A pseudo-optimal inexact stochastic interval T2 fuzzy sets approach for energy and environmental systems planning under uncertainty: A case study for Xiamen City of China

Applied Energy 138 (2015) 71–90

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A pseudo-optimal inexact stochastic interval T2 fuzzy sets approach for energy and environmental systems planning under uncertainty: A case study for Xiamen City of China L. Jin a,⇑, G.H. Huang a,b, Y.R. Fan b, L. Wang c, T. Wu d a

College of Environmental Science and Engineering, Xiamen University of Technology, Xiamen 361024, Fujian Province, China Faculty of Engineering and Applied Science, University of Regina, Regina, SK S4S 0A2, Canada College of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, Fujian Province, China d Jackson School of Geosciences, The University of Texas at Austin, 2305 Speedway, Stop C1160, Austin, TX 78712-1692, United States b c

h i g h l i g h t s  Propose a new energy PIS-IT2FSLP model for Xiamen City under uncertainties.  Analyze the energy supply, demand, and its flow structure of this city.  Use real energy statistics to prove the superiority of PIS-IT2FSLP method.  Obtain optimal solutions that reflect environmental requirements.  Help local authorities devise an optimal energy strategy for this local area.

a r t i c l e

i n f o

Article history: Received 4 January 2014 Received in revised form 18 August 2014 Accepted 6 October 2014

Keywords: Pseudo-optimal programming Stochastic programming Interval type-2 fuzzy sets boundary Energy systems planning

a b s t r a c t In this study, a new Pseudo-optimal Inexact Stochastic Interval Type-2 Fuzzy Sets Linear Programming (PIS-IT2FSLP) energy model is developed to support energy system planning and environment requirements under uncertainties for Xiamen City. The PIS-IT2FSLP model is based on an integration of interval Type 2 (T2) Fuzzy Sets (FS) boundary programming and stochastic linear programming techniques, enables it to have robust abilities to the tackle uncertainties expressed as T2 FS intervals and probabilistic distributions within a general optimization framework. This new model can sophisticatedly facilitate system analysis of energy supply and energy conversion processes, and environmental requirements as well as provide capacity expansion options with multiple periods. The PIS-IT2FSLP model was applied to a real case study of Xiamen energy systems. Based on a robust two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs between economic and environmental requirements, and among seasonal volatility energy demands of the right hand side constraints of Xiamen energy system. Thus, the lower and upper solutions of PIS-IT2FSLP would then help local energy authorities adjust current energy patterns, and discover an optimal energy strategy for the development of Xiamen City. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Energy is one of the building blocks to improve and/or maintain human daily life. The reasonable allocation of energy sources is one key to achieve high efficiency of energy usage and environmentally friendly society. Since Xiamen City was developed as one of ⇑ Corresponding author at: College of Environmental Science and Engineering, Xiamen University of Technology, Xiamen 361024, Fujian Province, China. E-mail addresses: [email protected] (L. Jin), [email protected] (G.H. Huang), [email protected] (Y.R. Fan), [email protected] (L. Wang), tiffany.y.wu@gmail. com (T. Wu). http://dx.doi.org/10.1016/j.apenergy.2014.10.024 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

‘‘Special Economic Zones’’ in 1980 China, it has achieved great economic growth. However, at the same time, the rate of its energy consumption has increased significantly from that time. In order to increase of economic, many energy consumption industries, for example the power industries, have expanded their output capacity. This trend of increasing energy consumption will continue to rise due to the obligation of the national ‘‘12th five-year plan’’ with a proposed economic growth yearly rate of 7% [1]. However, China national energy conservation and low-carbon policies require industrial emissions to be done in an environmentally friendly manner [2]. Thus, the planning of greenhouse-gas (GHG) emission control and energy systems management, (especially

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with coal as main energy sources in China) is necessary and has attracted many scholars’ interest over recent years. Energy authorizes need to concern themselves with the balance of energy consumption with emissions’ control [3]. However, in energy systems, there are uncountable influencing factors, upon which energy managers should reflect in their allocation strategies [4,5,6,7,8,9,10]. Uncertainties also exist in energy collection, treatment and the conversion processes. For example, the heating value of coal has different values in different production areas. This may cause uncertainties in the consumption of coal to reach a specific gross heating value for an electricity plan. The energy transportation, as a coal property, may have uncertain factors, which are represented in interval data, fuzzy vague and stochastic features. Those uncertain issues may result in a complicated a management procedure, which may be connected with environmental and social economic factors for Decision Makers (DMs) [11,12,13,14,15]. Therefore, development of effective optimization methods to support energy and environmental management under uncertainties and complexities are desired, especially in such ‘‘economic zone city’’ with its limited energy sources and high standards of environmental requirements in the east of China. 1.1. Research background In past decades, a large number of optimal research works made proposals to deal with such uncertainties and resulted in a compromise between environmental and economic targets [16] required in the planning of energy systems [17,18,19,20,21,22,23,24,25]. In these works, optimization programming played a significant role by providing desired decision alternatives under such complex energy systems [26,27,28,29,30,31,32,12,13,14,10,33,34,24]. For example, a hybrid inexact chance-constrained missed-integer linear programming method was introduced by Liu et al. [19] for nonrenewable energy resources management under uncertainty. This method emphasized an energy allocation pattern with dynamic features. Shrestha and Marpaung [35] examined the implications of a carbon tax for power industries, consuming side programs and pollution emissions in Indonesia. Zhang et al. [36] analyzed the relationship between GHG emission and the power industry to reveal difficulties between regional variations and economic constraints. Lin et al. [37] proposed a longer term energy model to evaluate the economic and environmental performance of the Saskatchewan energy systems [31] proposed a general model for minimizing the cost that finds an optimal combination of energy modules for a country community. Cai et al. [12–14] developed a fuzzy-random interval programming model to identify optimal strategies in the planning of energy management systems under multiple uncertainties. Li et al. [10] developed a multistage interval-stochastic regional-scale energy model to reflect dynamic decisions for power generation schemes. Liu et al. [38] introduced an inexact mix-integer two-stage programming model for management of low carbon energy systems to handle complexities related to carbon mitigation issues which can be effectively reflected. Zhang and et al. [39] compared new-types of bricks make of fly ash and coal gangue and conventional types of bricks to take as examples to analyze the energy saving. Pisello et al. [40] investigate how buildings energy performance is influenced by Inter-Building Effects (IBE) by using building modeling and energy performance assessment models. Ferrante [41] presented alternative ways of investigating, planning and managing sustainable urban environments, by discovering the possibility to use energy retrofitting options as a socio-economic leverage toward nearly Zero Energy Buildings (nZEBs). Aerts et al. [42] developed a probabilistic model which generates realistic occupancy sequences to simulate the more accurate energy demands. Although previous research papers were actual illustrated problems in energy generation, none of them connected energy systems with both the

