Stochastic and Extreme Scenario Generation of Wind Power and Supply–Demand Balance Analysis Considering Wind Power–Temperature Correlation

Abstract

In the context of large-scale wind power access to the power system, it is urgent to explore new probabilistic supply–demand analysis methods. This paper proposes a wind power stochastic and extreme scenario generation method considering wind power–temperature correlations and carries out probabilistic supply–demand balance analysis based on it. Firstly, the influence of temperature on wind power output is analyzed via Pearson coefficient to obtain the correlation between wind power and temperature. Secondly, based on the historical wind power curve, a large number of wind power output scenarios are randomly generated while fully preserving its characteristics, and probabilistic supply–demand analysis is carried out. Thirdly, for the extreme case of continuous multi-day extreme heat without wind, extreme scenarios are selected from the generated scenarios for supply–demand balance analysis. Finally, a practical example in a province in central-eastern China is used to verify the effectiveness of the proposed method. The results indicate that the scenario generation method can effectively capture the historical wind power characteristics and can be better applied to the diversified supply and demand balance analysis to obtain more accurate analysis results.

1. Introduction

With the consumption of traditional fossil energy and the continuous growth of social demand, renewable energy has attracted great attention [1]. The power grid with a high proportion of renewable energy has become an inevitable trend and significant feature of future development. The output of renewable energy, represented by wind power, is closely related to meteorological factors. Its strong randomness and volatility bring both short-term and long-term supply and demand imbalance risks to the power system [2,3]. Using the traditional deterministic planning method presents difficulty in accurately describing the operation characteristics of the new power system, which will lead to the gradual increase of the deviation between the planning research and the actual situation [4]. In order to further adapt to the source-side uncertainty caused by the volatility and randomness of wind power output, it is necessary to achieve transformation and upgrading from the planning strategy and method level. The application of multi-scenario probabilistic planning can make a more detailed modeling of the uncertainty factors, which is conducive to evaluating the medium and long-term power supply and demand situation and providing the power system with a more stable optimization scheme [5].

The output of renewable energy is closely related to meteorological conditions, so it is of great significance to study extreme meteorological conditions to grasp the operation law of renewable energy. The meteorological factors that have a greater impact on the output of renewable energy include extreme weather such as continuous days without wind and light, ice disaster and typhoon. Among these factors, typhoon and ice disaster are the focus of existing research. In analyzing the impact of ice disaster on power systems, Ref. [6] quantified the temporal and spatial effects of ice disaster on components, and established an active scheduling model of power system considering the temporal and spatial distribution characteristics of ice disaster weather based on a semi-Markov decision process. In Ref. [7], considering the temperature and relative air humidity, a regression model of transmission line icing based on support vector machine is proposed to predict the short-term icing of transmission lines. Ref. [8] established a model to describe the relationship between meteorological conditions and power grid faults under the scenarios of icing and insulator flashover, which realized the multi-variable and multi-time scale hybrid simulation of power system considering line icing and insulator flashover. Ref. [9] established the ice–wind load curve of overhead lines design and the ice–wind load risk model of lines based on the random characteristics and interference theory of line load-strength, so that the system operators can provide early warning information of power systems in extreme ice disaster weather. In analyzing the impact of typhoons on power systems, Ref. [10] studied the unsteady characteristics of wind turbines in the typhoon active area by establishing models for wind fields with different turbulence intensities, wind speeds and wind directions. Ref. [11] evaluated the long-term effects of offshore wind farms under typhoon conditions, and the extreme wind speed of typhoon is identified as the main cause of structural fatigue of wind turbines. Ref. [12] considered four fault conditions of transmission lines under typhoon disasters, and used an exponential function to fit the relationship between transmission line failure rate, wind speed and line parameters under different fault conditions. In Ref. [13], the typhoon meteorological information, power grid information and geographic information were added to modify the theoretical model of damage risk, and then the comprehensive failure probability of the transmission line tower–line system was obtained. In Ref. [14], the Batts model was used to describe the wind speed of each point in the wind field during the typhoon attenuation process, and the failure rate model of tower and line was established according to the interaction mechanism between typhoon and power pole. Based on Bayesian networks, Ref. [15] used conditional probability to obtain the relationship between weather conditions and line faults, which enables the calculation of the predicted line failure rates under typhoon disasters.

