1. Introduction
Since the Industrial Revolution, while society has developed rapidly, humans have developed and utilized conventional fossil energy sources on a large scale. Facing the multiple pressures of energy depletion, environmental pollution, and climate deterioration, it is urgent to vigorously develop renewable energy and achieve an energy structural transformation [
1,
2]. Renewable energy sources, represented by wind power and photovoltaic power generation, boast abundant reserves, low development costs, and pollution-free characteristics. Compared to traditional energy sources, renewable energy is the optimal choice from both ecological and resource perspectives, gradually becoming the preferred option for sustainable human energy development [
3]. With large-scale and high-percentage integration of new energy into the power grid, controllable power sources such as thermal power plants need to frequently adjust their output and, when necessary, start or stop operations to track peak and off-peak load changes. Currently, thermal power units generally suffer from insufficient peak shaving depth and lack of initiative in peak shaving. When the operating state of a thermal power unit deviates from its rated operating condition, the power generation efficiency decreases with the reduction in load rate, leading to decreased operational economy [
4].
In formulating dispatch decisions for high-penetration renewable energy power systems, the uncertainty associated with renewable energy output scenarios often leads to conservative decision-making and increased economic investments. Scenario reduction methods serve as an effective tool for characterizing this uncertainty. In recent years, substantial research has been conducted by scholars both domestically and internationally on the generation of typical wind/photovoltaic (PV) scenarios in power systems [
5]. Among them, scenario analysis enables the analysis of renewable energy uncertainty based on potential wind/PV output scenario datasets. By selecting reasonable typical renewable energy output scenarios, it characterizes the stochastic nature of the regional renewable energy output, thereby mitigating the negative impacts of uncertainty [
6,
7] and providing a decision-making basis for grid dispatch planning and other related tasks. Existing methods for generating typical scenarios mainly encompass probability modeling, deep learning, and clustering-based scenario generation. Probability modeling primarily utilizes statistical methods in conjunction with sampling techniques such as Monte Carlo for joint density modeling, generating typical wind and PV output or load scenarios. Reference [
8] employs Gaussian kernel functions to generate probability density functions for wind and PV output at each time interval, combined with Copula theory to construct typical wind–solar output scenarios. Reference [
9] assumes that the renewable energy output and load forecast errors approximately follow normal distributions, simulating prediction error scenarios through Markov chain multi-scenario approaches. Reference [
10] describes regional wind speeds based on the Weibull distribution and probabilistically models light intensity using the Beta distribution. Reference [
11] integrates quantile regression theory with Gaussian distribution theory, leveraging the concept of the Cartesian product to construct a statistical scenario set for renewable energy. Reference [
12] predicts wind speeds using an autoregressive integrated moving average model and combines Latin Hypercube Sampling to generate future wind power output scenarios. Reference [
13] performs probability modeling of wind power, electricity, and heat demand using Monte Carlo simulation methods, conducting uncertainty analysis based on scenario methods. Reference [
14] proposes a method for acquiring wind speed scenarios based on C-vine Copula theory, which significantly increases the number of modeled random variables due to its consideration of spatio-temporal tail dependence structures.
To efficiently solve planning and operation models, many scholars have adopted clustering analysis to reduce scenarios. This involves classifying scenarios based on their original characteristics to decrease the number of scenarios, thereby enhancing solution efficiency. Considering the uncertainty of distributed generation in distribution networks, Reference [
15] constructs a multivariate time-series dataset based on wind, solar, and load power levels and employs clustering based on correlation features to obtain typical scenarios and their corresponding weights. In the field of typical scenario generation, traditional methods such as K-means clustering [
16], the Analytic Hierarchy Process, and Fuzzy C-Means clustering [
17] have matured. Among them, K-means clustering is widely used due to its good clustering performance and high computational efficiency. Reference [
18] applies multi-scenario analysis and K-means clustering to address distributed generation uncertainty; Reference [
19] generates typical scenarios to describe distributed generation uncertainty through an improved bi-level clustering method; Reference [
20] proposes a bi-level clustering algorithm that considers both micro- and macro-grid structures to achieve the similarity analysis of distribution network structures; Reference [
21] employs a multi-scenario analysis method based on improved FCM clustering to describe the uncertainty of wind and solar power output for solving distribution network reconfiguration problems; Reference [
22] adopts a multi-scenario analysis method based on K-means clustering to describe the uncertainty of wind and solar power output. However, the above clustering methods rely heavily on the selection of initial clustering centers, which is subject to subjective factors, and the improper selection of initial clustering centers can increase the error in clustering results. Reference [
23] utilizes the Density-based Spatial Clustering of Applications with Noise algorithm, which is a density-based clustering method. By processing the electricity consumption behaviors of different users, it can efficiently analyze large-scale user behaviors. Nevertheless, this method also depends on the initial parameter settings.
