed
• Scenario 3: 100% of cluster projects (all 10 sites) are completed

Adjustment of inter-cluster distances

Sensitivity scenarios for adjusting distances between the hypothetical project area and each cluster site (1–10) were devised. Minimum inter-cluster distance guidelines such as Taiwan’s 1.2 km and the UK’s 5.0–7.5 km were referenced, and four representative distances (0 km, 1 km, 3 km, and 5 km) were adopted for the analysis:

• Scenario 1: No inter-cluster distance is applied (clusters are contiguous)
• Scenario 2: All cluster distances set to 1 km
• Scenario 3: All cluster distances set to 3 km
• Scenario 4: All cluster distances set to 5 km

Final sensitivity analysis scenarios

Table 3 summarizes the final sensitivity analysis scenarios. The “Base case” assumes that only the hypothetical project is sited, and no external wake-induced energy losses occur. Scenarios range from Case 1 (no spacing inter-cluster with 30% operation) to Case 12 (5 km inter-cluster distance with 100% cluster operation), evaluating annual energy yield across 12 scenarios. Quantitative estimation of energy and economic losses for Cases 1–12 is provided relative to the Base case, which considers losses from internal wake effects only. The results of wind farm and turbine layouts for each scenario are shown in Fig 4.

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Table 3. Sensitivity analysis scenarios based on cluster operation ratios and inter-cluster distance (wind farm spacing). The base case represents only internal wake loss without considering any neighboring offshore wind farms.

https://doi.org/10.1371/journal.pone.0341955.t003

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Fig 4. Configuration of external wake scenarios considering wind farm cluster operation ratios and inter-cluster distance (wind farm spacing): (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, (e) Case 5, (f) Case 6, (g) Case 7, (h) Case 8, (i) Case 9, (j) Case 10, (k) Case 11 and (l) Case 12.

Coordinate system: EPSG 5181, WGS 84 / Pseudo-Mercator.

https://doi.org/10.1371/journal.pone.0341955.g004

Jensen wake model

Commonly known as the Park model, the Jensen wake model is an analytical framework that linearly simplifies and predicts far-wake wind speed deficits occurring downstream of wind turbines (see Equation 1) [30,31]. The model is based on the assumption that the low-speed, high-turbulence zone formed behind a turbine due to energy extraction diffuses linearly with distance, resulting in gradual wind speed recovery.

(1)

In this context, represents the relative wind speed at a downstream distance x from the turbine, while denotes the free-stream velocity upstream of the turbine. refers to the thrust coefficient, and k is the wake decay constant (WDC). For offshore conditions, a WDC value of 0.04–0.06 is typically applied; this study adopts a representative value of 0.04. denotes the rotor diameter of the turbine.

For each wind speed–direction bin (), the single-wake velocity deficit from an upstream turbine at the location of turbine is first expressed as

(2)

where is the free‑stream wind speed at hub height and is the local wind speed at turbine when only the wake from turbine is considered.

The combined velocity deficit at turbine due to multiple upstream turbines is then obtained using the root‑sum‑square superposition method as below:

(3)

where denotes the set of all turbines located upstream of turbine for the considered wind direction.

The effective hub‑height wind speed at turbine is thus given by:

(4)

The Jensen model is widely used in commercial software as a default wake model, valued for its computational simplicity and flexible parameterization, making it applicable across both offshore and onshore contexts. However, its limitations include inadequate representation of turbulence intensity changes, inter-turbine interactions in large arrays, nonlinear wind speed distribution, and atmospheric effects. Consequently, it is known to have accuracy limitations and a tendency to underestimate wake losses in practical wind farm applications.

TurbOPark wake model

Unlike the Jensen model, which assumes linear wake expansion, the TurbOPark (Turbulence Optimised Park) model accounts for wake expansion deceleration as turbulence generated within the wake dissipates with increasing distance [32–35]. TurbOPark complements the physical interpretation of inter-turbine interactions by more accurately reflecting nonlinear effects such as wind speed deficits, turbulence intensity, and thermal impacts when multiple wakes overlap. This approach enables the prediction of induced losses not only for single turbine wakes but also for complex aggregated scenarios within large wind farms [36–39].

In this study, the TurbOPark model as implemented in the WindPRO PARK module is used to represent far‑wake development and inter‑farm interactions. The model retains the top‑hat assumption of the Jensen/Park approach but links the wake expansion rate to the local turbulence intensity, allowing the wake to recover faster in highly turbulent conditions while remaining persistent in low‑turbulence offshore environments.

(5)

(6)

The single‑wake deficits obtained from Equation (6) are mapped to the turbine locations and combined using the root‑sum‑square superposition described in Equation (3), yielding the effective hub‑height wind speed at each turbine before converting to power and AEP.

