A Gramian angular field-based data-driven approach for multiregion and multisource renewable scenario generation

Abstract

Scenario generation is a pivotal method for providing system operators with a reasonable quantity of power scenarios that are capable of reflecting uncertainties and spatiotemporal processes to make exact and effective decisions for power systems. Aiming at improving the forecasting performance of renewable generation and capturing uncertainty as well as dependency over renewable site groups in different regions, this paper proposes a data-driven approach for parallel scenario generation. To capture the complex spatiotemporal dynamics of renewable energy sources (RESs), the proposed approach utilizes Gramian angular field (GAF) to process time sequences and constructs style-based super-resolution models that correspond with the idea of multi-model ensembles. Thereafter, a two-stage stochastic optimization strategy is adopted to accomplish scenario forecasting using point forecasts and historical error information as input. Based on two real-world datasets from the National Renewable Energy Laboratory (NREL) and the Belgian transmission operator ELIA, the effectiveness of the proposed approach is verified by methods including statistical analysis, spatiotemporal correlations, power system scheduling, and out-of-sample evaluations. Compared with three advanced benchmarks, the proposed approach has superior forecasting performance and spatiotemporal dynamic capture capability. At a 24-h lead time, the proposed model achieves continuous ranked probability scores (CRPSs) of 4–14% over the other models with consistent performance during the economic dispatching of actual power system operations.

Introduction

The increasing popularity of renewable energy sources (RESs) is fundamentally changing the operation of conventional power and microgrid systems around the world. However, the intermittency of RESs remains an obstacle to their large-scale integration, as in power systems with high renewable energy penetration, intermittency is partly responsible for variability and uncertainty in renewable energy utilization. Such inherent features force power system operators to change conventional decision-making and risk assessment methods, including unit commitment (UC) [1], economic dispatch (ED) [2], system reserve setting, optimal power flow, and storage sizing. Meanwhile, nonnegligible renewable generation is curtailed due to the limitations of the forecast technique and the internal constraints of the power system. To this end, energy management systems (EMSs) require accounting for the uncertainty of renewable energy and implementing reliable, effective scheduling strategies on these grounds. Recently, many works have concentrated on solving the uncertainty in renewable energy systems from the perspectives of renewable sources, including solar radiation and wind speed, energy management frameworks [3], economic uncertainty [4], and load as well as power generation synergy [5]. However, as a major source of uncertainty, renewable generation forecasting is still one of the main concerns of power system operations.

Generally, point forecasts provided by commercial power companies, whether derived from numerical weather predictions (NWPs) or physical simulations, seem incapable of containing inherently uncertain information. In contrast, probabilistic forecast methods aim to quantify renewable generation uncertainty, which can provide comprehensive and valuable probability distribution information for the operation of power systems.

For renewable generation, probabilistic forecast usually takes the form of probability density function (PDF) and cumulative distribution function (CDF), which can offer additional quantitative information about the uncertainty associated with expectations. For the moment, the construction of probabilistic forecast mainly includes parametric and non-parametric methods. Unfortunately, sometimes unreasonable assumptions of renewable generation distribution will impair the effectiveness of parameterization methods, while non-parametric methods are required to estimate massive densities or quantiles, which may lead to unaffordable computational costs.

As another form of probabilistic forecasting, the prediction interval (PI) is also recognized as a practical form for uncertainty quantification. A PI consists of three specified parts: an upper bound, lower bound and coverage probability. In recent years, a two-output neural network-based estimation method, called lower and upper bound estimation (LUBE) [6], has been used widely to directly perform upper and lower bound estimation of renewable profiles without any assumptions about the distribution. To solve LUBE problems, metaheuristic algorithms such as particle swarm optimization (PSO) [7] and the dragonfly algorithm (DA) [8] have been added to the optimization process in several studies. Considering the complex nonlinear patterns and spatiotemporal connections, Zhou et al. constructed a deep PI model based on a long short-term memory network (LSTM) and introduced a competitive learning mechanism to modify the parameter optimization strategy [9], which greatly improves the accuracy of current PI construction. Regrettably, the inherent form of PIs means that they are unable to contain specific probability information, which may result in overly conservative UC or ED solutions, and this inadequacy cannot be alleviated by model improvement alone.