Scenario analysis is one of the mainstream methods to describe the uncertainty of wind power output. This method generates multiple possible random scenarios by probabilistic modeling of historical wind power output curves. Most of the existing random scene generation methods of wind power belong to the explicit density model. It needs to make statistical assumptions about the probability density function obeyed by the output curve and use the historical wind power output curve to fit the parameters in the probability density function. Ultimately, the probability density function is sampled to obtain the random scene of wind power. Ref. [16] used Copula theory to connect the joint distribution function of multiple wind farms with their respective marginal distribution functions, and historical samples were used to fit the unknown parameters in the distribution. Finally, random scenarios of multiple adjacent wind farms were obtained by the Monte Carlo method. Ref. [17] used the autoregressive moving average model to generate wind power series, which can better control the autocorrelation characteristics of the generated wind power series. On this basis, Refs. [18,19] divided the wind power fluctuation process into several categories, such as large fluctuation, medium fluctuation and small fluctuation process, and then used the Markov chain Monte Carlo method for sequential sampling to generate wind power series, which well simulated the fluctuation characteristics of wind power. Ref. [20] proposed a wind power Monte Carlo sampling method based on the duration characteristics and fluctuation characteristics of the measured wind power series, which better reflected the duration characteristics and volatility of the original sequence. Ref. [21] proposed an Attention Conditional Generative Adversarial Network (ACGAN) model to generate daily curves of wind power and photovoltaic output, and then used the Markov chain-Monte Carlo (MCMC) method to generate daily series curves for 365 days of the year. This method retains the annual seasonal fluctuation attribute and daily variations characteristics of historical data while ensuring the randomness of the generated scenarios. In terms of wind power scenario generation considering correlation, Refs. [22,23] used the mixed copula function to describe the spatial correlation of multi-wind farm output, and constructed the joint probability distribution model of multi-wind farm output. Ref. [24] described the correlation of wind power based on Copula theory and established a probabilistic wind power model by considering the uncertainty of wind power through fuzzy C-means clustering method. Ref. [25] used multivariate normal distribution function and Copula function to establish a multi-wind farm spatio-temporal correlation analysis model. Ref. [26] used nonparametric estimation to describe the probability distribution of wind and solar power, and established the correlation model of wind and solar power output based on Frank-copula function. In Ref. [27], a scenario generation method considering multi-dimensional correlation is proposed for regional integrated energy systems with renewable energy. In Ref. [28], the researchers considered the correlation between wind power generation and load in different locations in the same area, established the probability distribution model of these related random variables based on Copula theory, and used the Monte Carlo method to generate uncertain scenarios. Ref. [29] considered the wind speed correlation of different wind farms, and used Copula function to model the correlation structure and prediction error of random wind speed. At the same time, the Sobol sequence is used to improve the quality of uniform distribution random numbers, which reduces the computational burden of the Monte Carlo sampling method. Ref. [30] focused on the correlation between electrical load and thermal load, and established a load correlation model using Copula function. Ref. [31] analyzed the nonlinear correlation between renewable energy outputs. In order to accurately evaluate the impact of wind power generation on the power system, Ref. [32] considered the spatial and temporal correlation between different wind turbines in the same wind farm, and constructed a new probability model based on Gaussian Copula function and Archimedean Copula function. The Euclidean distance and Kullback–Leibler divergence are used to prove the effectiveness of the developed model in merging the spatial and temporal correlation between turbine power generation.

