Method for Wind–Solar–Load Extreme Scenario Generation Based on an Improved InfoGAN

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This article developed an improved InfoGAN wind–solar–load extreme scenario generation approach that can inform power system evaluation in extreme scenarios.

Abstract

In recent years, extreme events have frequently occurred, and the extreme uncertainty of the source-demand side of high-ratio renewable energy systems poses a great challenge to the safe operation of power systems. Accurately generating extreme scenarios related to the source-demand side under a high percentage of new power systems is vital for the safe operation of power systems and the assessment of their reliability. However, at this stage, methods for extreme scenario generation that fully consider the correlation between wind power, solar power, and load are lacking. To address these problems, this paper proposes a method for extreme scenario generation based on information-maximizing generative adversarial networks (InfoGANs) for high-proportion renewable power systems. The example analysis shows that the method for extreme scenario generation proposed in this paper can fully explore the correlation between historical wind–solar–load data, greatly improve the accuracy with which extreme scenarios are generated, and provide effective theories and methodologies for the safe operation of a new type of power system.

1. Introduction

To achieve the dual-carbon goal, China is actively developing a new type of power system with a high proportion of renewable energy access [1]. However, with the large-scale use of renewable energy sources, mainly wind power and solar power, the intermittency and volatility of the power output affect the reliability and stability of power system operation, resulting in great challenges in the optimal scheduling of power systems [2]. On the demand side, with the rapid growth of flexible loads, such as electric vehicles, the uncertainty of the load profile of a power system is also increasing [3]. To address the source-demand uncertainty in a power system, the scenario generation method, which is a type of uncertainty modeling method used to generate wind–solar–demand power profiles by using historical wind–solar–load data and referring to various related factors, such as weather and data, has gained substantial attention [4].

In recent years, with the increasing severity of the El Niño phenomenon, extreme weather has frequently occurred. Under extreme weather conditions, wind–solar are often characterized by long-term low output or unpredictable fluctuations in power output [5]. On the one hand, long-term low renewable energy output makes it difficult to guarantee the reliability with which a power system will supply power to uncertain loads. On the other hand, power systems face serious consumption problems when the renewable energy output remains high for a long period [6]. Therefore, in power system operations, both typical and extreme scenarios need to be considered. Therefore, a method for extreme scenario generation is needed to explore in depth the characteristics of different extreme scenarios, such as wind–solar–load, and to provide extreme scenario boundary conditions for power system operations [7].

Currently, domestic and international research on scenario generation for renewable energy can be divided into two main categories: scenario generation methods based on probabilistic statistical features and data-driven scenario generation methods [8,9].

Statistical feature-based scenario generation methods require prior assumptions about the probability distribution of renewable energy output and relevant model parameters from historical data [10]. Reference [11] assumes that the wind speed follows a Weber distribution and that the solar intensity follows a Beta distribution, and it builds the wind-scenery output on the basis of these distributions. A copula function is used to capture the spatial correlation between wind farms, and Monte Carlo sampling is used to generate wind power scenarios [12]. These methods, although simple and easy to handle, suffer from major shortcomings in terms of accuracy. The method assumes that the statistical distribution is based on historical data; however, because of geographical location and time differences, wind power and solar power may not align with the assumed distribution. If assumptions from the distribution of sampling are used to generate scenarios, the calculated results will seriously deviate from the actual value, affecting the power system to make the right decision.

Methods for data-driven scenario generation are based on data [13]. With the development of artificial intelligence technology, this type of method has begun to receive widespread attention. This kind of method mainly generates scenarios by feature extraction from historical data via neural network training; this approach does not need the distribution type to be formulated in advance but adopts an unsupervised learning approach to learn the relevant features of the data itself [14]. Among them, generative adversarial networks are increasingly used in scenario generation. Reference [15] was the first to apply Generative Adversarial Networks (GANs) to the scenario generation of wind–solar power output, while Reference [16] introduced a GAN loss function based on Wasserstein distance and incorporated a gradient penalty term (Wasserstein Generative Adversarial Networks, WGAN-GP), thereby enhancing the stability of GAN model training and the quality of generated outputs. These GAN-based methods effectively capture the stochastic characteristics of renewable energy; however, due to the use of random noise as input, the types of generated scenarios exhibit randomness and unpredictability, making them difficult to control.

