Daily Variation and Regional Differences in Wind Power Output during Heat and Cold Wave Days in China

. China currently boasts the largest installed capacity of wind power; however, its output is unstable and highly dependent on weather variability. Despite this, the infuence of extreme weather events on wind energy production at the interprovincial scale in China has not been fully characterized. Tis study aims at investigating the daily variations and regional diferences in wind power output during heat wave (HW) and cold wave (CW) days in six regions of China. In addition, the study projects the monthly changes in HW and CW days in the coming decades by utilizing a stacking ensemble machine learning method. Te projections are under a real-world warming scenario that incorporates current and long-term actions or policies. Te fndings of the study reveal that, for most regions, the daily cumulative wind power generation on HW days is close to that on normal days; however, there is a lower output during the daytime and a higher output at night. Furthermore, the number of HW days is projected to increase by 2.3 to 21.8 days during the periods of 2031–2040, 2041–2050, and 2051–2060 in these regions. By comparison, the daily cumulative wind power generation increases signifcantly on CW days, and the monthly distribution of CW days is expected to undergo notable changes in the future. Tese fndings provide valuable insights into wind resource planning and operation under extreme weather conditions in China.


Introduction
China boasts the world's largest installed capacity and second-largest technical resource potential for onshore wind power [1][2][3].By the end of 2021, China's installed wind power capacity and electricity generation had reached 328 GW and 655.8 PWh, respectively, accounting for 13.8% and 7.8% of the country's total volumes and playing an irreplaceable role in the country's industrial sectors [4].At the national level, wind power ranks second among all clean energy resources (nuclear and renewables) after hydropower in China, while wind energy is unevenly distributed at the provincial level.Te installed capacity or electricity generation from wind power ranks frst among all renewables for 13 provinces, including Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Ningxia, Xinjiang, Henan, Gansu, Shanghai, Jiangsu, and Shandong.Although wind power makes an important contribution to the electric system for many provinces in China, the energy output of a wind farm is unstable and highly dependent on weather variability.Te wind power output sufers signifcant fuctuations with the occurrence of diferent weather conditions, especially regional extreme weather events [5][6][7][8][9][10].
China proposed to reach peak carbon emissions around 2030 and achieve carbon neutrality before 2060, which requires a substantial growth of renewable energies and collaborative optimizations among various energy resources [11].Specifcally, the onshore wind power installation is anticipated to reach 1866 GW [12,13].In addition, the frequency or intensity of extreme weather events in China is projected to increase for the next several decades in the context of global warming [14,15].For example, the average heat wave (HW) days and HW duration in 2020-2039 is projected to be 1.86 (2.53) and 1.56 (2.00) times higher than that in 1986-2015 under the 1.5 °C (2.0 °C) warming levels.Tis increase in extreme weather events poses challenges to uncertainty planning in distributed renewable energy systems [16,17].Terefore, it is essential to understand the characteristics of wind power output under extreme weather events such as HW and cold wave (CW).
Some case studies have investigated the impact of extreme weather events on wind energy variability in specifc regions by comparing wind power generation during normal and abnormal weather conditions using observed or simulated wind energy production data.In Western Europe, Leahy et al. found that the wind generation output was low during a prolonged spell of unusually cold conditions in Ireland [18].Correia et al. evaluated the impact of large-scale atmospheric circulation patterns on monthly wind power resources and production in Portugal [19].Garrido-Perez et al. assessed the change of wind capacity factors in the United Kingdom and Spain on eight distinct recurring largescale weather patterns [20].In China, Li et al. analyzed the characteristics of aggregated wind power generation based on eight typical weather systems in the western region of Inner Mongolia [21].In addition, scholars have developed many short-term wind power simulation models using physical, statistical learning and hybrid approaches [22][23][24].Tese models provide useful tools to explore the wind power output in abnormal weather conditions for a single wind farm.
However, previous studies have focused on specifc sites or relatively small regions, and research to date has not yet investigated the infuence of extreme weather events on wind energy production at the interprovincial scale in China.Note that when applying a wind power simulation model to a large number of farms in a wide area, the orientation of each wind farm needs to be considered.Tis aspect has been somewhat neglected in the model design, as most studies concentrate on the micrositing layout problem [25].Tis study aims to investigate the daily variation and regional diferences in wind power output during HW and CW days in six regions in China.We calculate the local prevailing wind direction to determine the orientation of wind farms.Moreover, we explore the monthly changes of HW and CW days in the next several decades under a medium pathway of future greenhouse gas emissions and discuss their potential impact on wind power generation in diferent regions.It is worth noting that ofshore wind farms are also important in China's power system, but their geographical distribution and related extreme weather conditions are completely diferent from onshore wind farms.Terefore, this study is intended primarily for the onshore wind energy.A description of the study area, wind power simulation model, the defnition of regional HW and CW events, and statistical climate projection methods are given in Section 2. Changes in wind power out during HW and CW days, as well as the future projection of HW and CW frequencies, are presented in Section 3. Te main conclusions are summarized in Section 4.