The uncertainty of renewable energy aggravates the risk of power system supply and demand imbalance. In the past decade, China’s energy consumption has shown a gradual growth trend, among which the growth of renewable energy is the most significant [33]. The uncertainty of renewable energy output will cause changes in the operating state of the system [34], which is likely to cause voltage fluctuations and load shedding [34,35]. In severe cases, it will also cause large-scale power outages and even cause fundamental damage to the power grid [36]. The research on supply and demand balance of power systems focuses on the evaluation and planning of supply and demand. In the assessment of power supply and demand risk, Ref. [37] proposed a rapid assessment method for the reliability of wind power grid-connected systems and the risk of peaking supply and demand based on the state clustering method of non-sequential Monte Carlo sampling. In Ref. [38], the supply and demand risks caused by the uncertainty of wind power output are considered in the economic dispatch of power systems and the economic dispatch model and risk decision method of power systems considering supply and demand risks are proposed from the perspective of risk management. Refs. [39,40] obtained system component states based on the Monte Carlo method, and analyzed the influence of wind power access on system economic loss risk. Ref. [41] proposed a refined operational risk assessment model based on the piecewise discrete model of wind power prediction error; at the same time, load shedding risk, voltage collapse risk, voltage over-limit risk and line active power over-limit risk indicators were introduced to comprehensively assess the operational risk of large-scale wind power grid-connected power systems. In addition to the evaluation of supply and demand indicators, the power supply and demand level of the system can also be described by a high-risk random fault set. In the unit operation scheduling mentioned in Ref. [42] and the transmission expansion planning mentioned in Ref. [43], the high-risk random fault set provides more direct reference information for identifying weak links and improving the reliability level of the system. In order to accurately and quickly screen random faults, the existing research often equates the fault screening problem of the transmission system to a two-layer programming of the ‘attacker’ and ‘defender’, where the ‘attacker’ of the upper model is used to select the fault event of the system, and the ‘defender’ of the lower model is used to simulate the minimum fault loss of the power grid. In Ref. [44], the minimum load shedding problem based on DC power flow was taken as the lower model, and the Karush Kuhn Tucher (KKT) condition and duality theory were further used to transform the double-layer model into a single-layer mixed integer linear programming, which could accurately screen the random fault events that cause the maximum load loss. Ref. [45] considered the constraints of reactive power and voltage in the lower operation model and proposed a random fault screening algorithm based on mixed integer nonlinear programming. In Ref. [46], the loss and probability of random fault events were considered in the upper model, and a mixed integer linear programming model with risk as the goal was proposed, which could realize the rapid risk ranking of high-order fault events in transmission system.

In summary, there are certain research foundations for the generation of scenarios considering the randomness of wind power and the work of supply and demand balance in new power systems. The application of the generated scenarios to the analysis of supply and demand balance has also produced fruitful results. However, the current research results still have deficiencies in the following two aspects. Firstly, meteorological factors are less considered in the identification and probabilistic modeling of conventional and extreme risk factors. The influence of meteorological factors such as temperature is uncertain in the operation of power system. Most of the literature focused on the impact of extreme weather such as ice disaster and typhoon on the operation of power system equipment, while relatively few studies focused on the impact of renewable energy output and meteorological characteristics. Secondly, the supply and demand risk assessment indicators of new power system have limitations. The supply and demand risk assessment indicators in the current research mainly include the probability of loss of load and the expectation of power shortage, which cannot fully reflect the various risks of the new power system with a high proportion of renewable energy connected to the grid for probabilistic scenarios. Therefore, it is imperative to study the method of generating wind power scenarios with meteorological correlation and analyze the probabilistic supply and demand balance.

The main contributions are as follow. Firstly, the influence of temperature on wind power output is analyzed via Pearson coefficient, and the correlation between wind power and temperature is obtained. Secondly, the general method of random scene generation and supply and demand balance analysis is proposed by fully retaining the correlation characteristics of the given original data. Finally, in the conditions of normal and continuous hot and windless weather, the corresponding scenarios are selected from the generated scenarios for supply and demand balance analysis.

The remainder of this paper is organized as follows: Section 2 analyzes the correlation between wind power and temperature in detail. Section 3 describes the K-means clustering method and improved Markov Chain Monte Carlo (MCMC) method used in the subsequent scene generation process, and details the wind power random scene generation method and the extreme scene screening strategy of continuous multi-day extremely hot and windless. Section 4 validates the proposed method through an example based on the actual historical wind power and meteorological data of a province in central-eastern China. Section 5 summarizes this paper and looks forward to the future research direction.

2. Research on Wind Power–Temperature Correlation

2.1. Pearson Correlation Coefficient

The uncertainty of wind power includes randomness and volatility. Analyzing the characteristic factors related to wind power and meteorological data can not only understand their characteristics more deeply, but also promote the generation and screening of random scenes of wind power, which is conducive to the analysis of supply and demand balance. Among many meteorological factors, temperature has obvious diurnal and seasonal variation characteristics, which is closely related to wind power output. Take the central and eastern regions of China as an example. In the lower part of the near-surface layer, intense turbulence occurs during the day due to heating of the ground, resulting in high daytime wind speeds. After sunset, as the ground radiation cooling, the gas layer is stable, and the lowest ground temperatures and minimum wind speeds occur around sunrise. However, in the upper part of the near-surface layer, the diurnal variation of wind speed with temperature is opposite to that in the lower part, showing that the wind speed at night is larger than that in the daytime. As a result, the wind power output changes with the wind speed, showing the anti-peaking characteristics of the night output larger than the daytime [47]. Similarly, wind power generation exhibits seasonal variations correlated with temperature. In most parts of China, due to the influence of Asian high pressure, high power and high wind are more likely to occur in cold winter, while the wind speed is low in summer. As a result, there is a seasonal imbalance between supply and demand in summer power load peak and low wind power output [48]. Therefore, this paper uses Pearson correlation to quantify the correlation between temperature and wind power data [49]. The formula is expressed as