To address this issue, Conditional Generative Adversarial Networks (CGANs) incorporate additional label information into the inputs of both the generator and the discriminator, thus guiding the scenario generation process. References [17,18] utilized renewable energy scenario prediction data as label information to develop a CGAN-based short-term scenario generation model for renewable energy. Although the conditional information within the CGAN model can guide scenario generation to some extent, the reliance on a single type of condition limits the interpretability of the adjustment process, while discretized condition information cannot achieve continuous and smooth control over scenario generation.

Most of the current literature about scenario generation focuses on a single typical scenario of wind and solar loads [19]. Few studies on extreme scenario generation consider the wind–solar–load correlation. On the one hand, in the same region, the wind–solar–load has a certain correlation [20], and the consideration of the wind–solar–load correlation in the process of scenario generation can help improve its accuracy. On the other hand, in the process of power system operation, extreme scenarios often threaten the power supply and consumption of the power system. Studying methods for extreme scenario generation that consider the wind–solar–load correlation to maintain the power supply and consumption of the power system is very important [21].

In summary, this paper mainly focuses on the wind–solar–load extreme scene generation problem and proposes information-maximizing generative adversarial networks (InfoGANs) for extreme scene generation extraction that considers the source–load correlation. First, on the basis of the hierarchical clustering technique, historical wind–solar–load data are evaluated to analyze the joint probability distribution of the historical wind–solar–load output data and the distribution characteristics under different extreme weather conditions and to verify the correlation of the wind–solar–load data. Subsequently, the basis for determining extreme scenarios, such as long-term wind–solar–load output, low output, and abnormal fluctuations considering extreme weather, is proposed. In the InfoGAN algorithm, the extreme scenario set is extracted from the scenario set. The extreme scenarios are used as boundary conditions to simulate the operation of a power system, analyze the operation of the power system under extreme scenarios, and propose risk warning indicators for the power system to protect the power supply and consumption. Finally, the effectiveness of the method proposed in this paper is verified with practical examples.

2. Extreme Scenario Feature Selection for Power Systems

In this section, the characterization of the output level of wind power–solar–demand in power systems under extreme weather conditions is investigated. First, the type of extreme weather studied in this paper is defined. On the basis of the selected weather conditions, the key features required for extreme scenario generation are extracted.

2.1. Extreme Weather Events

In recent years, under the influence of global climate change, extreme weather events have exhibited a trend characterized by “increased frequency, higher occurrence rates, greater severity, and simultaneous occurrences of multiple extreme weather events”. These changes have significantly constrained the stability and reliability of renewable energy generation within power systems due to wind and solar resources and climate risks, thereby threatening the security of power supply [22,23]. Currently, research on extreme scenarios in power systems primarily defines these scenarios based on climate conditions and their associated impacts on production and daily life. For instance, extremely high temperatures and drought conditions pose severe challenges to the power supply assurance of systems heavily reliant on hydropower [24,25], while typhoon conditions lead to a rapid increase in wind power generation, exerting significant pressure on the integration of renewable energy [26].

To further analyze the extreme scenarios faced by power systems in ensuring supply and renewable energy integration, this study introduces extreme meteorological factors as classification criteria [1]. Given that wind and solar power generation are significantly influenced by weather, meteorological conditions, and natural disasters, extreme scenarios such as prolonged high temperatures, extreme cold waves, typhoons, and conditions of no sunlight and no wind are regarded as typical extreme scenarios within power systems due to their broad impact and high occurrence frequency [22,27]. Therefore, this paper classifies extreme scenarios into five categories: prolonged high temperatures, extreme cold waves, typhoons, no sunlight, and no wind. Additionally, based on the “Extreme Low Temperature and Cooling Detection Indicators” released by China [28], we define the specific criteria for extreme scenarios as shown in

Table 1. Definition of extreme scenarios.

Extreme Weather Events	Selection of Features
Long-term high-temperature	Temperature A, duration T1
Extreme cold weather	Temperature B, duration T2
Typhoon weather	Air velocity C, rate of increase in wind turbine power T3
No wind for a long time	Air velocity D, duration T4
Prolonged absence of solar energy	Radiation intensity E, duration T5

.

