Accurate photovoltaic (PV) power forecasting is crucial for ensuring reliable power system operation under high renewable energy penetration. This study proposes a novel two-stage hybrid PV power forecasting framework that combines the MTF-MTS-Mixer for deterministic day-ahead forecasting and the Physics-Informed Bayesian Neural Networks (PI-BNN) for probabilistic intra-day forecasting. The framework integrates multi-scale temporal features (MTF), temporal-channel mixing, physics-informed modeling, and Bayesian uncertainty quantification. Using a two-year dataset from seven PV power stations, extensive experiments are conducted to evaluate forecasting accuracy, robustness, and uncertainty representation. For deterministic forecasting, the proposed MTF-MTS-Mixer leverages MTF and temporal-channel mixing operations, achieving superior performance across all stations. It attains an average correlation coefficient (CC) of 0.811 and reduces NRMSE and NMAE by 14.12% and 16.43%, respectively, compared with TCN. It also maintains relatively favorable performance under different weather conditions, particularly rainy scenarios. For probabilistic intraday forecasting, the PI-BNN incorporates real-time meteorological inputs and physical guidance, enhancing forecasting performance and uncertainty estimation. It increases the average CC by 0.141 compared with day-ahead forecasting. In terms of probabilistic evaluation, it achieves a 40.29% improvement in CRPS compared with DeepAR and produces better-calibrated prediction intervals, with reduced PINAW and PICP closer to the nominal confidence level. In addition, the PI-BNN shows improved reliability in uncertainty estimation across different weather conditions. Overall, the proposed framework demonstrates competitive and stable forecasting performance across multiple PV stations and weather conditions. It provides useful information for PV operation and scheduling under uncertainty, supporting more reliable decision-making in renewable-integrated power systems.

Large-scale hydro–wind–photovoltaic (HWP) bases are increasingly important for expanding clean-energy supply, yet their cross-regional operation is challenged by renewable variability and strongly coupled hydraulic and transmission constraints. This study develops a feasibility-enhanced, cluster-guided optimization framework for source–grid coordinated HWP dispatch under cross-regional power delivery (CRPD). A topology-explicit model links cascade reservoir regulation, bank-side hydropower allocation, channel-specific transmission limits, and receiving-end residual-load smoothing. A water-volume reallocation strategy (WRS) and dynamic constraint-handling strategy (DCHS) are integrated to restore terminal reservoir states and progressively guide the search toward feasible regions, while a cluster-guided optimization algorithm assigns differentiated search roles according to population structure and solution quality. A multi-level evaluation demonstrates the effectiveness of the framework. At the feasibility-enhancement level, WRS restored final water levels to the prescribed tolerances in all runs, and the selected DCHS reduced mean residual-load root-mean-square error (RLMSE) by 34.00%–67.16% relative to the fixed-rigid-constraint setting while increasing the mean proportion of feasible population (PFP) from 0% to 100%. At the algorithmic level, CGO ranked first in the Friedman analysis of 23 benchmark functions and retained the best average rank under a unified total function-evaluation budget. At the application level, it maintained a mean PFP of 100% across three representative HWP conditions and produced schedules that balanced residual-load smoothing, solution stability, and operational feasibility. The proposed framework therefore provides an effective means of leveraging hydropower flexibility to smooth receiving-end residual-load processes and support reliable cross-regional clean power delivery.

The Muskingum model is the most well-known and commonly used method for flood routing in water resources engineering, and the variable-parameter nonlinear Muskingum model has become a hot topic today. However, there is no consensus on how to construct variable-parameter nonlinear Muskingum models and determine the final model structure in practice. In this study, a generalized determination framework is proposed for variable-parameter nonlinear Muskingum models with lateral flow. In the proposed generalized determination framework, a new four-parameter variable-parameter nonlinear Muskingum model with lateral flow (4P-VPNLMM) is proposed, which is constructed by partitioning the inflow hydrograph into L sub-regions and considering the lateral flow in reality. Then an efficient optimization approach (Improved Stochastic Fractal Search, ISFS) is developed. Finally, with the help of ISFS, the final number of sub-regions is determined based on expected model improvement. The applicability of the proposed generalized determination framework is verified by solving four representative flood routing applications, including a flood event with significant lateral flow contribution. Results show that the proposed generalized determination framework can effectively determine the final number of sub-regions of variable-parameter nonlinear Muskingum models, improving model performance by more than 80