$${\mathsf{\rho }}_{\mathrm{x},\mathrm{y}}=\frac{\mathrm{E}\left[\left(\mathrm{X}-{\mathsf{\mu }}_{\mathrm{x}}\right)\left(\mathrm{Y}-{\mathsf{\mu }}_{\mathrm{y}}\right)\right]}{{\mathsf{\sigma }}_{\mathrm{x}}{\mathsf{\sigma }}_{\mathrm{y}}}$$

(1)

where X and Y represent wind power output and air temperature, respectively, ${\mathsf{\sigma }}_{\mathrm{x}}$ and ${\mathsf{\sigma }}_{\mathrm{y}}$ represent the variance of wind power output and air temperature, respectively, and ${\mathsf{\mu }}_{\mathrm{x}}$ and ${\mathsf{\mu }}_{\mathrm{y}}$ are the mean values of wind power output and air temperature.

2.2. Case Analysis of Wind Power–Temperature Correlation

This paper conducts a correlation analysis using the wind farm hourly output data of a province in central-eastern China in a certain year, along with the hourly average temperature of the whole province in China Meteorological Data Service Centre. The correlation coefficient between wind power and temperature in the province is −0.143.

In order to analyze the correlation between temperature and wind power data intuitively, the scatter diagram of wind power on temperature is shown in Figure 1.

The correlation coefficient between wind power output and temperature shows a weak negative correlation. When the temperature rises, it is more likely to have a scenario with smaller wind power output. When the temperature is higher than 20 °C, the proportion of scenarios with wind power output less than 0.06 reaches 29.91%. When the temperature is higher than 26 °C, the proportion of low wind power scenarios increases sharply to 36.42%. When the temperature is higher than 30 °C, the proportion of low wind power scenarios is close to 40%, which is mainly affected by the extremely hot windless weather.

3. Wind Power Random Scene Generation and Extreme Scene Screening Method

In order to describe the uncertainty of wind power output, this section proposes a method that considers wind power–temperature correlation for generating random and extreme scenarios of wind power. Firstly, a sequential wind power random scene is generated based on K-means and improved MCMC algorithm. Then, according to the wind power–temperature correlation, the extreme wind power output scenarios are screened to meet the actual needs of supply and demand balance analysis.

3.1. Typical Day Division Based on K-Means

In the extraction of wind power scenarios, the extraction data of continuous time series scenarios is large, and the optimization efficiency is low. Therefore, it is necessary to simplify the wind power scenario. Through clustering technology, the output scenario set that conforms to the typical characteristics of the original power can be obtained, and the analysis efficiency of the wind power sequence can be effectively improved.

K-means algorithm is an efficient unsupervised clustering algorithm, which plays an important role in clustering analysis [50]. It can fully mine the data characteristics of the sample, and divide the sample set into K categories according to this. This paper mainly studies the generation method of annual 8760 h of wind power output curve for stochastic production simulation, which needs to extract key features from historical data. Therefore, this paper adopts a K-means method to generate typical days month by month. The specific steps are as follows:

(1)

The given specific historical wind power 8760-h curve data is artificially divided into 12 parts according to the month.

(2)

The historical curve of each month is divided into about 30 pieces of data according to the number of days per month. Each piece of data corresponds to 24 h of renewable energy output per day in each of the 30 days.

(3)

By using the K-means algorithm, 30 data per month are divided into K clusters to complete the clustering division of historical data.

3.2. Random Scene Generation Based on Improved MC-MC Method

The MCMC method is a special Monte Carlo simulation method. It introduces the Markov chain in the random process into the Monte Carlo simulation, which is of great significance in simulating the wind power output sequence. The state transition matrix is a core concept in the Markov chain, which describes the probability of the system transferring from one state to another. By combining with Monte Carlo sampling, a large number of random samples are generated to generate the required wind power sequence.