The formulation of the TurbOPark model builds upon the Jensen framework while introducing probabilistic and weighting methods to quantify the cumulative wake effects from multiple turbines downstream [40]. This model is particularly suitable for simulating external wake effects in large clusters, although it may conservatively estimate the magnitude and persistence of offshore external wake influences, potentially resulting in conservative annual energy yield predictions.

Selection of wake models for external wake assessment

For the analysis of external wake losses in offshore wind cluster developments, both the Jensen and TurbOPark wake models were selected, and an ensemble modelling approach was adopted by equally weighting the results from each model (weighting factor of 0.5). This methodology accounts for the inherent bias tendencies of each model: the Jensen model’s tendency to oversimplify wake expansion and thus underestimate wake losses, and TurbOPark’s propensity to overestimate losses by capturing nonlinear cumulative wake effects. To address these contrasting characteristics, model outputs were independently derived and then integrated with equal weights to arrive at the final loss estimate.

Meanwhile, the Eddy Viscosity (EV) wake model was excluded from consideration, as it requires detailed atmospheric turbulence and flow field data not available during the early-stage, pre-feasibility assessment targeted in this project. The EV model is subject to considerable uncertainty in the absence of ample site measurements and detailed flow parameters, and its computational complexity limits practicality for large offshore wind cluster early-phase reviews [40,41]. Consequently, it was excluded from the model shortlist. Table 4 presents internal wake loss simulation results for the 390 MW project area under the Base case scenario (internal wake effects only) using the selected models.

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Table 4. The summary result of preliminary EYA simulation for internal wake losses including blockage effect. The adjusted final wake loss was estimated from Jensen and TurbOPark as an ensemble methodology considering same weighting value.

https://doi.org/10.1371/journal.pone.0341955.t004

Due to its tendency to underestimate internal wake loss, the Eddy Viscosity model was also excluded from the ensemble methodology. The final internal wake loss estimate was derived by applying a weighting factor of 0.5 to each of the Jensen and TurbOPark model results. This ensemble approach was also consistently applied to simulations of external wake effects.

Core assumptions for energy yield assessment

The P50 energy yield represents the 50th percentile of long-term average energy production, meaning there is a 50% probability that actual generation will meet or exceed the predicted value. The P50 figure is routinely used for project feasibility evaluations, profitability analyses for investors, and credit/bond assessments by financial institutions, often serving as the ‘Best Case’ scenario during feasibility studies [6]. More conservative risk evaluations such as P75 and P90 percentiles are also commonly calculated, but P50 remains the technical and economic decision-making baseline.

(7)

P50 is determined by predicting the long-term energy yield of a wind project, incorporating a range of loss factors (Equation 7). These loss factors include wake losses (turbine interactions), electrical losses, mechanical or turbine availability losses, environmental losses, curtailment (grid restrictions), non-availability due to maintenance and inspections, and other exceptional losses [42,43]. Each loss factor is applied multiplicatively after the theoretical annual energy production (Gross AEP) is calculated, producing the ‘Net AEP’, the P50 yield expressed from a probabilistic perspective. In this study, loss rates assumed for all factors except wake losses are shown in Table 5.

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Table 5. The breakdown of general loss assumptions excluding turbine interactions (wake losses).

https://doi.org/10.1371/journal.pone.0341955.t005

(8)

Based on equation 8, the loss rate excluding wake losses is set at 10.8%, which is considered a suitable benchmark in the context of domestic environmental conditions [6]. The P90/P50 ratio serves as a supplementary indicator for rapid estimation of P90 yields when detailed uncertainty analysis is unavailable [44]. This ratio reflects the spread of project energy yield distribution; values close to 1 indicate low prediction uncertainty. Generally, offshore wind projects exhibit lower resource variability than onshore sites, allowing P90/P50 ratios of 0.87–0.93 to be considered commercially sound, indicating that loss and uncertainty are at an acceptable level for reliable investment and financial review.

Given the absence of dedicated wind resource measurements in this study, an independent uncertainty analysis could not be performed. Therefore, the P90/P50 ratio was presumed to be 0.9 for P90 yield estimation.

Wind speed deficit

Figs 5 and 6 illustrate the spatial variability of wake-induced wind speed deficits within the Shinan offshore wind cluster under various inter-farm spacing scenarios, where 11 individual sites (10 in red delineated cluster areas plus 1 project site outlined in dashed black) are assumed fully outfitted and operational with turbines. The scenarios model wind farm spacing at 0 km (Case 3), 1 km (Case 6), 3 km (Case 9), and 5 km (Case 12) to investigate the influence of cluster layout density on wake interactions and resultant wind speeds at turbine hub height (150 m).