On the other hand, energy storage systems, due to their charging and discharging characteristics, can maintain real-time power balance and are therefore widely deployed in power systems. Addressing the issue of energy storage deployment in power grids, Reference [
24] analyzes the impact of distributed generation integration into distribution networks on power quality and protective device operations, proposing an adaptive current protection method by altering wiring configurations, albeit with a relatively long computation time. References [
25,
26,
27] consider and analyze the optimal deployment of multiple or various types of distributed generations into the grid, establishing a series of mathematical models. By applying data-mining algorithms, they develop optimized dispatch schemes and verify their accuracy. Reference [
28] establishes a grid dispatch model incorporating distributed generations, calculating the differences in costs between distributed generations and market electricity prices. Through a specific case study, it investigates the influence of distributed generations on network losses and marginal node prices within the power system. Reference [
29] presents an optimization method for the power and capacity of energy storage devices utilizing a hierarchical control approach. By analyzing various control methods, it identifies the optimal rated power and capacity of energy storage devices that minimize output errors and total costs. Reference [
30] introduces a capacity optimization method for energy storage devices that considers the load demand and state-of-charge (SOC) partitioning. It translates different operating ranges into impacts on the energy storage device lifespan and wind curtailment, which are further converted into economic implications. An improved particle swarm optimization algorithm is employed to optimize and obtain the results. However, current research has yet to consider the configuration model when wind power, photovoltaic generation, and energy storage are jointly integrated into a distribution network within a specific region. Currently, some researchers are also embarking on studies of more efficient and environmentally friendly new transportation modes from the perspectives of engine performance and fuel properties. This, to a certain extent, has promoted the popularization and consumption of new energy sources, reduced greenhouse gas emissions, and is of great environmental protection value [
31,
32,
33,
34,
35,
36,
37,
38,
39].
The innovative points of this paper can be summarized as follows:
- (1)
This paper proposes a GAN-based scenario analysis method and scenario reduction technique to model and optimize the uncertainties associated with renewable energy generation. By selecting typical scenarios, the complexity of the problem is reduced, providing a solid foundation for the construction of the optimization model.
- (2)
This paper constructs a flexible cloud energy storage scheduling model that leverages the widely available small-capacity energy storage units within the system. This model employs flexible scheduling strategies to assist in renewable energy consumption, enhancing the flexibility and reliability of the energy system.
2. Method for Characterizing the Uncertainty of Renewable Energy Output Based on Multi-Scenario Analysis
2.1. Modeling Uncertainty in Renewable Energy
- (1)
Probability Model of Wind Power Generation
Wind turbines installed at the user side are typically small-capacity units. The output power of these turbines varies according to changes in wind speed, exhibiting characteristics such as random fluctuations. As a result, modeling the probability of wind turbine output can essentially be transformed into modeling the probability of wind speed. Typically, the two-parameter Weibull distribution is employed to model the probability distribution of wind speed, with its probability density function expressed as shown in Equation (1):
In the equation, v represents the wind speed, is the shape parameter, and is the scale parameter. Meanwhile, and , respectively, represent the standard deviation and mean of the wind speed.
The corresponding mathematical model for the active power output of the wind turbine is shown in Equation (2). In this paper, a constant power factor model is adopted to model the wind power output, with its reactive power output expressed as shown in Equation (3):
Here, represents the active power output of the wind turbine; and , respectively, represent the rated power and rated wind speed of the wind turbine; and , respectively, represent the cut-in wind speed and cut-out wind speed; and are constants; represents the power factor of the wind turbine.
- (2)
Probability Model of Photovoltaic Power Generation
Numerous studies have shown that the irradiance over a certain period of time can be represented by a Beta distribution, as shown in Equation (4):
Here, represents the gamma function; represents the maximum irradiance (W/m²); and are the shape parameters of the Beta distribution, which can be calculated based on the mean and variance of the irradiance over a certain period of time.