Study Area and Historical Climate
Data.Tis study classifes China's provinces into six contiguous regions based on their climate classifcation and interprovincial power network [26].Te spatial distribution of these regions is illustrated in Figure 1, and Table 1 provides a list of the provinces belonging to each region.Northeast China, consisting of four provinces, is mainly located in the midtemperate and humid or semihumid climate zones.North China spans six provinces and ranges from the warm temperate and semihumid climate zone to the midtemperate and arid climate zone.Northwest China, comprising fve provinces, is mainly located in the midtemperate and arid climate zone.East and Central China encompass four and six provinces, respectively, and they extend across the north to midsubtropical and humid climate zones.South China spans six provinces and ranges from the south subtropical and humid climate zone to the tropical and humid climate zone.
As of May 24, 2022, according to the statistics from Global Energy Monitor (GEM), there are 4184 onshore wind farms in China, and their locations are depicted in Figure 1.Notably, Tibet's installed wind power capacity is only 10 MW, accounting for 0.25% of the province's total volume, and its geospatial information is not recorded by GEM.Tus, Tibet is not considered in our further analysis.To explore the infuence of HW and CW events on regional wind energy production, we extract historical hourly climate data (surface maximum and minimum temperature, wind speed, and wind direction) from the ERA5 reanalysis [27] for the past ten years (2012-2021).

