Multidimensional Uncertainty Integration based on Spatiotemporal Hybrid Copula: A Resilience-Oriented Modeling Paradigm for IES and Virtual Power Plant
DOI:
https://doi.org/10.4108/ew.12159Keywords:
IES, Spationtemporal hybrid copula, Dynamic correlations, Multi-dimensional uncertaintiesAbstract
Integrated Energy Systems (IES) and Virtual Power Plants (VPPs) are pivotal for achieving the "dual-carbon" goals, yet they face significant challenges from multidimensional spatiotemporal uncertainties. Traditional uncertainty modeling methods, relying on static correlation assumptions, are inadequate for dynamically capturing the complex fluctuations in source-load-market parameters, especially the aggregation uncertainties inherent in VPPs. This paper proposes a novel resilience-oriented modeling paradigm centered on a spatiotemporal hybrid Copula (ST-HC) framework. The primary innovation lies in its dynamic correlation capture mechanism, which integrates time-decay and spatial-distance factors to accurately characterize nonlinear, time-varying dependencies among cross-regional uncertainties. Furthermore,a comprehensive five-dimensional evaluation system is established, incorporating metrics for storage flexibility, degradation, market volatility, risk preference, and system efficiency—including a novel data security risk entropy indicator. Validated through case studies, the proposed approach demonstrates superior performance over conventional static models, enhancingplanning accuracy and reducing total costs by approximately 9.98%, while effectively quantifying the economic-low-carbon trade-offs under different risk strategies for IES-VPP synergy.
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[1] Smith JA, Müller T, Johnson RW. Spatiotemporal vine copula modeling for correlated uncertainties in multi-energy grids[J]. Applied Energy. 2024; 367: 123301.
[2] Dubois L, Rossi F, Schmidt M. Data-driven nonparametric dependence modeling of wind-solar-load uncertainties using optimal transport copulas[J]. IEEE Transactions on Sustainable Energy. 2023; 14(4): 2101-2115.
[3] Anderson KL, Williams PD. Multimodal uncertainty propagation in renewable-integrated energy hubs: A Gaussian mixture copula approach[J]. Renewable and Sustainable Energy Reviews. 2024; 192: 114201.
[4] Müller S, Braun H, Fischer K. Resilience quantification of IES under spatiotemporally correlated uncertainties using conditional value-at-risk[J]. Energy Economics. 2023; 128: 107261.
[5] García-Sánchez C, Fernández-Guillamón A, Gómez-Lázaro E. Dynamic weighting of temporal-spatial factors in hybrid copula models for energy system uncertainty characterization[J]. Energy Conversion and Management. 2024; 308: 118152.
[6] Patel RK, Jackson ST. Information-theoretic security risk assessment for cyber-physical integrated energy systems[J]. IEEE Transactions on Smart Grid. 2023; 14(5): 4021-4033.
[7] Kazempour J, Pinson P, Papaefthymiou G. Regime-switching copulas for modeling electricity-carbon price dependencies in low-carbon energy planning[J]. Operations Research. 2024; 72(1): 1-19.
[8] Viehweider F, Moser A, Leimgruber F. Exergy efficiency degradation under multi-uncertainty coupling in district energy networks[J]. Energy. 2023; 282: 128742.
[9] Bessa RJ, Matos MA, Costa IC. Multidimensional flexibility metrics for energy storage in correlated uncertainty environments[J]. IEEE Transactions on Power Systems. 2024; 39(1): 511-525.
[10] Hodge BM, Orwig KD, Lew DJ. Copula-entropy frameworks for probabilistic forecasting of multi-energy demand under extreme weather[J]. Renewable Energy. 2023; 218: 119312.
[11] Zima M, Andersson G, Hug G. Adaptive mixed copula models for dynamic correlation analysis of source-load-market uncertainties[J]. Electric Power Systems Research. 2024; 226: 109991.
[12] Smith TJ, Brown MH. CVaR-constrained optimization of integrated energy systems under spatiotemporal uncertainty correlations[J]. International Journal of Electrical Power & Energy Systems. 2023; 152: 109232.
[13] Giannelos S, Konstantelos I, Strbac G. Sparse vine copula constructions for high-dimensional uncertainty modeling in energy systems[J]. Applied Energy. 2024; 355: 122178.
[14] Wogrin S, Tejada-Arango DA, Centeno E. Robust-copula optimization for capacity planning of multi-energy systems under data scarcity[J]. European Journal of Operational Research. 2023; 309(2): 789-803.
[15] Palmintier B, Webster MD. Dynamic correlation risk premiums in electricity-carbon markets: Implications for IES investment[J]. The Energy Journal. 2024; 45(2): 1-28.
[16] Zucker A, Hinz F, Most D. Nonparametric Bayesian networks for uncertainty propagation in integrated heat-electricity networks[J]. Energy. 2023; 274: 127352.
[17] Pinson P, Madsen H, Nielsen HA. Temporal adaptive copulas for short-term forecasting of correlated renewable generation[J]. Wind Energy. 2024; 27(3): 301-317.
[18] Dehghan S, Amjady N, Kazemi A. Resilience-oriented stochastic scheduling of IES under cyber-physical contingencies using hybrid copula[J]. IEEE Transactions on Industrial Informatics. 2023; 19(7): 8201-8212.
[19] Zugno M, Morales JM, Pinson P. Equilibrium models for electricity markets with correlated wind and price uncertainties[J]. Mathematical Programming. 2024; 201(1-2): 1-32.
[20] Bottieau J, De Grève Z, Vallee F. Multiscale copula-based scenario generation for coordinated energy storage dispatch[J]. Journal of Energy Storage. 2023; 68: 107732.
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