An Integrated Methodology for Assessing Wind Power Curtailment Using Anemometric Measurements and Operational Data in the Brazilian Context

Abstract

The increasing share of wind power generation has intensified the occurrence of curtailment events in power systems worldwide, mainly driven by transmission constraints, operational limitations, and imbalances between generation and demand. In the Brazilian context, this phenomenon has become more pronounced since 2023, highlighting structural challenges of the Brazilian Interconnected Power System and the need for reliable methodologies to estimate curtailed wind generation. This study presents a methodology to estimate wind power potential during curtailment events, aiming to support forecasting models and the economic compensation of affected generating agents. The proposed approach integrates measured power generation data, technical information of wind farms, and anemometric measurements from SCADA systems, combining data filtering and consistency procedures, gap-filling based on spatial correlation among wind farms, and regression models supported by statistical and computational techniques for wind-to-power conversion. The methodology was applied to more than 1000 wind farms connected to the Brazilian transmission grid and achieved accuracy levels above 95% on a semi-hourly basis and exceeding 99% for annual aggregations.

1. Introduction

The continuous growth in electricity demand, combined with the need to reduce greenhouse gas emissions, has driven the expansion of renewable energy sources as a cornerstone of sustainable development [1]. In this context, wind power has consolidated as one of the most attractive options, exhibiting remarkable growth over the past decades [2]. Currently, global installed wind capacity has reached approximately 1 TW, accounting for nearly 25% of the total renewable capacity worldwide [3]. Projections indicate that by 2030 wind power generation will surpass hydropower in terms of global energy production, being exceeded only by solar photovoltaics [4].

Despite this positive evolution, the increasing penetration of wind power introduces significant operational challenges due to its inherent variability and strong dependence on meteorological conditions [5]. Key challenges include the growing need for power and energy reserves to compensate for production fluctuations, as well as increased complexity in power system planning and operation [5,6,7]. In this context, comprehensive knowledge of wind power generation and accurate forecasting become strategic assets, serving as essential inputs to support operational and dispatch decisions [5,6,7,8].

However, as wind power penetration intensifies, the frequency of curtailment events has increased, often associated with transmission constraints, operational limitations, and temporary imbalances between supply and demand. In such cases, the analysis of observed generation alone, even when supported by accurate forecasts, is insufficient to characterize the actual performance of wind farms. Estimating the potential generation that would have occurred in the absence of constraints becomes necessary to disentangle curtailment effects from natural wind variability, enabling a proper assessment of energy losses, fairer management of operational restrictions, and the evaluation of economic impacts, particularly in compensation processes for affected generators.

Considering these factors, a relevant scientific challenge is the reliable estimation of potential wind power generation in power systems with a high penetration of wind energy. Although several approaches for wind power estimation and forecasting have been proposed in the literature, their application in large-scale operational environments remains limited, particularly in the context of large independent system operators (ISOs), where available data are often heterogeneous, incomplete, and subject to inconsistencies. Furthermore, few studies systematically address the counterfactual estimation of suppressed generation due to operational constraints, which is a key aspect for the proper quantification of energy losses associated with curtailment events.

In this context, this work proposes the development of a methodology for estimating potential wind power generation, with a specific focus on identifying and quantifying energy losses associated with curtailment. The proposed approach is based on the application and adaptation of techniques for data processing and generation estimation, considering both the particularities of the Brazilian power system and practices and experiences adopted internationally. The proposed methodology presents an innovative character and, although developed for the Brazilian context, has broader applicability, potentially serving as a reference for other system operators and for the scientific community. The main contributions of this paper are summarized as follows:

• An objective review of the literature on wind power generation estimation methods and their application to evaluating energy losses due to wind curtailment, covering institutional practices, operational requirements, and experiences from international power system operators.
• An overview of the Brazilian power sector, with a focus on wind power generation characteristics and wind power curtailment in the Brazilian Interconnected Power System (SIN).
• A data processing and qualification framework is proposed to address challenges related to the availability, quality, and consistency of operational wind data. The approach integrates anemometric measurements from Brazilian sectoral institutions and wind farms, applying systematic procedures for data treatment and validation in large-scale operational environments with heterogeneous and incomplete datasets.
• A novel wind power potential generation estimation model is proposed, with strong emphasis on practical applicability for large-scale system operators, particularly Independent System Operators (ISOs) such as the Brazilian National Electric System Operator (ONS). The methodology adopts a hybrid approach, combining physical and statistical concepts and incorporating advanced techniques for the large-scale construction of wind speed–power (W–P) curves, which is a key requirement for systems with a large number of wind farms.
• Results obtained to date indicate robust performance of the proposed model in estimating curtailment within the ONS context, highlighting its potential as a significant contribution to the improvement of estimation practices and operational analysis in power systems with high penetration of variable renewable energy sources.

To achieve these objectives, the paper begins by presenting in Section 2 a brief review of curtailment practices on a global scale, approaches used for wind power generation estimation, and an overview of wind power generation in the Brazilian context. Next, Section 3 describes the data used for model development, the methods applied to process these data, and the resulting model. Section 4 then presents the results obtained, followed by the main discussions, presented in Section 5. Finally, Section 6 summarizes the conclusions of the paper.

2. Background and Literature Review

2.1. Curtailment Practices at the Global Scale

2.1.1. Concept and Causes of Curtailment

The increasing share of variable renewable energy sources, particularly wind and solar power, in the global electricity mix has made curtailment an increasingly relevant challenge for power system operation in many countries [9].

Curtailment is defined as the reduction of a power plant’s electricity generation to levels below its available potential [10]. In such cases, even when energy resources such as wind or solar irradiance are available, generation is limited by operational or structural constraints of the power system, including transmission congestion, restricted grid access, or excess generation during periods of low demand. Operational security requirements, such as voltage control, interconnection limits, and frequency regulation, may also lead to curtailment, particularly in small or isolated systems [11].