A Markov process is a stochastic process in the state space that undergoes a transition from one state to another. The process requires ‘non-memory’, meaning that the probability distribution of the next state can only be determined by the current state, and the previous events in the time series are independent of it. This particular type of ‘memoryless’ is called Markov property. The discrete Markov process is called the Markov chain, and its mathematical expression is as follows:

$$\mathrm{P}\left\{{\mathrm{X}}_{\mathrm{n}+1}={\mathrm{x}}_{\mathrm{n}+1}\left|{\mathrm{X}}_0={\mathrm{x}}_0,{\mathrm{X}}_1={\mathrm{x}}_1,\dots ,{\mathrm{X}}_{\mathrm{n}}={\mathrm{x}}_{\mathrm{n}}\right.\right\}=\mathrm{P}\left\{{\mathrm{X}}_{\mathrm{n}+1}={\mathrm{x}}_{\mathrm{n}+1}\left|{\mathrm{X}}_{\mathrm{n}}={\mathrm{x}}_{\mathrm{n}}\right.\right\}$$

(2)

where ${\mathrm{X}}_0,{\mathrm{X}}_1,{\mathrm{X}}_2,\dots ,{\mathrm{X}}_{\mathrm{n}}$ are the state sequences. The formula shows that the conditional probability of ${\mathrm{X}}_{\mathrm{t}+1}$ state at time t + 1 only depends on ${\mathrm{X}}_{\mathrm{t}}$ at time t.

In the random process, the random quantity at any time can be regarded as the state of the Markov chain. For a non-periodic Markov chain, there exists a state transition matrix P, and any two states are connected, then $\mathrm{l}\mathrm{i}{\mathrm{m}}_{\mathrm{n}\to \infty }{\mathrm{P}}_{\mathrm{i}\mathrm{j}}^{\mathrm{n}}$ is independent of i, and at the same time

(1)

$\mathrm{l}\mathrm{i}{\mathrm{m}}_{\mathrm{n}\to \infty }{\mathrm{P}}_{\mathrm{i}\mathrm{j}}^{\mathrm{n}}=\mathsf{\pi }\left(\mathrm{j}\right)$

(2)

$\mathsf{\pi }\left(\mathrm{j}\right)={\displaystyle \sum _{\mathrm{i}=0}^{\infty }}\mathsf{\pi }\left(\mathrm{i}\right){\mathrm{P}}_{\mathrm{i}\mathrm{j}}$

(3)

$\mathrm{l}\mathrm{i}{\mathrm{m}}_{\mathrm{n}\to \infty }{\mathrm{P}}^{\mathrm{n}}=\mathsf{\pi }\left(\begin{array}{ccccc}\mathsf{\pi }\left(1\right)& \mathsf{\pi }\left(2\right)& \dots & \mathsf{\pi }\left(\mathrm{j}\right)& \dots \\ \mathsf{\pi }\left(1\right)& \mathsf{\pi }\left(2\right)& \dots & \mathsf{\pi }\left(\mathrm{j}\right)& \dots \\ \dots & \dots & \dots & \dots & \dots \\ \mathsf{\pi }\left(1\right)& \mathsf{\pi }\left(2\right)& \dots & \mathsf{\pi }\left(\mathrm{j}\right)& \dots \\ \dots & \dots & \dots & \dots & \dots \end{array}\right)$

where $\mathsf{\pi }$ is the unique nonnegative solution of $\mathsf{\pi }=\mathrm{P}\mathsf{\pi }$ equation, and ${\displaystyle \sum _{\mathrm{i}=0}^{\infty }}\mathsf{\pi }\left(\mathrm{i}\right)=1,$ $\mathsf{\pi }=\left[\mathsf{\pi }\left(1\right),\mathsf{\pi }\left(2\right),\dots ,\mathsf{\pi }\left(\mathrm{j}\right),\dots \right]$ is usually called the stationary distribution of the Markov chain. The stationary distribution of the Markov chain is the expected target distribution. When the chain is long enough, the obtained simulation sequence can be regarded as an independent sample from the target distribution.

The specific steps of generating wind power time series by traditional MCMC method can be referred to Ref. [51]. In this paper, K-means is introduced into the MCMC algorithm. The daily wind power output sequence is clustered into K classes via K-means, and the same class sequence is extracted and reconstructed into a new sequence. However, when extracting and reconstructing a new sequence for the same class days, the days of the same class are not necessarily adjacent in the original sequence, and there may be a jump in the connection of each day in the process of reconstructing the new sequence. Therefore, this paper improves the traditional MCMC method by adding screening conditions to correct the unrealistic fluctuations of renewable energy output from 12:00 AM to 1:00 AM. In addition, when generating the typical daily curve under the corresponding clustering, the wind power daily curve fitting results before Gaussian filtering are easy to fluctuate due to the small number of 8760 h of historical curve samples. Therefore, this paper uses a 24-element Gaussian-copula function to randomly generate a typical daily curve of wind power to improve the fitting accuracy.

