A copula-based flexible-stochastic programming method for planning regional energy system under multiple uncertainties: A case study of the urban agglomeration of Beijing and Tianjin

Abstract

In this study, a copula-based flexible-stochastic programming (CFSP) method is developed for planning regional energy system (RES). CFSP can deal with multiple uncertainties expressed as interval values, random variables and fuzzy sets as well as their combinations employed to objective function and soft constraints. It can also reflect uncertain interactions among random variables through using copula functions even having different probability distributions and previously unknown correlations. Then, based on the developed CFSP approach, a CFSP-RES model is formulated for planning RES of the urban agglomeration of Beijing and Tianjin (China). Results disclose that uncertainties existed in the system components have significant effects on the outputs of decision variables and system cost, and the variation of system cost is reached 16.3%. Results also reveal that air pollutant emissions can be mitigated if the urban agglomeration can co-implement renewable energy development plans (REDP) over the planning horizon, with the reductive rates of [3.3, 7.6] % of sulfur dioxide (SO2), [2.7, 4.1] % of nitrogen oxides (NOx) and [7.0, 11.5] % of particulate matter (PM10). Compared to joint-probabilistic chance-constrained programming (JCP), the CFSP method is more effective for handling multiple random parameters associated with different probability distributions in which their correlations are unknown. Thus, it is not limited to some unjustified assumptions and can be applied to a wider range of problems than previous studies. The findings are helpful to explore the influence of interaction among random variables on modeling outputs and provide in-depth analysis for identifying desired decision schemes for planning RES.

Uncertainties towards a fossil-free system with high integration of wind energy in long-term planning

“…The use of PROMETHEUS, for sampling of the joint probability distributions of the parameters, significantly differs from this study, in which the probability distributions of the uncertain inputs are ad hoc, mainly based on literature. Chen et al (2017) found no report on interactions among multiple parameters in electric systems planning models; however, methodologies dealing with joint probability distributions might be recommended, as also suggested by Yu et al (2018). Marcucci et al (2019) found that the availability of biomass resources, the rapid decrease of the costs of renewables and improvements in energy efficiency were the factors with the largest effect on the cost of carbon on a global level.…”

Data Driven Stochastic Energy Management for Isolated Microgrids Based on Generative Adversarial Networks Considering Reactive Power Capabilities of Distributed Energy Resources and Reactive Power Costs

“…The probability distributions are not guaranteed to be accurate in representing the uncertain variables. Whereas in [26]- [27], copula methods were utilized in the scenario generation process. However, it is hard to capture the temporal and spatial dynamics of RESs power profiles depending only on the first and second statistics when using copula methods.…”

Evolution of the Industrial Innovation Ecosystem of Resource-Based Cities (RBCs): A Case Study of Shanxi Province, China

“…In Brazil, financial mechanisms were used to compensate for the negative environmental impacts of mining. There are 262 RBCs in China [18]. RBCs, as strategic energy resource bases, are important supports for the sustained and sound development of the national economy [19].…”