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Journal ArticleDOI

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

TL;DR: 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.
About: This article is published in Applied Energy.The article was published on 2018-01-15 and is currently open access. It has received 52 citations till now. The article focuses on the topics: Stochastic programming & Copula (probability theory).

Summary (3 min read)

1. Introduction

  • Over the past decades, the world has undergone rapid economic development and social revolution corresponding to the increasing energy demand.
  • Air pollution is a major public health crisis, with many of its root causes and cures to be found in the energy sector.
  • Interval-parameter programming (IPP) can deal with uncertainties expressed as interval numbers without distributional information [22, 23].
  • In the CFSP-RES model, fifteen scenarios under different joint constraint-violation levels and various individual constraint-violation levels are selected to verify the interaction of electricity demands between the urban cities of Beijing and Tianjin.

2.1 Copula-based stochastic programming

  • The ‘‘copula” approach for modeling multivariate joint distributions was proposed by Sklar in 1959 [24].
  • This approach shows that a multivariate joint distribution can be completely characterized by its respective marginal distributions and a copula function for binding them together independent of the types of individual marginal distributions [15].
  • Modeling joint distributions using copulas has effectiveness in allowing researchers to take into account marginal distributions and dependence as two separate but related issues [25-29].

2.2 Interval-flexible programming

  • Flexible programming (FP) is effective for handling flexibility on target value of goals and soft constraints [33].
  • The FP model has advantage of dealing with uncertain parameters in virtue of various fuzzy ranking approaches and different satisfaction degrees.
  • In many practical problems, uncertainties are often existed as discrete intervals with known lower and upper bounds.
  • IPP is capable of handling the uncertainties expressed as intervals without probability distributions and flexibility on target value of goals [22, 38].

2.3 Copula-based flexible-stochastic programming

  • In decision-making problems, acquired data may subject to some errors owing to spatial and 9 temporal variations, as well as the incompleteness or impreciseness of observed information.
  • This can lead to multiple uncertainties of interactive random variables, interval values, and flexible constraints.
  • Therefore, one effective approach for dealing with such complex uncertainties can be developed by coupling IFP into CSP.

3. Case Study

  • The CFSP method is applied to planning RES of the urban agglomeration of Beijing and Tianjin that are both located in the northern part of the North China Plain .
  • In addition, one of problems for RES planning faced by decision makers is the multi-uncertainty associated with various characteristic features in the study system [39, 40].
  • Such variations of renewable energy availabilities would then affect operating statuses of relevant power-conversion facilities (i.e. hydro power, wind power and photovoltaic power), resulting in changes in their energy outputs [42].

4.1 Result analysis

  • Beijing is a typical power-import city; its domestic electricity production is far below the city’s electricity consumption which occupies lower than 60%.
  • Compared to Beijing, Tianjin is a self-supporting based city, the electricity generated by domestic production accounts for 75.6%.
  • Summarily, coal-fired power is the primary emitter for the entire power-conversion facilities owing to the higher pollutant discharge coefficient and lower coal price.
  • For each planning year, the pollutant emissions would be reduced with time in response to the implement of air pollution controls, reform of coal-burning boils, stimulation of renewable energy resources, as well as improvement of energy transmission capacities and efficiencies in the RES.

4.2 Uncertainty analysis

  • Three joint constraint-violation levels (i.e. p = 0.05, 0.1 and 0.2) of violating electricity demand of RES in Beijing and Tianjin were considered to reflect energy demand-supply risk.
  • Besides, by making a comparison of various scenarios at the same joint constraint-violation level, the authors could find that the system cost would be varied with different individual constraint-violation levels and the minimum system cost would occur in the scenario that 1 2p p= .
  • And the system cost, imported electricity and renewable energy-based electricity would be ascended with the α and β levels.
  • High α and β levels would correspond to decision maker’s desire 17 to achieve the minimized system cost with high violation degrees in soft constraints, thus resulting in a low satisfactory attitude to prohibiting not opened facilities costs.

5.1 Impacts of REDP policy

  • Figure 9 depicts the pollutant emissions with- and without implementing REDP in years of 2016-2020.
  • Since the RES including two urban cities, the detailed pollutant emissions in each urban city would be different.
  • Moreover, the primary emitter for the air-pollutants in Beijing would be the transportation sector after the shutdown of coal-fired power plants, and the air-pollutants in Tianjin are mainly derived from the sectors of industry and transportation.
  • Therefore, additional efforts need to be undertaken to reduce the pollutant emissions and improve the air quality with a sustainable way (e.g., implement of air quality plans, development of electric vehicles, improvement of energy utilization efficiencies and upgradation of power transmission infrastructures, ae well as adoption of regional co-control plans toward power-supply security and air-pollution mitigation) [3, 49, 50].