3.3. Wind Power Random Scene Generation Framework

3.3.1. Overview of Wind Power Random Scene Generation Process

Figure 2 shows the algorithm flow chart of the wind power curve generation method for random 8760-h production simulation. According to 8760 h of historical wind power data, the algorithm randomly generates several 8760-h output curves under the premise of considering the seasonal and daily characteristics of wind power. The generation algorithm flow can be divided into three steps. The first step is the input of 8760 h of wind power history data and enter the original wind power output curve into the algorithm program after processing. The second step is to reasonably split the historical data and identify the characteristics. Through the K-means clustering model, the MCMC method based on the time series state transition matrix and other algorithms, the wind power data is preprocessed before randomization. Based on the first two steps, the improved MCMC method is used to randomly simulate the corresponding wind power curve. The third step is to randomly generate the renewable energy output curve.

3.3.2. Detailed Explanation of Sequence Scene Generation Process

The algorithm flow chart shown in Figure 2 is explained in detail in three steps.

(1)

Step 1: Input the historical data

In the wind power curve generation method for random 8760-h production simulation, the input is a historical wind power 8760-h data of a certain province. After the original curve enters the program, the program divides the curve data into 12 parts according to the month, and each part corresponds to one month in the 12 months. The subsequent logic of the program will process the original curve month by month. When 12 months have been processed by the program, the program will splicing 12 N random sequences generated by the aforementioned algorithm into N 8760-point curves one by one to obtain N probabilistic 8760-h scenes.

(2)

Step 2: Data analysis and processing

On the basis of Section 3.1, the data is divided into K clusters by K-means clustering, and the state transition matrix between each state is obtained. Then, for the daily 24 points, the improved MC method considering time dependence is used to solve the problem that the wind power jumps between adjacent time points in the 24 points daily curve randomly generated by each cluster, and the 24 points daily random curve in a certain cluster is randomly generated.

(3)

Step 3: Generation of random curve

Taking the obtained state transition probability matrix between clusters in a certain month and the random curves under different clusters as input, the improved MC-MC method is used to generate N monthly random output curves after N times of sampling. After splicing the monthly random curve in chronological order, N annual random curves can be obtained. Due to the regional differences in the annual utilization hours of wind power in the actual power system, this paper uses the annual utilization hours checking module to screen out the scenarios where the number of hours exceeds the limited range, and finally generates an annual random curve that conforms to the characteristics of wind power output.

Through the above three steps, the whole process of source-load annual timing scene generation is completed. In the Section 4, this paper will verify the engineering practicability of the algorithm process proposed in this chapter through a random generation example of 8760 h of actual wind power data in a certain province.

3.4. Extreme Scene Screening

According to the correlation analysis of wind power and temperature in Section 2, when the temperature is too high, the scene of extremely low wind power output is easy to observe. In the high proportion of renewable energy power system, if there is a continuous multi-day extremely hot windless situation, it will seriously affect the supply and demand balance of the power system [52]. However, the probability of extreme scenes is extremely low. If there is no relevant scene in historical information, it is difficult to carry out correlation analysis in extreme scenes. In order to solve this problem, a large number of wind power random scenes can be generated by Monte Carlo sampling in advance, and then combined with the correlation analysis results of wind power and temperature, the screening conditions of continuous multi-day extremely hot windless scenes can be set. The specific screening methods are as follow:

Firstly, according to the meteorological data of 8760 h in a province, the scenario of continuous h-hour temperature higher than C is defined as the continuous multi-day extreme heat state. Then, the N scenes generated by Monte Carlo method are verified one by one. If the continuous hourly wind power output coefficient corresponding to the 8760 h of the weather is lower than the minimum value w, the scene is retained, otherwise, the scene is not retained.

4. Case Study

In this paper, the actual system of a province in central-eastern China is selected for example analysis. Firstly, N wind power random scenarios are generated based on the actual wind power output data, and then the supply and demand balance analysis is carried out for normal scenarios and extreme scenarios, which verifies the effectiveness of the proposed method in practical engineering applications. The models in this paper are programmed based on Python 3.10.

