Research on short-term optimization and scheduling of multi-energy complementary systems based on forecast scenario dynamic correction 基于预测情景动态修正的多能互补系统短期优化与调度研究
Xinyang Ji ^(a){ }^{\mathrm{a}}, Guohua Fang ^(a){ }^{\mathrm{a}}, Ziyu Ding ^(a,b,^(**)){ }^{\mathrm{a}, \mathrm{b},{ }^{*}} 纪欣阳 ^(a){ }^{\mathrm{a}} ， 方国华 ^(a){ }^{\mathrm{a}} ， 丁 ^(a,b,^(**)){ }^{\mathrm{a}, \mathrm{b},{ }^{*}} 子宇^(a){ }^{a} College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China ^(a){ }^{a} 河海大学 水利水电工程学院， 中国 南京 210098^(b){ }^{\mathrm{b}} College of Computer and Information Science, Hohai University, Nanjing, 211100, China ^(b){ }^{\mathrm{b}} 河海大学 计算机与信息科学学院， 江苏 南京 211100
A R T I C L E IN F O
Keywords: 关键字：
Dynamic scene correction 动态场景校正
Wind-solar-hydro complementary system 风光水互补系统
Short-term optimization dispatch 短期优化调度
Forecast uncertainty 预测不确定性
Source-load matching 源负载匹配
Abstract 抽象
The inherent unpredictability and instability of renewable energy sources, such as wind and solar power, hinder the precise execution of power generation plans in complementary systems, posing significant challenges to their integration into power grids. Therefore, this study proposes a dynamic correction method for wind and solar output forecast scenarios in the short-term scheduling of wind-solar-hydro complementary systems. The method utilizes statistical analysis of forecast errors in wind and solar power outputs to characterize uncertainty patterns across different forecast levels and constructs a typical forecast scenario set based on single-day forecasts. This approach probabilistically models each scenario according to the temporal migration patterns of wind and solar power outputs and develops a neural network-based dynamic correction fusion model to refine the forecasts. Application of this method in a case study of the Yalong River Basin demonstrated that, after applying dynamic correction to the forecast scenarios, the mean absolute error in total wind and solar output predictions during the wet and dry seasons was reduced by 50.73%50.73 \% and 47.95%47.95 \%, respectively. Additionally, the dynamic correction reduced the maximum residual load on typical wet and dry days by 82.70%82.70 \% and 62.37%62.37 \%, respectively, and decreased the total intraday residual electricity by 91.17%91.17 \% and 73.24%73.24 \%, compared to single-day forecasts. The study concludes that the proposed dynamic correction method enhances power system stability and improves power generation efficiency and reliability. 风能和太阳能等可再生能源固有的不可预测性和不稳定性阻碍了互补系统中发电计划的精确执行，对它们并入电网构成了重大挑战。因此，本研究提出了一种风-光-水互补系统短期调度中风光发电量预测情景的动态修正方法。该方法利用对风能和太阳能发电量输出的预测误差进行统计分析，以描述不同预测水平的不确定性模式，并根据单日预测构建典型的预测情景集。这种方法根据风能和太阳能输出的时间迁移模式对每个情景进行概率建模，并开发基于神经网络的动态校正融合模型来优化预测。该方法在亚砻河流域的案例研究中的应用表明，在对预测情景进行动态校正后，雨季和旱季风电总量预测的平均绝对误差分别减少了 50.73%50.73 \% 和 47.95%47.95 \% 。此外，与单日预报相比，动态校正将典型潮湿日和干日的最大剩余负荷分别降低了 82.70%82.70 \% 和 62.37%62.37 \% ，并将日内总剩余电量减少了 91.17%91.17 \% 和 73.24%73.24 \% 。该研究得出结论，所提出的动态修正方法增强了电力系统的稳定性，提高了发电效率和可靠性。
1. Introduction 1. 引言
Clean energy sources like wind, solar, and hydropower have gained a lot of attention in light of the world’s depleting fossil fuel reserves, rising energy consumption, and the worsening effects of climate change [1-4]. The increasing contribution of wind and photovoltaic energy, characterized by their inherent randomness and intermittency, heightens the unpredictability of the power system and complicates the maintenance of a stable supply-demand balance [5-7]. Currently, the dispatch plans based on forecast data cannot effectively achieve the optimization objectives [8]. Once significant forecast errors occur, it will not only affect the reliability of hydropower plans but may also lead to situations of power wastage and power rationing. To lessen the effects of adding solar and wind power to the grid, it is crucial to develop more dependable hydropower generation plans, take into account the uncertainty of forecast errors in the optimization scheduling process, and guarantee the safe, stable, and cost-effective operation of multi-energy complementary systems [9,10]. 鉴于全球化石燃料储量的枯竭、能源消耗的增加以及气候变化的影响恶化，风能、太阳能和水力发电等清洁能源受到广泛关注 [1-4]。风能和光伏能的贡献不断增加，其特点是其固有的随机性和间歇性，这增加了电力系统的不可预测性，并使维持稳定的供需平衡变得复杂 [5-7]。目前，基于预测数据的调度计划无法有效实现优化目标 [8]。一旦出现重大预报误差，不仅会影响水电计划的可靠性，还可能导致电力浪费和限电的情况。为了减少太阳能和风能并网的影响，制定更可靠的水力发电计划至关重要，在优化调度过程中考虑预测误差的不确定性，并保证多能源互补系统的安全、稳定和经济高效的运行 [9,10]。