2.2. Extreme Scene Feature Extraction for Power Systems

In the previous section, extreme weather events are defined. In this section, power system extreme scenarios are analyzed on the basis of the defined extreme weather events, and key features affecting the generation of extreme scenarios are extracted. As shown in Section 2.1, a power system’s wind–solar–load output is affected by various weather conditions, and in this paper, the five types of extreme weather described above are selected. In addition to weather factors, the load power demand is equally affected by time factors. Therefore, the input features are selected for extreme scenario generation, as shown in

Table 2. Hidden influencing factors for the generation of wind–solar–load scenarios.

Hidden Influencing Factors	Categorization
Seasons	Spring
	Summer
	Autumn
	Winter
Date type	Working days
	Nonworking day
Climatic factor	Temperature
	Humidity level
	Pneumatic
	Air velocity
	Dew point
	Solar intensity
	Type of weather

. Among the selected extreme weather events, each extreme scenario affects the wind–solar–load output.

Under extremely hot and windless conditions, wind power is associated with long-term low output, solar power long-term high output, and long-term high load demand. During cold waves and typhoon weather, the wind power output rapidly increases, and PV’s long-term low output and long-term low load demand increase. When extreme weather is considered, the change in the wind–solar–load output is concentrated on the mathematical features of the mean and slope. Therefore, for the classification of extreme scenarios, the extraction of mathematical features related to the wind–solar–load output is needed.

The process of extracting features from the data in this paper is shown in Equations (1)–(4). First, the input features are compressed to the same interval by uniform distribution normalization.

Uniform distribution normalization involves mapping input data to a specified uniform distribution. This process operates by calculating the cumulative distribution function (CDF) of the input data and subsequently mapping the data to the corresponding percentiles of the target distribution. The implementation steps are as follows:

• Calculate the percentiles:

  $$F(x_i)={\displaystyle \frac{rank(x_i)}{n}}$$

  (1)

  where $rank(x_i)$ represents the position of $x_i$ in the dataset after sorting the data in ascending order, and $n$ is the total number of data points.
• Generate a uniform distribution:

Define a uniform distribution U over the interval [0, 1], which will be used to generate values corresponding to the percentiles of the input data in the uniform distribution.

3.

Map the percentile of each data point to the corresponding position in the target uniform distribution using linear mapping.

The means and slopes of these variables are subsequently computed by (3) and (4). Finally, the quantitative data features are weighted. To synthesize the impact of the extreme scenario on the considered wind–solar–load to obtain the scenario’s eigenvalues, the extreme scenario is judged to be a power-protection or consumption-protection scenario.

$$Av{e}_t={\displaystyle \frac{x_t}{{\displaystyle {\sum }_{i=m}^n{x}_t}}}$$

(2)

$$Sl{o}_t={\displaystyle \frac{x_{t-m}-x_{t+n}}{m+n}}$$

(3)

$$S_t={\mu }_{ave,t}Av{e}_t+{\mu }_{slo,t}{B}_t$$

(4)

where, in this context, $Av{e}_t$ represents the mean index of extreme scenarios, describing the power levels of $x_t$, and $x_t$ refers to wind power, photovoltaic output, and load output. $Sl{o}_t$ denotes the slope index of extreme scenarios, indicating the growth trend or decline of xxx under extreme conditions. $S_t$ represents the characteristic value of extreme scenarios, considering both the mean and the growth rate. $m$ and $n$ indicate the start and duration of the extreme scenarios, respectively. ${\mu }_{ave,t}$ and ${\mu }_{slo,t}$ represent the weighted coefficients for the two categories of indicators.

3. Improved Information Maximizing Generative Adversarial Nets Extreme Scene Generation

The core idea of the generative adversarial network (GAN) is the two-player zero-sum game in game theory, and this is a type of unsupervised learning. In the zero-sum game of GAN, the participating parties are composed of a generator and a discriminator, and the accuracy of the model is improved as they both learn the game. The training of the model is considered to be completed when the equilibrium of the game is reached.

The InfoGAN generative network divides the input into two parts: (1) incompressible random noise $z$ and (2) control parameter $c$, which has interpretable features and can control the characteristics of the generated samples. By maximizing the mutual information between control parameter c and generated samples $G(z,c)$ and reducing the loss of coding information in the generating process, the generator is interpretable and practical for control parameter $c$. Finally, the mapping relationship between control parameter c and generating samples $G(z,c)$ and interpretable features is established. The controlled generation of generating samples is achieved by adjusting control parameter $c$.

