Intelligent estimation of wind farm performance with direct and indirect ‘point’ forecasting approaches integrating several NWP models

Paid Open Access

section_content: Electric power industries and related markets face new challenges due to the increased wind power penetration into electric grids. One of the significant challenges in this large-scale integration of windgenerated electricity is the stochastic nature of wind. The speed and direction of the wind at a given site may significantly vary even within short intervals of time. As the power contained in the wind stream is proportional to the cube of wind velocity, these fluctuations in the velocity will be reflected in the wind power production on a magnified scale. This results in uncertainties in the generation expected from wind power plants. This is critical for System Operators (SOs) as they have to deal with these variabilities and uncertainties when scheduling and dispatching decisions. Moreover, these uncertainties pose challenges to Generating Companies (GENCOs) in operating their wind farms efficiently by providing stable and dispatchable energy, avoiding possible power quality issues and economic losses [1]. 

In many countries, wind power producers must participate in electricity markets in the same way as conventional power generators [2]. A good example is the Nordic power market (Nord Pool), which operates in 16 European countries, including the Nordic region. This market has three main alternatives: the day-ahead 'Elspot', the continuous intraday 'Elbas', and the balancing market. 

In 'Elspot', the producers and consumers submit bids and offers to cover every hour of the following day, which is cleared before noon. Whereas in 'Elbas', the trade is settled individually between two parties which closes 1 h before the delivery hour in Norway. The balancing market regulates production or consumption up or down depending on keeping the grid's instantaneous balance [3]. 

Therefore, wind power forecasting (WPF) is becoming essential for realizing energy balance and scheduling decisions, particularly in regions with a significant share of wind electricity generation. Short-and medium-term forecasts are essential for successful participation in the electricity markets, particularly the day-ahead market, i. e., 36 h ahead, which traditionally has been the leading market mechanism for power trading. However, due to the increased penetration of wind electricity generation, the trading market moved to shorter horizons than the dayahead market. The participants in the short-term markets use intra-day forecasts to adjust their day-ahead bids avoiding the associated imbalance costs, which are also used by system operators who must balance supply and demand in real-time, guaranteeing the system's security [4]. 

Moreover, The power producers are accountable for the cost of real-time balancing of their deviations from their forward-contracted volumes [2]. Hence, it is essential to estimate the day-ahead and hour-ahead productions from the wind farms with an acceptable level of accuracy to avoid financial losses. Hour-ahead predictions are also crucial for formulating the dispatch schedules for the grid operation. Therefore, reliable short-to medium-term wind power forecasting (WPF) has become increasingly important in the efficient management of wind farms. 

The WPF can be classified into several categories depending on the governing characteristics and the need for the forecast [5]. As shown in Fig. 1, in general, the forecast can be classified as either deterministic or probabilistic. Deterministic forecasts comprise a single value estimation for estimated future wind power generation. In contrast, under the probabilistic forecast, wind power is modelled as a stochastic process with confidence levels that can quantify the uncertainties in the predicted wind power generation [6] [7] [8]. Nevertheless, with the advances in the deterministic forecasting methods evolved over the years [9] [10] [11], many end-users still prefer the deterministic approach with a single forecasted value as interpreting the probabilistic forecasting results could be challenging [4, 10, 12]. 

Both the deterministic and probabilistic forecasts can further have several sub-categories, as shown in Fig. 1 and discussed below. 

• Based on the temporal scale, WPF can be classified into five subcategories [13] as seen in Fig. 1. The very short-term and short-term forecasts range from a few seconds to 30 min ahead and up to 6 h ahead, respectively, while the medium-term forecast can be up to 1 day ahead. In comparison, the long-term and very long-term forecast can be up to 3 days and more ahead, respectively. However, this forecast classification is not universal (see Ref. [14] ). • Based on the spatial scale, WPF can be divided into 3 categories: point forecasting for a single wind turbine [15], wind farm forecasting for a cluster of wind turbines as a single entity [16, 17], and regional forecasting for a specific region with several wind farms [18]. Coefficient of Determination • Based on the method used [19], WPF can generally be classified as physical methods such as Numerical Weather predictions (NWP) and mesoscale models use physical conservation laws considering terrain obstacles, air pressure, humidity and temperature to forecast the weather, thus the wind power [20, 21]. Traditional statistical methods such as autoregressive integrated moving average models (ARIMA) make the forecasts by establishing the relationship of the observed wind speed time series -in other words forecasting the wind speed based on observed historical data [22], and, more recently, the modern statistical or the so-called learning methods like artificial neural network (ANN) and support vector machines (SVM), which are getting wider attention among the forecasting community [10, [23] [24] [25]. These approaches can also be combined to yield hybrid methods [11, 26]. • Based on the input data, WPF can be classified as numerical weather predictions (NWP) based [17, 27, 28] or without utilizing the NWP [22, 29]. • Based on the output type, WPF can be classified as either indirect forecast (which results from forecasting the wind speed first and then using this forecasted wind speed with the turbines' power curve for estimating the power) or direct forecast (which forecasts the wind power directly, without forecasting the wind speed [4, 22, 30, 31]. 