1.1. Literature review 1.1. 文献综述
Recently, as renewable energy has rapidly evolved, the significance of power generation forecasting has grown markedly. To improve forecasting accuracy, researchers have proposed various methods for forecasting improvements and corrections, including static and dynamic corrections, error prediction corrections, and methods combining multiple learning models. However, these methods have certain limitations in practical applications. The following is a summary of some research approaches (see Table 1). 近年来，随着可再生能源的迅速发展，发电预测的重要性显著增加。为了提高预测准确性，研究人员提出了各种预测改进和校正的方法，包括静态和动态校正、误差预测校正以及结合多个学习模型的方法。但是，这些方法在实际应用中存在一定的局限性。以下是一些研究方法的摘要（见表 1）。
At present, research on improving renewable energy power generation forecasting primarily focuses on enhancing accuracy through various methods, including error correction models, hybrid approaches, and the integration of multiple forecasting techniques. However, these methods face several challenges. One key issue is the high complexity and computational demands of the models, such as those using complex neural networks or requiring multi-step corrections, which limit their practical applicability. Additionally, many methods, including those 目前，改进可再生能源发电预测的研究主要集中在通过各种方法提高准确性，包括纠错模型、混合方法和多种预测技术的集成。然而，这些方法面临一些挑战。一个关键问题是模型的高复杂性和计算需求，例如那些使用复杂神经网络或需要多步校正的模型，这限制了它们的实际适用性。此外，许多方法，包括
Table 1 表 1
Comparison of existing research methods for improvements and corrections in renewable energy output forecasting. 改进和修正可再生能源产量预测的现有研究方法的比较。
Author 作者
Year 年
Contribution 贡献
Drawbacks 缺点
Liang et al. [11] Liang 等 [11]
2016
A short-term wind power forecasting method that corrects prediction errors is proposed. 提出了一种修正预测误差的短期风电功率预测方法。
The error correction model may not perform well in multi-step forecasting. 误差校正模型在多步预测中可能表现不佳。
Gulin et al. [12] Gulin 等 [12]
2017
A method combining static and dynamic online correction was proposed to improve the power generation forecasting of photovoltaic arrays. 提出了一种静态与动态在线校正相结合的方法，以改进光伏阵列的发电预测。
The forecasting quality is highly dependent on the quality of meteorological variable predictions. 预报质量在很大程度上取决于气象变量预报的质量。
Andrade & Bessa [13] 安德拉德和贝萨 [13]
2017
Utilizing numerical weather prediction grid information to improve the accuracy of wind and solar energy forecasting. 利用数值天气预报网格信息来提高风能和太阳能预报的准确性。
It requires substantial computational resources, which may limit its practical application. 它需要大量的计算资源，这可能会限制其实际应用。
Zhou et al. [14] 周等 [14]
2019
A novel grey forecasting model was proposed for robust prognostics in renewable energy technologies. 提出了一种新的灰色预测模型，用于可再生能源技术的稳健预测。
The model has high complexity, and its computational efficiency needs improvement. 该模型复杂度高，计算效率有待提高。
Yan & Ouyang [15]
2019
A data-driven error correction method has been proposed to enhance the initial wind energy forecasting model's performance. 已经提出了一种数据驱动的纠错方法，以提高初始风能预测模型的性能。
It is difficult to handle unpredictable errors, leading to a decrease in forecasting accuracy. 难以处理不可预测的错误，从而导致预测准确性下降。
Muñoz et al. [16] Muñoz等[16]
2020
A feature-driven method was proposed to improve renewable energy forecasting and trading. 提出了一种特征驱动方法来改进可再生能源预测和交易。
It relies on a large amount of external data, which may pose challenges in data acquisition. 它依赖于大量的外部数据，这可能会给数据采集带来挑战。
Costoya et al. [17] Costoya等[17]
2020
An error correction method was adopted to improve future offshore wind energy resource forecasting. 采用纠错方法改进未来海上风能资源预测。
The forecasting accuracy may vary significantly across different regions. 不同地区的预测准确性可能会有很大差异。
Liu et al. [18] Liu等[18]
2021
A hybrid neural network model based on decomposition, multi-learner ensemble, and adaptive multiple error correction was proposed. 提出了一种基于分解、多学习器集成和自适应多元纠错的混合神经网络模型。
The model training is complex, and the computational cost is high. 模型训练复杂，计算成本高。