According to [10], curtailment often occurs due to transmission congestion or local network constraints associated with thermal or stability limits, leading system operators to reduce generation in order to prevent overloads and instabilities. It may also arise from imbalances between generation and demand in the absence of sufficient flexibility or storage, a common condition in systems with high solar or wind penetration, as well as from the need to ensure adequate system inertia and proper response to disturbances. Beyond technical factors, economic curtailment is also observed, being related to dispatch logic and merit-order considerations, including low or negative electricity prices and strategic bidding behavior in energy markets [12].

2.1.2. Evolution of Curtailment in Systems with High Renewable Penetration

At the global level, wind power curtailment has intensified in regions such as Europe, China, Canada, and the United States, following the expansion of variable renewable energy sources [9]. This trend reflects both the growth of these sources and the limitations of power systems in handling high variability. In this context, ref. [9] analyzes curtailment through an international comparative approach that relates curtailment rates to the share of wind and solar generation in national electricity mixes. Based on at least ten years of historical data, the study classifies systems according to curtailment magnitude and its temporal evolution, showing that high renewable penetration does not necessarily imply high curtailment levels and highlighting the role of infrastructure and flexibility. For example, while curtailment has increased in countries such as the United Kingdom, Germany, and Ireland, several regions in China have experienced reductions despite higher renewable shares.

Curtailment has become a strategic indicator for transmission system operators, as it reflects structural and operational constraints. It signals the need for transmission expansion, greater flexibility, and ancillary services, while also supporting regulatory and market decisions [9]. From a technical perspective, limited transmission capacity tends to increase curtailment. In countries such as Germany and the United Kingdom, higher renewable shares have been accompanied by increased costs and greater reliance on redispatch, highlighting its relevance for reserve management and ancillary services [13].

From an economic perspective, curtailment reduces marketable energy and expected revenue of Variable Renewable Energy (VRE) projects, potentially affecting financial performance and increasing investor risk. Evidence indicates that, as the share of these sources in the power system grows, both the economic loss per event and the marginal cost of curtailment increase [14]. To mitigate these effects, compensation mechanisms are adopted, such as payments for non-dispatched energy and revenue protection instruments, which rely on robust methods to estimate generation in the absence of curtailment [15].

2.2. Approaches for Wind Power Generation Estimation

Wind power generation estimation is essential for system operators in curtailment analysis, as it enables the separation of effects caused by operational constraints from those related to the natural variability of the wind resource. By providing a reference for expected generation in the absence of curtailment, these estimates support operational monitoring, post-operational analyses, and the assessment of energy and economic impacts, while also contributing to real-time decision-making, short-term planning, and the implementation of compensation mechanisms. Various approaches have been used to estimate generation under curtailment conditions [16], including data-driven methods based on meteorological variables, as well as empirical, statistical, and machine learning techniques [17]. This section reviews these approaches, with a focus on data treatment, gap filling, and potential generation estimation.

Wind power generation exhibits strong spatial and temporal dependence, allowing the use of information from nearby wind farms to complement incomplete time series, reduce noise, and improve the robustness of estimates [18]. Common techniques include the use of neighboring wind farms, spatial interpolation, clustering of plants, and combinations of these strategies for missing data imputation. Data from nearby wind farms or meteorological stations can be used for model calibration or as auxiliary variables. A relevant approach is the use of spatial lags, which represent inter-regional dependence through weighted averages [19]. In the absence of local measurements, generation can be estimated by combining wind–power methods with spatial interpolation techniques such as Natural Neighbor and Inverse Distance Weighting [20,21].

Clustering wind farms with similar patterns reduces data heterogeneity and enables the development of cluster-specific models based on power profiles, wind series, or inter-farm correlations [22]. These approaches are particularly useful in scenarios involving data gaps or newly commissioned wind farms, providing relevant operational benefits [23].

Estimation methods can be classified into physical, statistical, and machine learning approaches [24]. Physical methods rely on technical characteristics and do not require historical data. Statistical methods explore relationships between variables and are suitable for incomplete time series and contexts where interpretability is important. Machine learning methods, also grounded in statistical principles, offer greater flexibility and are capable of capturing both linear and nonlinear relationships more efficiently.

Wind–power curve-based methods model the relationship between wind speed and generated power and can be either parametric or nonparametric [25,26]. Nonlinear regression methods, such as Generalized Additive Models (GAM) and Multivariate Adaptive Regression Splines (MARS) [26,27], are widely applied. Machine learning techniques, including Support Vector Regression (SVR), decision trees, and Gradient Boosting methods, particularly XGBoost [28,29,30,31], stand out for their robustness and ability to model complex relationships.

2.3. Overview of Wind Power Generation in Brazil

For the proper development of wind power generation estimation models, it is essential to consider the specific characteristics of the Brazilian wind power fleet, as well as the different wind regimes that shape the observed generation behavior. Unlike models strictly aimed at forecasting, estimation models primarily seek to reconstruct the counterfactual potential generation that was not realized, particularly under operational constraints such as curtailment events. These models support the assessment of energy losses, the reconstruction of consistent historical time series, and the technical substantiation of economic compensation mechanisms.

Brazil currently has more than one thousand large-scale wind power plants in operation. Figure 1 illustrates the geographical distribution of these plants across the national territory. Circles represent wind farms, with their sizes proportional to the density of adjacent points, allowing the identification of areas with higher concentration. Density was calculated based on the geographical distances between wind farms, considering plants separated by less than 0.5 degrees as neighboring points.

The Brazilian wind power fleet is composed exclusively of onshore wind farms. Its spatial distribution is strongly concentrated in the Northeast and South regions, as illustrated in Figure 1, highlighted by the areas outlined in green and blue, respectively. Approximately 94% of wind farms are located in the Northeast, a concentration that increases the complexity of power system operation and the management of curtailment events in this region, particularly during periods of high wind resource availability. In contrast, about 6% of wind farms are located in the South.