WPF has been explored and researched intensively for around 20 years [13] [14] [15] [16] [17] [18] [19] 22, 23, [32] [33] [34]. In the present study, we propose a new short-medium term point WPF approach, incorporating inputs from several NWPs, adopting an optimized machine learning pipeline. The proposed forecasting scheme is applied and compared in both direct and indirect approaches generating several WPFs. These forecasts are to be later weighted to establish a combined single value WPF merging the strengths of different NWPs based WPF. 

The features of the proposed forecasting scheme, differentiating it from the previous approaches, are highlighted below:

• The automated learning process: In conventional wind power forecasting, the model type, its architecture and hyperparameters are selected based either on a trial-and-error basis or by applying the domain knowledge and experience as discussed in Refs. [35, 36]. In contrast, the present study adopts a new approach to automate the process of selecting the most optimal model, its architecture and configuration in all the development phases. This approach uses a tree-based structure (see section 3. 2. 1) to represent the development process while performing genetic programming to achieve a stochastic global optimization of the selected pipeline process [37] [38] [39]. This could improve the efficiency of the proposed forecasting scheme. • Integrating inputs from several NWPs: The performance of NWP models, which are used to forecast the input flow conditions in the WPF, significantly varies depending upon several factors [6, 9, 12 ]. An extensive literature review [14] concluded that for short-and medium-term WPF, NWP data is required to get accurate results. The author in Ref. [17] investigated the role of NWP data in WPF for the next 36 h using an ensemble model with 10 members known as MetCoOp Ensemble Prediction System (MEPS). Several models were built using the XGboost method based on different combinations of the latest observations and MEPS predictions while considering both MEPS generation time and members used. The author concluded that the quality of WPF based only on NWP does not vary much with lead time, and the latest observation would mainly impact the forecast up to 3 h ahead, while beyond 12 h ahead, it would have a negative impact. Regardless of the advances NWP models have reached, specific NWP models would perform well in some regions and worse in others for different reasons [20]. Therefore, to achieve reliable WPF, three NWP models are combinedly used in this study which is rarely reported in WPFs. 

• The point forecasting approach: Most previous studies follow a wind farm level forecasting approach, while the point-wise level is rarely researched and has not been evaluated for different terrains and wind conditions, mainly due to the size and complexity of the modelling part. Here, we adopt a point-wise forecasting method in which the power output of each turbine in the farm, under a forecasted wind flow condition, is estimated. These are then aggregated to estimate the expected wind farm level power generation. This is expected to give better forecasting performance, as observed in Refs. [4, 17]. In Ref. [4], the authors compared different techniques based on turbine level and farm level approaches applied on two wind farms in the UK. The results show the superiority of the turbine level based techniques (point approach) over the farm level approach. The authors concluded that simple aggregated individual turbine forecast and direction conditioned aggregated individual turbine forecast performed both better than the direct wind farm level forecast, where the root means squared error (RMSE) is reduced by 6-12% considering forecasts up to 48 h ahead.
section_name: Introduction