economic requirement and the environmental standards to produce solutions to satisfy each aspects of these components in one general optimization modeling work. Other problems are that those studies barely revealed a multi-factories, multi-time and multi-option with multi-expert experiences. There studies however, deal little with the ambiguity in data estimation, poor variable measurements, or the imprecise information from the subjective assessment. Of the above mentioned optimization methods, the Interval Linear Programming (ILP) approach is deemed the most effective tool to deal with uncertainties. The desirable feature of this method is that it handles uncertainties as interval numbers without distribution or membership functions. Interval parameters can exist in both the object function and right/left hand of constraints. Its characteristics allow uncertain numbers, for example [10, 10.2], to directly communicate into processes of energy management. This ILP model can be solved by Two-Step Method (TSM) developed by Huang et al. [43]. It does not cause complicated intermediate models, and it requires a relative lower level of computations. The typical application of this method is the grey linear programming approach for solid waste management by Huang and Moore [44]. Bass et al. [45] also proposed a grey mathematical program with interval parameters for assessing the sensitivity of a decision to climatically sensitive parameters. However, this conventional interval method only solves a small range interval numbers. This methodology may generate highly uncertain solutions if the interval ranges, (such as [2, 20,000]) are very large. Furthermore, ILP only solve those intervals which contain deterministic boundaries. It is based on determined boundary conditions. However, in real world energy systems, this assumption cannot reflect all uncertain issues. Therefore, the ILP method may not be able to fully describe uncertain issues. In management of energy systems, uncertainty is always accompanied by random and imprecise information or data records. The Fuzzy Linear Programming (FLP) method is an effective method for handling such uncertain problems as fuzzy sets as extensions of the corresponding definitions for ordinary sets. It allows uncertainties to be linked into the optimization process and result in a deductively rational solution of linguistic ambiguity [46,47]. For example, [48] developed an interactive fuzzy MultiObjective Programming (MOP) model for planning water resources under uncertainties which are represented in terms of fuzzy sets. However, the conventional FLP can only solve problems with determined membership functions, which may be difficult to obtain in a real cases. Therefore, [49] proposed a hybrid method integrating ILP and FLP into an optimal model called as IntervalFuzzy Linear Programming (IFLP). Following this proposal many studies of interval analysis with fuzzy sets theory were undertaken. The most in-depth study is that of Moore and Lodwick [50]. In this study, the relationship of intervals to fuzzy sets had been provided. IFLP improved on the deficiencies of ILP and enhanced the applicability of FLP. However, it contains shortages of input data which may only be discrete intervals, while deterministic values may still be hard to be estimated under all cases of uncertainties. Stochastic Mathematical Programming (SMP) is an effective tool to analyze of random variables with probability distribution. It divides decision variables into two subsets. The fundamental concept behind the SMP is its ability to take corrective actions after a random event takes place [51]. It reflects the dynamic variations features of management problems, particularly for large-scale problems. For example, during the typhoon season in Xiamen City, the energy supply has critical importance for people who live in this city. Typhoons in this city bring random factors. Thus, during typhoon season, the use of energy including power, natural gas, renewable energy as well as energy costs show random uncertain. The cost of energy can be expressed as the random interval of