As the irradiance increases, the output power of the photovoltaic power generation equipment gradually increases until it reaches the rated power
. The active power output of the photovoltaic system
can be expressed by Equation (5):
where
represents the rated value of irradiance.
2.2. Introduction to Scenario Generation Method
In this paper, a Generative Adversarial Network (GAN) is employed to construct a scenario set for renewable energy output. A GAN is an unsupervised neural network that continuously fits a model by training on real datasets, implicitly learning the intrinsic probability distribution of the data. Its basic structure comprises a generator and a discriminator, as shown in
Figure 1. GANs are widely used in generating large amounts of similar data and improving data quality, even when the quality of the original data is not high. They have been applied to solve problems such as generating power data samples for new energy scenario generation and unit fault diagnosis. In the operation of power systems, the advantages of using GANs to generate typical operating scenarios are primarily embodied in the following aspects: GANs are capable of automatically learning the complex data distributions within power systems, such as the power output characteristics of renewable energy sources like wind and solar, which are often characterized by high levels of uncertainty and volatility. Through the generator of GANs, it is possible to simulate operating scenarios that closely resemble real-world conditions, providing robust support for power system planning and dispatch. The samples generated by GANs possess high fidelity, enabling the creation of diverse and typical operating scenarios. These scenarios can encompass the various operational states of power systems under different conditions, facilitating the assessment of power system stability and reliability. In contrast to traditional scenario generation methods that may require vast amounts of historical data and complex computational processes, GANs, through their adversarial training mechanism, can generate a large number of high-quality scenarios in a relatively short time. This significantly enhances the efficiency of scenario generation and reduces computational costs. Furthermore, GAN models exhibit high flexibility, allowing for customization and optimization according to different requirements and application scenarios. For instance, they can be trained to generate operating scenarios that are more tailored to the specific characteristics of power systems in particular regions.
In
Figure 1, the generator G is used to capture the data distribution, while the discriminator D is used to determine the probability that a generated sample comes from the real data. The two models are trained simultaneously. The training objective of the generator G is to deceive the discriminator D with generated data, maximizing the probability of the discriminator D making a mistake. The loss functions of the generator and discriminator can be calculated according to the following equations:
Here,
E(·) represents the expectation function;
G(·) and
D(·) are the functions of the generator and discriminator, respectively;
pz(
z) and
pdata(
x) are the distributions of the input noise
z and the sample input
x, respectively.
V(D,G) is a binary cross-entropy function. The ultimate goal of (8) is to minimize the Jensen–Shannon distance between the probability distribution of the generated samples and the real data distribution.
In the space of any functions G and D, the unique solution that allows G to reproduce the distribution of the training data is when D = 0.5. Throughout the training process, no Markov chain or unfolded approximate inference network is required. Additionally, when the generator G and discriminator D are composed of multi-layer perceptions, the entire system can be trained using backpropagation.
2.3. Typical Scenario Screening Method
In
Section 2.2, the strategy for generating renewable energy output scenarios was introduced. However, while a large number of scenarios can accurately characterize the uncertainty of renewable energy output, they also increase the computational complexity of the model. Therefore, this section focuses on screening typical scenarios through a selection strategy. This approach not only accurately captures the uncertainty of renewable energy but also significantly reduces the computational complexity. Current methods for screening typical scenarios include the intra-period mean method, intra-period typical day method, backward reduction method, etc. In this paper, we primarily adopt the Clustering by Fast Search and Find of Density Peaks clustering method.
Density-based clustering methods classify data based on data density. Compared to partition-based clustering algorithms, density-based clustering algorithms can identify data with arbitrary distributions. The Fast Search and Find of Density Peaks clustering method focuses on selecting cluster centers. The cluster centers are chosen based on the principles of “having a high density and being surrounded by points with lower densities” and “being far away from other high-density points.” Points with a high product of local density and relative distance are selected as initial cluster centers.