Reliable synthetic streamflow sequences are essential for water resources planning and management under hydrological uncertainty. However, existing streamflow simulation methods often have difficulty balancing distributional flexibility, temporal dependence representation, and structural parsimony. Within the Gaussian mixture model (GMM) framework, this challenge is further aggravated by the sensitivity of expectation–maximization (EM)-based training to initialization and its dependence on mixture-component selection. To address these limitations, this study proposes a greedy learning–optimized GMM (GL-GMM) framework for streamflow stochastic simulation. The proposed method integrates a splitting-based candidate generation strategy, a two-phase parameter optimization mechanism, and dual-threshold constraints to adaptively determine model complexity and ensure robust parameter estimation. Instead of repeatedly retraining mixtures with pre-specified complexities, the framework progressively expands the model through data-guided candidate generation, local screening, and full-model refinement, while suppressing unreliable or redundant components. In synthetic datasets, GL-GMM increased the average log-likelihood by 5.52% and 5.28% relative to EM for D = 2 and D = 5, respectively, indicating stronger probabilistic fitting ability and a more reliable basis for stochastic streamflow generation. In real-data stochastic simulation experiments using long-term streamflow records from the Pingshan Hydrological Station, GL-GMM identifies substantially more parsimonious mixture structures than EM-GMM across monthly, ten-day, and daily resolutions and, relative to benchmark methods, provides better overall performance in preserving statistical characteristics, temporal autocorrelation, tail- and drought-related behaviors, and uncertainty description. Overall, GL-GMM provides an efficient and parsimonious framework for long-term streamflow simulation and offers stochastic inflow data support for subsequent reservoir and energy-system planning and operation studies.

Accurate short-term load forecasting (STLF) is crucial for ensuring the stable operation of power systems and promoting the development of electricity markets. However, current research for STLF overlooks model optimization methods and the need for more flexible weighted ensemble methods, which leads to less research on excavating the prediction performance of the models and improving their utilization efficiency. To address these issues, this paper proposes a novel STLF model based on Hierarchical Optimization and Ensemble Networks (HOEN), which sequentially applies a deep learning model optimization method, a multi-model ensemble method, and a residual correction method to perform hierarchical optimization and ensemble of LSTM, GRU and MTS-Mixers. Firstly, a Spiral Fitting Optimization (SFO) method is proposed based on the theory of Stochastic Weight Averaging (SWA). This method explores the optimal model parameter matrix by fitting the logarithmic spiral curve between the parameter weights and loss values of models, thereby excavating and optimizing the predictive performance of the model. Secondly, an Optimal Model Classification Ensemble (OMCE) method is proposed, which dynamically assigns the weights of each model by constructing a data-driven dynamic weighting mechanism, improving the utilization efficiency of the optimized models. Finally, residual correction method is applied to optimize the forecast residuals of the ensemble model, further enhancing its predictive performance. The proposed methods and models are validated using load data from Hubei Province, China, and Belgium in this paper. The results demonstrate that our methods and models exhibit clear advantages in terms of accuracy, stability, and generalization ability in STLF.