section_content: The present study focuses on short-to medium-term forecasts with temporal resolutions corresponding to the Nord Pool's continuous intraday 'Elbas' and day-ahead 'Elspot' trade requirements. Hence, the proposed methods can support the efficient integration of wind energy in the Nordic power market • Comparison between the direct and indirect approaches for the same wind farm: Some previous studies [22] reported that the direct WPF approach yields better accuracy. The authors compared the direct and indirect short-term WPF performance for a single 2 MW offshore turbine. The auto-regressive integrating moving average (ARIMA) models of both approaches were tested for 1-h ahead forecast (achieved at each 10 min), rendering the direct approach outperforming the indirect approach. In contrast, some other investigations favour the indirect approach [12, 31, 40]. The authors in Ref. [12] proposed a novel approach for an indirect wind farm level forecast by decomposing the wind speed into the mean trend and the stochastic component using the empirical mode decomposition method (EMD). The two components were later forecasted separately using two different techniques. In addition to that, the speed-power conversion was obtained from the historical data using polynomial fitting. This resulted in better performance for both direct power and direct speed forecasts for 1-4 h ahead. Similarly, the authors in Ref. [40] proposed an improved EMD to decompose wind speed measurements and then integrated it with a hybrid forecasting engine using bagging neural networks combined with the K-means clustering technique. The proposed approach was applied on three different wind farms and compared to several previously published approaches, where the proposed approach outperformed all of them for different forecast horizons. In the same track, research was carried out in Ref. [31] investigating wind farm power forecasts in the scope of energy markets (24-48 h) using both direct and indirect approaches while integrating NWP data. The authors studied several wind farms and applied several machine learning techniques, mainly tree-based ones. The ML techniques utilized data from the supervisory control and data acquisition system (SCADA) and weather data extracted from several grid points around the wind farms from the European Centre for Medium-Range Weather Forecasts (ECMWF) model. The results showed that the indirect approach performed better than the direct due to improving the wind forecast. The authors emphasized that having a good speed-power conversion in the indirect approach is essential for a better forecast. The previous studies do not clearly identify which WPF approach (direct/indirect) to best tackle the short-term forecast. 

In this paper, we compare the accuracies of both the direct and indirect approaches at the turbine level and an aggregated farm level. The WPF models are formulated in the scope of the main electricity markets the day-ahead and the intraday and optimized using an automated learning process while integrating data from several NWP models. 

The remainder of the paper is organized as follows. The next section describes the data used to develop the forecast models and the preprocessing procedure to detect and process the outliers. This is followed by the descriptions of the methods used to develop and optimize individual turbine power forecast models and the weighing technique which is applied to combine the predictions. Thereafter, we discuss the performance of different models at both turbine and farm levels, which is finally summarized in the last section.
section_name: • The temporal resolution matches the Nordic energy market requirements:

section_name: Data description and pre-processing

section_content: One of Norway's first commissioned wind farms, the 'Smøla' wind farm, was chosen for the proposed research. Smøla wind farm is composed of 68 wind turbines distributed in 6 rows. On average, the wind farm produces 356 GWh of electricity annually. It is situated in a flat and open terrain, which is 10-40 m above sea level. The wind farm was constructed in two phases. The first construction phase had 20 wind turbines (2 MW each) and became operational in September 2002, while the second phase had 48 wind turbines (2. 3 MW each) and was commissioned in September 2005. As seen in Fig. 2, blue and green dots represent the two commissioning phases, respectively. The turbines have rotor diameters of 76-82. 4 m, and the towers are 70 m high [41]. 

The turbine's production, operating conditions, and nacelle wind speed were retrieved from the wind farm's (SCADA) system with a frequency of 10-min from January 2017 to December 2020. The retrieved data, particularly production and wind speed measurements, are converted to an hourly average to be compatible with the scope of the studied electricity markets.
section_name: Wind farm and SCADA data

section_content: Historical weather forecasts from 3 NWPs' archives, with different spatial resolutions, were used in this study. The NWP source selection was based upon the temporal resolution (1-h scale) and the availability of the model's coverage at the wind farm's terrain. This model is an ensemble model with 10 members [42]. However, in this study, we used data from only one member (the control member) as recommended by MET Norway. 

It should be noted that the NWP sources have an update rate of times per day at 00, 06, 12 and 18 UTC, except for IFS, which is updated twice a day since 2018. 

As seen in Fig. 3, the NWP grid coordinates, within and surrounding the wind farm, were chosen according to the highest NWP spatial resolution (MEPS). Therefore, the data from IFS and EURO sources were interpolated to the chosen coordinates. Both IFS and EURO data were retrieved from a third-party database, while MEPS data were retrieved directly from the MET Norway database. 

Moreover, the air temperature (Temp) was retrieved at 2 m above the ground from the prementioned NWPs' archives. Wind speed, gust, and direction (WS, WG, WD) were extracted at 10 m above the ground from the MEPS source due to availability, while they were extracted at the hub height (70 m) from the IFS and the EURO sources.
section_name: NWP' weather forecasts

section_content: Initially, the data were cleaned by removing the outliers. There were four types of outliers which are indicated in Fig. 4 and listed below. 