In the InfoGAN generative network, to reduce the loss of control parameter $c$, the objective function is as follows:

$$\underset{G}{min}\underset{D}{max}{V}_I(D,G)=V(D,G)-\lambda I(c;G(z,c))$$

(5)

$$I(c;G(z,c))=H(c)-H(c|G(z,c))$$

(6)

where $D(\cdot )$ represents the discriminator, while $G(\cdot )$ represents the generator.$\lambda$ denotes the weight of mutual information in the objective function and $I(c;G(z,c))$ denotes the relationship information between $c$ and $G(z,c)$, as indicated by (6). $H(c)$ denotes the information entropy of the control parameter $c$, which represents the quantification of the amount of information contained in the control parameter $c$ and $H(c|G(z,c)$ denotes the information entropy of the control parameter $c$ under the known conditions of the production sample $G(z,c)$.

3.1. Improved InfoGAN Framework

In unsupervised learning, the generation of extreme scenarios for wind power, solar energy, and electricity load involves discrete categories and continuously adjustable interpretable features. By adjusting these interpretable features, the generation process of extreme scenarios can be effectively controlled, thereby enhancing the model’s interpretability and generalizability. The framework of the improved InfoGAN model established in this paper is illustrated in Figure 1.

To enhance the quality of extreme scene generation and improve the stability of model training, this paper integrates a convolutional neural network (CNN) with a generative adversarial network (GAN) to establish a deep convolutional adversarial generative network as the core structure of the improved InfoGAN. The model comprises three main components: the generator (G), the discriminator (D), and the subsidiary network (Q). The generator is composed of fully connected layers, convolutional sampling layers and ConvNextBlock layers. The discriminator includes ConvNextBlock layers, a fully connected layer, and an output layer. Given the high temporal correlation of the input sample data in this study, a symmetric convolutional model structure is employed to preserve rich contextual information. This approach enhances detail recovery through feature fusion, simplifies the end-to-end training process, and improves model flexibility. The framework of the ConvNextBlock layer is illustrated in Figure 2. The time embedding module incorporates time step information into the input data, which, after passing through the convolution module, is added to the output data. This design allows gradients to flow directly through the network, mitigating the vanishing gradient problem.

3.2. The Model Training Process

In this paper, historical power output profiles of wind power, solar, and load, as well as historical extreme weather data, are used as real samples to train the improved InfoGAN network. The proposed InfoGAN model can learn the latent distribution patterns of interpretable features from the data. During model training, a control parameter sequence ($c$) is generated, and by adjusting this sequence, the statistical characteristics of the generated scenarios can be dynamically altered, thus enhancing the model’s flexibility. The training steps are as follows [29]:

(1)

Data preprocessing: the sample data is uniformly normalized according to Equations (1) to (4).

(2)

Generator G training: random noise z is generated, and the initial control parameter sequence c is fed into the generator G.

(3)

Discriminator D training: The generated data and real data are fed into the discriminator D, and the loss function of D is computed.

(4)

Control parameter update: The generated results are input into the subsidiary network Q, where the control parameter (c) is trained. Both the control parameters c and the generator G’s parameters are updated. The detailed training process of the control parameters c will be discussed in the next section.

(5)

Iterative process: this process is repeated until the set number of iterations is reached or the model converges.

By adjusting the control parameter ($c$) during training, the statistical characteristics of the generated scenarios can be effectively controlled, thereby enhancing the model’s flexibility.

3.3. Sequence of Control Parameters

In traditional InfoGAN generative networks, the control parameter c is often assumed to be a discrete sequence obeying a fixed uniform probability distribution, as shown in (7).

$$c ~ S\left(K=k,P={\displaystyle \frac{1}{k}}\right)$$

(7)

where $S$ represents the discrete probability distribution that the control parameter c follows, which is commonly assumed to be a uniform distribution. $k$ denotes the category of the discrete sequence and $P$ denotes the probability of each category.

However, in practical scenarios, the probability of occurrence of each extreme event is not the same, and there are also large differences in the wind, solar, and load output forces under uniform extreme events, which means that each output force does not obey a uniform distribution. In our proposed improved InfoGAN model, the training process of control parameter c is shown in Figure 3.

