Search Results (180)

Accurate and uncertainty-aware wind power forecasting is essential for reliable and cost-effective power system operations. This paper presents a novel probabilistic forecasting framework based on diffusion probabilistic models. We adopted a two-stage modeling strategy—a deterministic predictor first generates baseline forecasts, and a conditional diffusion model then learns the distribution of residual errors. Such a two-stage decoupling strategy improves learning efficiency and sharpens uncertainty estimation. We employed the elucidated diffusion model (EDM) to enable flexible noise control and enhance calibration, stability, and expressiveness. For the generative backbone, we introduced a time-series-specific diffusion Transformer (TimeDiT) that incorporates modular conditioning to separately fuse numerical weather prediction (NWP) inputs, noise, and temporal features. The proposed method was evaluated using the public database from ten wind farms in the Global Energy Forecasting Competition 2014 (GEFCom2014). We further compared our approach with two popular baseline models, i.e., a distribution parameter regression model and a generative adversarial network (GAN)-based model. Results showed that our method consistently achieves superior performance in both deterministic metrics and probabilistic accuracy, offering better forecast calibration and sharper distributions. Full article

In response to the challenge of multi-objective optimal scheduling and efficient solution of hydropower stations under large-scale renewable energy integration, this study develops a multi-objective optimization model with the dual goals of maximizing total power generation and minimizing the variance of residual load. Four complementarity evaluation indicators are used to analyze the wind–solar complementarity characteristics. Building upon this foundation, Hyper-dominance Evolutionary Algorithm (HEA)—capable of efficiently solving high-dimensional problems—is introduced for the first time in the context of wind–solar–hydropower integrated scheduling. The case study results show that the HEA performs better than the benchmark algorithms, with the best mean Hypervolume and Inverted Generational Distance Plus across nine Walking Fish Group (WFG) series test functions. For the hydro-wind-solar scheduling problem, HEA obtains Pareto frontier solutions with both maximum power generation and minimal residual load variance, thus effectively solving the multi-objective scheduling problem of the hydropower system. This work provides a valuable reference for modeling and efficiently solving the multi-objective scheduling problem of hydropower in the context of emerging power systems. This work provides a valuable reference for the modeling and efficient solution of hydropower multi-objective scheduling problems in the context of emerging power systems. Full article

Fractional-order differential equations are prevalent in many scientific fields; hence, their study has seen a renaissance in recent years. The fascinating realm of fractional calculus is explored in this research study, with particular emphasis on the Harry Dym equation. To solve this problem, we use the Laplace Residual Power Series Method (LRPSM) and introduce the New Iterative Method (NIM). Both the mathematical complexity of the Harry Dym problem and the viability of the Caputo operator in this setting are investigated in our work. We go beyond the limitations of traditional mathematical methods to provide novel insights into the results of fractional-order differential equations via careful analysis and cutting-edge procedures. In this paper, we combine theory and practice to provide a novel perspective to the results of high-order fractional differential equations. Our efforts pay off by expanding our knowledge of mathematics and revealing the latent potential of the Harry Dym equation. This study expands researchers’ and mathematicians’ perspectives, bringing in a new and exciting period of progress in the field of fractional calculus. Full article

In the context of the clean and low-carbon transformation of power systems, addressing the challenge of day-ahead electricity market price prediction issues triggered by the strong stochastic volatility of power supply output due to high-penetration renewable energy integration, as well as problems such as limited dataset scales and short market cycles in test sets associated with existing electricity price prediction methods, this paper introduced an innovative prediction approach based on a multi-modal feature fusion and BiGRUSA-ResSE-KAN deep learning model. In the data preprocessing stage, maximum–minimum normalization techniques are employed to process raw electricity price data and exogenous variable data; the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) methods are utilized for multi-modal decomposition of electricity price data to construct a multi-scale electricity price component matrix; and a sliding window mechanism is applied to segment time-series data, forming a three-dimensional input structure for the model. In the feature extraction and prediction stage, the BiGRUSA-ResSE-KAN multi-branch integrated network leverages the synergistic effects of gated recurrent units combined with residual structures and attention mechanisms to achieve deep feature fusion of multi-source heterogeneous data and model complex nonlinear relationships, while further exploring complex coupling patterns in electricity price fluctuations through the knowledge-adaptive network (KAN) module, ultimately outputting 24 h day-ahead electricity price predictions. Finally, verification experiments conducted using test sets spanning two years from five major electricity markets demonstrate that the introduced method effectively enhances the accuracy of day-ahead electricity price prediction, exhibits good applicability across different national electricity markets, and provides robust support for electricity market decision making. Full article