• Type 1 represents a horizontal cluster at the bottom of the power curve due to downtime for several reasons, such as maintenance and error in the log. • Type 2 represents random scatters due to sensor malfunction, noise in signal processing or power curtailment. • Type 3 represents a dense cluster below the rated power where the wind turbine production is limited for reasons like power curtailment. 

• Type 4 represents a vertical cluster at zero wind speed due to icing or malfunction of the anemometer. 

Missing values and outliers represent a fraction between 5% and 30% of the data for each turbine. This data was discarded before developing the forecasting models. However, it should be mentioned that not all turbines suffered from all types of outliers.
section_name: Data pre-processing

section_name: Methods

section_content: Models for direct and indirect WPF are developed under the study. Forecasts on wind speed (WS), wind gust (WG), wind direction (WD) and temperature (Temp) from the 4 NWP grid cells nearest to the turbines are directly correlated with the turbine's power output in the direct forecasting approach. On the other hand, in the case of indirect WPF, these forecasts from NWPs were first correlated with the nacelle's wind speed measurements for developing the downscaling model, which estimates the velocity 'felt' by the turbines at its hub coordinates. Then, the power corresponding to these velocities are estimated using the sitespecific performance model of the turbine. In both cases, power estimates from individual turbines are accumulated together to arrive at the Wind forecasts from the three NWP sources considered under the study (IFS, EURO and MEPS) were used individually and in combination (MIX) to develop each wind turbine's direct and indirect WPF. The MIX models were built upon using the three NWP's data together as input. Thus, as shown in Fig. 5, each wind turbine has 4 direct WPF models, 4 wind speed downscaling models and 1 turbine's site-specific performance model. In addition to this, the above-discussed WPFs based on direct and indirect approaches are individually combined to form single WPFs based upon direct and indirect approaches and both together, as shown in Fig. 5. More details are described in section (3. 3). 

It should be noted that, for forecasting the wind power at the time (t+1), we used weather data from the NWP sources at the start and the end of the hour, i. e., at time (t) and (t+1). 

The historical data records for each turbine were divided into two sets, one for model development and calibration (train and validation) and the other for testing (unseen). The data division was done by preserving the first 10 days of each month from the years 2017-2019 for testing while using the rest for model calibration. The test set was almost 1 year out of the 4 years used in this study.
section_name: Forecasting models

section_content: The model development process had mainly three phases summarized as follows:

• The pre-processing phase which consisted of feature selection, feature pre-processing (division, scaling), and feature construction. 

The main objective of this phase was to select and prepare the inputs for the model in proper form and shape. • The model selection phase involved model architecture development (selection and calibration) and optimization of hyperparameters. This phase aimed at achieving high accuracy associated with high generalization ability. • The model evaluation phase was focused on the performance evaluation of the developed models by applying several error metrics and statistical methods.
section_name: Model development process

section_content: In the present study, we adopted a new approach to fully automate the process of selecting the most optimal techniques and configurations for all the development phases. This approach was developed by researchers from the University of Pennsylvania which was initially applied in the biomedical field [37] [38] [39]. It uses a tree-based structure to represent the development process for a predictive modelling problem, including data preparation, model selection and hyperparameters tuning while performing genetic programming (GP) to optimize the selected pipeline process. In other words, this approach tries a pipeline, evaluates its performance, and randomly changes parts of it using a genetic search (natural selection) to find a better-performing pipeline. Fig. 6 shows the end-to-end pipeline development process, where the pipeline search elements include feature selection, feature processing, feature construction, model selection, and hyperparameter optimization. The GP used in this study searches over several well-known regression models, data processing techniques (pre-processing, construction and selection) to generate the search space, and optimizing each pipeline. So, the population consists of a list of randomly generated pipelines. For each generation, copies of the best-performing pipelines are created and imposed with random changes (e. g., the addition or removal of an operation or the parameter tuning of an operation), enabling the development of new pipelines that were never explored before. The worst-performing pipelines are removed from the population at the end of each generation before starting the next generation. Table 1 presents the models and the data processing techniques utilized in the genetic search. However, each of these models/techniques has several hyperparameters which were tuned during the search. A full description of the models/techniques used can be seen in Refs. [43, 44]. 