Regional Wind Energy Simulation.
To obtain the regional wind power output curve (WPOC) for a given day, we use a methodology that utilizes wind speed and direction data to calculate the wind power generation normalized by the total installed capacity for each wind farm.Tis calculation is performed using a single wind farm analytical model from Kunakote et al. [28].Te model applies Jensen's wake model to estimate the decay of wind speed after passing through a rotating turbine.Te initial wake area is assumed to have the same diameter as the turbine and expands linearly to infuence downstream turbines, as illustrated in Figure 2. Based on the conservation of momentum, the velocity in the wake cone can be computed as follows: where D represents the turbine rotor diameter, D(x) is the diameter of the wake disk at a distance of x behind the turbine, V 0 is the initial wind velocity, V(x) is the wind velocity at distance x, C T is the turbine thrust coefcient, and k is a constant that relies on the hub height and terrain roughness.Additionally, the distance between the centres of the wake cone and the swept area of the downstream turbine    International Transactions on Electrical Energy Systems is denoted as d; therefore, their intersection area (A) can be computed using the following equation: . ( Real wind industry statistical data and certain assumptions are utilized to determine the layout of wind turbines in each farm.Firstly, referring to the onshore wind power installation list from GEM, it is observed that most existing farms in China were built since the 2010s, with over 65% of them having a capacity of 50 MW (Figure 3).Considering the typical lifespan of a wind farm ranging from 25 to 40 years [29,30], a capacity of 50 MW will remain the predominant size for Chinese wind farms until 2060.Terefore, for this study, the capacity of individual wind farms is set at 50 MW.Secondly, the primary type of newly installed wind turbines in China is 2 MW [31], corresponding to a mean rotor diameter of 90 m [32], which suggests that each wind farm comprises 25 turbines.Following the design principles of general wind farms [33], these 25 turbines are arranged in a 5-by-5 crossed layout pattern (Figure 4).In this pattern, the orientation of the wind farm (the alignment of turbine rows) is perpendicular to the local prevailing wind direction, and the distance between the rows and columns is set at 7D and 4.5D, respectively.As mentioned earlier, Kunakote's model is employed for a single wind farm, and when applying it to multiple farms in a large region, the orientation of each wind farm needs to be determined.To accomplish this, we divide the compass into 36 directions at 10 °intervals and calculate the most frequent wind direction for each wind farm.Tis calculation is based on hourly eastward and northward wind data at a height of 100 m from ERA5 spanning the period 2012-2021.
After positioning individual wind farms at optimal orientations and simulating their power outputs, we calculate the regional WPOC by averaging the curves from all farms shown in Figure 1 within that region.Since the wind power generation from diferent farms does not follow an idealized Gaussian distribution, and the arithmetic mean may not be unbiased, we use the biweight robust method [34] to estimate the mean WPOC and mitigate the impact of outliers.Te biweight mean y * for time t is iteratively computed as follows: where y i represents the wind energy output of the farm i and w i is a symmetric weight function defned as follows: where c is a constant typically ranging from 6 to 9 (set to 7.5 in this study) and S is a robust measure of the standard deviation of the frequency distribution, computed as the median absolute deviation as follows: To initiate the iteration process and compute the fnal y * , the median is used as an initial estimate.Due to the nonmonotonicity behaviour of the biweight function w i , the iteration based on equations ( 3)-( 5) may not converge to a constant.However, typically, only three to four iterations are needed to achieve an estimation that changes by no more than 10 −3 [35].In this study, the maximum number of iterations is set to 10. Finally, we use a linear-scaling approach [36] to adjust the biases in the mean of capacity factors between observations and simulations.Te observed capacity factors are extracted from the China Electric Power Yearbook [37].It is important to note that we assume the wind farm density remains unchanged as shown in Figure 1, even with an increasing number of wind farms over years, to ensure the applicability of the regional WPOC in the future.
To evaluate the performance of our wind farm model under diferent weather conditions at local and regional levels, we compare our model simulation with observed power outputs from recent publications [38,39] for real wind farms in China.For a single wind farm with weather and power output data from 2019-2020 provided by Chen and Xu [38], the correlation coefcients between simulations and observations for hourly mean power output on HW days, CW days, and normal days are 0.988, 0.880, and 0.884, respectively.All correlation coefcients are signifcant at the 0.001 level, indicating that our model is capable of accurately simulating local wind power under extreme weather conditions.For multiple wind farms within a province, Wan et al. [39] presented the output distribution of several main wind farms in Hubei for three extremely hot days during summer 2016.We also simulate the wind power outputs for the corresponding farms and days to calculate their frequency distribution.Te comparison between International Transactions on Electrical Energy Systems observations and our simulations reveals a similar distribution pattern on hot days (Figure 5).Specifcally, the wind power output is below 0.1 for nearly 60% of the time, between 0.1 and 0.2 for approximately 15% of the time, and the output falls into other intervals for less than 10% of the time.Te comparison demonstrates the efectiveness of our model at the regional level.

Identifcation of Regional Heat Wave and Cold Wave
Events.HW and CW events are commonly defned using various criteria, and there is no universally accepted defnition for these terms [40].For a specifc location, a basic absolute standard for a hot day is when the daily maximum temperature exceeds 35 °C, as proposed by the China Meteorological Administration (CMA).An HW occurs when this hot day condition persists for at least three consecutive days.However, this fxed threshold corresponds to diferent temperature percentiles across a large region, and it is more reasonable to defne a hot day based on a relative threshold that represents regional heat conditions [41][42][43].In this study, we adopt the defnition used in previous research [41] and defne a hot day at the regional level as one where the daily maximum temperature, averaged over the entire region, exceeds the 98th percentile.Similarly, a regional HW is defned as a hot day condition that lasts for three or more consecutive days.
Te criterion for identifying a CW at a specifc weather station is when the daily minimum temperature is lower than 4 °C and decreases by at least 8/10/12 °C within the previous 24/48/72-hour period, as established by the CMA.For the regional CW, previous studies suggest that it occurs when the number of sites in a region that meet the stationlevel criterion exceeds a predefned percentage threshold, such as 20% or 30% for midlatitudes [44,45].However, the percentage threshold may be lower (e.g., 10%) for regions in tropical provinces [46].In this study, we set the percentage threshold as 10% in South China and 20% in other regions.Furthermore, we exclude CW days with a daily minimum temperature below −20 °C from the wind power generation analysis since wind turbines may shut down due to extremely low temperatures, resulting in unreliable operation.