Deep learning has become a widely used approach in photovoltaic (PV) power generation forecasting due to its strong self-learning and parameter optimization capabilities. In this study, we apply a deep learning algorithm, known as the time-series dense encoder (TiDE), which is an MLP-based encoder–decoder model, to forecast PV power generation. TiDE compresses historical time series and covariates into latent representations via residual connections and reconstructs future values through a temporal decoder, capturing both long- and short-term dependencies. We trained the model using data from 2020 to 2022 from Australia’s Desert Knowledge Australia Solar Centre (DKASC), with 2023 data used for testing. Forecast accuracy was evaluated using the $R^2$ coefficient of determination, mean absolute error (MAE), and root mean square error (RMSE). In the 5 min ahead forecasting test, TiDE demonstrated high short-term accuracy with an $R^2$ of 0.952, MAE of 0.150, and RMSE of 0.349, though performance declines for longer horizons, such as the 1 h ahead forecast, compared to other algorithms. For one-day-ahead forecasts, it achieved an $R^2$ of 0.712, an MAE of 0.507, and an RMSE of 0.856, effectively capturing medium-term weather trends but showing limited responsiveness to sudden weather changes. Further analysis indicated improved performance in cloudy and rainy weather, and seasonal analysis reveals higher accuracy in spring and autumn, with reduced accuracy in summer and winter due to extreme conditions. Additionally, we explore the TiDE model’s sensitivity to input environmental variables, algorithmic versatility, and the implications of forecasting errors on PV grid integration. These findings highlight TiDE’s superior forecasting accuracy and robust adaptability across weather conditions, while also revealing its limitations under abrupt changes. Full article

In this work, we first develop the modified time Caputo fractional Kawahara Equations (MTCFKEs) in the usual Hilbert spaces and extend them to analogous structures within the theory of Hilbert algebras. Next, we employ the residual power series method, combined with the Laplace transform, to introduce a new effective technique called the Laplace Residual Power Series Method (LRPSM). This method is applied to derive the coefficients of the series solution for MTCFKEs in the context of Hilbert algebras. In real Hilbert algebras, we obtain approximate solutions for MTCFKEs under both exact and approximate initial conditions. We present both graphical and numerical results of the approximate analytical solutions to demonstrate the capability, efficiency, and reliability of the LRPSM. Furthermore, we compare our results with solutions obtained using the homotopy analysis method and the natural transform decomposition method. Full article

In this paper, we develop an analytical approximate solution for the nonlinear time-fractional Fisher’s equation using a right starting space function and a unique analytic-numeric technique referred to as the Laplace residual power series approach. The generalized Taylor’s formula and the Laplace transform operator are coupled in the aforementioned method, where the coefficients, obtained through fractional expansion in the Laplace space, are determined by applying the limit concept. In order to validate and illustrate the theoretical methodology of the LRPS technique, as well as to show its effectiveness, adaptability, and superiority in solving various types of nonlinear time and space fractional differential equations, numerical experiments are generated. The obtained analytical solutions are compatible with the precise solutions and concur with those proposed by the other approaches. The outcomes show that the Laplace residual power series strategy is incredibly successful, straightforward to implement, and well suited for handling the complexity of nonlinear problems. Full article