Although GP is faster and more efficient than traditional optimization methods, the utilized GP had to be configured to maintain a good diversity to achieve an optimal or near-optimal solution in a reasonable time. The adopted GP had to iterate for 10 generations having a population size of 70, off-spring size of 10, mutation and crossover rates were set to 90% and 10%, respectively. Moreover, the cross-validation method was implemented, dividing the calibration set into 3 folds, 2 for training and 1 for validating. In other words, each pipeline in the genetic search had to be trained and evaluated 3 times using different combinations of folds. Nevertheless, an automatic termination mechanism was implemented to terminate the search if no improvements were detected during the last 3 generations. Furthermore, a scoring function was implemented to rank the established pipelines depending on the mean absolute error (MAE) as it is robust to outliers.
section_name: Model's architecture (pre-processing, model selection and optimization)

section_content: The accuracy of the developed forecasts was quantified through different metrics, including (RMSE), normalized RMSE (NRMSE), MAE, normalized MAE (NMAE), coefficient of determination (R 2 ) and the index of agreement (IoA), which are expressed in the equations given below. 

Where, P k and Pk represent the observed and the predicted values of the studied parameter at the time instant k, whereas n represents the number of data used in the test stage. Note that the rated power is either 2 or 2. 3 MW depending on the turbine (see section 2. 1). RMSE and MAE are most commonly used for measuring the variations between predicted and measured values [28, [45] [46] [47]. However, normalized versions of both metrics are used generally for comparisons with other study cases. Both RMSE and MAE express average model prediction error in units of the variable of interest. However, the errors are squared before being averaged in RMSE. Therefore, it gives high weights to significant errors, which is useful in case large errors are undesirable. In comparison, MAE is more robust to large errors due to the way it is calculated. R 2 indicates how well the recorded data can be forecasted by the proposed model (goodness of fit) [48]. 

The highest possible score can be 1, but it can also display negative scores, indicating an arbitrarily worse predicting model than a linear one. 

The metric IoA is a ratio between the mean squared error and the potential error [49]. It is a standardized measure of the degree of model prediction error which varies between 0 and 1. This metric evaluates the agreement between the prediction and the observed values by detecting additive and proportional differences in the observed and predicted means and variances. However, it is overly sensitive to extreme values due to the squared differences. 

Where, P is the mean of the observed values over the test set for the studied parameter.
section_name: Model's performance evaluation (post-processing)

section_content: As mentioned previously, each wind turbine has 6 wind power predictions depending on both the forecast approaches (direct and indirect) and the NWP model used (IFS, EURO and MEPS). In addition to those, 2 WPFs are created based on merging all the NWPs parameters together, denoted as the MIX models as seen in Fig. 5. In general, The NWPs' performance varies depending on the period of the year, location and other model's configurations. Therefore, it is essential to have a single combined wind power prediction to represent the wind power predictions from the developed models. This is achieved by using a weighting multiplier for the developed models' predictions according to each forecast's short-term historical performance. The predicted value of multiple forecasting models for the single turbine is determined by:

where NWP i ∈ [IFS, EURO, MEPS], App j ∈ [Direct, Indirect] and W NWP are the weighting multipliers of different forecasting models, which were determined using RMSE as the performance index. The performance index for each forecasting model was calculated using the last 6 h' observations of the NWPs updates. Thus,

)

)

So, the less the magnitude of RMSE for a particular model, the more would be the weightage multiplier W in Eq. ( 7 ), and vice versa. It should be noted that the Δt is chosen to be 2 h as this study focuses on the intraday market (in Norway) to reduce the balancing costs. 

To illustrate more, the 3 WPFs (IFS, EURO and MEPS) developed using the direct approach are combined, producing a forecast denoted as 'Direct Combined', whose performance is compared to the direct MIX forecast. The same is applied to the WPFs using the indirect approach scheme producing a forecast denoted as 'Indirect Combined'. Moreover, both approaches' forecasts (in total 6) are combined in a single forecast denoted as the 'Combined', as illustrated in Fig. 5, whose performance is compared with both the MIX and the combined ones resulting from both approaches.
section_name: Multiple forecast weighing (combined forecast)

section_content: The turbine as well as farm-level performances of the proposed wind power forecasting models, under both the direct and indirect forecasting approaches, are discussed in this section. As 8 forecasting models were developed for each studied turbine, for concisely presenting the results, the average performances of the models across all the turbines and the corresponding standard deviation are presented.
section_name: Results and discussion

section_content: As mentioned previously, the indirect forecast scheme comprises two models, the wind downscaling and the turbine's performance model. In this subsection, the wind downscaling results will be presented and discussed. 