Machine Learning to Optimize Projection of Regional Heat and Cold Waves.
To estimate the monthly changes in HW and CW days for six regions in the future, we utilize multiple model results from the Coupled Model Intercomparison Project Phase 6 (CMIP6).CMIP6 ofers various standard scenarios that represent diferent socioeconomic environments and the intensity of the additional radiative forcing in the future [47].Among these scenarios, the SSP245 scenario closely aligns with the real-world warming projections, taking into account current and long-term actions or policies such as China's carbon dioxide peaking and carbon neutrality targets [48].Terefore, we project the potential   CMIP6 encompasses more than 30 general circulation models (GCMs) and fve of them (ACCESS-CM2, FGOALS-g3, IPSL-CM6A-LR, MPI-ESM-2-0, and NESM3) are selected to use for this study.Tese models have demonstrated superior performance in simulating temperature change trends compared to observed records during the historical period of 1979-2014 [49].Detailed information on the selected models is provided in Table 2. Te model simulation data is obtained from the NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP-CMIP6) [50], which applies bias correction and spatial disaggregation procedures to the original CMIP6 output.Te processed datasets from NEX-GDDP-CMIP6 maintain a spatial resolution of 0.25 °× 0.25 °and exhibit better consistency with historical climate records.
Te most commonly used approach to project future changes in climate variables from multiple models is to calculate their arithmetic mean.However, recent studies have highlighted the signifcant advancements of the stacking ensemble method in the machine learning framework.Tis method involves using the prediction results of the previous level learners as input for the next level [51,52].Terefore, in this study, we use the stacking ensemble machine learning method to project changes in HW and CW days under the SSP245 scenario.Te model structure is illustrated in Figure 6 and implemented using the ensemble learning toolbox (ELT, available at https://github.com/vhrique/ELT).To calibrate the stacking ensemble model, we utilize historical simulations of daily maximum and minimum temperature from the fve selected CMIP6 models, along with ERA5 data as observational reference, covering the period from 1990 to 2014.Te dataset is divided into a training set and a testing set in a 2 : 1 ratio, with every 3rd value in the time dimension selected [53].Te base learner for the stacking ensemble is the random forest model initialized by support vector regression, and the hyperparameters are predefned using the inbuilt confgurations from ELT.In order to assess the model performance, we calculate three metrics: the correlation coefcient (r), rootmean-squared error (RMSE), and mean absolute error (MAE), as recommended by prior studies [52,53].

Prevailing Wind Direction in China.
Figure 7 shows the prevailing wind direction at a height of 100 m in China with a spatial resolution of 0.25 °based on hourly ERA5 reanalysis data over a 10-year period (2012-2021).Te wind patterns exhibit a distinct association with the topography of the region.Te Northeast China Plain and the North China Plain experience predominantly southwest winds, while the middle and lower reaches of the Yangtze River are characterized by east and southeast winds.Te Inner Mongolia Plateau and the hilly and mountainous regions of South China are marked by north and northwest winds.Te Sichuan Basin and the Tarim Basin frequently encounter east winds.Te Tibet Plateau and the Yunnan-Guizhou Plateau exhibit strong south and southwest winds.Tese wind regime characteristics are considered in determining the optimal orientations of wind farms in diferent locations, and wind energy simulations are conducted for each farm under diverse weather conditions.