In this work, the novel general formula for a time-dependent nuclear reactor system of equations with delayed neutron effect has been formulated using a fractional calculus model. We explore the properties of this model, including two analytical approximation methods, the Temimi–Ansari method (TAM) and the Sumudu residual power series method (SRPSM), for solving the equation. These methods allow for the computation of approximate solutions at specific points. This is particularly useful for partial differential equations (PDEs) arising in various fields like physics, engineering, and finance. This work is hoped to improve the advancement of nuclear modeling and simulation, providing researchers and engineers with a powerful mathematical tool for studying the complex dynamics of these critical energy systems. Full article

As the popularity of smartphones, wearable devices, intelligent vehicles, and countless other devices continues to rise, the surging demand for mobile data traffic has resulted in an increasingly crowded electromagnetic spectrum. Spectrum sharing serves as a solution to optimize the utilization of wireless communication channels, allowing various types of users to share the same frequency band securely. This paper investigates spectrum allocation and power control problems in overlay spectrum sharing, with a focus on promoting green communication. Maximizing weighted sum energy efficiency (WSEE) requires solving complex multiple-ratio fractional programming (FP) problems. In contrast, weighted sum power (WSP) minimization offers a more straightforward approach. Moreover, because WSP is directly related to users’ power consumption, we can dynamically adjust their weights to balance their residual energy. We prioritize WSP minimization over the more common WSEE maximization. This choice not only simplifies computation but also maintains users’ quality of service (QoS) requirements. The joint optimization for multiple primary users (PUs) and secondary users (SUs) can be decomposed into two components: a weighted bipartite matching problem and a series of convex resource allocation problems. Utilizing Newton’s method, our system-level simulation results show that the proposed scheme achieves optimal performance with minimal computational time. We explore strategies to accelerate the proposed scheme by refining the selection of initial values for Newton’s method. Full article

The development of numerical or analytical solutions for fractional mathematical models describing specific phenomena is an important subject in physics, mathematics, and engineering. This paper’s main objective is to investigate the approximation of the fractional order Caudrey–Dodd–Gibbon ($CDG$) nonlinear equation, which appears in the fields of laser optics and plasma physics. The physical issue is modeled using the Caputo derivative. Adomian and homotopy polynomials facilitate the handling of the nonlinear term. The main innovation in this paper is how the recurrence relation, which generates the series solutions after just a few iterations, is handled. We examined the assumed model in fractional form in order to demonstrate and verify the efficacy of the new methods. Moreover, the numerical simulation is used to show how the physical behavior of the suggested method’s solution has been represented in plots and tables for various fractional orders. We provide three problems of each equation to check the validity of the offered schemes. It is discovered that the outcomes derived are close to the accurate result of the problems illustrated. Additionally, we compare our results with the Laplace residual power series method (LRPSM), the natural transform decomposition method (NTDM), and the homotopy analysis shehu transform method (HASTM). From the comparison, our methods have been demonstrated to be more accurate than alternative approaches. The results demonstrate the significant benefit of the established methodologies in achieving both approximate and accurate solutions to the problems. The results show that the technique is extremely methodical, accurate, and very effective for examining the nature of nonlinear differential equations of arbitrary order that have arisen in related scientific fields. Full article