Deep learning has been widely applied in runoff forecasting, focusing primarily on temporal features but neglecting the influence of spatial heterogeneity. Capturing complex spatiotemporal atmosphere-land-hydrology interactions by deep learning remains challenging in rainfall-runoff forecasting. This study proposes a hybrid deep learning framework, Runoff Forecasting Model Integrating Spatiotemporal Features (RFMISF), which leverages the complementary strengths of multiple deep learning architectures to construct five modules, thereby fusing multi-source data. Specifically, the framework integrates the Convolutional Neural Networks for extracting spatial features of underlying surface, the LSTM for capturing temporal dependencies in rainfall and runoff, and the Convolutional LSTM (ConvLSTM) for learning spatiotemporal features of meteorological inputs. Two case studies of daily runoff forecasting have been deviced for the BHT and SBY hydrological stations with distinct hydrological regimes. At the BHT, the RFMISF reduced RMSE by 31.53% and MAE by 33.39% compared to the Xinanjiang baseline; at the SBY, the RFMISF improved NSE by 13.6% and decreased MAE by 27.39%. Ablation experiments of excluding station rainfall, underlying surface, and meteorological data are further conducted to underline the importance of multi-source data. At the BHT, the experiments led to RMSE increases of 9.29%, 4.69%, and 5.59% during flood season, respectively. At the SBY, the experiments resulted in reductions of NSE by 15.08%, 4.46%, and 12.94%. Additionally, model performance varies with rainfall intensity, indicating the differentiated contributions of multi-source data in complex runoff responses. Although reanalysis data enhance spatial representativeness, their systematic errors require careful treatment. Overall, this study introduces a novel, robust framework for enhancing runoff prediction and improving water resource management in hydrologically complex environments.

Toward low-carbon and sustainable power systems, hydro–wind–solar complementarity provides an important pathway for enhancing renewable energy accommodation and operational flexibility, while accurate characterization of uncertainty and cross-energy dependencies is essential for system optimization, operational risk assessment, and sustainable utilization of renewable resources. This study proposes a conditional Wasserstein generative adversarial network with gradient penalty integrating one-dimensional multi-scale channel attention (MSA) and an exponential moving average (EMA) mechanism (MSA-cWGAN-GP) for joint runoff–wind–photovoltaic (PV) scenario generation. The generator employs parallel depthwise 1D convolutions with multiple temporal receptive fields to capture multi-timescale variations, while an EMA shadow generator is used for model validation and scenario generation. Conditional labels are obtained by clustering joint 24 h runoff–wind–PV profiles, enabling generation under typical resource states. Case studies using historical runoff observations from Shuibuya Hydropower Station and wind and PV power series derived from ERA5 reanalysis data show overall absolute errors of the autocorrelation function (ACF) and Kendall coefficient of 0.0113 and 0.0495, respectively. The proposed model achieves the best average performance among the evaluated models in preserving intraday temporal dependence, cross-energy dependencies, and distributional characteristics, providing representative scenarios for uncertainty analysis and subsequent optimization of hydro–wind–solar complementary systems.

The large-scale integration of wind and solar photovoltaic (PV) power is a cornerstone of low-carbon, sustainable energy systems. However, the uncertainty of the output brings great challenges to the operation and dispatching of power systems. To clearly describe the fluctuation characteristics of wind–PV power output and the spatial–temporal coupling relationship, a two-stage wind–PV scenario-generation method is proposed. This method is based on Difference-Constrained Variational Autoencoder and Mixture of Factor Analyzers (DVAE-MFA). In the first stage, a differential constraint term is added to the reconstruction loss of the Variational Autoencoder (VAE) to build the Difference-Constrained Variational Autoencoder (DVAE) model. This helps the model better learn the fluctuation characteristics of output sequences. In the second stage, to solve the problem of the posterior distribution of the DVAE latent variables deviating from the standard normal prior, the Mixture of Factor Analyzers (MFA) model is introduced for secondary probability modeling of the latent space. The simulation experiment results show that the proposed DVAE-MFA model outperforms comparison models in terms of the scenario temporal fluctuation characteristics, spatial–temporal correlations, and statistical distribution similarity. The generated output scenarios can reproduce the features of historical data, providing high-quality data support for the stochastic optimization scheduling of sustainable power systems.