4.1. Parameter Description

The total number of samples in the Monte Carlo sampling process is set to N = 10,000, the photovoltaic guarantee output coefficient is 0, and the wind farm guarantee output coefficient is 0.06. In the process of screening extremely hot and windless extreme scenes, it is defined that the atmospheric temperature for h consecutive hours is higher than C degree Celsius to represent extreme heat, and the wind power output for h consecutive hours is lower than w per unit value to represent no wind. In order to keep generality, h = 72, c = 26, w = 0.06 are selected.

4.2. Scene Generation and Supply–Demand Balance Analysis under Normal Conditions

4.2.1. Wind Power Random Scene Generation

Firstly, the annual wind power output per unit value curve of 8760 h in a province in the central and eastern regions is input into the process of time series scene generation algorithm. The wind power curve is shown in Figure 3.

Secondly, the 8760 data of the whole year are divided into 12 parts month by month, and then the monthly data are optimized and clustered by day.

As shown in Figure 4, taking March as an example, the 744 data points (24 × 31) of the 31 days of the month are optimized and clustered on a daily basis. Among them, a total of 10 days of data belong to cluster I (24 × 10), 16 days of data belong to cluster II (24 × 16), and 5 days of data belong to cluster III (24 × 5).

The benchmark curve of each cluster is shown in Figure 5. Known from the curve, the average curve output of cluster III is higher, showing bimodal characteristics in the late night and daytime. The average curve output of cluster I is in the middle, showing high characteristics in the middle of the night. The average curve output of cluster II is lower, and it is high in the middle of the night. It can be seen that the unsupervised learning clustering ability of K-means can better extract the characteristics of various curves and automatically classify them accordingly.

At the same time, according to the divided clusters, the state transition probability matrix of random jump between different clusters is obtained month by month. The state transition probability matrix focuses on the analysis of the probability of transition between different clusters on two adjacent natural days, supporting the random generation of subsequent monthly and annual data.

Taking March as an example, the state transition probability matrix at K = 3 and the transition probability between states are shown in Figure 6. When the current state is in cluster I, the probability of remaining in cluster I state in the next step is 0.5, the probability of the next jump to the cluster II state is 0.063, the probability of jumping to cluster III state in the next step is 0.438. The rest may be deduced by analogy.

Furthermore, in the generation of 24-point daily random curves, the improved MC method considering time correlation can solve the problem that the wind power jumps between adjacent time points in the 24-point daily curve randomly generated by each cluster. Taking cluster I as an example, the 24-point random generation curve based on cluster I is shown in Figure 7. The red solid line is the benchmark curve of cluster I, with other curves randomly generated from it. Each random curve follows a similar trend as the red one, displaying the characteristics of high output in the morning and low output in the evening.

According to the state transition diagram shown in Figure 6, N times of Monte Carlo sampling are carried out month by month, and then spliced into N annual 8760 h random output curves. In addition, due to the randomness of various parameters of the generated random curve, the program can filter out the scenarios where the utilization hours exceed the limited range by using the annual utilization hours checking module.

Figure 8 shows an example of annual random curve generation. Based on the historical wind power output data of a certain year in a central and eastern province, the maximum output coefficient of the randomly generated curve appears in August–September, which is consistent with the historical curve. The random utilization hours are close to the historical curve, with a fluctuation range of about 5%.

4.2.2. Supply–Demand Balance Analysis under Normal Conditions

Although the power generation capacity of the power supply side is constantly improving, power shortages on the demand side persist due to ongoing grid construction and steadily increasing power loads, especially during the evening peak hours in summer and winter. To maintain generality, this paper adopts the level year load data of Qinghai Province, China, and randomly selects 10 wind power output curves from N curves and inputs them into the production simulation platform to obtain 10 sets of corresponding provincial power surplus curves. For probabilistic analysis, the power shortage situation of 10 groups of power surplus curves is counted for any time, and the differentiation conversion is carried out to obtain the curve reflecting the probabilistic power shortage situation. For example, at a certain moment, six of the 10 groups of the province’s 8760 power surplus curve show a lack of electricity, and four groups of curves do not lack electricity, which indicates that the probability of shortcomings at this moment is 60%.

According to this idea, the probability statistics of 8760 h of power shortage can be obtained as follows.