Li et al. [19] Li等 [19]
2023
A method of decomposition, integration, and error correction has been proposed to improve the accuracy of photovoltaic power generation. 为提高光伏发电的精度，提出了一种分解、积分和纠错的方法。
The method is highly complex, involving the training and integration of multiple models, resulting in significant computational costs. 该方法非常复杂，涉及多个模型的训练和集成，导致巨大的计算成本。
Smolarz et al. [20] Smolarz等[20]
2023
By improving data processing and model optimization, the prediction accuracy of renewable energy in the power system has been enhanced. 通过改进数据处理和模型优化，提高了电力系统中可再生能源的预测精度。
The data processing procedure is complex, relying on high-quality input data, and model optimization requires significant computational resources and time, which may pose challenges in practical applications. 数据处理过程复杂，依赖于高质量的输入数据，模型优化需要大量的计算资源和时间，这在实际应用中可能会带来挑战。
Liu et al. [21] Liu等[21]
2023
A method for hourly solar radiation prediction based on stepwise error correction and variational mode decomposition has been proposed, which improves prediction accuracy through dynamic adjustment and correction. 提出了一种基于逐步误差校正和变分模态分解的每小时太阳辐射预测方法，通过动态调整和校正提高预测精度。
The model is complex, involving multiple steps and parameter tuning, with strong data dependency and high requirements for the quality and integrity of input data. 模型复杂，涉及多个步骤和参数调优，数据依赖性强，对输入数据的质量和完整性要求高。
Wang et al. [22] Wang等[22]
2024
By integrating various forecasting models and error correction methods, the accuracy and reliability of wind power prediction have been enhanced. 通过集成各种预测模型和纠错方法，提高了风电功率预测的准确性和可靠性。
The method is highly complex and demands significant computational resources. 该方法非常复杂，需要大量的计算资源。
Author Year Contribution Drawbacks
Liang et al. [11] 2016 A short-term wind power forecasting method that corrects prediction errors is proposed. The error correction model may not perform well in multi-step forecasting.
Gulin et al. [12] 2017 A method combining static and dynamic online correction was proposed to improve the power generation forecasting of photovoltaic arrays. The forecasting quality is highly dependent on the quality of meteorological variable predictions.
Andrade & Bessa [13] 2017 Utilizing numerical weather prediction grid information to improve the accuracy of wind and solar energy forecasting. It requires substantial computational resources, which may limit its practical application.
Zhou et al. [14] 2019 A novel grey forecasting model was proposed for robust prognostics in renewable energy technologies. The model has high complexity, and its computational efficiency needs improvement.
Yan & Ouyang [15] 2019 A data-driven error correction method has been proposed to enhance the initial wind energy forecasting model's performance. It is difficult to handle unpredictable errors, leading to a decrease in forecasting accuracy.
Muñoz et al. [16] 2020 A feature-driven method was proposed to improve renewable energy forecasting and trading. It relies on a large amount of external data, which may pose challenges in data acquisition.
Costoya et al. [17] 2020 An error correction method was adopted to improve future offshore wind energy resource forecasting. The forecasting accuracy may vary significantly across different regions.
Liu et al. [18] 2021 A hybrid neural network model based on decomposition, multi-learner ensemble, and adaptive multiple error correction was proposed. The model training is complex, and the computational cost is high.
Li et al. [19] 2023 A method of decomposition, integration, and error correction has been proposed to improve the accuracy of photovoltaic power generation. The method is highly complex, involving the training and integration of multiple models, resulting in significant computational costs.
Smolarz et al. [20] 2023 By improving data processing and model optimization, the prediction accuracy of renewable energy in the power system has been enhanced. The data processing procedure is complex, relying on high-quality input data, and model optimization requires significant computational resources and time, which may pose challenges in practical applications.