In addition to differences in spatial concentration, there are also relevant structural differences between the wind regimes of the major Northeast and South regions, as well as their respective subregions. These particularities result in distinct patterns of observed wind generation. As shown in Figure 1, it is possible to identify more characteristic behaviors in coastal areas—represented as Northeast Coast and South Coast, which include wind farms located up to 40 km from the shoreline, as indicated in [32]—and in inland areas, classified as South Inland, Bahia/Piauí Inland, and Other Regions. These regional and subregional differences directly influence the estimation of potential generation, especially in curtailment analyses. In such cases, an accurate characterization of the typical behavior and intrinsic variability of the wind resource is essential to avoid biases in the quantification of energy losses.

3. Materials and Methods

This study presents a methodology for estimating wind power generation suppressed by curtailment events. The proposed approach integrates technical information and observed generation data with anemometric measurements obtained from the Supervisory Control and Data Acquisition (SCADA) systems of the Brazilian National Electric System Operator (ONS) and the Brazilian Energy Research Office (EPE) [33]. The methodology begins with a wind farm-level data filtering stage, in which measurement errors are identified and relevant information is systematically selected and consolidated from multiple data sources.

Subsequently, a gap-filling procedure is applied to the wind data time series, using information from nearby wind farms with similar anemometric behavior. Regression models combined with statistical and computational techniques are then employed to convert wind measurements into energy generation estimates, following an approach similar to that adopted in [34]. The methodology further incorporates correction mechanisms designed to mitigate the effects of curtailment events and atypical operational conditions.

The overall structure of the proposed model is presented in Figure 2, which illustrates the information flow underlying the wind power generation estimation process.

3.1. Input Data

3.1.1. Technical Data of Wind Farms

Although several technical attributes of wind farms are relevant for power system planning and operation, in the context of modeling aimed at estimating potential generation and analyzing curtailment events, the most essential information is limited to the geographical coordinates of the plants, their total installed capacity, and the commercial operation start date. Other technical characteristics, while important for real-time operation and asset management, are predominantly operational in nature and do not directly influence the ability of estimation models to reconstruct historical time series or to quantify generation losses associated with operational constraints. The technical data used in this study were obtained from the ONS and the Brazilian Electricity Regulatory Agency (ANEEL).

3.1.2. Observed Data

The data used in this study comprise information from ONS and other institutions within the Brazilian electricity sector. Electric power generation measurements were obtained from the ONS SCADA system. Wind speed anemometric data were collected from the ONS SCADA system and the EPE Anemometric Measurement Monitoring System.

Within the scope of this study, 1043 large-scale wind farms are considered. These wind farms are connected to the transmission network, generally at voltage levels of 230 kV or higher, or, due to their size, have significant impacts on the planning and operation of the SIN by the ONS. These wind farms correspond to all wind power plants operated by the ONS during the analyzed period and total approximately 33.5 GW of installed capacity.

The analysis covers the period from January 2023 to December 2025. The data used are spatially discretized by individual wind farms. Although the data are originally acquired with a temporal resolution of 4 s by ONS and 10 min by EPE, they are aggregated by averaging into 30-min intervals, which is the temporal discretization adopted by ONS in most operational processes. Considering the analysis period and the adopted spatial and temporal discretizations, the dataset corresponds to approximately 54.9 million records for each variable used in the model. However, some wind farms started commercial operation after January 2023; therefore, the effective number of records used in the analyses is approximately 50.1 million for each variable considered in the model.

3.2. Historical Data Preprocessing

As mentioned previously, measurements of the same variable are provided by different institutions, and all datasets exhibit issues related to missing data and/or the presence of spurious values (outliers), which are common in real-world data. As a result, the available data may present undesirable characteristics for estimation models and must be properly treated. Furthermore, due to data redundancy, it is necessary to construct consistent time series by integrating all available sources. For this purpose, a dedicated data preprocessing methodology was developed, based on the approaches described in [35,36].

3.2.1. Historical Data Cleaning Model

First, the observed wind power generation and anemometric data used in this study undergo a systematic quality control and treatment procedure, aiming to ensure physical and temporal consistency, identify instrumental faults, and remove spurious measurements before any integration or gap-filling stage. This process is designed to maximize the reliability of the observed time series and ensure that only statistically and physically consistent information is used in subsequent modeling steps. The methodological workflow adopted for cleaning historical wind data consists of the following steps:

(i)

Data input: raw hourly wind speed time series obtained from ONS and EPE databases, organized at daily resolution.

(ii)

Physical consistency filter: removal of measurements that are physically incompatible or that fall outside limits considered representative for the normal operation of wind farms.

(iii)

Low variability filter: identification and removal of nearly constant measurements over moving windows of 96 consecutive hours, aiming to detect sensors with insufficient temporal variation.

(iv)

Short-term frozen sensor detection: elimination of sequences of measurements with negligible variation over continuous periods of up to 3 h, characterizing temporary reading or data transmission failures.

(v)

Daily representativeness check: discarding days with an insufficient number of valid observations (fewer than five hourly measurements), ensuring a minimum level of statistical representativeness for the daily series.

At the end of this process, the result is a set of cleaned time series, with physically consistent and temporally reliable measurements, which constitute the input basis for the source combination and gap-filling models described in the following subsections.

3.2.2. Measurement Source Combination Model

After the historical data cleaning and consistency stage, wind speed time series from different measurement sources (ONS and EPE) are integrated using a hierarchical source combination model. The objective of this stage is to maximize the use of available information, prioritizing local observed data, and ensuring that any supplementation is statistically consistent, physically coherent, and fully traceable. The methodological workflow for the measurement source combination is structured as follows:

(i)

Verification of valid data availability: assessment of the presence of clean and valid wind observations from the ONS and EPE databases over the period of interest. Not all wind farms have both sources available simultaneously.

(ii)

Linear regression model adjustment between sources: when both sources provide valid data, a linear model is fitted between the corresponding wind speed time series from ONS and EPE, with statistical consistency evaluated through the coefficient of determination ($R^2$).