Figure 9 shows the probability statistics of the probability of power shortage and the number of power shortage hours based on the actual surplus. From the perspective of loss of load probability (LOLP), throughout the year, there are 28 h with a 100% probability of power shortage, 225 h with a probability of power shortage exceeding 50%, 136 h with a probability ranging from 20% to 50%, 66 h with a 20% probability, and 84 h with a 10% probability of power shortage. From the perspective of the expected annual power shortage hours and expected power shortage, the annual power shortage hours of 539 h, multiplied by the corresponding power shortage probability, the annual probability of power shortage hours is about 276 h.

Figure 10 shows the probability statistics of the probability of power shortage and the number of power shortage hours based on the surplus in the region. From the perspective of loss of load probability (LOLP), throughout the year, there are 163 h with a 100% probability of power shortage, 256 h with a probability of power shortage exceeding 50%, 151 h with a probability ranging from 20% to 50%, 68 h with a 20% probability, and 90 h with a 10% probability of power shortage. From the perspective of the expected annual power shortage hours and expected power shortage, the annual power shortage hours of 728 h, multiplied by the corresponding power shortage probability, the annual probability of power shortage hours is about 445 h.

Due to the effect of external power such as cross-regional transmission, the power shortage under the actual surplus of the province is greatly alleviated compared with the surplus in the region.

4.3. Scene Screening and Supply–Demand Balance Analysis under Extreme Conditions

4.3.1. Extreme Scene Screening

The meteorological 8760 data of the corresponding historical year in the province are substituted into the scene screening sub-module considering the extreme factor. The result show that among the N scenarios randomly generated, there are two extremely hot and windless scenarios. (72 h of continuous atmospheric temperature higher than 26 degrees Celsius and wind power output lower than 0.06).

The extremely hot and windless situation shown in Figure 11 appears in the 7717th of the 10,000 scenarios generated by the Monte Carlo method. The maximum value of the wind power output coefficient in the continuous 72 h from July 24 to July 27 of the scenario is 0.053. As can be seen from Figure 11, the wind power output coefficient in this extreme scenario is lower than the wind power guarantee output coefficient (0.06) for 72 h, which may cause greater pressure on the supply guarantee of the province.

4.3.2. Supply–Demand Balance Analysis under Extreme Conditions

The selected extremely hot and windless scenes are input into the production simulation platform. In the results of supply and demand balance analysis in extreme scenarios, the number of power shortage hours reaches 524 h, the maximum power gap reaches 11,220 MW, and the energy shortage reaches 1,825,550 MWh.

Figure 12 shows the power supply situation under extreme scenarios. When the extremely hot and wind-free scenario occurs for several consecutive days, the power supply is seriously insufficient, resulting in greater pressure on the supply guarantee. In addition, combined with the simulation results of production, the utilization rate of renewable energy is 98.7% in this extreme scenario. It can be seen that extreme scenarios will bring double pressure on power system supply and renewable energy accommodation.

5. Conclusions and Discussion

In the context of the increasing proportion of wind power, low wind power events caused by extremely hot and windless weather bring great pressure on the balance of supply and demand to the power system [53]. However, the traditional wind power scenario generation methods mainly focus on the generation of conventional wind power scenarios, which are applied to economic dispatch, stochastic programming and other occasions [54]. Therefore, this paper proposes a wind power stochastic and extreme scenario generation method considering wind power–temperature correlations and carries out probabilistic supply–demand balance analysis based on it. The method can make up for the deficiency of low wind power extreme scenario generation considering meteorological factors in previous studies, and effectively evaluate the risk of low wind power events to the supply and demand balance of power system. The conclusions are summarized as follows:

(1)

The wind power random scene generation method considering wind power–temperature correlation and extreme scenes can generate a large number of random scenes representing wind power characteristics under the condition of limited historical data and can provide sample data for low-probability extreme scene analysis.

(2)

The probabilistic supply and demand balance analysis and risk assessment are carried out, which provides a new method for the supply and demand analysis of the new power system and obtains more accurate analysis results.

However, it must be pointed out that this study still has some limitations. Due to the obvious periodic characteristics of photovoltaic and load output coefficients, the method proposed in this paper is not suitable for the generation of photovoltaic and load random scenarios. In addition, the method in this paper mainly considers the generation of random curves based on the historical characteristics of wind power output and does not consider the coupling effect of renewable energy and load curves under extreme hot and windless meteorological conditions. In the future work, the source–load–meteorology correlation can be considered, and the supply and demand balance analysis of extreme scenarios considering source–load–meteorology can be studied in combination with the generation of typical daily random curves.