Liu et al. [21] 2023 A method for hourly solar radiation prediction based on stepwise error correction and variational mode decomposition has been proposed, which improves prediction accuracy through dynamic adjustment and correction. The model is complex, involving multiple steps and parameter tuning, with strong data dependency and high requirements for the quality and integrity of input data.
Wang et al. [22] 2024 By integrating various forecasting models and error correction methods, the accuracy and reliability of wind power prediction have been enhanced. The method is highly complex and demands significant computational resources.| Author | Year | Contribution | Drawbacks |
| :---: | :---: | :---: | :---: |
| Liang et al. [11] | 2016 | A short-term wind power forecasting method that corrects prediction errors is proposed. | The error correction model may not perform well in multi-step forecasting. |
| Gulin et al. [12] | 2017 | A method combining static and dynamic online correction was proposed to improve the power generation forecasting of photovoltaic arrays. | The forecasting quality is highly dependent on the quality of meteorological variable predictions. |
| Andrade & Bessa [13] | 2017 | Utilizing numerical weather prediction grid information to improve the accuracy of wind and solar energy forecasting. | It requires substantial computational resources, which may limit its practical application. |
| Zhou et al. [14] | 2019 | A novel grey forecasting model was proposed for robust prognostics in renewable energy technologies. | The model has high complexity, and its computational efficiency needs improvement. |
| Yan & Ouyang [15] | 2019 | A data-driven error correction method has been proposed to enhance the initial wind energy forecasting model's performance. | It is difficult to handle unpredictable errors, leading to a decrease in forecasting accuracy. |
| Muñoz et al. [16] | 2020 | A feature-driven method was proposed to improve renewable energy forecasting and trading. | It relies on a large amount of external data, which may pose challenges in data acquisition. |
| Costoya et al. [17] | 2020 | An error correction method was adopted to improve future offshore wind energy resource forecasting. | The forecasting accuracy may vary significantly across different regions. |
| Liu et al. [18] | 2021 | A hybrid neural network model based on decomposition, multi-learner ensemble, and adaptive multiple error correction was proposed. | The model training is complex, and the computational cost is high. |
| Li et al. [19] | 2023 | A method of decomposition, integration, and error correction has been proposed to improve the accuracy of photovoltaic power generation. | The method is highly complex, involving the training and integration of multiple models, resulting in significant computational costs. |
| Smolarz et al. [20] | 2023 | By improving data processing and model optimization, the prediction accuracy of renewable energy in the power system has been enhanced. | The data processing procedure is complex, relying on high-quality input data, and model optimization requires significant computational resources and time, which may pose challenges in practical applications. |
| Liu et al. [21] | 2023 | A method for hourly solar radiation prediction based on stepwise error correction and variational mode decomposition has been proposed, which improves prediction accuracy through dynamic adjustment and correction. | The model is complex, involving multiple steps and parameter tuning, with strong data dependency and high requirements for the quality and integrity of input data. |
| Wang et al. [22] | 2024 | By integrating various forecasting models and error correction methods, the accuracy and reliability of wind power prediction have been enhanced. | The method is highly complex and demands significant computational resources. |
based on numerical weather prediction or large data-driven models, rely heavily on external data, raising concerns about data availability and quality. Another major challenge is the variation in forecasting performance across different regions and time periods, which complicates the generalization of models. Combining static and dynamic correction methods is promising, but they often require significant computational resources and parameter adjustments, leading to suboptimal performance in real-time applications. In conclusion, while the trend of increasing model complexity improves accuracy, it also introduces obstacles related to computational efficiency, data dependence, and regional adaptability. 基于数值天气预报或大数据驱动模型，严重依赖外部数据，引发了对数据可用性和质量的担忧。另一个主要挑战是不同地区和时间段的预测效果存在差异，这使得模型的泛化变得复杂。将静态和动态校正方法相结合是很有前途的，但它们通常需要大量的计算资源和参数调整，从而导致实时应用中的性能欠佳。总之，虽然模型复杂性增加的趋势提高了准确性，但它也引入了与计算效率、数据依赖性和区域适应性相关的障碍。