(iii)

Geometric consistency filter: application of an additional quality criterion based on the geometric distance of points to the fitted regression line, removing observations beyond a predefined distance threshold to eliminate inconsistent measurement pairs.

(iv)

Model performance test: validation of the linear adjustment based on a minimum statistical performance criterion, with the model considered eligible for supplementation only when $R^2$ exceeds the established threshold ($R^2>0.7$).

(v)

Hierarchical data supplementation: when the model is validated, gaps in the ONS series are filled using estimates derived from the adjusted EPE series, fully preserving the originally observed values and replacing only the positions with missing data.

As a result of this process, integrated and consistent wind time series are obtained, in which the source of information used at each time step is explicitly identified. This approach ensures transparency, traceability, and robustness in the combination of measurement sources, providing a solid basis for the subsequent spatially correlated gap-filling stage.

3.2.3. Spatially Correlated Data Gap-Filling Model

After integrating the measurement sources, the wind speed time series may still contain temporal gaps resulting from persistent measurement failures or from the simultaneous absence of valid data across the different databases. To address these cases, a spatial correlation-based gap-filling model is employed. This approach uses information from geographically proximate and statistically correlated wind farms, ensuring physical coherence, statistical consistency, and preservation of the observed data. The methodological workflow adopted for spatially correlated data gap filling is structured as follows:

(i)

Identification of neighboring wind farms: for each reference wind farm, geographically proximate wind farms within a maximum distance of 50 km are selected, ensuring spatial relevance.

(ii)

Linear adjustment of neighboring series: wind time series from each neighboring wind farm are individually adjusted to the reference wind farm series using linear regression models of the form $y\sim x$, with coefficient estimation and statistical consistency evaluated through the coefficient of determination ($R^2$).

(iii)

Ranking and selection wind farms: neighboring wind farms are ranked according to their $R^2$ values, and only those meeting a minimum statistical correlation criterion ($R^2\ge 0.6$) are considered eligible for gap filling, ensuring that only representative series contribute to the data supplementation.

(iv)

Hierarchical gap filling: missing values in the reference wind farm series are filled hierarchically, prioritizing the most strongly correlated neighboring series, replacing only positions with missing data while fully preserving the originally observed values.

This spatial correlation-based gap-filling approach enables the systematic exploitation of spatial redundancy among nearby wind farms, resulting in finalized wind time series that combine statistical robustness, physical coherence, and full traceability of the data used.

3.3. Wind-to-Power Model

3.3.1. Wind Speed–Power Scatter Filter

The subsequent stage of the model consists of constructing wind speed–power (W–P) curves. This step requires careful treatment of data dispersion for each wind farm in order to identify and mitigate records that deviate from typical operational behavior. Proper characterization of W–P scatter is crucial for the correction of outliers, as discussed in [37,38].

The adopted methodology, based on [39], employs a robust mathematical formulation for the identification of anomalous points, while preserving, as much as possible, data that are representative of the natural operational behavior of the wind farm. The approach defines upper and lower bounds that delimit the typical operating range of the wind power plant, as illustrated by the green and yellow curves in Figure 3, which is presented and discussed in Section 3.3.2 . The model proposed in this study advances beyond the original methodology by automating the estimation of the parameters of these boundary curves.

Initially, recent samples of power generation and wind speed are selected, with explicit treatment of null values and restriction to physically plausible ranges. In the absence of predefined limits, the curve parameters are automatically estimated using robust quantile-based statistics, allowing the characterization of cut-in, saturation, and rated power regions. The boundary curves are modeled using logistic functions [39], which provide smooth representations of the lower and upper envelopes of the power curve. The automation of this parameter estimation process is particularly relevant for system operators such as the ONS, which is responsible for supervising a large and heterogeneous wind power fleet comprising more than one thousand utility-scale wind farms.

It is important to note that the exclusion of certain records does not necessarily imply the presence of measurement errors. In many cases, these data are technically consistent but associated with atypical operational conditions, such as scheduled maintenance, equipment failures, or transmission capacity constraints, including curtailment events. As they do not represent the expected behavior of the plant under normal operating conditions, these records are removed from the calibration process of the potential generation estimation models. A similar methodology, with a higher level of detail, is presented in [34].

In addition, the behavior of the wind speed–power (W–P) scatter of each wind farm may vary over time. These variations may occur due to the natural degradation of equipment or operational limitations, such as the unavailability of part of the wind turbines. In principle, the observed data on turbine availability could be used to directly correct this behavior, as illustrated by the black points in Figure 3. However, in practice, these data do not always accurately reflect the actual operational condition of the wind farm, which justifies the adoption of more robust filtering procedures, such as the construction of boundary curves. Since these curves are estimated from the observed data scatter itself and the W–P relationship may evolve over time, both the boundary curves and the W–P curve are re-estimated weekly for all considered time series.

3.3.2. Dynamic Creation of Wind vs. Power Curves

To prevent the estimated wind speed–power curve from violating the physical limits of the wind farm under conditions of low data density in the saturation region, the methodology introduces fictitious points into the wind–power scatter. These points are defined based on robust statistics of the observed data or on previously estimated upper and lower bounds, prioritizing recent measurements and values close to rated power. The inclusion of these synthetic points ensures an adequate representation of the cut-in and saturation regions, stabilizing the curve fitting process and preventing physically inconsistent extrapolations when observations in these operational ranges are scarce.

Finally, the W–P curve is fitted using a logistic function, with parameters estimated through the Gauss–Newton algorithm. Figure 3 illustrates the application of the boundary curves and compares the estimation of the W–P curve parameters (yellow) obtained without the inclusion of fictitious points (No Fictitious Points—NFP) and that derived with their inclusion (With Fictitious Points—WFP).

Figure 3. Wind–Power Relationship Curves.

Figure 3. Wind–Power Relationship Curves.