5.2 Comparison with the conventional JCP

  • Figure 5 also indicates that when a joint probability level is given (i.e. p = 0.2), the system costs would increase with p2 (i.e. violating the second chance constraint) or decrease with p1 (i.e. violating the first chance constraint) under scenarios of S9-S14; conversely, the system costs would decrease with p2 or increase with p1 under scenario of S15.
  • Some differences among system costs would be generated owing to different marginal probability levels even if at a fixed joint probability level.
  • This assumption was not justified and might encounter difficulty in application to planning real-world RES problems.
  • These studies were based on the assumption that all the marginal probability levels were followed the determinative linear relationship.
  • Therefore, the CFSP approach proposed in this study is not limited to the assumptions, and thereby can be applied to a wider range of problems than the previous studies.

6. Conclusions

  • A copula-based flexible-stochastic programming (CFSP) method has been proposed for planning the energy system within a regional scale under multi-uncertainty.
  • CFSP simultaneously reflects interactive features of random variables and deals with uncertain parameters in target value of goals and soft constraints.
  • Therefore, the CFSP-RES model proposed in this study is not limited to the assumptions, and thereby can be applied to a wider range of problems than the previous studies.
  • Therefore, improvements would be desirable in further investigations to mitigate these limitations.

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Citations
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Bo Ming1, Pan Liu1, Lei Cheng1, Yanlai Zhou1, Xianxun Wang1 
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TL;DR: This study adopts nonparametric methods to estimate the total factor energy efficiency of 105 resource-based cities covering the period 2010-2016 in China and analyzes the spatiotemporal characteristics of changes in energy efficiency.

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TL;DR: In this article, the authors examined the historical CO2 emissions of Bangladesh's electricity sector from 1979 to 2018 and applied the logarithmic mean divisia index (LMDI) method to three distinct scenarios regarding future emissions.

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TL;DR: Compared to single level programming (SLP) and bi-level programming (BP) approaches, the MIFCP-WEFN model can help decision-makers identify the optimal agricultural water resources management schemes by means of the leadership of water resources managers as well as the feedback of two diverse followers.

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References
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Book
01 Jan 1999
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Abstract: The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study.

8,626 citations

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Ronald R. Yager1
TL;DR: A function to help in the ordering of fuzzy subsets of the unit interval is introduced, which is the integral of the mean of the level sets associated with the fuzzy subset.

1,302 citations


"A copula-based flexible-stochastic ..." refers methods in this paper

  • ...Based on the fuzzy ranking method suggested by [36, 37], t and r can be defuzzified as follows: '...

    [...]

Journal ArticleDOI
TL;DR: The ITSP is applied to a hypothetical case study of water resources system operation and results indicate that reasonable solutions have been obtained and the information obtained can provide useful decision support for water managers.
Abstract: An inexact two-stage stochastic programming (ITSP) model is proposed for water resources management under uncertainty. The model is a hybrid of inexact optimization and two-stage stochastic programming. It can reflect not only uncertainties expressed as probability distributions but also those being available as intervals. The solution meth od for ITSP is computationally effective, which makes it applicable to practical problems. The ITSP is applied to a hypothetical case study of water resources system operation. The results indicate that reasonable solutions have been obtained. They are further analyzed and interpreted for generating decision alternatives and identifying significant factors that affect the system's performance. The information obtained through these post-optimality analyses can provide useful decision support for water managers.

501 citations

Journal ArticleDOI
TL;DR: This paper addresses the problem of socially responsible supply chain network design under uncertain conditions by developing a bi-objective mathematical programming model, called robust possibilistic programming (RPP), and several varieties of RPP models are developed.

396 citations


"A copula-based flexible-stochastic ..." refers background in this paper

  • ...Flexible programming (FP) is effective for handling flexibility on target value of goals and soft constraints [33]....

    [...]

Proceedings ArticleDOI
Ronald R. Yager1
01 Jan 1978
TL;DR: This work investigates the question of ranking fuzzy subsets in the unit interval by presenting some initial ideas and concepts toward a solution of this problem.
Abstract: We are interested in investigating the question of ranking fuzzy subsets in the unit interval. We present some initial ideas and concepts toward a solution of this problem.

255 citations


"A copula-based flexible-stochastic ..." refers methods in this paper

  • ...Based on the fuzzy ranking method suggested by [36, 37], t and r can be defuzzified as follows: '...

    [...]

Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "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" ?

Wang et al. this paper proposed an inexact optimization approach based on Monte Carlo simulation ( MCS ), chance-constrained programming ( CCP ), two-stage stochastic programming ( TSP ) and flexible programming ( MSP ) for real-world regional energy system ( RES ) planning problems.