In the effective utilization of renewable energy, not only can its own uncertainties be reduced, but other energy sources can also be used to complement and adjust it. Multi-energy complementary systems, by utilizing the complementary characteristics of various energy sources, can balance the uncertainties of a specific energy to some extent and enhance the overall efficacy and stability of the system. However, it is necessary to adjust the multi-energy complementary system models when applying improved new energy output forecasting methods. For instance, Huang et al. [23] adjust the multi-energy complementary system models through multi-objective optimization and dynamic adjustment mechanisms, combining the complementary characteristics of different energies, thereby enhancing the system’s forecasting accuracy and stability. Lin et al. [24] improve system operational efficiency and accuracy by introducing real-time data and forecasting error correction mechanisms, along with dynamic adjustments to the system. Additionally, researchers adjust complementary systems using multi-objective optimization methods, incorporating the complementary features of various energies and considering the uncertainties in energy production, thereby enhancing the system’s accuracy and stability [25,26]. 在可再生能源的有效利用中，不仅可以减少其自身的不确定性，还可以利用其他能源对其进行补充和调整。多能互补系统，通过利用各种能源的互补特性，可以在一定程度上平衡特定能量的不确定性，增强系统的整体效能和稳定性。然而，在应用改进的新能源输出预测方法时，有必要调整多能源互补系统模型。例如，Huang等[23]通过多目标优化和动态调整机制来调整多能量互补系统模型，结合不同能量的互补特性，从而提高系统的预测精度和稳定性。Lin等[24]通过引入实时数据和预测纠错机制，以及对系统进行动态调整，提高了系统运行效率和准确性。此外，研究人员使用多目标优化方法调整互补系统，结合各种能量的互补特性，并考虑能量生产的不确定性，从而提高系统的准确性和稳定性 [25,26]。
Despite significant progress in enhancing the accuracy of renewable energy output forecasts, challenges remain. Firstly, the complexity and uncertainty of multi-energy complementary system models increase the difficulty of adjustments, and the uncertainties brought about by fluctuations in new energy production will continue to affect the stable operation of these systems. Secondly, current research mainly focuses on the construction and optimization of forecasting models, with less 尽管在提高可再生能源产量预测的准确性方面取得了重大进展，但挑战仍然存在。首先，多能源互补系统模型的复杂性和不确定性增加了调整的难度，新能源生产波动带来的不确定性将继续影响这些系统的稳定运行。（2）目前的研究主要集中在预测模型的构建和优化上，且
targeted adjustments and validations for actual application areas, limiting further optimization and application of the models. Lastly, the extensive integration of new technologies such as artificial intelligence and big data is not yet fully mature, requiring more practice and exploration. Efforts are still needed in the complexity of output models, practical application promotion, and integration of new technologies. 针对实际应用领域进行有针对性的调整和验证，限制了模型的进一步优化和应用。最后，人工智能和大数据等新技术的广泛融合尚未完全成熟，需要更多的实践和探索。在输出模型的复杂性、实际应用的推广和新技术的集成方面仍需做出努力。
1.2. Research objectives and novelty 1.2. 研究目标和新颖性
The primary objective of this research is to develop an optimized scheduling model for multi-energy complementary systems that integrates wind, solar, and hydroelectric power. This model aims to dynamically correct forecast scenarios by incorporating real-time data updates, addressing the inherent uncertainties in renewable energy output, particularly from wind and solar sources. This research aims to improve the reliability and efficiency of power generation within these systems, ensuring stable and cost-effective operations. 本研究的主要目标是为集成风能、太阳能和水力发电的多能源互补系统开发一个优化的调度模型。该模型旨在通过结合实时数据更新来动态纠正预测情景，解决可再生能源输出的固有不确定性，尤其是来自风能和太阳能的产量。本研究旨在提高这些系统内发电的可靠性和效率，确保稳定和具有成本效益的运行。