Accurate reservoir inflow forecasting is essential for sustainable watershed management and low-carbon hydropower operation. Traditional fixed-weight ensemble models lack adaptability under non-stationary hydrological conditions, limiting their reliability in reservoir operation. This study proposes a Context-Aware Localized Weighting Ensemble (CALWE) framework for reservoir inflow forecasting. The framework constructs a predictive response space from heterogeneous model outputs, enabling context identification based on similarities in model prediction behaviors. A localized weighting strategy is then employed to adaptively determine model contributions across contexts. The framework was evaluated using daily reservoir inflow data from Xiaowan Hydropower Station in the Lancang River Basin and monthly inflow data from Xiluodu Hydropower Station in the Jinsha River Basin. Results demonstrate that CALWE outperforms individual models and conventional ensemble approaches in both cases. Compared with the best-performing individual benchmark model for each basin (i.e., SVR for Xiaowan and XGBoost for Xiluodu), CALWE achieved a relative RMSE reduction of 4.93% and an absolute NSE improvement of 0.007 for daily inflow forecasting at Xiaowan, while achieving a relative RMSE reduction of 5.32% and an absolute NSE improvement of 0.027 for monthly inflow forecasting at Xiluodu. SHAP analysis revealed scale-dependent feature contributions, with daily forecasts dominated by antecedent inflow information and monthly forecasts influenced by meteorological, land surface, and hydrological factors. These findings demonstrate that CALWE captures context-dependent inflow responses while providing interpretable insights into model predictions, thereby supporting sustainable watershed management and reservoir operation.

Wind and solar resources are characterized by limited predictability and strong uncertainty. To maintain power system stability under high renewable penetration, sufficient flexibility resources are required to respond promptly to system regulation demands. Hydropower is the primary source of operational flexibility; however, quantitative assessments of grid flexibility demand and hydropower flexibility provision before and after wind and solar integration remain limited. To address this gap, this study develops a probabilistic uncertainty-based stochastic dispatch framework. First, an advanced forecasting model (FI-Transformer) that incorporates meteorological accumulation effects and uncertainty is constructed to predict key variables in the hydro-windphotovoltaic complementary system. Second, to rigorously propagate uncertainty into dispatch decisions, a hybrid scenario reduction technique is proposed by combining norm-constrained filtering and K-means clustering, with scenario probability distributions calibrated using the Wasserstein distance (WD). A flexibilityoriented decoupled multi-objective dispatch model (D-MODM) is then formulated. Using data from representative wet and dry seasons, probabilistic grid flexibility demand is explicitly integrated into the dispatch model, which jointly maximizes hydropower responsiveness to flexibility demand and total system generation. The results show that although flexibility demand variability increases significantly under low-probability scenarios, the hydro-wind-photovoltaic dispatch model maintains generation variations within 3% and limits flexibility provision fluctuations to below 6%, demonstrating enhanced system stability. Furthermore, the decoupled approach effectively improves the generation-flexibility Pareto front compared to traditional methods. Notably, the enhanced forecasting accuracy of the FI-Transformer narrows uncertainty boundaries, thereby reducing the need for overly conservative flexibility margins and safely enabling higher renewable energy generation. These findings indicate that the proposed framework enables explicit quantification of grid flexibility demand and effectively unlocks hydropower flexibility potential, underscoring the importance of probabilistic uncertaintyaware dispatch modeling for power systems with high shares of wind and solar generation.

To address the challenges posed by the direct integration of large-scale wind and solar power into the grid for peak-shaving, this paper proposes a short-term optimization scheduling model for hydro–wind–solar multi-energy complementary systems, aiming to minimize the peak–valley difference of system residual load. The model generates and reduces wind and solar output scenarios using Latin Hypercube Sampling and K-means clustering methods, capturing the uncertainty of renewable energy generation. Based on this, a new improved algorithm, Tent–Gaussian Enterprise Development Optimization (TGED), is introduced by incorporating chaotic initialization and Gaussian random walk mechanisms, which enhance the optimization capability and solution accuracy of the traditional enterprise development optimization algorithm. In a practical case study of a certain hydropower station, the TGED algorithm outperforms other benchmark algorithms in terms of solution accuracy and convergence performance, reducing the residual load peak–valley difference by over 600 MW. This effectively mitigates the volatility of wind and solar power output and significantly enhances system stability. The TGED algorithm demonstrates strong applicability in complex scheduling environments and provides valuable insights for large-scale renewable energy integration and short-term optimization scheduling of hydro–wind–solar complementary systems.