To describe uncertainties in a productive way, scenarios are introduced as a limited number of renewable time trajectories that represent stochastic features of uncertainty in the future [10], including the intermittency of RESs and multi-value characteristics in the power conversion process, and the scenario generation (SG) method aims to identify and integrate the spatiotemporal correlation among uncertainty information. Compared with other forecasting forms, the set of scenarios can be more flexible when solving stochastic UC and ED optimization problems. Thus, in recent years, researchers have developed numerous renewable SG methods, and the current works are mainly divided into four categories: sampling-based methods, optimization-based methods, forecasting-based methods and other methods [11]. Sampling-based methods directly take the measure of sampling from probability distributions to obtain scenario sets, and typical examples include the Monte Carlo (MC) [12] and Latin Hypercube Sampling (LHS) [13] methods. Given the single state of these two algorithms, [14] further proposed a modeling method based on hybrid vine copula functions to capture the nonlinear and asymmetric relations of stochastic renewable generation processes. Despite the simplicity of the algorithms, sampling-based methods require probabilistic distribution assumptions, such as the Weibull distribution of wind speed and the empirical cumulative distribution function (ECDF) for wind power [15], or probabilistic prediction results, which may deviate from reality. In comparison, the optimization-based approach focuses on reducing the number of scenarios for a given large-scale scenario set. Distance matching [16] and moment matching [17], as two representative technologies, were utilized to reduce the number of scenarios according to statistical characteristics and similar distances, respectively. However, due to the difficulty in capturing extreme scenarios and the involvement of NP-hard problems, the application environment is limited when adopting optimization-based methods. In addition to the aforementioned studies, several other competitive SG methods have been proposed recently, many of which are a fusion of different methods. For instance, Wang et al. combined a copula function and distance matching to effectively express the nonlinear relation of renewable power while reasonably controlling the computational complexity to prevent the dimension explosion problem [18]. Another method proposed in [19] also applied the same principle, which combined LHS and distance matching to obtain renewable scenarios. However, one commonality of the above SG methods is that most of them depend on certain assumptions as well as the law of historical statistics; thus, there is a lack of research on the nonlinear relationship of future generation profiles.

Modern forecasting-based methods, including the autoregressive moving average (ARMA) [20], transfer learning [21], and other machine learning models, are directly driven by historical data without excessive prior knowledge. In recent years, some deep learning-based techniques have been applied to identify the complex patterns of RES generation. In addition to the earlier artificial neural network (ANN) [22] and convolutional neural network (CNN) [23], which have been used to solve some shallow modeling problems, the LSTM autoencoder [24], gated recurrent unit (GRU) [25] and attention mechanism [26] have also been leveraged to capture correct spatiotemporal correlations and make reliable forecasts for wind and photovoltaic (PV) generation. With regard to the recently-developed generative adversarial network (GAN), several simulations and extensions have demonstrated that the GAN exhibits state-of-the-art performance in the field of sequence processing, including anomaly detection [27], missing value imputation [28] and synthetic data generation [29]. In [30], a GAN-based model was first proven to be efficient in the SG domain. Essentially, the GAN can provide highly generalized and expandable hypothesis spaces to implicitly capture the stochastic variation and irregular pattern, which dispenses with any feature extraction or manual annotation processes. Along this line, multiple studies have adopted GAN variants, including the deep convolutional GAN (DCGAN) [30] based on Wasserstein distance, the Bayesian GAN [31] and the multi-agent diverse GAN (MADGAN) [32], to simulate stochastic processes conforming to the characteristics of renewable probability distributions, fluctuations and ramping events, which is expected to improve the overall efficiency of GAN-based SG methods.

Nevertheless, one commonality of the above GAN-based methods is that they lack the ability to generate directed scenarios. That is, due to the random sampling of GAN input noise, the generated scenarios may represent the renewable generation profiles of arbitrary historical data rather than the designated forecast date, which is not suitable for actual day-ahead scheduling. Although the conditional GAN (cGAN) [30] can overcome this defect to some extent by using certain conditional information, the tunable characteristics are still insufficient because of the limited number of conditions. To address this issue, some auxiliary methods have been utilized under given forecast conditions (such as NWP, point forecast and wind speed information), and they are termed scenario forecasting. For the sake of distinction, hereafter, phrase scenario generation is only defined to represent the method that uses the GAN to randomly generate scenarios, while the abbreviation SG denotes an overall process that consists of both scenario generation and scenario forecasting. In this manner, Chen et al. further obtained forecasting scenarios by solving a single-objective optimization problem (DCGAN-SO) [33], [32] performed the same work. Moreover, Qiao et al. made the generation process transparent by building the link between latent space and scenario space (ctrl-GANs) [34]. To direct wind scenarios to possible profiles in the future, Yuan et al. employed a nondominated sorting genetic algorithm (NSGA-III) based on the progressive GAN (ProGAN-MO) to solve multi-objective problems and output day-ahead forecast scenarios [35]. In [36], Zhang et al. established an unsupervised label annotation framework for forecast error and combined it with an improved conditional GAN to realize the mapping from point forecasts to forecast error scenarios. Similarly, [37] integrated the GAN, reinforcement learning and LSTM (SeqGAN-LSTM) to directly predict real dynamics in the future by adopting the corresponding sequence of the previous days as input. To further improve the forecasting quality, [38] refines the latent space to the style-based level and broadens the control scale of renewable styles.