The main contribution of this study is the development of a dynamic correction method for optimizing the short-term scheduling of multienergy complementary systems that incorporate wind, solar, and hydroelectric power. This method significantly improves the accuracy and reliability of power generation forecasts by integrating real-time data updates and advanced probabilistic models, effectively addressing the uncertainties inherent in renewable energy sources. The research follows a structured approach, beginning with a comprehensive analysis of historical forecast errors and their distribution, which forms the basis for generating typical forecast scenarios. These scenarios are then dynamically corrected using a neural network-based fusion model, ensuring that the multi-energy system operates with greater stability and efficiency. The rest of the paper is organized as follows. Section 2 describes the methodology, including the dynamic correction method for forecast scenarios, determination of prediction error distribution features, and generation of typical forecast scenarios; Section 3 presents a case study of the multi-energy complementary system in the Yalong River basin; Section 4 presents the results and discussion; and conclusions are drawn in Section 5. 本研究的主要贡献是开发了一种动态校正方法，用于优化包括风能、太阳能和水力发电在内的多能源互补系统的短期调度。该方法通过整合实时数据更新和先进的概率模型，显著提高了发电预测的准确性和可靠性，有效解决了可再生能源固有的不确定性。该研究遵循结构化方法，首先对历史预测误差及其分布进行全面分析，这构成了生成典型预测情景的基础。然后使用基于神经网络的聚变模型对这些场景进行动态校正，确保多能源系统以更高的稳定性和效率运行。本文的其余部分组织如下。第 2 节描述了该方法，包括预测情景的动态校正方法、预测误差分布特征的确定以及典型预测情景的生成;第 3 节介绍了亚砻河流域多能源互补系统的案例研究;第 4 节介绍了结果和讨论;第 5 节中得出结论。
2. Methodology 2. 方法
2.1. Dynamic correction method for forecast scenarios considering wind and solar uncertainty 2.1. 考虑风能和太阳能不确定性的预测情景的动态修正方法
In addressing the optimization scheduling challenges of multi-energy combined systems with significant wind and photovoltaic output, relying solely on a single-day forecast of wind and photovoltaic output often fails to achieve satisfactory results. Therefore, this chapter proposes a dynamic correction method for forecast scenarios considering the uncertainty of wind and photovoltaic conditions. Firstly, a hierarchical statistical analysis is employed to analyze the historical forecasts and measured sequences of wind and photovoltaic outputs, describing the distribution patterns of forecast errors and transferred outputs. Based on this, according to the distribution law of forecast errors, a large number of uncertain scenarios are derived from the single day-ahead forecast, and a set of typical forecast scenarios is obtained. The occurrence probabilities of each typical scenario are then estimated using real-time data updated periodically according to the distribution of transferred output. Lastly, through the constructed artificial neural network model, the scenarios are integrated and dynamically corrected, generating converged forecast scenarios for short-term optimized scheduling of multi-energy complementary systems. 在应对风能和光伏发电量显著的多能源组合系统的优化调度挑战时，仅依靠风能和光伏发电量的单日预测往往无法取得令人满意的结果。因此，本章提出了一种考虑风能和光伏条件不确定性的预测情景的动态修正方法。首先，采用分层统计分析分析风能和光伏发电出力的历史预报和实测序列，描述预报误差和转移出力的分布模式;基于此，根据预报误差分布规律，从单日前预报中推导出大量不确定情景，得到一组典型的预报情景。然后，根据传输输出的分布，使用定期更新的实时数据估计每个典型场景的发生概率。最后，通过构建的人工神经网络模型，对情景进行整合和动态校正，生成收敛的预测情景，用于多能源互补系统的短期优化调度。
2.1.1. Determination of prediction error distribution features for wind and solar power output 2.1.1. 确定风能和太阳能发电量的预测误差分布特征
Utilizing data from actual measurements as well as past weather forecasts, multiple data records [p_(i),r_(i),e_(r,i)]\left[p_{i}, r_{i}, e_{r, i}\right] are established, 利用来自实际测量和过去天气预报的数据，建立多个数据记录 [p_(i),r_(i),e_(r,i)]\left[p_{i}, r_{i}, e_{r, i}\right] ，
where p_(i)p_{i} and r_(i)r_{i} stand for the predicted and real measurement data, respectively, of the power production from wind (or photovoltaic) at a specific time; e_(r,i)e_{r, i} represents the forecast relative error of wind (or photovoltaic) power output at that moment; ii is the data number, which is related to the data collection frequency in the historical database. If the forecast accuracy is 15min,9615 \mathrm{~min}, 96 records can be generated in a day. Owing to the intrinsic features of solar and wind energy generation, there is a comparatively high percentage of zero power times. Therefore, when calculating the relative error e_(r,i)e_{r, i}, certain adjustments are made to the normalization process according to the following formula:
where bar(p_(i))\overline{p_{i}} and bar(r_(i))\overline{r_{i}} represent the normalized values of wind (or photovoltaic) power outputs between [1,2][1,2].
To establish a conditional normal distribution model for forecasting errors [27,28][27,28], data records are segmented into NN strata based on the values of p_(i)p_{i} using a stratified statistical method. The range of p_(i)p_{i} for each stratum is defined as follows: [minp_(i),(1)/(N)maxp_(i)),[(1)/(N)maxp_(i),(2)/(N)maxp_(i)),dots\left[\min p_{i}, \frac{1}{N} \max p_{i}\right),\left[\frac{1}{N} \max p_{i}, \frac{2}{N} \max p_{i}\right), \ldots, [(N-1)/(N)maxp_(i),maxp_(i)]\left[\frac{N-1}{N} \max p_{i}, \max p_{i}\right].