Hydropower stations play a crucial role in meeting the demand for peak shaving in the power grid. A method called the adaptive segmented cutting load algorithm (ASCLA) is proposed to address the problem of the uneven distribution of regulation effects when formulating long-term peak-shaving dispatching plans for hydropower stations. This method mainly consists of three components: full-period load segmentation, sub-period end water level treatment, and staged cutting load optimization. It can improve the average regulation ability of hydropower stations for the power grid’s long-term load by combining the inflow conditions. In order to compare the progressiveness of the proposed method, the Three Gorges hydropower station and the Central China Power Grid were used as research objects, and its long-term peak-shaving performance was analyzed by comparing it with that of the classical HCL solution method. The simulation dispatching results show that the proposed method resulted in significantly improved peak-shaving indicators, such as the mean squared deviation of the rolling window, load fluctuation index, and peak value compared to HCL. In years with abundant reservoir runoff, the comprehensive improvement can reach about 25%, indicating that the proposed ASCLA has more advantages in responding to the long-term load regulation needs of the power grid compared to existing methods. The research results of this paper can provide a reference and guidance for peak-shaving dispatching in hydropower stations during the dry season, effectively improving the long-term peak-shaving benefits of hydropower stations.

Under the current context of the large-scale integration of wind and solar power, the coupling of hydropower with wind and solar energy brings significant impacts on grid stability. To fully leverage the regulatory capacity of hydropower, this paper develops a multi-objective optimization scheduling model for hydropower, wind, and solar that balances generation-side power generation benefit and grid-side peak-regulation requirements, with the latter quantified by the mean square error of the residual load. To efficiently solve this model, Latin hypercube initialization, hybrid distance framework, and adaptive mutation mechanism are introduced into the Strength Pareto Evolutionary Algorithm II (SPEAII), yielding an improved algorithm named LHS-Mutate Strength Pareto Evolutionary Algorithm II (LMSPEAII). Its efficiency is validated on benchmark test functions and a reservoir model. Typical extreme scenarios—months with strong wind and solar in the dry season and months with weak wind and solar in the flood season—are selected to derive scheduling strategies and to further verify the effectiveness of the proposed model and algorithm. Finally, K-medoids clustering is applied to the Pareto front solutions; from the perspective of representative solutions, this reveals the evolutionary trends of different objective trade-off schemes and overall distribution characteristics, providing deeper insight into the solution set’s distribution features.

Hydrological runoff prediction plays a crucial role in water resource management and sustainable development. However, it is often constrained by the nonlinearity, strong stochasticity, and high non-stationarity of hydrological data, as well as the limited accuracy of traditional forecasting methods. Although Wasserstein Generative Adversarial Networks with Gradient Penalty (WGAN-GP) have been widely used for data augmentation to enhance predictive model training, their direct application as forecasting models remains limited. Additionally, the architectures of the generator and discriminator in WGAN-GP have not been fully optimized, and their potential in hydrological forecasting has not been thoroughly explored. Meanwhile, the strategy of jointly optimizing Variational Autoencoders (VAEs) with WGAN-GP is still in its infancy in this field. To address these challenges and promote more accurate and sustainable water resource planning, this study proposes a comprehensive forecasting model, VXWGAN-GP, which integrates Variational Autoencoders (VAEs), WGAN-GP, Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory Networks (BiLSTM), Gated Recurrent Units (GRUs), and Attention mechanisms. The VAE enhances feature representation by learning the data distribution and generating new features, which are then combined with the original features to improve predictive performance. The generator integrates GRU, BiLSTM, and Attention mechanisms: GRU captures short-term dependencies, BiLSTM captures long-term dependencies, and Attention focuses on critical time steps to generate forecasting results. The discriminator, based on CNN, evaluates the differences between the generated and real data through adversarial training, thereby optimizing the generator’s forecasting ability and achieving high-precision runoff prediction. This study conducts daily runoff prediction experiments at the Yichang, Cuntan, and Pingshan hydrological stations in the Yangtze River Basin. The results demonstrate that VXWGAN-GP significantly improves the quality of input features and enhances runoff prediction accuracy, offering a reliable tool for sustainable hydrological forecasting and water resource management. By providing more precise and robust runoff predictions, this model contributes to long-term water sustainability and resilience in hydrological systems.