Changes of Wind Power Output on HW Days for Diferent
Regions.According to our defned criteria, regional HW occurred for 47, 41, 54, 48, 36, and 47   International Transactions on Electrical Energy Systems 7 10 years.We conducted simulations to estimate the WPOC for each HW day and normal day (days that were neither a hot day nor a CW day) in summer season (June to August).Subsequently, we calculated the biweight robust mean WPOCs for the six regions under these two weather conditions.Te results are presented in Figure 8.
In Northeast China (Figure 8(a)), the WPOC on a summer normal day exhibits two peaks and two valleys.Te highest peak output occurs at midnight, reaching 16.6%, while the other peak at 3 PM has an output power of 14.5%.Te output drops to 12.1% and 13.0% at 8 AM and 6 PM, respectively.In contrast, the WPOC for an HW day shows a signifcant reduction of 2-5% from early morning to the afternoon, with an increase of 2-4% in the evening.Te wind power production on an HW day is 94.6% of that on a summer normal day.
In North China (Figure 8(b)), the WPOC on a summer normal day is similar to that in Northeast China, but the output in the frst valley around 8 AM is slightly lower at 10.2%, and the time of the afternoon peak appears a little later at 5 PM.On the other hand, the WPOC for an HW day has a decline of 3-4% during the day (8 AM to 5 PM) and rises about 2% during the night (9 PM to 5 AM).Te wind power production on an HW day is 96.1% of that on a summer normal day.
In East China (Figure 8(c)), the WPOC on a summer normal day also follows a two-peak and two-valley pattern, but the range of wind power output is larger than that in Northeast China and North China.Te highest peak output occurs at 10 PM, reaching 19.9%.Te other peak is around 5 PM with an output power of 17.7%.Two output valleys are observed at 8 AM and 6 PM, with outputs of 14.5% and 16.2%, respectively.By comparison, the WPOC for an HW day drops about 2% during the day (8 AM to 5 PM) but grows by 2% during the night (9 PM to 5 AM).Te wind power production on an HW day is 99.3% of that on a summer normal day.
In Central China (Figure 8(d)), the WPOC on a summer normal day is similar to that in North China, but the daily output is slightly lower (about 1%), and the peak at night occurs a little earlier at 10 PM.By contrast, the WPOC for an HW day shows a remarkable increase of 2% at night (7 PM to 2 AM), a slight reduction in the morning (7 AM to 12 PM), and no signifcant changes in the afternoon (2 PM to 6 PM).Te wind power production on an HW day is 101.7% of that on a summer normal day.
In South China (Figure 8(e)), the WPOC on a summer normal day still exhibits a two-peak and two-valley pattern, with the highest peak of 21.0% occurring in the afternoon at 3 PM, which is 2% higher than the other peak at 9 PM.Additionally, the output falls to low points of 17.5% and 18.2% at 6 AM and 6 PM, respectively.By comparison, the WPOC for an HW day maintains almost the same output during the nighttime period (8 PM to 5 AM) but experiences a sharp decrease of 3-5% during the daytime period (6 AM to 5 PM).Consequently, the afternoon peak on an HW day is slightly lower than the evening peak.Te wind power production on an HW day is 93.2% of that on a summer normal day.
In Northwest China (Figure 8(f )), both summer normal days and HW days show a simple one-peak and one-valley pattern, where the valley occurs at 9 AM and the peak appears before midnight.Both WPOCs have comparable output from 9 AM to 6 PM, while the output on HW days can reach 25.4% at night, which is 5% higher than that on summer normal days.Terefore, the wind power production on an HW day is 109.2% of that on a summer normal day.
Taken together, most regions experience a reduction in wind power output from late morning to early afternoon on HW days.However, this period corresponds to the peak load   International Transactions on Electrical Energy Systems in the commercial sector and the second-highest power demand peak in residential and industrial sectors for typical daily power load curves in summer [54].Terefore, HW events challenge the daily dynamic supply-demand balancing capability of a power grid that relies on wind resources.