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[100(1 + a)pi, 120(1 + a)pi]  106 CNY/PJ. Where pi denotes random parameter of intervals. It requires a stochastic method to maintain the operation of this city. Therefore, through the improvement of SMP, DMs can use limited energy to service this region. However, the strengths of this method is also weaknesses because it requires probabilistic specifications. But in fact, when dealing with many practical problems, the numbers of the data obtained are not good enough to be used as probabilities [52]. One potential model extends the existing SMP approach to integrate SMP and IFLP within a Stochastic Interval Fuzzy Linear Programming (SIFLP) framework, where uncertainties are reflected as interval fuzzy membership functions and probability distribution. However, it is incapable of tackling higher level fuzzy uncertainties presented in terms of Type-2 Fuzzy Sets (T2 FS). T2 FS is the most attractive method to measure of dispersion the formal fuzzy sets. The important kinds of uncertainty are linguistic and random. Formal fuzzy sets (or call as type-1fuzzy sets) has a crisp grade of membership; comparatively, T2 fuzzy sets has grades of membership, which also has features of fuzzy uncertainty. Previous studies of the SIFLP method can be used to handle both random and linguistic certainties considering the noisy measurements under random disturbances. However, in practical energy problems, it is impossible to just use first-order moments to measurement random uncertainties because it needs additional understanding of dispersion about the mean [53]. The T2 FS approach is a previous method, which provides this measure of dispersion. The concept of T2 FS was proposed by L.A. Zadeh as an extension of ordinary fuzzy sets. It has also been seem as one method to increase the fuzziness of a relation. According to [54], the study shows that increased fuzziness in a description means an increased ability to handle uncertain information in a logically correct manner. The T2 FS method can assist in knowledge representation by using linguistic grades of membership. Thus, it improves inference of Type-1 Fuzzy Sets (T1FS) or the normal fuzzy sets method. The relationship between T1 FS and T2 FS just as determinism is embedded in randomness. In other words, if the higher level fuzzy uncertainty disappeared, the T2 FS then collapses to a T1 FS. For instance, [55] used the T2 fuzzy logic system to develop a ‘‘connection admission control method’’. Hagras [56] applied the T2 FS controller to overcome the limitations of the T1 method in intelligent environments’ control. Qui et al. [57] used the T2 fuzzy method to test whether their smart washing machine controls were reasonable and reliable. Mendez [58] employed T2 FS to obtain a base for boiler entry temperature prediction. They found that T2 systems improved performance in collier entry temperature prediction when compared with the T1 model. These studies show that the T2 FS method is superior with respect to robustness and flexibility. However, the most common reason that the T2 FS method has not been widely used is that it is more difficult to understand than the T1 FS method. Additionally, although T2 FS contains more freedom of membership degrees than others, reasonable evidence does not exist to prove how to best choose the secondary membership function. At this time, there has been a logical progression from T1 FS to the Interval T2 Fuzzy Sets (IT2FS) method or T2 fuzzy intervals. IT2FS is an accessible kind of general T2 FS method because it is easier to compute, especially when uncertain variables are large, and it can yield more promising solutions than T1 FS [58]. Baklouti and Alimi [59] designed an IT2 FS controller for navigating mobile robots in an unknown environment. In this study, they compared results obtained from T1 FS and IT2 FS systems. The IT2 FS method outperformed the results gained from the T1 FS method. Gu and Zhang [60] proposed an IT2 FS online decision support system for web shopping usage. In this study, an efficient IT2 FS method was applied to deal with all rules with T1 FS to perform T2 FS reasoning. The IT2 FS method simulated

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human decision making to deal with a higher level of uncertainty, and it provided judicious decisions for all users. However, there were few reports on incorporation of the IT2 FS method within an optimal SIFLP framework. Energy consumption in Xiamen, a special economic zone, keeps growing with the development of this city. The economic changes lead to energy demand variations throughout the year. Energy supply fluctuate among different years. This phenomenon can cause interval numbers in the management of energy systems. The energy demand also changes in difference seasons. For example, during summer, the power demand of municipality is higher than in other seasons. Industries need to consume more power during the winter season. Agriculture users usually use more energy during the spring and autumn seasons by the reason of planting and harvesting. Those seasonal changes in the use of energy demand is a typical stochastic problem. Moreover, IT2 FS is an effective method which can more accurately describe fuzzy uncertainties of energy management during the typhoon season from July to September of Xiamen. Such features of multiple uncertainties were not fully addressed in previous research. Consequently, in order to achieve better solutions for energy allocation in Xiamen, the approach for representing the above multiple uncertain issues is to integrate stochastic interval fuzzy linear programming and interval type-2 fuzzy set linear programming into an optimization framework. In the process, a dual interval or interval boundary interval will emerge to account such complexities. So, the reason of combining IT2 FS with SIFLP method is because the solution processes of IT2 FS contain a Lower Membership Function (LMF) and an Upper Membership Function (UMF), and both have interval characteristics. For example, interval IT2 FS can be formatted of  LMF ðx1 Þ; ½lUMF ðx1 0 Þ; l  UMF ðx1 0 Þ. ½½lLMF ðx1 Þ; l This kind of IT2 FS interval can thus be treated as a dual interval or intervals with T2 fuzzy boundaries. Joslyn [61] presented a dual interval method for handling random intervals. Liu et al. [62] has been applied the dual interval method into a linear programming of solid waste management. Jin et al. [25] developed a dual interval approach for irrigation water resources management. The dual interval method can effectively work within boundaries of uncertain intervals due to the complexities of practical problems. Thus, by incorporating the dual interval technique into the IT2 FS optimal framework, T2 FS programming can be easier calculated, and obtained more reliable solutions to real energy management problems. However, the previous IT2 FS method works only with single parameters. This means that the preceding study of the IT2 FS method does not communicate with an optimal linear programming framework but has an independent existence. Based on the classical optimization routines, there is a pseudo-optimal method [63] which is used to optimize the IT2 FS uncertainties within classical linear methods. Therefore, the objective of this study is to develop a Pseudooptimal Inexact Stochastic Interval T2 Fuzzy Sets Linear Programming (PIS-IT2FSLP) for the planning of Xiamen energy management in China. It will help plan the local energy options under multiple uncertainties, and manage the relative activities such as greenhouse-gas emission control and typhoon season energy supply problems in an integrated IT2FSLP optimal framework. The development of PIS-IT2FSLP approach can deal not only with the multiple uncertainties expressed as type-2 fuzzy sets, stochastic variables and interval type-2 fuzzy methods in both fuzzy parameters and fuzzy optimal linear framework. It improves the conventional IFLP method which is not very useful because multiple fuzzy or linguistic uncertainties require a measure of dispersion. (a) The proposed PIS-IT2FSLP method provides this measure of dispersion. This study will incorporation of ILP, FLP, SMP and IT2 FS techniques to formulate a PIS-IT2FSLP method for dealing with stochastic multiple energy management presented as dual interval type-2 fuzzy