First, the feature matrix is established on the basis of the selected meteorological feature scenarios and the historical wind, solar, and load output data. On the basis of the eigenmaps, the control parameter c is trained, and finally, a control parameter sequence that can reflect the probability distribution of the wind load under different extreme scenarios is obtained.

3.4. Power System Operation Simulation Model

To verify the effectiveness of the InfoGAN-generated scenario proposed in this paper, the following power system model is established. A power system to preserve power supply and consumption is taken as the objective function, and the level of the power system to preserve power supply and consumption under the scenario is evaluated.

$$\min \hspace{0.33em}F=F_L+F_{\mathrm{Re}}$$

(8)

where $F_L$ is the cost of shedding load; $F_W$ is the curtailment penalty of renewable energy. The specific calculation formulas are as follows:

$$F_L={\lambda }^{load}{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{g=1}^{N_G}\Delta P_{t,j,s}^D}}$$

(9)

$$F_W^S={\lambda }^{RE}{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^{N_{RE}}\Delta P_{t,j,s}^{\mathrm{Re}}}}$$

(10)

Power system constraints are below:

$${\displaystyle \sum _{i=1}^{N_f}{P}_{t,i,s}^G}+{\displaystyle \sum _{i=1}^{N_{\mathrm{Re}}}\left(P_{t,i,s}^{\mathrm{Re}}-\Delta P_{t,j,s}^{\mathrm{Re}}\right)}-{\displaystyle \sum B_{n,m}\left({\delta }_{t,n,s}-{\delta }_{t,m,s}\right)}={\displaystyle \sum _{j=1}^{N_D}\left(P_{t,j,s}^D-\Delta P_{t,j,s}^D\right)}$$

(11)

$$P_{t,i,s}^{W,f}-P_{t,i,s}^W\ge 0$$

(12)

$$-P_{n,m}^{L,\max }\le B_{n,m}\left({\delta }_{t,n,s}-{\delta }_{t,m,s}\right)\le P_{n,m}^{L,\max }$$

(13)

$$-\pi \le {\delta }_{t,n,s}\le \pi$$

(14)

$${\delta }_{t,1,s}=0$$

(15)

$$u_{t,i,s}^G{P}_{i,\min }^G\le P_{t,i,s}^G\le u_{t,i,s}^G{P}_{i,\max }^G$$

(16)

$$P_{t,i,s}^G-P_{t-1,i,s}^G\le \Delta P_{RU,i,\max }^G$$

(17)

$$P_{t-1,i,s}^G-P_{t,i,s}^G\le \Delta P_{RD,i,\max }^G$$

(18)

$$\left\{\begin{array}{c}{U}_{t,i,s}^{on}\ge \left(u_{t,i,s}^G-u_{t-1,i,s}^G\right)\\ U_{t,i,s}^{on}\ge 0\end{array}\right.$$

(19)

$$\left\{\begin{array}{c}{U}_{t,i,s}^{off}\ge \left(u_{t-1,i,s}^G-u_{t,i,s}^G\right)\\ U_{t,i,s}^{off}\ge 0\end{array}\right.$$

(20)

$$\left\{\begin{array}{c}\left(T_{t-1,i,s}^{on}-T_{i,\min }^{on}\right)\left(u_{t-1,i,s}^G-u_{t,i,s}^G\right)\ge 0\\ \left(T_{t-1,i,s}^{off}-T_{i,\min }^{off}\right)\left(u_{t,i,s}^G-u_{t-1,i,s}^G\right)\ge 0\end{array}\right.$$

(21)

Constraint (11) represents the energy balance of the power system. The wind power consumption constraint is depicted in Constraint (12). Constraint (13) imposes restrictions on the transmission line capacity. Constraints (14) and (15) constrain the voltage angle. The power outputs are denoted by Constraint (16), and the ramping up/down of units is governed by Constraints (17)–(19). Constraints (19) and (20) limit the on/off status of the units, while the on/off time constraint is expressed in Constraint (21).