Despite all of the aforementioned progress, several critical issues for GAN-based scenario forecasting methods remain unresolved.

• 1) Despite the attempts made by [34], a low-dimensional manifold form with a high degree of entanglement makes latent variables difficult to control, resulting in inferior quality and low accuracy for forecasted scenarios, which need to be fundamentally changed. The renewable style is an elegant solution but needs further improvement [38].

• 2) Forecasting models such as [30] have difficulties accounting for extreme cases and parsing high-frequency details due to their limited design, and they thus fail to capture the fluctuation of RESs in the case of complex datasets and large regions and often lack generalization and sufficient recognition of spatiotemporal correlation.

• 3) Most SG methods, including [33], [32], rely excessively on point forecasts or prelabeled condition types, and the corresponding scenarios are not always reliable.

To address the above challenges, this paper proposes a data-driven SG approach that accounts for the spatiotemporal dependence of multiple power sites and even multiple renewable sources, as shown in Fig. 1. Specifically, the proposed method reforms the renewable sequence data structure, and Gramian angular field (GAF) transformation [39] is adopted to process renewable sequences, which provides a generalized form of renewable generation data. Referring to the concept of multi-model ensembles, the architecture used for scenario generation is a combination of the style-based GAN [40] with adaptive discriminator augmentation (ADA) [41] and the enhanced super-resolution GAN (ESRGAN) [42]. Then, a generative model called StyleGAN-ADA-ESR is further constructed to generate a stochastic renewable GAF, which describes the random characteristics and uncertainties of RESs. Furthermore, alluding to scenario forecasting, an improved two-stage stochastic optimization (SO) is proposed considering the dependency problem of point forecasting. It is worth noting that the proposed method can perform parallel scenario forecasting under multi-region and multisource conditions, which is still a technical characteristic that is not mentioned in existing studies. The main contributions of this paper can be summarized as follows:

• 1) Advanced representation of renewable data. A GAF-based representation is provided to turn the multisequence problem into a multi-matrix problem. Compared with conventional data integration, the proposed method is proven to be superior in terms of preserving the temporal structure during training and providing support for subsequent models to generate multi-region and multisource scenarios in complex patterns and large-scale datasets.

• 2) Data-driven scenario generation. A novel scenario generation model is designed to capture the nonlinear characteristics and irregular spatiotemporal dynamics of RESs. Compared with existing studies, the proposed model provides outperforming quality for short-term forecasting. Moreover, the style-based control mode replaces the interpretation of conventional low-dimensional manifolds and improves the controllability of renewable scenarios.

• 3) Improved scenario forecasting based on optimization. Considering the distribution of historical point forecast errors, a style-based two-stage optimization model is developed to carry out renewable generation forecasting on a specified date. Compared with existing studies, the experimental results demonstrate the favorable performance of the proposed model in power system operations. Due to the lack of point forecast quality dependency, reliability is guaranteed for all possible day-ahead renewable power profiles.

Moreover, in this study, experiments are conducted for the aspects of machine learning, scenario quality, spatiotemporal dependence analysis, day-ahead scheduling and out-of-sample testing to evaluate the performance of the proposed SG method in detail, and the superiority of this method is verified by comparison with several benchmark methods.

The overall structure of this study is divided into five sections, including this introductory section. Section 2 describes the process of renewable GAF transformation and the details of the scenario generation models, including the architectures and training processes of StyleGAN-ADA-ESR. The framework of the scenario forecasting method is introduced in Section 3, and scenario evaluations and case studies are discussed in Section 4. Finally, Section 5 summarizes the whole paper and proposes some ideas for improvement in future studies.