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sets. (b) A case study of Xiamen City energy management with GHG emission control will then demonstrate the applicability of the PIS-IT2FSLP method. The results can help DMs not only satisfy people with energy usage to obtain maximizing systems profit, but also ensure energy supply in an effective manner during multiple situations of uncertainty such as during typhoon seasons. (c) The proposed PIS-IT2FSLP method can effectively address the fuzzy and random uncertainties in the energy management processes without unrealistic simplification, and thus improve system efficiency and energy supply security. 2. Case study Xiamen City is located in the southeast of Fujian province and belongs to the south coast area of China. It is the nearest city close to Taiwan. The main island of Xiamen City is surrounded by the sea, and it has three major bridges and one undersea tunnel to connect to the Chinese mainland. Xiamen City is administered as one of 15 sub-provincial cities of China and it has an area of 1699.39 square kilometers. In 2012, Xiamen City has about 3.67 million people and a GDP of 2535.80 billion RMB. The new Xiamen City is larger than before and covers six districts as shown in Fig. 1. It is the core city of the Minnan economical triangle, which consists of Quanzhou City to the north side and Zhangzhou city to the south. In the early 19th century, this city was treated as a treaty port. It is now one of the six original ‘‘Special Economic Zones’’ along with Shenzhen City, Shantou City, Zhuhai City and else. 2.1. Energy demand and supply With a stable cross-strait relationship, Xiamen marked a great period of development, in last decade with rapid growth in its economy and population. According to the investigation of the Xiamen Statistics Bureau, Xiamen consumed 2.07 million tonnes of coal in 2000, 3.88 million tonnes of coal in 2005, 3.22 million tonnes of coal energy in 2009, and it increased significantly to 5.98 million tonnes of coal in 2011. By comparing these data, it is easily noted that the energy consumption of Xiamen has greatly increased over the past years. Usage of raw coal and electric power has increased 21.3% and 5.4% respectively in 2011. However, Xiamen City is very short in energy resources and relies on energy from other cities. If the energy supply is lower than its demand, the extra amount of energy is either imported from other places or expanded by city energy industries. In ‘‘Twelfth Five-year Plan’’, the total energy consumption target of China will meet 40 billion tonnes of coal in 2020. The goal of this development strategy will strongly effect the Xiamen energy system and seriously challenge the local environmental conditions. 2.2. Energy flow In China, energy supply depends mainly on the resource of raw coal and Xiamen has no exception. This city’s energy resources are imported from Jiangxi mining places. However energy transportation from one place to another cause higher costs. The electric power resource of Xiamen comes from the National power grid and combustion generating units. However, these resources are always limited due to the regional differences. The majority of energy supplies in Xiamen relies heavily on domestic imports. For example, there are no gasoline factories on Xiamen island of Xiamen. Most of gasoline is transported onto the island by ship. If meet a long typhoon season, Xiamen Island would face a shortage of gasoline. However, because this city is surrounded on the mainland by a few large oil refinery factories, Xiamen easily achieves a cheaper price of oil products. These products, including

gasoline, diesel and relative organic liquid, can be exported to benefit by taking advantage of Xiamen Port. The import of oil products from Quanzhou and Zhangzhou cities, and the import of coal from Jiangxi province is due to the limitations of energy sources in Xiamen. Although, raw coal causes environmental damage, raw coal is a major import for Xiamen energy supply. 100% of the raw coal in Xiamen has been imported or purchased from other cities, and most of the raw coal has been used for power generation, though a small part of this raw coal has been sold to benefit energy companies. In 2011, the total coal consumption of Xiamen industries was 5.98 million tonnes of which 4.815 million tonnes of raw coal were used for energy conversion. Unlike support of raw coal, Xiamen has its own crude oil supply system by integrating the resources of Quanzhou City. Most oil products are consumed by the population’s daily transportation activities. The capacity of Quanzhou City’s oil refinery is 5 million tonnes per year. Gasoline and diesel fuels are used for land transportation and fuel oil is used for water shipping activities. There are no natural-gas resources in Xiamen. Most natural-gas resources are shipped from Indonesia. Natural-gas is first shipped to Putian City to LNG industrial park. It helps deliver natural gas to Xiamen as well as to Guangzhou. Natural gas was first introduced as a clean energy source for Xiamen City in 2006. Since then, it has become one of the major energy source of Xiamen. 1.7 billion m3 was consumed in 2010. The main of natural gas is consumption by households and public transportation while a small part of it is domestically exported for economic profit. Table 1 shows more details of the energy consumption of Xiamen City from 2003 to 2012. The consumption of electricity in Xiamen is far greater than its capacity. The Songyu power plant of Xiamen can produce 6 billion kilowatt hours every year. However, Table 1 clearly shows that electrical power consumption reached 6.3 billion kilowatt hours in 2003. The generation of power cannot meet the energy needs of Xiamen’s development. In 2009, the amount of electricity generated by the Songyu power plant was only 46.8% of total power consumption of Xiamen. In the past 5 years, the local government is trying to apply other available technologies to generate power and satisfy the city’s demands. The most important one is hydropower technology. It is one of China’s domestic and mature technologies. In 2012, Xiamen government invested 6 billion RMB to construct a Hydro-pumped-storage power plant and tried to make up consumption power of 23.45 TW h. Other relative power technologies are mainly focused on emission requirements and combustion efficiency. However, none of these facilities make up for the insufficiency of power supply in this city. By 2010, the total consumption of power was 150.59 TW h, and the power generation from the power plant only 70.0 TW h. At present, total power consumption is 182.89 TW h. Nearly 100 TW h power need to be purchased from other cities. However, the local government will install other hydro-power plant including a tidal power plant and two gas fire generation plants in the next decade. These new power plants may mitigate the contradiction between consumption and production in the future, and thus make the Fujian province power grid more robust. Xiamen has very convenient conditions for the utilization of renewable energy. Renewable energy has been regarded as new energy resources to relieve the shortage of power supply. Its characteristics are longer life and pollution free. It is treated as ‘‘cleanenergy’’. Thus, it has been listed as one of the key areas to develop. Xiamen City, which is located on the south coast of China, has 8 months of summer weather. The average annual sunshine reach of 2233.5 h per year because it has a subtropical climate with sunny weather every year. Since it is close to the East China Sea, Xiamen City has 2800 h of effective wind speed every year. These advantages mean that this city has great potential to engage renewable energy as a power source. However, the shortage of