4. Case Study

In this section, a case study is performed to verify the correctness and validity of the model proposed in this paper. The relevant parameter settings are as follows: the wind, solar, and load historical datasets are taken from the publicly available measured data of the Belgian grid, and the meteorological data are provided by the Wunderground website. The dataset includes all historical data from 2018 to 2022, and the time step is set to 15 min; therefore, there are 96 data points in the 24 h daily output/load curve. Eighty percent of the dataset is used as a training set, and the remaining 20% is used as a test set. All the simulations are performed on the Python-based TensorFlow 2.3.0 platform. The computer configuration is an Intel i7-8700 3.20 GHz CPU, 16.0 GB of RAM, and an NVIDIA GTX 1660 GPU.

• Case 1: Traditional probability sampling models [11,12];
• Case 2: Traditional generative adversarial network models [15];
• Case 3: The proposed improved information maximizing generative adversarial network model.

In Case 1, empirical probability distributions are used for sampling, with wind speed following a Weibull distribution, solar intensity following a Beta distribution, and load following a normal distribution [11,12]. The relevant parameters for each distribution are provided in

Table 3. Parameter settings of the distribution.

Categories	Parameter	Value
Wind power	Scale1	4.738
Wind power	Variance β1	2.684
Solar power	Scale α2	0.326
Solar power	Variance β2	1.764
Load	Average μ (MW)	724.3701
Load	Variance σ (MW)	147.3181

.

4.1. Analysis of the Effectiveness of Different Models

To accurately evaluate the performance of the three models in capturing the characteristics of historical wind, solar, and load series data, we introduce extreme scene ensemble validity indexes, focusing on two primary metrics: extreme scene coverage and the average width of power intervals. The formula for calculating the coverage rate is given in (22), while the formula for the validity index is presented in (23).

$$C={\displaystyle \frac{T^{\prime }}{T}}\times 100\%$$

(22)

$$W={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T\left(P_t^{up}-P_t^{down}\right)}$$

(23)

where $T^{\prime }$ is the number of moments when the real scene data is enclosed within the scene set; $T$ denotes the total number of moments in the outgoing force sequence; $C$ is the cover rate, the larger its value, the more reliable the generated set of scenarios; $P_t^{up}$ is an upper bound on the set of scenes generated at time t; $P_t^{down}$ is the lower bound of the set of scenes generated at time t; and $W$ is the average width of the power interval of the generated scene, and the smaller its value, the closer the generated scene data is to reality.

By applying the validity indexes to analyze the generated scenes, the validity indexes for the scene data produced by the three models were obtained through comparative experiments, as shown in

Table 4. Ensemble validity indexes of scenario sets under Cases 1–3.

Categories	Wind Power		Solar Power		Load
	$W$	$C$	$W$	$C$	$W$	$C$
Case 1	8.46	76.14	5.66	85.61	8.69	92.09
Case 2	8.23	78.00	5.79	87.00	8.01	96.31
Case 3	8.11	96.82	5. 28	92.65	6.14	98.82

. This comparison highlights the differences in the models’ ability to fit extreme scene data and their effectiveness in capturing variations in power intervals.

By analyzing

Table 5. Mean of Wasserstein distance of scenario sets under Cases 1–3.

Categories	Wind Power	Solar Power	Load
Case 1	1.643	1.019	1.438
Case 2	1.283	0.924	1.361
Case 3	1.036	0.582	0.914

, it can be observed that the data generated by the proposed improved InfoGAN model in Case 3 for wind power, solar power, and electric load scenarios demonstrate a higher coverage index $C$ compared to the other cases. Additionally, Case 3 exhibits a smaller average width index $W$ of the power intervals than the other models. This comparison shows that the InfoGAN model in Case 3 achieves higher coverage while maintaining a lower average width of power intervals, indicating that the proposed model generates scenario data that more realistically and reliably aligns with real-world conditions.

4.2. Error Analysis of Different Models

To assess the ability of the model described above to fit the historical data, wind, solar, and load data are used. The mean values of the Wasserstein distance measure for generating the set of extreme scenarios are given in

Table 6. Comprehensive error scores of scenario sets under Cases 1–3.

Model	RMSE	MAPE
Case 1	0.9710	7.82
Case 2	0.9176	6.59
Case 3	0.8914	5.17

, with smaller values indicating a higher accuracy of the model in fitting the historical data. The Wasserstein distance measures the difference between two probability distributions by calculating the minimum effort required to transform one into the other. In this model, a smaller Wasserstein distance indicates that the generated extreme scenarios closely resemble the historical data, reflecting a higher model accuracy.