The W–P curve is intended to represent wind farm operation under full availability. However, in practice, this condition is not always met, which limits the current formulation. When turbine availability data are reliable, they can be used to correct the scatter during curve fitting and to adjust the curve during application, better reflecting actual operating conditions. This approach, discussed in [34], enables the explicit incorporation of turbine availability and represents a potential improvement for future model developments.

The experimental results indicate that generation estimation based on aggregated sets of wind farms exhibits higher robustness and accuracy than plant-level estimation, due to the reduction of the intrinsic variability of wind power generation—a phenomenon widely associated with the portfolio effect. This aggregation enhances the statistical stability of the models, which is particularly relevant in curtailment analyses, where distinguishing between the natural variability of the wind resource and operational constraints is essential.

However, aggregated generation time series exhibit a structural upward trend resulting from the continuous expansion of installed capacity. In addition, transmission constraints, often transient in nature, affect these aggregated sets heterogeneously over time, temporarily altering the observed generation patterns. Consequently, the training of estimation models must explicitly account for the dynamics of these time series, whose growth patterns are nonlinear and characterized by discrete increments associated with the commissioning of new wind farms.

To mitigate these effects, a weighted historical average series is constructed based on the number of active wind farms in each time interval, reducing the bias introduced by the expansion of the generation fleet. At the daily scale, a linear regression is applied between the total observed generation and the historical average of the preceding five days, allowing for an indirect capture of the influence of dynamic operational constraints, including curtailment events.

In addition, the dynamic modeling of the wind speed–power curves involves normalizing generation between its extreme values and standardizing wind speed using the historical mean and standard deviation of the series. This procedure leads to the formulation of Equation (1), which establishes the functional relationship between observed wind conditions and the estimated potential generation.

$$\begin{array}{c}\hfill G_e^T={\alpha }_{mt}((P_{mi}+{\displaystyle \frac{(P_{ma}-P_{mi})}{{\left(1+{10}^{b\left(V_{mid}-\frac{(V_o-\overline{V_o})}{{\sigma }_{V_o}}\right)}\right)}^s}})\\ \hfill ·(G_{ma}-G_{mi})+G_{mi})+{\beta }_{mt}\end{array}$$

(1)

where $G_e^T$ denotes the total estimated generation of the plant; $G_{ma}$ and $G_{mi}$ are the computed maximum and minimum generation values, respectively; $\overline{V_o}$ and ${\sigma }_{V_o}$ represent the calculated mean and standard deviation of the observed wind speed, respectively; $V_o$ denotes the observed wind speed; ${\alpha }_{mt}$ and ${\beta }_{mt}$ are the slope and intercept of the regression that relates the mean to the total generation of the plant; the parameters $P_{mi}$ and $P_{ma}$ represent the lower and upper asymptotic bounds, corresponding to the estimated normalized minimum and maximum power, respectively; b and $V_{mid}$ denote the slope and the x-coordinate of the inflection point, respectively; and s is a coefficient.

3.4. Validation, Uncertainty, and Performance Criteria

Validation aims to demonstrate that the estimates are robust, stable, and physically consistent under different operational and meteorological conditions. To this end, criteria based on bias metrics, absolute and relative errors, and the ability to explain variability are employed, explicitly accounting for observational, model-related, and random uncertainties [40]. Isolated performance metrics are generally insufficient to fully characterize model performance; therefore, sets of complementary performance metrics are typically used.

Several metrics are applied to evaluate the performance of estimation models, including Mean Error (ME), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). ME is primarily used to identify systematic bias, MAE assists in detecting outliers, RMSE penalizes large errors, and MAPE expresses the percentage deviation between estimates and observations [41]. Error metrics can also be normalized, such as nME, nMAE, nMAPE, and nRMSE, typically by installed capacity, the range of the time series, or other scaling factors, allowing comparisons across wind farms with different characteristics [42].

MAPE, however, is not recommended when observed values approach zero, as its normalization may produce artificially inflated errors even for well-performing models. For this reason, analyses of wind power generation commonly adopt the normalized Mean Absolute Percentage Error (nMAPE). The mathematical definitions of these metrics are provided in [36]. In addition to error-based metrics, the coefficient of determination ($R^2$) is used to assess the degree of model fit to the observed data.

4. Results

4.1. Results of Historical Data Preprocessing

As described in Section 3.2, the wind time series data were subjected to rigorous quality control and consistency assessment. This process includes the removal of physically inconsistent measurements, the automatic identification of sensors exhibiting anomalous behavior, and the hierarchical integration of multiple observed data sources. In addition, remaining temporal gaps were filled using information from geographically proximate wind farms, selected based on spatial and statistical criteria. Gap filling is performed only when a high level of consistency between the series is observed, thereby preserving the originally measured data and ensuring full traceability of the information used.

Figure 4 presents an example of the application of wind data selection, treatment, and completion procedures, as well as their relationship with observed wind power generation. The raw wind series corresponds to the originally available measurements, whereas the filtered series results from the application of consistency criteria. In turn, the completed wind series incorporates the filling of remaining data gaps, producing a signal more suitable for use in estimation models. Observed wind power generation is shown on the secondary axis, allowing a direct comparison between relative variations of wind speed and power output, which facilitates the assessment of physical coherence between the processed wind data and the wind power response.

Figure 5 shows the distribution of the percentage of wind data failures by wind farm, allowing an assessment of the quality of the time series used in this study. Black markers represent the percentage of invalid data identified in the raw series prior to the application of data treatment procedures, whereas red markers indicate the percentage of remaining gaps after the gap-filling process. Wind farms are ordered according to the percentage of failures in the original series, facilitating the visualization of heterogeneity in data quality across different projects.

It can be observed that, although some wind farms exhibit high percentages of invalid data in the raw series, the data completion procedure significantly reduces the presence of gaps, resulting in more complete time series that are suitable for the application of estimation and forecasting models.