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N

Fig. 1. Geographical position of Xiamen.

Table 1 Energy consumption of Xiamen. Year

Coal consumption 104 tonne

Fuel oil consumption 104 tonne

Natural-gas consumption 104 tonne

LPG consumption 104 tonne

Power consumption 109 kW h

Water consumption 104 tonne

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

197.20 241.63 279.19 344.22 443.47 438.88 449.74 413.03 513.44 542.37

29.51 28.83 20.87 17.45 14.61 13.79 13.95 12.16 7.26 6.11

n/a n/a n/a n/a n/a 510 977 9084 9856 17,052

7.94 8.35 9.47 10.51 11.07 9.97 8.20 9.00 9.67 10.84

68.37 75.92 89.97 103.22 118.88 125.12 128.18 150.59 169.3 182.89

20,548 19,784 23,755 25,782 28,298 28,954 29,454 31,666 33,739 35,700

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accumulator technologies limits Xiamen exploitation and utilization of renewable energy. Consequently, a few renewable energy resources have been commissioned compared with fossil fuel sources, even though the local government provides beneficial policies and financial support. Other disadvantages of using renewable energy are the higher upfront costs and a monopolized power market. Investors are not willing to put their capital into this market. They invest in the high profit real estate market of China. Therefore, the renewable energy of Xiamen need further utilized, and this will have to wait the energy market being more mature. 2.3. Energy participants Xiamen’s energy systems have an integral network with complex interactive subsystems including those that involve distribution energy system, power generation system and environmental emission control system. Fig. 2 shows these complex relationships within each individual subsystem including the primary energy resources such as raw coal, crude oil and natural gas. These resources involve their own energy production and imported energy sources. Other types of energy, for example, the relation of secondary energy resources are also represented in Fig. 2. According to previous statistical research, the energy sources of Xiamen depend seriously on import from other cities.

Consequently, the city’s energy conversion industries consist of a power generation plant and a few oil refining factories. However, these energy resources are finally converted into electricity or heat by the industrial, commercial, or residential sectors. These subsystems depend on each other and are connected in many ways. Each subsystem has multiple input energy sources, and each energy source has multiple outputs. In other words, the energy flow in this city has a complicated relationship. For example, since prices of natural gas are lower than other energy products, it can be used as a resource in the gas-fired plant. However, it is also one key energy source for public transportation. Thus, available natural gas resources need multiple demand or supply decisions. Therefore, these complex patterns in the energy systems should be taken into careful consideration to reduce operation cost of energy systems. Table 2 shows the relationships between GDP and energy consumptions from 1999 to 2012. In 1999, the total amount of energy consumption was 356.46  104 tonnes; in 2005, the energy consumption of Xiamen was 651.96  104 tonnes; and in 2012, this city consumed 1255.52  104 tonnes energy of standard coal. Respectively, during these three years, the GDP of this city was 4,405,368  104 RMB, 10,065,830  104 RMB and 28,170,7 00  104 RMB. As a result, the united GDP energy consumption was 123.58 million Yuan per tonnes (standard coal) in 1999, while it was 224.37 million Yuan per tonnes in 2012.

Resident coal consumption

Coal processing technologies Industrial coal consumption

Raw coal Industrial consumption

Industrial natural gas consumption

Natural gas

Hydro-energy

Commercial and resident consumption

Commercial and resident natural gas consumption Transportation natural gas consumption

Renewable energy

Coal-fired power plant Agricultural power consumption

Electricity

Gas-fired power plant Industrial and construction power consumption

Washed coal

Public transportation, commercial and resident consumption

Commercial and residential power consumption Transportation industry power consumption

Coke Hydro-power technology Crude oil

Industry and construction coke consumption

Renewable energy technology Commercial and residential coke consumption

Gasoline Diesel

Coal coking Industrial consumption

Kerosene Energy Export for profit LPG

Transportation consumption

Agriculture consumption

Crude oil refinery Industrial, commercial and residential LPG consumption

Fuel oil Water transportation

Environment systems: air pollution control (NO x, SO2, VOC, PM2.5) Fig. 2. The interaction between energy and environmental systems in Xiamen City.