As shown in Table 5, Case 3, which is proposed in this paper, achieves a high accuracy improvement in the generation of wind, solar, and load scenarios. Compared with Case 1, the Wasserstein distance measure of the wind scenario obtained by Case 3 is reduced by 38.7%, that of the solar scenario is reduced by 45.1%, and that of the load scenario is reduced by 40.1%. Among the three scenarios, the model proposed in this paper has the greatest accuracy improvement in the generation of the solar scenario and the smallest accuracy improvement in the generation of the wind scenario. This is because the diurnal nature of solar power is reflected in the highest temporal correlation in the time series features, and the effect of using the improved InfoGAN model to extract data features is more obvious.

Table 6 compares the error values of the test scenarios generated by the three cases, where two error metrics are considered, namely, MAPE (mean absolute percentage error, mean absolute percentage error) and RMSE (root mean square error, root mean square error); the formulae for each of the metrics are shown in Equations (24) and (25).

$$MAPE={\displaystyle \frac{100\%}{\mathrm{n}}}{\displaystyle \sum _{i=1}^n\left|\frac{p_i^{Gen}-p_i^{\mathrm{Re}}}{p_i^{\mathrm{Re}}}\right|}$$

(24)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n(p_i^{Gen}-p_i^{\mathrm{Re}}}{)}^2}$$

(25)

where $p_i^{\mathrm{Re}}$ and $p_i^{Gen}$ denote the real scene power and the generated scene power, respectively.

As shown in Table 6, it can be seen that the method proposed in this paper not only outperforms the traditional probabilistic generation method but also improves substantially over the traditional GAN model in Case 2. This can prove the effectiveness of the proposed model in wind, light, and load scene generation.

4.3. Timing Autocorrelation Analysis

Since the wind, solar power, and load scenarios generated in this paper form a continuous time series process, they exhibit a strong temporal correlation. Therefore, the autocorrelation function (ACF) is employed to capture and describe this temporal dependency. The calculation formula for the ACF is provided in Equation (26):

$$AC{F}_k={\displaystyle \frac{{\displaystyle \sum _{t=1}^{n-k}(X_t-\overline{X}})(X_{t+k}-\overline{X})}{{\displaystyle \sum _{t=1}^n(X_t-\overline{X}}{)}^2}}$$

(26)

where $AC{F}_k$ is the autocorrelation function (ACF); $K$ indicates the number of time intervals; $X\left(t\right)$, $X\left(t+k\right)$ denote the load values at time t and time t + k, respectively. $\overline{P}$ indicates the daily average of load data. The value of $AC{F}_k$ ranges from [−1, 1]; the closer the value is to 1, the higher the positive correlation of the time of the variable force; the closer it is to −1, the higher the negative correlation, and 0 means no correlation

The generated scenarios were analyzed using the autocorrelation function (ACF). The ACF results for the scenario data produced by the three models in the comparative experiments are illustrated in Figure 4, Figure 5 and Figure 6.

As illustrated in Figure 4, Figure 5 and Figure 6, the scenarios generated in Case 3 exhibit trends similar to those of historical scenes, demonstrating the effectiveness of the improved InfoGAN model proposed in this paper. Overall, Case 3 shows a significant advantage over the other two methods in terms of error range and temporal correlation.

4.4. Intercorrelation Analysis

There is a complex coupling relationship between the wind, solar, and load scenario sets. The mutual correlation among these sets must be considered when jointly generating scenarios. Therefore, the Pearson correlation coefficient is used to measure the correlation between wind, solar, and load in the generated scenario sets.

Figure 7, Figure 8 and Figure 9 display scatter plots of historical and generated data for wind and solar loads. The shading of the color represents the probability magnitude of the wind, solar power output, or load values occurring in a given region. The histograms above and to the right of each subplot show the probability distributions for the data corresponding to the horizontal and vertical coordinates, respectively. The correlation between the data can be analyzed through the color shades of the scatter plots and the trends in the probability histograms.

From these figures, it is evident that the wind–solar–load scenario set generated by the proposed model more accurately preserves the inter-correlation and probability distribution of historical data compared to the historical data itself. Comparing the Pearson correlation coefficient values of the generated scenario set and the historical data reveals an error of approximately 10%, indicating that the generated scenarios effectively capture the complex inter-correlation of source and load observed in the historical scenes.