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Fig 5. Quantitative distribution of hub-height (150 m) wind speed deficits induced by internal/external wakes in the Shinan cluster under different scenarios.

All scenarios assume 100% operational ratio of the cluster, with inter-farm spacing varied across the following cases: (a) Case 3 − 0 km, (b) Case 6 − 1 km, (c) Case 9 − 3 km, and (d) Case 12 − 5 km. Coordinate system: EPSG 5181, WGS 84 / Pseudo-Mercator.

https://doi.org/10.1371/journal.pone.0341955.g005

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Fig 6. Quantitative distribution of wind speed difference at hub-height (150 m) between free wind stream and wake-effected wind speed induced by internal/external wakes in the Shinan cluster under different scenarios.

All scenarios assume 100% operational ratio of the cluster, with inter-farm spacing varied across the following cases: (a) Case 3 − 0 km, (b) Case 6 − 1 km, (c) Case 9 − 3 km, and (d) Case 12 − 5 km. Coordinate system: EPSG 5181, WGS 84 / Pseudo-Mercator.

https://doi.org/10.1371/journal.pone.0341955.g006

Fig 5 presents the Vortex MAPS mesoscale modelling wind resource dataset depicting the spatial distribution of wind speeds at hub height for each spacing scenario. The colour gradient from red to green indicates decaying wind speeds due to wake effects, with green corresponding to greater deficits. Notably, Case 3 (0 km inter-farm spacing) demonstrates extensive areas of pronounced wind speed reduction, particularly near turbine clusters, as evidenced by the deep green shading. This intensified velocity deficit arises from overlapping wakes caused by the close proximity of wind farms, producing compounded aerodynamic interference, increased turbulence intensity, and subsequent momentum depletion in the wake region.

Fig 6 visualizes the quantitative wind speed difference between free-stream undisturbed winds (turbine-free conditions) and wake-affected winds within the same cluster scenarios. The blue shading reflects the magnitude of wind speed deficit attributable to wake effects, with darker blue regions indicating a deficit of up to 0.9 m/s relative to free-stream conditions. As in Fig 5, Case 3 exhibits the most extensive and severe velocity deficits, illustrating substantial wake-induced wind speed reduction when turbine arrays are densely packed without spatial separation.

Increasing inter-farm spacing from 0 km to 5 km progressively mitigates these wake interactions, as the additional distance allows greater wake recovery and dispersion before encountering subsequent turbines. This spacing improvement is manifested by weakening green and blue regions in Figs 5 and 6 for Cases 6, 9, and 12, indicating higher hub-height wind speeds and smaller wake-induced deficits.

Fig 7 further illustrates the cross-sectional spatial variation of wind speed deficit across the Shinan cluster. It is evident that the magnitude of the difference between the free-stream wind speed and the waked wind speed progressively increases toward the central region of the cluster. This trend is attributable to the cumulative effect of overlapping wakes generated by upstream turbine arrays, which become more pronounced as the wind progresses into the denser core of the cluster. Furthermore, a clear distinction is observed among the different spacing scenarios: as the inter-farm spacing increases from Case 3 to Case 12, the severity of the wake-induced wind speed reduction is markedly alleviated. This finding demonstrates that greater spacing between wind farm sub-clusters effectively mitigates the adverse impact of wake losses on the available wind resource, thereby reducing the expected negative effect on annual energy production. These results underscore the importance of optimized spatial planning for large-scale offshore wind clusters, ensuring that wake interactions are minimized to maximize power yield and operational efficiency.

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Fig 7. Cross-sectional spatial variation of the wind speed deficit (free-stream wind speed minus wake-effected wind speed) at hub height (150 m) along the blue arrow transect indicated in the Shinan cluster map.

(a) The cross section is oriented along the prevailing wind direction approximately, traversing most wind farm zones. (b) Each curve represents the spatial profile of wind speed deficit for different inter-farm spacing scenarios, quantifying the impact of cluster wake interactions on available wind resource. Red solid line (Free-Sc 3), Blue double line (Free-Sc 6), Green dashed line (Free-Sc 9), Grey dotted line (Free-Sc 12).

https://doi.org/10.1371/journal.pone.0341955.g007

The observed phenomenon where tighter spacing exacerbates wake-induced wind speed deficits can be primarily attributed to the physics of wake formation and recovery in clustered wind farm environments. Turbulent wakes generated behind wind turbines lead to a low-momentum region with reduced wind speeds and heightened turbulence, which slowly recovers with downstream distance due to turbulent mixing and ambient flow entrainment. When wind farms are positioned with minimal separation, these wakes overlap and interact, producing cumulative deficits that reduce available wind energy for downstream turbines, thereby impacting energy yield.