L. Jin et al. / Applied Energy 138 (2015) 71–90 Table 2 Relationship between GDP and energy consumption in Xiamen City. Year

GDP/ 104 RMB

Annual electricity consumption/ 104 kW h

Standard coal consumption/ 104 tonnes

Daily maximum load/ 104 kW h

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

4,405,368 5,018,706 5,583,268 6,483,570 7,596,934 8,877,149 10,065,830 11,737,984 14,025,849 16,107,098 17,372,349 20,600,738 25,393,132 28,170,700

365,912 433,332 498,364 590,278 699,310 759,200 899,691 1,032,294 1,188,788 1,251,154 1,281,795 1,505,881 1,693,046 1,848,006

356.46 403.47 453.76 507.33 564.17 547.59 651.96 744.19 844.54 n/a 952.47 1076.96 1188.96 1255.52

67.67 79.80 87.95 100.00 121.00 132.00 161.30 188.50 215.00 232.80 249.60 286.20 316.50 n/a

Energy consumption increased more than 3.5 times since 1999. However, the GDP increased more than 6.39 times. This phenomenon indicates that Xiamen is constantly improving its efficiency of energy consumption. It shows that a single energy resource such as coal cannot meet the requirements of this city is development. Consequently, local government set up a natural gas project to purchase other energy sources to satisfy energy needs. Natural gas is one of these important energy sources, which is imported from other countries to Xiamen as a kind of clean energy to replace coal energy. Although energy management employed natural gas or other high combustion technologies to enhance energy efficiency, there is still a great need for the operating structure of the energy system of this city to achieve an optimal pattern. Crude oil is imported from Quanzhou City as a satellite city of Xiamen. It is converted into Liquefied Petroleum Gas (LPG), diesel fuel and gasoline by domestic companies in Xiamen. Taking the high cost of conversion into consideration, this type of energy is not suitable for power generation in Xiamen. However, the prices of petroleum products in Xiamen are relatively lower than in other places. Xiamen can profit by exporting part of these oil products. Thus, according to the Xiamen Statistical Yearbook, a half of its petroleum products have been exported to other cities. The rest of the products are ensured residential usage in Xiamen. In Table 2, the electricity generation and consumption are displayed. Social development cannot survive without a power supply. As a key energy, the annual consumption was 365,912  104 KW h in 1999. The daily maximum load was 67.67  104 KW h. In 2005, the annual power consumption was 899,691  104 KW h, and in 2012, it is 1,848,006  104 KW h. The large increase in the amount of power needs to either be supported by Xiamen City or imported from other cities. In 2005, local government installed a gas-fired power plant, but it was hard to make up the shortage of power supply. In the mean time, a waste to energy project was built to for support city demands in 2009 as well as hydro energy or other types of renewable energies. However, these projects cannot produce enough power to meet the energy requirements of city development. Under recent harsh strict environmental conditions, these primary or secondary energy sources need to be well allocated to end users. To utilize a primary energy sources cannot satisfy local demands but damage the environment, while it increases the cost to deal with polluted air or water. Therefore, energy system planning can certainly help to achieve a harmonious development between socio, economic, and environmental objectives within such limited energy sources.

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2.4. Statement of problems Based on the above discussion, the complex energy systems of Xiamen need an optimal pattern to coordinate the relationship between supply and demands for energy production, energy transportation, energy conversion and utilization under strict environmental requirements. However, these system factors including resource availability, utilization purposes, and conversion efficiency, and the ability to transport have uncertain characteristics. These uncertain parameters may influence the rationality of Xiamen’s energy structure. Moreover, they may cause economic penalties of environment disruption in Xiamen. These uncertainties could also affect the judgments of decision makers in choosing the appropriate optimal processes. From energy to environmental systems, these uncertainties can be expressed as crisp intervals and fuzzy intervals, which depending the preciseness of local data records and individuals. Some of these uncertain data are described as interval T2 FS with a lower and upper boundary. It is based on the uncertain utilizations for different persons in different situations. Thus, a complex local energy system allocation strategy is desired to address such multiple uncertain factors. In Xiamen energy system, multiple energy sources and conversion processes and relative parameters need a reasonable planning with limited input energy amount to satisfy municipal energy consumption. This can lead to a suitable application of Pseudo-optimal Inexact stochastic Interval Type-2 Fuzzy Sets Linear Programming (PIS-IT2FSLP) approach. This is a challenge for decision makers because if the energy supply cannot meet the requirements of city, energy departments need set up a new project to expand current facilities or pay a higher prices into energy markets to purchase certain amounts of energy sources. However, the small island of Xiamen cannot tolerate disorderly expansion due to the limited land area. The decision makers of the energy department should respond to such deficiencies of energy resources. Under that circumstance, bad decisions would negatively affect local people and no one would benefit from such mistakes. Therefore, the problem under the current situation is to find a reasonable allocation energy pattern and decide when and how to expand energy facilities to minimize the net system cost. Energy authorities need to identify uncertain factors and quantify them into countable numbers to optimize’s Xiamen energy sources with minimized pollutants discharge and cost. Therefore, the issues of the Xiamen energy system should be divided into 4 main areas: (a) measure all multiple uncertainties in the energy system between demand and supply, (b) find an optimal energy strategy to allocate limited resources, (c) tackle T2 FS interval boundaries with stochastic feature uncertainties existing in constraints, and (d) generate an optimal schedule for capacity expansion of energy facilities with sophisticated considerations of the energy markets. 3. Methodology and modeling formulation 3.1. Interval linear programming Interval linear programming [44] is a typical optimization analytical method for planning under uncertainty. It provides satisfactory solutions by allowing uncertainty to be effectively reflected in coefficients and objective functions without distribution functions. A general ILP model can be formulated as follows: 

