Hongsheng Su¹, Wenyao Su¹, Yulong Che^1,*, Xiping Ma², Tian Zhao¹, Limiao Ren¹

Energy Engineering, Vol.122, No.11, pp. 4777-4797, 2025, DOI:10.32604/ee.2025.068134 - 27 October 2025

Abstract Aiming at the issues of insufficient carrying capacity, limited flexibility, and weak source-network-load-storage coordination capability in distribution networks under the background of high-proportion new energy integration. This study proposes a bi-level optimization model for ADN integrating hybrid wind-solar-hydrogen-storage systems. First, an electro-hydrogen coupling system framework is constructed, including models for electrolytic hydrogen production, hydrogen storage, and fuel cells. Meanwhile, typical scenarios of wind-solar joint output are developed using Copula functions to characterize the variability of renewable energy generation. Second, a bi-level optimization model for ADN with electrolytic hydrogen production and storage systems is established: the… More >

Jiaqing Wang¹, Yuming Shen^2,*, Xuli Wang², Jiayin Xu²

Energy Engineering, Vol.122, No.7, pp. 2751-2766, 2025, DOI:10.32604/ee.2025.064317 - 27 June 2025

Abstract To adapt to the uncertainty of new energy, increase new energy consumption, and reduce carbon emissions, a high-voltage distribution network energy storage planning model based on robustness-oriented planning and distributed new energy consumption is proposed. Firstly, the spatio-temporal correlation of large-scale wind-photovoltaic energy is modeled based on the Vine Copula model, and the spatial correlation of the generated wind-photovoltaic power generation is corrected to get the spatio-temporal correlation of wind-photovoltaic power generation scenarios. Finally, considering the subsequent development of new energy on demand for high-voltage distribution network peaking margin and the economy of the system More >

Osnamir E. Bru-Cordero¹, Cecilia Castro², Víctor Leiva^3,*, Mario C. Jaramillo-Elorza⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 1401-1431, 2025, DOI:10.32604/cmes.2025.064487 - 30 May 2025

Abstract Most reliability studies assume large samples or independence among components, but these assumptions often fail in practice, leading to imprecise inference. We address this issue by constructing confidence intervals (CIs) for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework. Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures. The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix, achieving near-nominal coverage probabilities even in small samples or highly dependent settings. More >

Caifeng Wen¹, Feifei Xue^1,*, Hongliang Hao², Edwin E. Nyakilla², Ning Yang^1,*, Yongsheng Wang³, Yuwen Zhang²

Energy Engineering, Vol.122, No.4, pp. 1511-1529, 2025, DOI:10.32604/ee.2025.060810 - 31 March 2025

Abstract This paper presents a new capacity planning method that utilizes the complementary characteristics of wind and solar power output. It addresses the limitations of relying on a single metric for a comprehensive assessment of complementarity. To enable more accurate predictions of the optimal wind-solar ratio, a comprehensive complementarity rate is proposed, which allows for the optimization of wind-solar capacity based on this measure. Initially, the Clayton Copula function is employed to create a joint probability distribution model for wind and solar power, enabling the calculation of the comprehensive complementarity rate. Following this, a joint planning… More >

Haoyuan Li, Lingling Li^*

Energy Engineering, Vol.122, No.4, pp. 1337-1358, 2025, DOI:10.32604/ee.2025.060105 - 31 March 2025

Abstract Rational distribution network planning optimizes power flow distribution, reduces grid stress, enhances voltage quality, promotes renewable energy utilization, and reduces costs. This study establishes a distribution network planning model incorporating distributed wind turbines (DWT), distributed photovoltaics (DPV), and energy storage systems (ESS). K-means++ is employed to partition the distribution network based on electrical distance. Considering the spatiotemporal correlation of distributed generation (DG) outputs in the same region, a joint output model of DWT and DPV is developed using the Frank-Copula. Due to the model’s high dimensionality, multiple constraints, and mixed-integer characteristics, bilevel programming theory is… More >

Ming Li^1,*, Cairen Furifu¹, Chengyang Ge², Yunping Zheng¹, Shunfu Lin², Ronghui Liu²

Energy Engineering, Vol.120, No.8, pp. 1775-1801, 2023, DOI:10.32604/ee.2023.027215 - 05 June 2023

Abstract As an effective carrier of integrated clean energy, the microgrid has attracted wide attention. The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids. This paper proposes an optimization scheme based on the distributionally robust optimization (DRO) model for a microgrid considering solar-wind correlation. Firstly, scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function; then the generated scenario results are reduced by K-means clustering; finally, the probability confidence interval More >

Yonghua Li^1,*, Xiaoning Bai², Shanshan Shi¹, Shenxuan Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 1077-1092, 2022, DOI:10.32604/cmes.2022.018181 - 13 December 2021

Abstract Multiple failure modes and strength degradation are usually inherent in the gear transmission system, which brings new challenges for conducting fatigue reliability analysis and design. This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of the Copula function and Gamma process. Firstly, the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history. The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model. The marginal distribution functions of tooth contact More >

Xueping Fan^*, Guanghong Yang, Zhipeng Shang, Xiaoxiong Zhao, Yuefei Liu^*

Structural Durability & Health Monitoring, Vol.15, No.1, pp. 69-83, 2021, DOI:10.32604/sdhm.2021.011922 - 22 March 2021

Abstract This article presented a new data fusion approach for reasonably predicting dynamic serviceability reliability of the long-span bridge girder. Firstly, multivariate Bayesian dynamic linear model (MBDLM) considering dynamic correlation among the multiple variables is provided to predict dynamic extreme deflections; secondly, with the proposed MBDLM, the dynamic correlation coefficients between any two performance functions can be predicted; finally, based on MBDLM and Gaussian copula technique, a new data fusion method is given to predict the serviceability reliability of the long-span bridge girder, and the monitoring extreme deflection data from an actual bridge is provided to More >

Ramadan A. ZeinEldin^1,2, Christophe Chesneau^3,*, Farrukh Jamal⁴, Mohammed Elgarhy⁵, Abdullah M. Almarashi⁶, Sanaa Al-Marzouki⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 791-819, 2021, DOI:10.32604/cmes.2021.012169 - 21 January 2021

Abstract Understanding a phenomenon from observed data requires contextual and efficient statistical models. Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations. Modern examples include the distributions of the truncated Fréchet generated family. In this paper, we go even further by introducing a more general family, based on a truncated version of the generalized Fréchet distribution. This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters, as well as the skewness and weight of the tails. We also investigate the More >