SMP and REC scenarios

To estimate the economic impact of external wake losses for a hypothetical offshore wind project in the Shinan cluster, both the System Marginal Price (SMP) and Renewable Energy Certificate (REC) values were considered. RECs certify the environmental value of electricity produced from renewable sources and are issued to large-scale producers under Korea’s Renewable Portfolio Standard (RPS), enabling them to fulfil renewable energy supply obligations.

In fixed-price contract competitive bidding, long-term (20-year) contracts are awarded based on the combined price of SMP and REC (or REC price adjusted by weighting factors), negotiated between power producers and obligated suppliers. According to the revised RPS management guidelines (July 2021), coastal offshore wind is assigned a base REC weight of 2.0 (tidal flat or seawall), while offshore wind receives a base weight of 2.5, with final composite weightings determined by site-specific factors (such as transmission distance and water depth). Project revenue is calculated by multiplying actual energy output by the combined SMP and REC prices; any reduction in output (due to external wake losses, for example) directly reduces economic returns.

Therefore, evaluating economic loss sensitivity through combinations of SMP and varying REC weights is a critical tool for assessing project feasibility and financial security in offshore wind development. This study analysed changes in annual energy revenues, under different SMP + REC scenarios, to quantify long-term economic impacts attributable to external wake effects.

Reference values were drawn from the ‘2025 Korea Offshore Wind Fixed-Price Contract Competitive Bidding Announcement (first half)’, which set an upper price limit for land-based projects at 176,565 KRW/MWh (SMP + 1 REC). The reference SMP for land was 86,350 KRW/MWh, yielding a REC price of 90,215 KRW. Economic loss sensitivity was assessed for several REC weights (2, 2.5, 3.5, and 4.5). These scenarios cover basic weights (coastal: 2, offshore: 2.5) and the maximum expected REC weighting for deep water, remote floating wind clusters, such as Ulsan, which could reach 4.5 based on local depth and transmission distance. In Section 4.3.2, economic losses are compared for each combination of SMP and REC unit price and weighting factor, quantifying the annual energy yield impacts of external wake losses and providing concrete evidence for domestic offshore wind developers to support project feasibility decisions.

Economic loss sensitivity analysis

Table 7 summarizes the results of economic loss sensitivity analysis based on annual energy shortfall simulations caused by external wakes. The analysis focuses on P90 annual energy yield, as this conservative metric is typically used during financial structuring and debt due diligence for wind projects. Assessing losses based on P90 more accurately reflects the true financial risk and potential economic impact to investors and lenders.

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Table 7. Summary of sensitivity analysis on economic losses based on P90 AEP due to external wake losses, comparing four (4) SMP and REC scenarios (2.0, 2.5, 3.5, 4.5 RECs). All economic losses are presented as the difference from the Base case which was estimated without external wake effects.

https://doi.org/10.1371/journal.pone.0341955.t007

For the hypothetical offshore wind project considered (as spatially described in Fig 2), the average water depth is below 20 m and grid connection distance is approximately 20 km, so the REC weighting is not expected to exceed 3.5. However, a range of REC weighting scenarios were evaluated to enable project developers to quantitatively understand the range of potential losses. The results indicate that, under Case 3 (representing the most significant external wake impact) annual economic losses reach 20.83 billion KRW at a REC weight of 2, and escalate to 38.43 billion KRW at a REC weight of 4.5. Assuming a conservative 20-year project life, this could result in a maximum cumulative loss of 770 billion KRW.

These findings are consistent with Ryu et al. (2025), which cited that Orsted's Hornsea project submitted documentation to the UK government indicating potential compensation claims ranging from €5.5 million to €199 million (approx. 9–32.3 billion KRW at 1 EUR = 1,630 KRW) over its operational period due to external wakes from the Outer Dowsing project, even though the average separation was 20–30 km. In this study's Case 3 (with no inter-farm separation) the potential losses are reasonably expected to exceed those referenced in the UK case.

In Case 12 (5 km inter-cluster distance, 100% cluster operation), annual losses increase from 12.98 billion KRW (REC weight 2.5) to 16.73 billion KRW (REC weight 3.5) and 20.48 billion KRW (REC weight 4.5), but are reduced by roughly 47% compared to Case 3, demonstrating the benefits of adequate project spacing.

Overall, annual energy shortfalls due to external wakes have profound implications for project long-term profitability and financial stability. This is especially important as the trend toward large, closely clustered offshore wind zones can lead to direct conflicts of interest between multiple developers. Thus, policy and regulatory responses including compensation frameworks, minimum inter-project distance rules, and the adoption of technical mitigation measures are essential subjects for further discussion and implementation.