With the increasing connection between integrated natural gas, thermal energy, and electric power systems, the integrated energy system (IES) needs to coordinate the internal unit scheduling and meet the different load demands of customers. However, when the energy subjects involved in scheduling are engaged in conflicts of interest, aspects such as hierarchical status relationships and cooperative and competitive relationships must be considered. Therefore, this paper studies the problem of achieving optimal energy scheduling for multiple subjects of source, storage, and load under the same distribution network while ensuring that their benefits are not impaired. First, this paper establishes a dual master-slave game model with a shared energy storage system (SESS), IES, and the alliance of prosumers (APs) as the main subjects. Second, based on the Nash negotiation theory and considering the sharing of electric energy among prosumers, the APs model is equated into two sub-problems of coalition cost minimization and cooperative benefit distribution to ensure that the coalition members distribute the cooperative benefits equitably. Further, the Stackelberg-Stackelberg-Nash three-layer game model is established, and the dichotomous distributed optimization algorithm combined with the alternating direction multiplier method (ADMM) is used to solve this three-layer game model. Finally, in the simulation results of the arithmetic example, the natural gas consumption is reduced by 9.32%, the economic efficiency of IES is improved by 3.95%, and the comprehensive energy purchase cost of APs is reduced by 12.16%, the proposed model verifies the sustainability co-optimization and mutual benefits of source, storage and load multi-interested subjects.

Fully tapping into the load regulation capacity of cascade hydropower stations on a river, in coordination with wind and photovoltaic power stations, can effectively suppress power fluctuations in new energy and promote grid integration and the consumption of new energy. To derive the peak shaving dispatching rules for cascaded hydropower stations in provincial power systems with a high proportion of new energy integration, a short-term peak shaving dispatching model for cascaded hydropower stations was first established considering large-scale new energy consumption; secondly, based on statistical learning methods, the peak shaving and dispatching rules of cascade hydropower stations in response to large-scale new energy integration were derived. Finally, taking wind farms, photovoltaic power stations, and the Qingjiang cascade hydropower stations in the power grid of Hubei Province, China, as research objects, the compensation effect of Qingjiang cascade hydropower stations on new energy output and the peak shaving performance for the power grid load were verified. The research results indicate that cascade hydropower can effectively reduce the peak valley load difference in provincial power grids and improve the overall smoothness of power grid loads while suppressing fluctuations in new energy output. After peak regulation by cascade hydropower, the residual load fluctuation indices of the power grid are improved by more than 20% compared to those after the integration of new energy. The probabilistic dispatching decisions for the facing period’s output through the optimal dispatching rules of cascade hydropower stations can provide dispatchers with richer decision-making support information and have guiding significance for the actual peak shaving dispatch of cascade hydropower stations.

Electricity price forecasting is of significant practical importance, and improving prediction accuracy has become a key area of focus. Although substantial progress has been made in electricity price forecasting research, the unique characteristics of the electricity market make prices highly sensitive to even minor market changes. This results in prices exhibiting long-term trends while also experiencing sharp fluctuations due to sudden events, often leading to extreme values. Furthermore, most current models are “black-box” models, lacking transparency and interpretability. These unique features make electricity price forecasting particularly complex and challenging. This paper introduces a forecasting framework that incorporates the Seasonal Trend decomposition using Loess (STL), Gated Recurrent Unit (GRU), Light Gradient Boosting Machine (LightGBM), and Shapley Additive Explanations (SHAPs) and applies it to forecasting in the electricity markets of the United States and Australia. The proposed forecasting framework significantly improves prediction accuracy compared to nine other baseline models, especially in terms of RMSE and R2 metrics, while also providing clear insights into the factors influencing the forecasts. On the U.S. dataset, the RMSE of this framework is 12.7% lower than that of the second-best model, while, on the Australian dataset, the RMSE of the SLGSEF is 2.58% lower than that of the second-best model.