Changes of Wind Power Output on CW Days for Diferent
Regions.In the past 10 years, there were 106, 96, 21, 5, 8, and 8 days of regional CW in Northeast China, North China, East China, Central China, South China, and Northwest China, respectively.Figure 9 presents the biweight robust mean WPOCs for CW days and normal days in autumn, winter, and spring (AWS) in the six regions.Since the daily minimum temperature typically occurs from midnight to early morning, we also include the mean WPOC for one day before and after the CW event, and these two days are excluded from the count of normal days.
In Northeast China (Figure 9(a)), the WPOC on an AWS normal day follows the same two-peak and two-valley pattern as a summer normal day.However, the average output is 7.9% higher, with the peak output reaching 24.9% before midnight (11 PM).In contrast, the output from the day before CW until noon on the CW day shows a signifcant increase of 15-20%, followed by a rapid decline.By the evening of the CW day and throughout the next day, the WPOC is about 3-4% lower than that on an AWS normal day.
In North China (Figure 9(b)), the WPOC on an AWS normal day also exhibits two peaks and two valleys.Te highest peak output is 21.1%, which appears in the afternoon (3 PM).Te other peak is around midnight with an output power of 20.7%.Te output drops to low points of 16.4% and 18.0% at 10 AM and 7 PM, respectively.Te WPOCs on the CW day and adjacent days are all higher than that on an AWS normal day.Te largest increase (about 10-12%) occurs from the CW day to the afternoon of the next day, while the output on the day before the CW only has a slight growth of 2-6%.
In East China (Figure 9(c)), the WPOC on an AWS normal day follows a simple one-peak and one-valley pattern, with the valley (16.6%) observed at 10 AM and the peak (21.2%) occurring before midnight.By comparison, the output is about 4% lower in the morning of the day before the CW, then sharply increases, reaching a peak of 47.8% at 3 PM on the CW day, and gradually returns to the normal level on the day after the CW.
In Central China (Figure 9(d)), the WPOC on an AWS normal day is similar to that in East China, but the output is lower (about 6%).By contrast, the output remains at the normal level in the early morning of the day before the CW and then gradually increases.It reaches over 60% generation from early morning until 4 PM on the CW day, and then slowly decreases but remains above the normal WPOC on the day after CW.
In South China (Figure 9(e)), the WPOC on an AWS normal day also exhibits a one-peak and one-valley pattern, with the valley (19.5%) observed at 10 AM and the peak (26.0%) occurring in the afternoon (5 PM).By comparison, the increase in output on the CW day is about 15%, but it can reach 20-25% within the 12-hour period before and after the CW day.
In Northwest China (Figure 9(f )), the WPOC on an AWS normal day also shows a one-peak and one-valley pattern, with the valley (14.2%) observed at 11 AM and the peak (18.2%) occurring in the evening.In contrast, the output starts to increase from the early morning of the day before the CW and reaches a peak of 43.7% in the afternoon of the CW day.It then gradually decreases to the normal level on the day after the CW, with a signifcant upturn around 2 PM.
In summary, all regions experience higher wind power generation on the CW day and the day before.Residential, commercial, and industrial sectors typically demand less energy during winter, as refected in typical daily power load curves [54].Terefore, power supplies face fewer challenges on CW days compared to HW days.However, it is worth noting that on the day after a CW event, there is a signifcant reduction in wind power output while electricity consumption experiences notable growth, particularly in the residential sector, due to cold weather [55].Tis situation may increase the risk of wide-area power outages.
3.4.Future Changes of the HW and CW Days.Table 3 shows the performance of applying stacking ensemble models in the test phase for predicting HW and CW days over 6 regions, respectively.All models obtain skilful performance, with r ranging from 0.792 to 0.976, RMSE ranging from 0.065 days to 0.420 days, and MAE ranging from 0.039 days to 0.290 days.Although models for CW days exhibit superior results than that for HW days, all the correlation coefcients pass the 0.01 signifcance level, which indicates that they efectively capture the temporal characteristics of HW and CW days among regions and could be used to project future changes.
Figure 10 depicts the change in the number of HW days for each month during the past decade and the next three decades under the SSP245 scenario.Te fgure reveals a continuous increase in the number of HW days in each region during 2031-2040, 2041-2050, and 2051-2060, with signifcant regional diferences in the number of increasing days.When compared to 2012-2021, the total number of HW days per year will increase by 1.5 to 3.9 times in 2031-2040, 1.4 to 4.2 times in 2041-2050, and 2.5 to 6.5 times in 2051-2060.Te minimum increase in HW days is expected in North China, while Central China and South China are expected to have the maximum increase.For instance, Central China and South China will have approximately 10 HW days in July during 2051-2060.Furthermore, the month with the highest number of HW days will gradually shift from August to July in these two regions.Prior studies have mostly focused on the mean summer temperature change in the future and reported that the warming trend in Northeast China is large but small over South China [56][57][58].However, a roughly reversed spatial pattern is seen for high temperatures, such as the number of in 2031-2040, from 55% to 120% times in 2041-2050, and from 87% to 128% times in 2051-2060.Specifcally, the number of annual CW days increases signifcantly in Central China, decreases slightly in East China and Northwest China, but remains steady in the other three regions.Moreover, the monthly distribution of CW days changes a lot for most regions, i.e., CW days decline in February and November but grow in December and     [56][57][58], but the frequency of cold extremes will not experience a notable decline along with the warming trend [60], including the CW events in this study.Consequently, the impacts of CW  4 summarizes the relative wind power output anomaly on HW and CW days, as well as the expected change in the number of HW and CW days per year in the future.