As illustrated in Figure 5, some wind farms exhibit high percentages of wind data failures in their original time series. Approximately 42 out of the 1043 utility-scale wind farms considered in the analyses present more than 50% missing or invalid data in their measurement histories, which often hampers the estimation of generation associated with these units. Considering the full set of observations—corresponding to approximately two years of half-hourly data from the 1043 monitored wind farms—about 12% of the records are classified as invalid. After the application of the data treatment and completion steps, this percentage is substantially reduced, resulting in approximately 2% of missing data in the historical series.

Nevertheless, all wind farms are included in the generation estimation model, even in the presence of measurement failures. Although this issue may be more critical for certain groups of wind farms, its impact on the total estimated generation volumes is limited. Therefore, occasional failures or inaccuracies at specific time steps tend not to significantly affect the aggregated results.

4.2. Results of the Estimation Model Application

As discussed in Section 3.3.2, applying the model to aggregated groups of wind farms rather than to individual plants results in improved performance when assessing aggregated generation, which represents the main operational focus of the ONS. As presented in Section 3.1.2, the results analyzed in this study consider 1043 utility-scale wind farms over the period from 2023 to 2025. The data are discretized at half-hour intervals and organized into 153 wind farm groups according to their connection to the SIN.

Currently, generation curtailment requests issued by the ONS are directed at these wind farm groups, while the operating agents are responsible for allocating the restrictions among the individual plants within each group. In this context, model performance is assessed at the group level. Based on this approach, the following analyses present representative examples of the estimation model performance, highlighting both cases of strong agreement between observed and estimated generation and situations in which limitations in the input data negatively affect the results.

Figure 6 presents two representative cases of wind farm groups exhibiting contrasting performance of the generation estimation model. The left panel shows a case with strong agreement between observed and estimated generation, indicating good explanatory capability of the model for this group. In contrast, the right panel illustrates a poorer performance case, characterized by greater dispersion and systematic deviations.

The plots in Figure 6 were constructed considering only time periods in which no generation curtailment events were identified. In general, the behavior observed in the right panel is associated not only with inconsistencies in wind data but also with issues in the observed generation data itself. It is worth noting that, in many cases, the degradation in model performance is further aggravated by widespread failures in the wind data from the wind farms composing the group.

Although the model aims to estimate generation during periods with curtailment, its validation requires time intervals not affected by this phenomenon. Additionally, the observed generation data incorporate other sources of uncertainty and operational limitations that are not fully reflected in the data reported to the ONS. While part of these inconsistencies is addressed during data preprocessing, some still persist in the time series, impacting performance indicators in ways that are difficult to quantify.

Considering the three-year analysis period and the 153 wind farm groups evaluated throughout their commissioning and operation between 2023 and 2025, the dataset comprises approximately 7.9 million generation records. Of this total, about 0.2% could not be estimated due to the absence of wind data, even after the data preprocessing procedures described in Section 4.1. Among the remaining records, approximately 35% correspond to periods in which generation curtailment occurs or in which failures or other limitations in the observed generation data can be identified. Consequently, approximately 5.1 million records remain available for validating the results of the estimation model.

As described in Section 3.4, for an adequate evaluation and a more comprehensive interpretation of the performance of the proposed model, it is recommended to use more than one performance metric. The adoption of complementary metrics allows different aspects of the estimation error to be analyzed and provides a more robust view of the quality of the obtained results.

Figure 7 presents the values of the nRMSE and nMAE metrics computed for different groups of wind farms. Normalization was necessary because the groups have significantly different generation capacities; to make the errors comparable, each time series was normalized by its amplitude, defined as the difference between its maximum and minimum values. Each point in the chart corresponds to the performance of a group, allowing a direct comparison of the relative generation estimation error across regions with distinct operational characteristics.

Filled circles represent the nRMSE values, while the “x”-shaped symbols represent the nMAE values, enabling simultaneous visualization of the behavior of both metrics. The colors of the points indicate the geographic region to which each group belongs, as shown in the upper legend. This categorization makes it possible to observe that, although there are well-defined regional patterns in wind regimes (such as differences between coastal and inland areas), these patterns do not directly translate into differences in the estimation model’s errors. This is because the observed wind data used in the model already captures the local aerodynamic and climatic characteristics adequately. As a result, factors such as measurement quality, anemometer availability, and the consistency of operational information provided to the system operator exert a much stronger influence on estimation performance than geographic location.

It is important to emphasize that this observation is restricted to the context of generation estimation. In wind power forecasting models, meteorological variability across regions exerts a much more significant influence on performance, directly affecting the quality of wind speed forecasts and, consequently, wind power forecasts, as evidenced in [43].

Finally, the combined use of nRMSE and nMAE provides a more comprehensive assessment of model error: while nRMSE places greater weight on large deviations, nMAE is more robust to outliers. Comparing both metrics therefore offers a consistent and balanced view of the generation estimation accuracy for each group analyzed.

Figure 8 presents a forest plot showing the normalized mean errors for each group analyzed, along with their respective 98% confidence intervals. Each point represents the average value of the normalized error obtained for the group, while the horizontal bars indicate the uncertainty associated with this estimate. The vertical dashed line at zero corresponds to the ideal scenario of no bias. From a statistical perspective, the confidence interval is computed from the sample mean error, the sample standard deviation, and the sample size. Since the population variance is unknown and the sample sizes are finite, Student’s t-distribution is employed, providing an appropriate critical value for each degree of freedom.

As shown in the Figure 8, the mean values of the normalized error reveal a tendency toward positive bias in some groups, indicating that in these cases, the estimated values are, on average, slightly higher than the observed values. This occurs because, at certain times, some wind farms operate under internal operational constraints that are not always reliably reflected in the data submitted to the system operator. Consequently, part of this operational limitation effect is interpreted by the model as estimation error, resulting in positive bias.