With the high proportion of clean energy connected to the grid, accurately characterizing its uncertainty emerges as a pivotal challenge for the planning and optimizing Hydro-Wind-Photovoltaic (HWP) multi-energy complementary systems. To address the complex modeling requirements of HWP resources in terms of high-dimensional variables and spatiotemporal stochastic dependencies, this study proposes a novel high-dimensional scenario generation method, jointly driven by multiple correlations. Firstly, the temporal autocorrelation models based on Gaussian mixture model (GMM) were constructed alongside the spatial cross-correlation model utilizing Copula functions, with synergistic modeling of multiple correlations being achieved through cumulative distribution functions. Second, the accuracy and reliability of the constructed models were validated through evaluation of root mean square errors between empirical data distributions and theoretical model distributions, supplemented by Kolmogorov-Smirnov goodness-of-fit tests. Then, based on established multiple correlations modeling framework and integrated with inverse transform sampling, daily-scale scenario sets were generated for streamflow, wind power output, and photovoltaic (PV) output. Finally, the performance of the proposed method was comprehensively evaluated through multiple metrics from diverse perspectives. The novelty of this work lies in: (1) The synergistic GMM-Copula modeling mechanism enables decoupled modeling of multiple correlations characteristics among HWP resources, with time-varying parameters reflecting dynamic evolution of correlations; (2) The application of the conditional distribution strategy reduced modeling complexity and improved computational feasibility, effectively addressing the challenges of modeling high-dimensional temporal variables and high-dimensional resource variables. Applied to the Xiluodu Hydropower Station and its associated wind-PV resources, the proposed method demonstrates superior performance in preserving statistical properties, describing multiple correlations, and characterizing uncertainties, thereby enhancing the accuracy and practicality of scenario generation. This advancement provides robust data support for optimizing the dispatch of HWP multi-energy complementary systems.

Hydropower is a vital strategic component of China’s clean energy development. Its construction and optimized water resource allocation are crucial for addressing global energy challenges, promoting socio-economic development, and achieving sustainable development. However, the optimization scheduling of cascade hydropower stations is a large-scale, multi-constrained, and nonlinear problem. Traditional optimization methods suffer from low computational efficiency, while conventional intelligent algorithms still face issues like premature convergence and local optima, which severely hinder the full utilization of water resources. This study proposed an improved whale optimization algorithm, the Black-winged Differential-variant Whale Optimization Algorithm (BDWOA), which enhanced population diversity through a Logistic-Sine-Cosine combination chaotic map, improved algorithm flexibility with an adaptive adjustment strategy, and introduced the migration mechanism of the black-winged kite algorithm along with a differential mutation strategy to enhance the global search ability and convergence capacity. The BDWOA algorithm was tested using test functions with randomly generated simulated data, with its performance compared against five related optimization algorithms. Results indicate that the BDWOA achieved the optimal value with the fewest iterations, effectively overcoming the limitations of the original whale optimization algorithm. Further validation using actual runoff data for the cascade hydropower station optimization scheduling model showed that the BDWOA effectively enhanced power generation efficiency. In high-flow years, the average power generation increased by 8.3%, 6.5%, 6.8%, 4.1%, and 8.2% compared to the five algorithms while achieving the shortest computation time. Significant improvements in power generation were also observed in normal-flow and low-flow years. The scheduling solutions generated by the BDWOA can adapt to varying inflow conditions, offering an innovative approach to solving complex hydropower station optimization scheduling problems. This contributes to the sustainable utilization of water resources and supports the long-term development of renewable energy.

Exploring efficient and stable solution methods for hydropower generation optimization models is crucial for enhancing reservoir power generation efficiency and achieving the sustainable use of water resources. However, existing studies predominantly focus on single-timescale scheduling models, failing to fully exploit multi-timescale runoff information. Additionally, commonly used solution algorithms often face challenges such as premature convergence, susceptibility to local optima, and dimensionality issues. To address these limitations, this paper proposes the Migrating Particle Whale Optimization Algorithm (MPWOA), which initializes the population using chaotic mapping, incorporates a particle swarm mechanism to enhance exploitation during the spiral predation phase, and integrates the black-winged kite migration mechanism to improve stochastic search performance. Validation on classical test functions and the Jiangpinghe River of the multi-timescale nested optimal scheduling model demonstrates that MPWOA exhibits faster convergence and stronger optimization capabilities and significantly improves power generation. The multi-timescale nested scheduling scheme derived from this algorithm effectively utilizes runoff information, offering a practical and highly efficient solution for hydropower scheduling.