This algorithm defines two parameters for each sample: the local density of the sample
and the distance to points with higher density than the sample point
. A cutoff distance
is selected as a hyperparameter input into the system. The local density
can be approximately viewed as the number of sample points within a distance less than the cutoff distance
from sample point
i. There are two forms of calculating local density: Gaussian kernel and cutoff kernel. To make it less likely for data points with the same density to be clustered together, this paper selects the Gaussian kernel to determine the cutoff distance. The local densities
are then arranged in descending order. The calculation formulas are shown in Equations (9)–(12). Among them, the formula for the cutoff kernel is given in Equation (9):
Here,
represents the Euclidean distance between data points
xi and
xj.
is a constant. The operational meaning of the function
is given in Equation (10):
The formula for the Gaussian kernel calculation is given in Equation (11):
Given that the algorithm is more sensitive to local density, it sets that only points with
and
relatively large distances to their neighboring points are considered as cluster centers. In other words, a sample can be regarded as a cluster center when both its local density and the distance to points with a higher density are relatively large, while the remaining sample points are considered as non-cluster centers. To adaptively determine the number of cluster centers, this paper selects a comprehensive consideration of the product parameter of
and
, as shown in Equation (12):
Then, the initial cluster centers and the number of clusters are determined through a clustering decision graph. This graph sorts the data in descending order of , and the data points with relatively high values of are selected as cluster centers by observation.
After the cluster centers are determined, the remaining sample points are assigned to the cluster of the sample with a higher local density and the closest distance to it. The cutoff distance
represents the neighborhood radius, and the number of samples within the cutoff distance indicates the local density. The Fast Search and Find of Density Peaks clustering algorithm has a simple structure and requires fewer parameters. By selecting cluster centers through the clustering decision graph, it can overcome the shortcomings of the subjective selection of cluster centers in clustering algorithms such as K-means and Density-based Spatial Clustering of Applications with Noise. However, the selection of cluster centers relies on the local density
and relative distance
, and these two parameters depend on the distances
between data points. When the dataset is large, the computational complexity grows exponentially with the number of samples. In summary, the steps of the Fast Search and Find of Density Peaks algorithm are shown in
Table 1.
2.4. Evaluation Index
In the field of typical scenario generation for power systems, unsupervised learning methods are often employed for clustering due to the absence of class information or prior knowledge in the input scenario samples. To further validate the scientific selection of typical output scenarios and the effectiveness of the proposed improvement methods, the Davies–Bouldin index (DBI) and the Calinski–Harabasz index (CHI), which are commonly used evaluation metrics for clustering performance, are utilized to comprehensively assess the clustering results.
The DBI index quantifies the similarity between different clusters by measuring the Euclidean distance between clusters and the size of the clusters themselves. A larger cluster size combined with a smaller distance between clusters indicates a higher similarity between the two clusters. Conversely, a smaller cluster size with a larger distance between clusters suggests a lower similarity. A lower DBI value indicates a better clustering performance. The corresponding formula is expressed as follows:
In the formula, IDBI represents the calculated Davies–Bouldin index; K is the number of clusters in the clustering; is the similarity between the cluster center of the w-th cluster and the cluster center of the q-th cluster; corresponds to the diameter of the w-th cluster, which is the average distance between each sample within the cluster and the corresponding cluster center; and is the inter-cluster distance, representing the Euclidean distance between the cluster centers of the w-th and q-th clusters.
Similar to the DBI index, the CHI is also a common parameter used to measure the effectiveness of clustering. The CHI index relies on the between-cluster and within-cluster dispersion matrices to characterize the degree of separation between clusters and the degree of cohesion within clusters, respectively. The ratio between these two quantities is used to represent the clustering quality. A higher value of the CHI index indicates that the distances between clusters are larger, resulting in a higher dissimilarity between different clusters, while the distances within clusters are smaller, indicating a higher similarity within the same cluster. The specific expression is as follows:
Here, n represents the number of input samples; represents the distance between the various clusters in the clustering result; represents the intra-cluster distance within each cluster in the clustering result; represents the average Euclidean distance between all samples in the input sample set; is the average Euclidean distance between the samples within the j-th cluster.
3. Scheduling Strategy for Renewable Energy Based on a Cloud Energy Storage Model
3.1. Concept and Working Mechanism of Cloud Energy Storage
Cloud Energy Storage (CES) represents a new form of shared service based on existing, established energy storage devices. It aggregates decentralized energy storage resources and enables their sharing through the cloud, leveraging internet technology. The cloud-based energy storage capacity is primarily provided by large-scale energy storage facilities, supplemented by distributed energy storage devices, allowing users to access storage resources anytime, on demand, without the additional costs of installing and maintaining their own energy storage equipment. Users interact with CES capacity similarly to physical energy storage devices, controlling charging and discharging according to their needs. This eliminates the burden of managing and maintaining energy storage infrastructure. CES service providers aggregate these dispersed storage devices, managing them centrally for maintenance, operation, and scheduling. By leveraging shared resources, they achieve economies of scale, improving the utilization of idle resources and reducing overall costs.