Conclusions and Discussion
In this study, we calculate the local prevailing wind direction to determine the orientation of wind farms and then simulate the daily wind power output during HW and CW days for six regions in China.Te major fndings can be drawn as follows.(1) Most regions (except for Northwest China) experience a signifcant wind power output reduction from late morning to early afternoon on HW days, which challenges the daily dynamic supply-demand balancing capability of a power grid.(2) All regions receive more wind power generation on the CW day and the previous day than on normal days.Te output peak occurs in the evening of the previous day for Northeast China and South China, while it appears in the early afternoon for other regions.However, a rapid decline in wind power is seen on the day after the CW for all regions, which may increase the risk of wide-area power outages.
In addition, we apply the stacking ensemble machine learning method to project the changes of regional HW and CW days during 2031-2040, 2041-2050, and 2051-2060 based on the SSP245 scenario.In the future, HW days have coherent growing trends among regions but CW days mainly show monthly redistributions without notable changes in total occurrences throughout the year.Terefore, HW and CW events will mainly infuence the intraday and interday supply-demand balances of the power grid that depends on wind resources.
In view of the method, the originality of this study is that it explores wind energy production at the interprovincial scale by placing individual wind farm models into a prevailing wind direction network and applying an ensemble learning algorithm to estimate the extreme weather change in the future from multiple GCMs.Tis method can better extract complex dynamical processes and implicit wind patterns within climate models and it difers from previous regional wind power simulators mainly based on statistical relationships [7,61].
A number of limitations need to be noted regarding the present study.Firstly, we only focus on the wind power sector during HW and CW days; further work is required to identify the output of hybrid renewable energy systems under diferent extreme weather conditions.Secondly, we simply assume that the wind farm density remain unchanged in the future with a growing number of wind farms, which will induce gradually increased bias of regional WPOCs.Further research might develop a dynamic wind farm network based on long-term planning of wind projects to reduce such bias.

Figure 1 :
Figure 1: Map of the six regions and locations of wind farms (indicated by yellow plus markers) in China.

Figure 2 :
Figure 2: Wind turbine wake decay model and its infuence on the downstream turbine.

Figure 3 :
Figure 3: Construction of onshore wind farm in China.
v a il in g W in d D ir e c ti o n

Figure 4 :
Figure 4: Layout of 25 turbines in a wind farm and the prevailing wind direction.

Figure 5 :
Figure 5: Distribution of wind power output from observations and simulations for wind farms in Hubei during three extremely hot days in summer 2016.

Figure 7 :
Figure 7: Prevailing wind direction at a height of 100 m in China based on hourly ERA5 reanalysis data.

Figure 8 :
Figure 8: Comparison of the ensemble mean WPOCs on HW days and normal days for six regions in China.(a) Northeast China.(b) North China.(c) East China.(d) Central China.(e) South China.(f ) Northwest China.

Table 1 :
Provinces included in the six regions.

Table 2 :
List of CMIP6 general circulation models (GCMs) used in this study.
Figure6: Structure of the stacking ensemble learning model for projecting regional HW and CW.

Table 3 :
Te stacking ensemble model performance (r, RMSE, and MAE) during the test phase for predicting HW and CW days over six regions in China.