The quantity and distribution of historical data have an impact on how many layers NN there are. Having too many layers may reduce the effectiveness of describing the error distribution in each layer. On the other hand, having too few layers cannot effectively depict the probability distribution relationship of relative forecast errors at different forecast levels.
The data is divided into several layers, and it is assumed that the prediction errors within each layer follow a Gaussian distribution [29, 30]. Let e_(r,1),e_(r,2),dots,e_(r,m)e_{r, 1}, e_{r, 2}, \ldots, e_{r, m} be the samples of forecast relative errors contained in the aforementioned layer. Then, the probability density function of variable e_(r)e_{r} in that layer is defined as: 数据分为几层，并假设每层内的预测误差遵循高斯分布 [29， 30]。设 e_(r,1),e_(r,2),dots,e_(r,m)e_{r, 1}, e_{r, 2}, \ldots, e_{r, m} 为上述层中包含的预测相对误差样本。然后，该层中变量 e_(r)e_{r} 的概率密度函数定义为： f(e_(r))=(1)/(sigmasqrt(2pi))e^(-((e_(r)-mu)^(2))/(2sigma^(2)))f\left(e_{r}\right)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{\left(e_{r}-\mu\right)^{2}}{2 \sigma^{2}}}
where sigma\sigma denotes the sample standard deviation and mu\mu denotes the sample mean. 其中 sigma\sigma 表示样本标准差， mu\mu 表示样本均值。
2.1.2. Determination of wind and solar power migration distribution characteristics 2.1.2. 风能和太阳能迁移分布特性的确定
Multiple data records [r_(i),r_(i+1)]\left[r_{i}, r_{i+1}\right] are generated based on past wind and solar power measurements, in a manner akin to extracting error distribution information for wind and solar power forecasts. Among them, r_(i)r_{i} and r_(i+1)r_{i+1} represent the measured wind (or photovoltaic) power values at a certain moment and the measured transferred power values of wind (or photovoltaic) at the next moment. According to the values of r_(i)r_{i} in each data record, the records are divided into MM layers, and stratified statistics are performed. The range of r_(i)r_{i} in each layer is [minr_(i):}\left[\min r_{i}\right., {:(1)/(M)maxr_(i)),[(1)/(M)maxr_(i),(2)/(M)maxr_(i)),dots,[(M-1)/(M)maxr_(i),maxr_(i)]\left.\frac{1}{M} \max r_{i}\right),\left[\frac{1}{M} \max r_{i}, \frac{2}{M} \max r_{i}\right), \ldots,\left[\frac{M-1}{M} \max r_{i}, \max r_{i}\right]. 根据过去的风能和太阳能发电量测量结果生成多个数据记录 [r_(i),r_(i+1)]\left[r_{i}, r_{i+1}\right] ，其方式类似于提取风能和太阳能发电量预测的误差分布信息。其中， r_(i)r_{i} 和 r_(i+1)r_{i+1} 表示在某一时刻测得的风（或光伏）功率值和在下一时刻测得的风（或光伏）传输功率值。根据每条数据记录 r_(i)r_{i} 中的值，将记录划分为 MM 多个层次，并进行分层统计。每层中的 范围 r_(i)r_{i} 是 [minr_(i):}\left[\min r_{i}\right. ， {:(1)/(M)maxr_(i)),[(1)/(M)maxr_(i),(2)/(M)maxr_(i)),dots,[(M-1)/(M)maxr_(i),maxr_(i)]\left.\frac{1}{M} \max r_{i}\right),\left[\frac{1}{M} \max r_{i}, \frac{2}{M} \max r_{i}\right), \ldots,\left[\frac{M-1}{M} \max r_{i}, \max r_{i}\right] 。
The probability density function of r_(i+1)r_{i+1} inside each layer is obtained by using a normal distribution to describe the samples within each layer. This allows for a probabilistic characterization of the pattern of transferred wind (or photovoltaic) energy at the next moment. 每层内部的 r_(i+1)r_{i+1} 概率密度函数是通过使用正态分布来描述每层内的样本来获得的。这允许对下一刻转移的风能（或光伏）能量的模式进行概率表征。
2.1.3. Generation of typical forecast scenarios for wind and solar power output and calculation of their occurrence probabilities 2.1.3. 生成风能和太阳能发电量的典型预测情景并计算其发生概率