Table 2 shows the performance of the wind downscaling models, which enhances the spatial resolution of the wind predictions from the NWPs to the hub coordinates of the wind turbines. Compared with the models based on a single NWP, the downscaling accuracy (reduced error) is improved using the three NWPs together (MIX model). These improvements varied between 8%, 14% and 22%, on average across all the turbines, compared to individual IFS, EURO and MEPS downscaling models, respectively. Moreover, in comparison with the raw wind forecast from the NWP models used, it is observed that the downscaling models improve the NWP raw wind forecasts from IFS, EURO and MEPS by around 15%, 11% and 22%, respectively. The increased improvement performance found for the MEPS model indicates that the downscaling enhances the wind forecast in vertical coordinates as well, as the MEPS data were extracted at 10 m above the ground. It should be noted that the rated wind speed of 16 m/s is used to normalize both MAE and RMSE.
section_name: Turbine level wind downscaling models for indirect WPF

section_content: Performance of the site-specific wind speed-power characteristics, computed for all the turbines and then averaged, are shown in Table 3. 

The relatively low values of the error indices and the high values of IoA and R2 imply the proposed algorithms' capability to model the turbine's performances. This is further illustrated in Fig. 7, where the power production of a representative turbine predicted using the developed model is compared with the actual observations.
section_name: Turbine level site-specific performance models for the indirect WPF

section_content: Performances of both the direct and indirect forecasting models, implemented at the turbine level, are presented in Tables 4 and 5, respectively. It is evident that the models' performances are significantly improved by using several NWP sources together (MIX). For example, RMSE and MAE of direct forecasting models could be enhanced, depending on the NWP used, by (8%-22%) and (9%-25%), respectively, by using the MIX. Corresponding improvements in the indirect forecasts were (8%-21%) and (8% 10%) respectively. Similar improvements (but in lesser magnitude) could be seen in the case of IoA and R 2 as well. Additionally, the combined forecast in each approach resulted in improved performance compared to the 3 individual WPFs (IFS, EURO and MEPS) to the same degree as for the MIX forecast. However, the latter performs slightly better with an improved RMSE and MAE below 4%. This confirms that the use of several NWPs yields better overall forecasts. 

Despite its lowest spatial resolution among NWP sources used, WPF using IFS data achieved better performances than EURO and MEPS sources. The improvements achieved are in the range of 4%-18% in both approaches. In contrast, the highest spatial resolution of MEPS is not reflected in the performances of the forecasting models in which it is integrated. One possible reason for this could be that the data from MEPS were only available at 10 m, whereas the turbines' hub height was at 70 m. It should be noted that the performances of WPF using different NWP sources could be site-dependent, and further research with varying site conditions is required for arriving to a more generalized conclusion. 

The standard deviation of the error metrics is also found to be reduced while using several NWPs together, indicating the consistency of the models while predicting the performances of different turbines. These are further evident in Fig. 8, where the medians, ranges and the percentiles of these matrices are illustrated. Tables 4 and 5 and Fig. 8 show that the WPF models based on direct and indirect methods performed somewhat equally well for the wind turbines under the study. Interestingly, this is in contrast to the findings of some of the previous studies. For example, the conclusions of [22] indicate that the forecasting based on the direct approach is more reliable than the indirect one, whereas the findings of [31] are contrary. The performance differences for all the models across both approaches are almost identical, where the differences are around 2% for different error metrics. This is evident in the comparison between Figs. 9 and 10. 

The 'Combined' forecast resulted from combining the six developed WPFs for each turbine through Eqs. ( 7 ) and ( 8 ), which are evaluated in Table 6. Combined forecast performances are comparable with the mixed NWP forecasting scheme (MIX) and the combined forecasts based on each approach. However, in some hours, the combined forecast yielded better predictions, especially in comparison with the direct predictions approach, as seen in Fig. 11. 