Conversely, some groups exhibit negative bias, indicating that the estimate was lower than the observed generation. This behavior is generally associated with the recent entry of new plants into the group, which alters its total generation capacity. Since the estimation model depends on a minimum historical dataset for calibration and training, a temporal lag may occur between the expansion of the wind fleet and the availability of sufficient data to properly configure the model, resulting in temporary underestimation. Despite these isolated behaviors, the vast majority of groups display very small average deviations—typically below 5%, whether positive or negative. This indicates that, overall, the model performs well in estimating group generation, with reduced systematic bias.

Results at the wind farm group level are particularly relevant for the assessment of generation accounting and are essential in the compensation procedures for affected generation agents. In addition, these results are important for real-time operation, as the estimated generation values can serve as a reference for releasing operational constraints without compromising system security. This is because, if an operator releases a restriction without a reliable estimate of wind power generation, excess generation may occur, potentially leading to overfrequency events and more severe operational issues.

Aggregated results at the electrical subsystem level are also relevant, particularly in the Brazilian context, which is characterized by two major regions with significant installed wind capacity—the South and the Northeast. Such aggregation is important for managing curtailment associated with power transmission between these subsystems. To assess the overall curtailment behavior in the country, even broader aggregations are required, enabling strategic-level analyses. These results are essential for improving system operation planning, reducing economic losses, guiding investments in transmission infrastructure and energy storage, and increasing the effective utilization of clean energy.

Figure 9 presents an example of a comparison between observed and estimated wind power generation for the SIN over ten days, in October 2025, considering a half-hourly temporal resolution. The lower panel shows the evolution of the number of wind farm groups that recorded at least one curtailment request, represented by the blue line. Currently, 153 groups are identified as having experienced operational restrictions, which enables a systematic analysis of the relationship between curtailment events and the aggregated behavior of wind power generation in the SIN. This indicator provides an indirect measure of the spatial and temporal extent of the restrictions imposed on wind generation over the analyzed period.

The upper panel presents the observed wind power generation (red line) and the generation estimated by the model (black line). A high level of agreement between the two series is observed during periods without curtailment, highlighting the model’s ability to consistently reproduce the actual behavior of wind power generation under normal operating conditions. This agreement is a fundamental aspect for the application of the model in counterfactual analyses, as it ensures that differences observed during restriction events can be more confidently attributed to the effects of curtailment rather than to deficiencies in the modeling of potential generation.

To enable a more comprehensive assessment of the model performance for the entire Brazilian power system, the metrics presented in Section 3.4 were applied. Unlike the normalization by amplitude used in the performance evaluation for groups of wind farms, in the following analysis the raw errors were normalized by the installed capacity at each time step multiplied by the average capacity factor over the analyzed period, approximately 33.2% for the SIN. In interpretative terms, this reference is equivalent to considering the average wind generation of the SIN.

This normalization approach was adopted because, when aggregating data for the entire SIN, there are significant differences in installed capacity between the beginning and the end of the analyzed period—approximately 22.7 GW and 33.5 GW, respectively—which lead to variations in the amplitude of the series over time. Therefore, this normalization allows error comparisons under different operating conditions and generation scales, reducing the influence of the growth in installed capacity on the analysis. The normalized performance metrics are presented in

Table 1. Error metrics obtained for the evaluated dataset.

	nME	nMAE	nRMSE	nMAPE (%)
Values	−0.0281	0.0401	0.0680	4.0121

.

The results presented in Table 1 indicate that the normalized Mean Error remains close to zero, suggesting the absence of a relevant systematic bias in the estimates. The small bias observed may be associated with atypical operational conditions that temporarily affect the generation of some wind farms for reasons not related to curtailment events.

The values obtained for nMAE and nRMSE indicate that the average deviations remain relatively low and that the occurrence of higher-magnitude errors is limited. In addition, the nMAPE value of approximately 4% indicates that, in relative terms, the average error level of the model is low. Taken together, these metrics indicate a consistent performance of the model in estimating the aggregated wind generation of the system.

Finally, the monthly aggregation of estimated generation by electrical subsystem provides a consolidated view of potential generation and the energy losses associated with curtailment events over time. This analysis constitutes a relevant input for medium- and long-term energy planning, as well as for the evaluation of policies and strategies aimed at integrating renewable energy sources into the Brazilian power system.

Figure 10 presents a synthesis of the monthly curtailment analyses. The upper panel shows the monthly average number of curtailment requests, while the lower panel depicts the effectively curtailed energy, obtained by comparing observed generation with that estimated by the model. This approach allows for a direct quantification of the energy impact of operational constraints, highlighting periods in which the gap between potential and observed generation is more pronounced.

Based on the application of the model to periods affected by curtailment, average annual wind power generation losses were estimated at approximately 5% in 2023, 10% in 2024, and 17% in 2025, with indications of a continuing upward trend throughout 2026. These results reflect the increasing frequency and severity of operational constraints associated with the rapid expansion of installed capacity, particularly in regions facing limitations in energy transmission to other regions.

The numerical evaluation of the results confirms the robustness of the proposed methodology. When considering exclusively periods without the occurrence of curtailment, the model achieves an accuracy exceeding 95% at the half-hourly resolution and above 99% when evaluated on an annual aggregated basis.

5. Discussion

5.1. Limitations of the Historical Data Preprocessing and Wind-to-Power Models

Although the gap-filling procedure presented in Section 4.1 is able to address most cases, some wind farms may still exhibit low-quality wind data or, in more critical situations, a complete absence of measurements. Quantifying the impact of these deficiencies remains challenging, as in many cases the generation data also appear inconsistent, as illustrated in Figure 6, even after the data preprocessing steps.

In addition, there are other conditions, difficult to quantify, that reduce the observed generation and are not related to curtailment, such as limitations in turbine availability and other operational effects not fully reflected in the data reported to the ONS. The strategy for constructing boundary curves, presented in Section 3.3.1, helps mitigate these effects in the development of the W–P curves. However, in scenarios with severe data issues or low representativeness in the saturation region, these curves may present less accurate fits.