4.5. Analysis of Example Results

To evaluate the performance of the power system under extreme scenarios, simulation tests are conducted with actual data from a power grid in Xinjiang, China, with a simulation duration of one year.

Table 7. Practical simulation analysis of scenario sets.

Extreme Weather Events	LOLP	LOLF	EENS (MW)	REDS
long term high temperature	0.032	11.534	454.790	0.471
Extreme cold weather	0.057	20.951	542.627	0.335
Typhoon weather	0.012	4.566	180.922	0.561
No wind for a long time	0.026	9.307	366.150	0.134
Prolonged absence of solar	0.018	6.636	358.136	0.182

shows the indicators of the power system’s loss of load probability, loss of load frequency, power shortage expectation, and renewable energy discard rate under extreme scenarios.

Loss of load probability:

$$\mathrm{LOLP}={\displaystyle \sum _{L_i\in L}Prob(L_i)}={\displaystyle \raisebox{1ex}{$T_{loss}$}\!\left/ \!\raisebox{-1ex}{$T_{all}$}\right.}$$

(27)

Loss of load frequency:

$$\mathrm{LOLF}={\displaystyle \sum _{L_i\in L}Fre(L_i)}={\displaystyle \raisebox{1ex}{$F_{loss}$}\!\left/ \!\raisebox{-1ex}{$F_{all}$}\right.}$$

(28)

Expectation of power shortage:

$$\mathrm{EENS}={\displaystyle \sum _{F_i\in F}Prob(L_i)\times \left(L_i-R\right)}$$

(29)

Renewable energy discard rate:

$$\mathrm{REDR}={\displaystyle \sum _{P_i\in G_{re}}Fre(P_i)}={\displaystyle \raisebox{1ex}{$P_{dis,i}$}\!\left/ \!\raisebox{-1ex}{$P_{re,i}$}\right.}$$

(30)

where $\mathrm{LOLP}$ represents the loss of load probability, where $T_{loss}$ denotes the loss of load duration and $T_{all}$ is the total simulation time; $\mathrm{LOLF}$ refers to the Loss of Load Frequency, with $F_{loss}$ representing the number of loss of load occurrences and $F_{all}$ the total number of simulation instances. $\mathrm{EENS}$ stands for the Expected Energy Not Supplied, where $L_i$ represents the load and $R$ is the reserve capacity. $\mathrm{REDR}$ indicates the Renewable Energy Dispatch Ratio, where $P_{dis,i}$ is the dispatched renewable energy and $P_{re,i}$ is the total renewable energy capacity.

Table 7 shows that the probability of power system load loss is the highest and that the average annual load loss time is the longest under conditions of prolonged hot weather and extreme cold weather. This is because, under these two extreme weather conditions, the power system load will be at a high level for a long period of time. However, the probability of load loss under long-term hot weather conditions is lower than that under cold weather conditions because long-term high-temperature solar power generation increases to compensate for the energy gap in the power system to a certain extent. However, because the solar system has no output at night, it cannot completely replace conventional power sources. The loss of load probability also increases when there is no wind for a long period and when there is no solar energy for a long period, resulting in a low level of renewable energy for a long period and a lack of energy input to the power system. When typhoon weather occurs, wind power generation increases rapidly, but it is difficult for the power system to absorb this rapid increase in wind power, so the renewable energy discard rate is highest at this time.

5. Conclusions

In this paper, we propose an improved InfoGAN method for the generation of extreme wind–solar–load scenarios in the context of the frequent occurrence of extreme weather events and uncertainty in the rapid growth of source load in a power system. First, the key factors affecting the generation of extreme wind–solar–load scenarios, including season, month, date type, and meteorological factors, are obtained through the feature extraction method. Then, an improved info neural network model is built, and the model control parameters are trained with historical data to capture the complex mathematical relationships between historical data when generating scenarios. Through case testing on the Belgian grid, the following conclusions can be drawn:

The improved InfoGAN wind and load extreme scenario generation method proposed in this paper can significantly reduce the number of errors in scenario production and improve the coverage of extreme scenarios. Compared with traditional statistical methods and GAN neural networks, the proposed method in this paper has a higher accuracy and generates more superior scenarios. Finally, the performance of the power system under extreme scenarios is evaluated from the perspectives of power supply preservation and consumption preservation through the production simulation of real power grids.