Given that users’ energy consumption patterns vary both within and between days, there is inherent complementarity in their storage needs. CES enables meeting these needs with minimal investment in storage equipment. The entities offering CES services are known as CES service providers. They set prices for cloud storage capacity and energy usage, and users purchase the right to use CES devices based on their storage needs. Information and financial transactions flow bidirectionally between CES providers and users through communication and financial systems, with energy exchanges occurring over the power grid. When the distributed renewable energy output cannot meet charging demands, users can purchase electricity from the grid at real-time prices to charge CES devices. If users utilize their own renewable energy for charging, no charging fees apply. Discharging from CES devices is also free. When users have surplus renewable energy and their net load is negative, they can sell electricity back to the grid, earning repurchase revenue. As a third-party platform, CES providers connect with both the grid and users, collecting critical information such as user loads, grid prices, and storage system configurations. Through comprehensive analysis and optimization, they provide users with optimal charging and discharging plans for cloud batteries. The typical working mechanism of CES is illustrated in the diagram below. As shown in
Figure 2 below, this model benefits both users, who save on electricity costs, and grid companies, which can generate additional revenue. The peak-to-valley difference in power system loads, a crucial indicator for studying peak shaving measures and energy conservation, can be mitigated by harnessing the dynamic response capabilities of energy storage systems. By reducing this difference, CES systems significantly enhance grid efficiency and offer substantial application value.
3.2. Optimal Dispatching Model for Renewable Energy with the Participation of Cloud Energy Storage
Without energy storage, the power
that user
i needs to obtain from the grid during time period
t is as follows:
The power that user
i still has left after meeting its own load during period
t and sends back to the grid is as follows:
In Equations (20) and (21), represents the load of user i during period t, and represents the renewable energy power generated by user i during period t.
The rules for the functions
and
are defined as follows:
By weighing the relationship among electricity price, load, and renewable energy output, the charging and discharging strategy for user
i during period
t is formulated as follows: Charge when the electricity price α
t is lower than the critical charging price threshold
or when the renewable energy output
exceeds the load
; discharge when the electricity price α
t is higher than the critical discharging price threshold
and the renewable energy output
is less than the load
, as shown in Equations (24)–(26):
Here, and are the charging and discharging power of user i’s energy storage device during period t, respectively. is the maximum energy storage capacity of user i. and are the maximum and minimum energy levels, respectively, of user i’s energy storage device. and are the charging and discharging efficiencies of user i’s energy storage device, respectively. ΔT represents the unit time interval.
As can be seen from the above equations, the user’s charging power is composed of two parts: when the electricity price is low, the grid power is used to charge the cloud-based battery; and when there is excess renewable energy output, it is used to charge the cloud-based battery. It is stipulated that renewable energy generation first satisfies the user’s load, and any excess renewable energy output is then used to charge the cloud-based battery. If the charging demand cannot be met solely by renewable energy, the grid power will be used.
The charging and discharging demands generated by the user are responded to and executed by the cloud-based energy storage service provider. When the user uses grid power to charge the cloud-based energy storage device, there will be an electricity charge incurred, which is collected by the cloud-based energy storage service provider and ultimately settled with the grid. When the user discharges from the cloud-based energy storage device, there is no cost incurred. If the user still has excess renewable energy power after satisfying their own load and the charging demand of the cloud-based energy storage device, they can feed this excess power back to the grid, and the grid will pay a certain amount of repurchase electricity fee. This fee is also first collected by the cloud-based service provider and ultimately settled with the user. Without considering the service fees paid by the user for the cloud-based energy storage device, the electricity purchase cost of user
i from the grid during period
t is as follows:
In summary, the renewable energy consumption and user electricity purchase model based on cloud-based energy storage services can be described by the following Equations (28)–(33):
The primary focus of this paper is on scheduling strategies, rather than planning strategies. For power system operators, the investment costs associated with renewable energy construction are primarily considered during the planning stage. In other words, in the discussion of power system scheduling in this paper, more emphasis is placed on technical feasibility, system stability, or environmental benefits, while economic feasibility is implicitly assumed or taken as given background information.