It is important to note that the boundary curves are not applied in the final results. Therefore, uncertainties in the generation data may influence the model performance indicators, even though spurious data are removed whenever identified.

Finally, the aggregation of wind farms, as discussed in Section 3.3.2, contributes to mitigating the aforementioned impacts. In general, these effects tend to be less significant when analyzed at the aggregated level of wind farm clusters.

5.2. Assessment of the Results

One of the main challenges in proposing large-scale wind power forecasting and estimation methods is the validation and direct comparison with results reported in the literature. In the case of the present study, for example, it was not possible to establish a benchmarking comparison with similar studies, since there are currently no equivalent datasets or studies in the Brazilian context that consider a dataset with a comparable scale in terms of the number of wind farms and operational groups analyzed. In addition, public datasets containing detailed operational information for hundreds of wind farms are not widely available worldwide, which limits the possibility of performing standardized comparisons across different studies.

Another relevant aspect is that the estimation method proposed in this work was specifically developed to address the characteristics and limitations of the operational data received by the ONS. These data present important particularities, such as heterogeneity in data availability, operational constraints, and measurement inconsistencies, which directly influence the design of the adopted estimation strategy. Therefore, the proposed approach emphasizes data treatment procedures and estimation strategies tailored to this specific operational environment, although the underlying ideas may still be useful in other contexts if appropriately adapted.

Although it would be possible to implement other estimation methods reported in the literature, such approaches would require significant adaptations to account for the structure and limitations of the ONS dataset. These adaptations would essentially result in the development of alternative estimation models rather than a direct comparison between equivalent methods. Therefore, instead of performing a benchmarking exercise between models that would require substantial methodological redesign, this work focuses on evaluating the proposed method within the operational context for which it was developed, using a comprehensive dataset that includes several years of observations and more than one thousand wind farms.

5.3. Curtailment Dynamics in the Brazilian Power System

In the Brazilian context, characterized by the rapid expansion of wind power generation and its concentration in regions with structural transmission constraints, the estimation of unrealized generation plays a strategic role. Beyond a descriptive step, this estimation directly supports operational and regulatory analyses and contributes to greater transparency between market agents and the system operator. In this sense, robust models are essential for improving planning, operation, and forecasting processes.

The results obtained in this study should be interpreted in light of the main drivers of curtailment, which are generally associated with transmission constraints and limitations in the balance between load and generation [10,44]. In Brazil, the regulatory classification into external unavailability, reliability, and energy-based curtailment reflects the different nature of these events, ranging from physical constraints external to the power plants to system security requirements and conditions of energy oversupply [44,45]. This diversity of causes poses additional challenges for modeling, as different operational mechanisms may produce effects in the observed data.

The significant increase in curtailment between 2023 and 2025, particularly in reliability- and external unavailability-related events, highlights the mismatch between the expansion of renewable generation and the available transmission capacity, especially in the Northeast region [45]. In addition, the intensification of energy-based curtailment during daytime hours, driven by high solar generation and the growth of distributed generation, shifts balancing adjustments toward centralized power plants, with a stronger impact during the wind season [45,46].

In this context, the estimation of reference generation has direct implications for the application of mechanisms such as constrained-off. Its accuracy is essential to ensure adequate financial compensation and to avoid operational and economic distortions, particularly in the presence of structural limitations and data-related uncertainties.

6. Conclusions

This work presents an innovative methodology for estimating potential wind power generation, designed for large-scale power systems with a high penetration of wind energy. Although developed to address the specific needs of the Brazilian system operator, the proposed approach is general in nature and demonstrates strong potential for application in other power systems, as well as relevance to the academic community focused on large-scale generation estimation techniques.

The main contribution of this study lies in the integrated treatment of wind power generation estimation challenges in complex operational environments, covering data processing, data qualification, and wind–power relationship modeling. Special emphasis is placed on the automatic and dynamic estimation of wind speed–power curves, a key requirement for system operators managing a large number of wind farms with heterogeneous and incomplete datasets.

Despite inherent limitations related to the availability, consistency, and quality of observational data, particularly anemometric measurements, the model demonstrates robust performance in estimating potential wind power generation, enabling the identification and quantification of energy losses associated with curtailment events. The strong agreement between estimated and observed generation during periods without curtailment reinforces the suitability of the adopted approach to represent the physical wind–power conversion process, in line with findings from previous studies employing deterministic models and regression techniques.

In comparison with the existing literature, the results reinforce the importance of employing anemometric measurements and other SCADA data, as well as spatial correlation techniques among wind farms, to address data gaps and inconsistencies, as widely reported in studies on wind power forecasting and estimation. Nevertheless, whereas most previous works primarily aim to minimize forecasting errors, the methodology proposed here specifically focuses on the counterfactual estimation of suppressed generation, an aspect that has received limited systematic investigation, particularly in large-scale power systems such as the SIN.

The large-scale application of the method demonstrates that, beyond its operational use, the proposed methodology constitutes a strategic tool for planning and operation studies in power systems with a high share of variable renewable energy sources (VREs). The approach enables the reconstruction of historical time series and the technical quantification of energy losses associated with dispatch constraints. In addition, it provides qualified support for regulatory analyses and economic compensation mechanisms for affected generators by enabling the transparent, consistent, and reproducible estimation of unrealized generation.

As directions for future research, the proposed methodology can be expanded through the incorporation of additional data sources and its application to other renewable technologies, particularly solar photovoltaic generation, for which curtailment levels have been increasing in Brazil. Furthermore, the integration of probabilistic approaches may allow the explicit representation of uncertainty in wind power generation estimation and the assessment of future curtailment projections under different operational and expansion scenarios. In this context, the integration of stochastic modeling and scenario-based analysis could provide a more comprehensive characterization of curtailment risks associated with transmission constraints, renewable penetration, and demand evolution. Additionally, further developments may address regulatory aspects, supporting the valuation of curtailment and the definition of transparent and consistent criteria for economic compensation mechanisms.