With the increase in photovoltaic installed capacity year by year, accurate photovoltaic power prediction is of great significance for photovoltaic grid-connected operation and scheduling planning. In order to improve the prediction accuracy, this paper proposes a photovoltaic power prediction combination model based on Pearson Correlation Coefficient (PCC), Complete Ensemble Empirical Mode Decomposition (CEEMDAN), K-means clustering, Variational Mode Decomposition (VMD), Convolutional Neural Network (CNN), and Bidirectional Long Short-Term Memory (BiLSTM). By making full use of the symmetric structure of the BiLSTM algorithm, one part is used to process the data sequence in order, and the other part is used to process the data sequence in reverse order. It captures the characteristics of sequence data by simultaneously processing a ‘symmetric’ information. Firstly, the historical photovoltaic data are preprocessed, and the correlation analysis of meteorological factors is carried out by PCC, and the high correlation factors are extracted to obtain the multivariate time series feature matrix of meteorological factors. Then, the historical photovoltaic power data are decomposed into multiple intrinsic modes and a residual component at one time by CEEMDAN. The high-frequency components are clustered by K-means combined with sample entropy, and the high-frequency components are decomposed and refined by VMD to form a multi-scale characteristic mode matrix. Finally, the obtained features are input into the CNN–BiLSTM model for the final photovoltaic power prediction results. After experimental verification, compared with the traditional single-mode decomposition algorithm (such as CEEMDAN–BiLSTM, VMD–BiLSTM), the combined prediction method proposed reduces MAE by more than 0.016 and RMSE by more than 0.017, which shows excellent accuracy and stability. Full article

With the evolving urbanization process in modern cities, the tertiary industry load and residential load start to take up a major proportion of the total urban power load. These loads are more dependent on stochastic factors such as human behaviors and weather events, demonstrating frequent abnormal variations that deviate from the normal pattern and causing consequent large forecasting errors. In this paper, a hybrid forecasting framework is proposed focusing on improving the forecasting accuracy of the urban power load during abnormal load variation periods. First, a quantitative method is proposed to define and characterize the abnormal load variations based on the residual component decomposed from the original load series. Second, a sample augmentation method is established based on Generative Adversarial Nets to boost the limited abnormal samples to a larger quantity to assist the forecasting model’s training. Last, an advanced forecasting model, TimesNet, is introduced to capture the complex and nonlinear load patterns during abnormal load variation periods. Simulation results based on the actual load data of Chongqing, China demonstrate the effectiveness of the proposed method. Full article

This paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlinear ion acoustic waves and thus helping us to understand wave dynamics in plasmas. We introduce a new approach that relies on a new fractional expansion in the natural transform space and residual power series method to construct analytical solutions to the governing models. We investigate the theoretical analysis of the proposed method for these equations to expose this approach’s applicability, efficiency, and effectiveness in constructing analytical solutions to the governing equations. Moreover, we present a comparative discussion between the solutions derived during the work and those given in the literature to confirm that the proposed approach generates analytical solutions that rapidly converge to exact solutions, which proves the effectiveness of the proposed method. Full article

In the current study, the integration of finite element simulation and machine learning is used to find the optimal combination of processing parameters in the directed energy deposition of SS316L. To achieve this, the FE simulation was validated against previously implemented research, and a series of simulations were conducted. Three inputs, namely laser power, scanning speed, and laser beam radius, and two outputs, namely residual stress and displacement, were considered. To run the machine learning model, artificial neural networks and a non-dominated sorting genetic algorithm were applied to determine the optimal combination of processing parameters. In addition, the current study underscores the novelty of combining FE simulation and machine learning methods, which provides enhanced precision and efficiency in controlling residual stress and displacement (geometrical deviation) in the Directed Energy Deposition (DED) process. Then, the results obtained via machine learning were validated with confirmatory tests and reported. The findings offer a practical solution for process parameter optimization, contributing to the progression of additive manufacturing technologies. Full article

This investigation focuses on the study of the fractional damped Burgers’ equation by using the natural residual power series method coupled with the new iteration transform method in the context of the Caputo operator. The equation of Burgers under the damped context is useful when studying one-dimensional nonlinear waves involving damping effect, and is used in fluid dynamics, among other applications. Two new mathematical methods that can be used to obtain an approximate solution to this complex non-linear problem are the natural residual power series method and the new iteration transform method. Therefore, it can be deduced that the Caputo operator aids in modeling of the fractional derivatives, as it provides a better description of the physical realities. Thus, the objective of the present work is to advance the knowledge accumulated on the behavior of solutions to the damped Burgers’ equation, as well as to check the applicability of the proposed approaches to other nonlinear fractional partial differential equations. Full article