It should be mentioned that the results had been tested and validated for several hours ahead. In particular, they are valid for up to 12 h ahead for the IFS WPFs and 6 h ahead for the remaining WPFs. This is mainly because WPFs models are trained with historical NWPs, which were updated according to the earlier mentioned update rate.
section_name: Turbine level wind power forecasts (indirect versus direct)

section_content: The performance of the models in estimating the power generated from the whole wind farm by aggregating the individual power estimates from all the turbines is shown in Table 7. This is further shown in Fig. 12, in which the percentile variations from the predictions are also illustrated. It should be mentioned that the prediction interval is a quantitative representation of several developed forecasts. It does not reflect the confidence interval or the probability of a specific value associated with certain conditions. As in the case of turbine level forecasts, the mixed and combined modelling approaches outperformed all other options with individual NWP inputted models. The aggregated forecasts have shown lower overall errors than those for the single turbines. This is because the over and under predictions of the turbine's power output could have been cancelled out to some extent while aggregated. Similar improvements can also be observed in the case of accuracy measures like R 2 and IoA. 

More in-depth error quantification for the wind farm aggregated forecasts is presented in Table 8 and visualized in Fig. 13. The forecasts' errors have, generally, slightly negative medians and positive means, which means having slightly more than 50% of the predictions being overestimated (negative median). In contrast, the rest of the predictions were underestimated with a higher magnitude (positive average). It should be noted that the error is calculated based on the observed minus the prediction. In addition, all the developed forecasts are right-skewed, i. e., medians are closer to the first quartile (Q1) than to the third quartile (Q3). However, by comparing the interquartile range (IQR), which contains 50% of the predictions, the MEPS forecasts show the highest IQR ranges, 9. 1 and 10. 4 MW, indicating that the predictions are more dispersed than other forecasts, which is also valid by comparing the standard deviations (SD). This strongly reflects having a wide fence range. Nevertheless, approximately 85% of the error falls into the fence ranges across all the developed forecasts, as shown in Fig. 13.
section_name: Wind farm-level power forecasts

section_name: Acknowledgement

section_content: The work presented in this paper is funded by the University of Agder, Norway (project number: 19/04543-1 ). The authors acknowledge Jørgen Olsen for his contributions to this research through fruitful interactions and discussions. Thanks are also due to Statkraft for providing the data required for this study.
section_name: Acknowledgement

section_name: Data availability

section_content: The data that has been used is confidential.
section_name: Data availability

section_name: Conclusions

section_content: In this study, we have explored the relevance of using several NWP sources in power forecasting from the perspective of individual wind turbine and aggregated wind farm level forecasts. The direct and indirect forecast approaches were also compared. The forecast models were built by implementing a genetic optimization search to find the most optimum machine learning pipeline utilizing various possible algorithms and configurations. The conclusions can be summarized as follows:

• Using several NWPs could improve the accuracies in WPF irrespective of the direct or indirect approaches used. By this, normalized RMSE and MAE of various forecasts were reduced by (8%-22%), depending on the NWP and approach used. • In the present study, there is no clear evidence proving that the direct WPF outperforms the indirect WPF, nor on the contrary. • The wind downscaling model, which extrapolates the wind flow conditions to the hub coordinates of the turbine, could improve the WPF accuracies. • The combined WPF, which resulted from either direct or indirect approaches, performed as accurately as the MIX WPF. This further confirms that using several NWP models yields a better forecast, irrespective of whether they are integrated into one "MIX" model or the forecasts based on individual NWPs are combined together as in the case of the discussed "combined" models. • The point forecasts aggregated to the wind farm level yielded a lower-normalized error, which could be mainly due to the cancellation of positive and negative errors in the forecasts of individual turbines. 

One specific advantage of the proposed point forecasting approach, in contrast with the farm level forecasts, is that it could be successfully implemented even if some of the turbines in the farm are down or are curtailed due to various reasons and operational settings. 

The point (turbine level) forecasting approach proposed under this study is currently being compared with the farm level approach and the results of this comparison would be shared with the wind power forecasting community through a later publication. Further, the present study, which was on a land based wind farm over a relatively flat terrain, has to be extended to other operating environments like complex terrains and offshore conditions.
section_name: Conclusions

section_content: Ghali Yakoub: Conceptualization, Methodology, Software, Visualization, Investigation, Validation, writing the original draft. Sathyajith Mathew: Supervision, Conceptualization, Validation, Writing review and editing. Joao Leal: Co-Supervision, Conceptualization, Validation, Writing review and editing.
section_name: Credit authors statement

section_content: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
section_name: Declaration of competing interest