Typical forecast scenarios for wind and solar power output are extensions of the original forecasts combined with the characteristics of forecast error distribution. The occurrence probabilities of each typical scenario are further descriptions based on the characteristics of the migration power output distribution. The specific generation processes of both are as follows. 风能和太阳能发电量的典型预测情景是原始预测的扩展，并结合了预测误差分布的特征。每个典型场景的发生概率是根据迁移功率输出分布的特点进一步描述的。两者的具体生成过程如下。
Step 1: Applying the wind and solar output forecast data for the next day, using the forecast error distribution characteristics extracted in Section 2.1.1, determine the hierarchical levels of forecasted wind power p_(w,i)p_{w, i} and forecasted photovoltaic power p_(s,i)p_{s, i} for the intra-day time period ii, and extract the relative forecast error distribution characteristics within that level. The hierarchical numbers represent the levels to which the forecasted wind output p_(w,i)p_{w, i} and forecasted photovoltaic output p_(s,i)p_{s, i} belong for each time period are denoted as nwn w and msm s, respectively. 第 1 步：应用第二天的风能和太阳能发电量预测数据，使用第 2.1.1 节中提取的预测误差分布特征，确定日内时间段内预测的风电功率 p_(w,i)p_{w, i} 和预测光伏功率 p_(s,i)p_{s, i} 的层次结构级别 ii ，并提取该级别内的相对预测误差分布特征。分层数字表示每个时间段的预测风能输出 p_(w,i)p_{w, i} 和预测的光伏输出 p_(s,i)p_{s, i} 所属的级别，分别表示为 nwn w 和 msm s 。 p_(w,i)in[(nw-1)/(N)maxp_(w),(nw)/(N)maxp_(w))p_{w, i} \in\left[\frac{n w-1}{N} \max p_{w}, \frac{n w}{N} \max p_{w}\right) p_(s,i)in[(ms-1)/(M)maxp_(s),(ms)/(M)maxp_(s))p_{s, i} \in\left[\frac{m s-1}{M} \max p_{s}, \frac{m s}{M} \max p_{s}\right)
where nwn w and msm s represent the interval numbers corresponding to the forecasted wind and photovoltaic output, respectively, with nw and ms being integers ranging from 0 to NN and 0 to MM, respectively. 其中 nwn w 和 msm s 分别表示与预测的风能和光伏输出相对应的区间数字，其中 NW 和 MS 分别是介于 0 到 NN 和 0 到 MM 之间的整数。
Obtain the mean as well as the standard deviation for the samples e_(r,w)e_{r, w} and e_(r,s)e_{r, s} that fall inside the level designated by the level number of the prediction value. Determine the probability density functions f_(w,i)(e_(r,w),mu:}f_{w, i}\left(e_{r, w}, \mu\right., sigma)\sigma) and f_(s,i)(e_(r,s),mu,sigma)f_{s, i}\left(e_{r, s}, \mu, \sigma\right) for relative forecast errors in each time period within a day. 获取样本的均值和标准差，这些样本 e_(r,w)e_{r, w}e_(r,s)e_{r, s} 落在预测值的水平编号所指定的水平内。确定 probability density functions f_(w,i)(e_(r,w),mu:}f_{w, i}\left(e_{r, w}, \mu\right. ， sigma)\sigma) 以及 f_(s,i)(e_(r,s),mu,sigma)f_{s, i}\left(e_{r, s}, \mu, \sigma\right) 一天内每个时间段的相对预测误差。
Step 2: Using the probabilistic density function of relative errors in forecasting for wind and solar power that was established in Step 1, perform Latin hypercube sampling to obtain a large number of relative forecast error sequences for each time period within a day. Transform them into actual values using Eq. (1) to generate the forecast scenario sets P_(w)P_{w} and P_(s)P_{s}. Regarding the wind and solar energy outputs in each time period, the predicted values in the initial set of 第 2 步：使用第 1 步中建立的风能和太阳能预测中相对误差的概率密度函数，执行拉丁超立方体采样，以获得一天内每个时间段的大量相对预测误差序列。使用方程 （1） 将它们转换为实际值，以生成预测情景集 P_(w)P_{w} 和 P_(s)P_{s} 。关于每个时间段的风能和太阳能输出，初始集合
Corresponding author. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China. E-mail address: dingzy@hhu.edu.cn (Z. Ding). 通讯作者。河海大学水利水电工程学院，中国 210098南京。电子邮件地址：dingzy@hhu.edu.cn （Z. Ding）。