Min f ¼ C  X 

ð1aÞ

S:t: A X  6 B

ð1bÞ

X P 0

ð1cÞ

78

L. Jin et al. / Applied Energy 138 (2015) 71–90 mn

1n

m1

n1

where A 2 fR g , C  2 fR g ; B 2 fR g ; X  2 fR g ; R± represented a set of interval numbers; A ¼ ða C ij Þmn ,    T        T ¼ ðc ; c ; . . . ; c Þ, B ¼ ðb ; b ; . . . ; b Þ and X ¼ ðx ; x ; . . . ; x 1 2 m 1 2 n 1 2 nÞ ; X± denoted a set of decision variables; ‘’ and ‘+’ superscripts indicated lower and upper bounds of variables. The (a±) was defined as a± = [a, a+] = {t e a| a 6 t 6 a+} [43]. Thus, these interval numbers can deal with uncertainties by corresponding lower and upper bounds. 3.2. Interval fuzzy linear programming However, in many cases, the ILP method has difficulties in dealing with uncertainty when lower or/and upper bounds contains ambiguous or vague information, for example, a [inadequate, sufficient] interval number for natural gas supply. This means that some boundaries can only be defined as linguistic fuzzy sets. In such cases, such vague information cannot be well represented by using ILP method. More importantly, ILP may provide an infeasible solution when the model’s coefficients have a distance interval number. For example, an interval number [100, 8000] is meaningless to management authorities [64]. However, these problems are often raised when some conditions, data is barely reliable making it difficult to precisely assess these uncertainties. To solve these issues, a grey fuzzy linear programming approach (IFLP) [44] has been introduced as an effective method to deal with such uncertain information [65]. Fuzzy programming can handle uncertainties with a fuzzy goal and constraints, which represent a flexible target value in both the objective function and the constraints. The formula of fuzzy programming is correspondingly as follows:

lD ¼ MinflG ; lE g

ð2aÞ

where lD, lG and lE denotes membership functions of fuzzy decision (D) by given (G) as a fuzzy goal as (E), a fuzzy constraint. Then, the decision variable can be described as an intersection space of (G) and (E). Using symbol lEi ðXÞ, it indicates membership functions of constraints Ei (i = 1, 2, . . . , m); lGi ðXÞ denote function goal Gj (j = 1, 2, . . . , n); therefore the decision variables can be defined as follows [66]:

lD ðXÞ ¼ lEi ðXÞ  lGj ðXÞ; i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; n

ð3aÞ

where X denotes as fuzzy decision variables. Thus, by integrating the fuzzy sets theory into the previous ILP model, the IFLP can be defined as follows: 

Min f ffi

n X C j X j

ð4aÞ

  lf x ; b _; b ^ ¼

i ¼ 1; 2; . . . ; m

ð4bÞ

j ¼ 1; 2; . . . ; n

b ^x

b ^b _ > > > : 0;

_





; b _6x6b ^

ð5Þ



x P b ^

th

i

set, aij is the (i, j)th element of A, ði; jÞ 2 Nn . Thus, coefficient b has been defined as interval fuzzy sets for this mathematic programming problem. Then, Feasible Fuzzy Region (FFR) [63] of this programming is defined as the fuzzy polyhydric sets produced by x 2 Rn which satisfy all fuzzy and Boolean frontiers as follows: m \  Di ðx Þ; bi

FFR ¼

ð6Þ

i¼1

where x 2 Rn , all elements of x± can be interpreted as a set of solu tions which satisfies both interval bi and fuzzy Di ; i 2 Nn . With upon statement, given a Fuzzy Feasible Set (FFS) [63], it denotes all values, which satisfy all fuzzy and crisp restrictions with non-negative membership degrees as follows:

( FFS ¼

Xj x 2

m \

)  bi



Di ðx Þ;

ð7Þ

i¼1

where Di ðx Þ is the a-cut membership degree regarding the ‘‘ith’’ ~ is the fuzzy restriction [67], bi is the ‘‘ith’’ crisp restriction and b i ‘‘ith’’ interval fuzzy restriction, i 2 Nn . Thus, in the domain of x, solutions of this interval T2 fuzzy sets programming is following,

( max a

! ) m \   \ ~   f x Di x

ð8Þ

i¼1

By introducing a variable [68,66], this interval T2 fuzzy set problem can thus be converted into a normal linear programming model. In model (8a), it focuses to find an a-cut, which maximizes the membership degree by applying formulate    Pn  Di ðx Þ ¼a bi ; 8i 2 Nn . This a-cut represents an optij¼1 aij xj mal solution for overall satisfaction for the model’s objective and constraints [44]. According to the fuzzy sets theory [69], ab = {x| lb(x) P a} has been denoted as a definitive solution of a conventional fuzzy sets. Thus, a higher level, a-cuts for the type-2 fuzzy sets are defined [63] as follows:

ab~ ¼

ð4cÞ

"Z

Z

Z

#,

u2J x Pa

x2X

j¼1

X j P 0;

x 6 b

   Pn  ; 8i 2 Nn , it indicates that an aGiven Di ðx Þ ¼a bi j¼1 aij xj ~ cut degree that the ‘‘i ’’ fuzzy restriction has regarding the b

j¼1 n X e Bi ; Aij X j 6 S:t:

8 > 1; > > <

Z

f x ðuÞ=u

x;

ab~ ¼

3.3. Interval type-2 fuzzy sets linear programming

Therefore, the interval of this a-cut of Footprint of Uncertainty (FOU) [70] for Interval T2 Fuzzy Set Parameter (IT2FSP) is denoted as a aI-cut, which is defined as follows:

According to previous studies [63], parameter b, in the right side of model, contains a higher level uncertain situation, which can be treated as a Type-2 (T2) fuzzy set. It is useful in a condition in which it is difficult to determine a membership function of a fuzzy set. As above mentioned, the interval number [inadequate, sufficient] means different things to different people who have the exact same backgrounds. Therefore, increased fuzziness in a description means increased ability to handle inexact information ~ in a logically correct manner [54]. Thus, _ ^ fuzzy sets b can be con  firmed by both possible values b and b . Its membership function is defined as follow:

aIb~ ¼ aIb~ ¼

u2J x Pa

Z

Z x2X

[

u2f x

fðx; uÞj J x ¼ ag; 

lb~ ðx; uÞj Jx ¼ a

a 2 ½0; 1; f x # ½0; 1

ð9Þ

e and ffi represent fuzzy inequality and equality. where symbols 6

x2X

fðx; uÞj J x P aÞ;

a 2 ½0; 1

a 2 ½0; 1; f x # ½0; 1

ð10Þ

ð11Þ

ð12Þ

x2J x

A aIb~ degree close to 1 would correspond to a high possibility of satisfying constrains or objectives as well as in normal fuzzy sets linear programming models.

79

L. Jin et al. / Applied Energy 138 (2015) 71–90

3.4. Dual interval type-2 fuzzy sets linear programming Thus, for handling such complex multiple interval fuzzy uncertainties, Dual Interval T2 Fuzzy Sets Linear Programming (DIT2FSLP) can be formulated as follows: 

Min f ffi

n X

C j X j

ð13aÞ

j¼1

S:t:

n X e; e B Aij X j 6 i

i ¼ 1; 2; . . . ; m

ð13bÞ

j¼1

X j P 0;

j ¼ 1; 2; . . . ; n

ð13cÞ

mn e  ~ , b ~ is a Dual Interval T2 Fuzzy Set Paramwhere A , Bi 2 b ij 2 R   ; b ; b   2 R e  2 b ; b eter (DI-T2FSP). Therefore, the DI-T2FSP B i i i i i and i e Nn [54,71,55,72,70,53,9,63]. Consequently, a single interval bound of membership function, which can be denoted as a fuzzy ~ is defined as follows: space, which represents interval bi # b,

~ ¼ b i

Z "Z bi

#, bi ;

1=u

i 2 Nn ; J bi # ½0; 1

u2J b

ð14Þ

i

~ is interpreted by two primary membership Therefore, a single b  b~ ðxÞ with functions (lower and upper bounds) called both l _

_

^

^

 b~ ðxÞþ with parameters b and b [73] parameters b and b, and l respectively, thus interval bounds of aIb~ are as follow:

h

i

h

n

aclb~ ðxÞ  ; acl b~ ðxÞ  ¼ inf x 2 X  : x 2 aIb~



o n oi  ; sup x 2 X  : x 2 aIb~

which can maximize approach. In other words, it can be treated as an optimal T1 fuzzy sets method embedded on FOU of constraints. This process is called a pseudo-optimal method in which a pre-defuzzification procedure finds an optimal solution of the IT2 FS which generates an interval parameter [76,63]. The general procedure for solving IT2 FS linear programming can be summarized as follows: (1) Select an overall pre-defuzzification level named k for all fuzzy parameters.  (2) Compute the aI -cut for all fuzzy sets, kcl~ ðbÞ , and it generb

   ates an interval kcl~ ðbi Þ ; kcl~ ðbi Þ . bi

bi

(3) Solve IT2 FS model by using an interval value LP approach in the form:



Min f ¼ c x ~ ; e b S:t: A x 6 

ð16aÞ ð16bÞ 



kcl~ ðbÞ 6 b 6 kcl~ ðbÞ ; b b

ð16cÞ



x P 0;

ð16dÞ

 n   m where x ; c 2 R ; b 2 R , and A± is an n  m matrix, nm

 A . The results of this model are guaranteed in limits nm 2 fR g of all restrictions, which are represented in FFS (7). Therefore, all aI± have a feasible solution.

ð15Þ Fig. 3 shows the membership function of DI-T2FSP. It is com^



^



_ _  

posed by eight parameters x , x , x , x and x , x , x , x , which can be considered as DILP [61] with a distance r, which is defined ^

^

^

3.6. Stochastic mathematic programming

^ ^ _ _ þ þ þ þ

^

as the distance between x and x , r ¼ x  x . According to previous studies [61,53,74], the advantages of DI-T2FSP major differently form FLP or IFLP or other kinds of fuzzy linear programming due to its ability to handle the uncertainties between the left and/or right side of constraints, plus the uncertainty of objective functions. While the formal fuzzy linear programming approaches only use a certain membership function to deal each of the parameters or relations, the newly developed DI-T2FSLP approach uses an infinite amounts of normal fuzzy sets such as (T1 FS) embedded in the ~i . It increases reliability of linear programFOU of T2 FS parameter b

When DI-T2FSLP constraints have stochastic features, which can be represented by Gaussian distribution, then, Stochastic Mathematic Programming (SMP) can be embedded into the linear programming model to deal with them. Considering the random~ , it then uses a SMP method as follows: ness in b

Max f ¼ CðtÞX

ð17aÞ

S:t: Pr½ftj Ai ðtÞX 6 bi ðtÞg P 1  pi ; xj P 0; xj 2 X;

ð17bÞ

j ¼ 1; 2; . . . ; n;

pi 2 ½0; 1; Ai ðtÞ 2 AðtÞ; bi ðtÞ 2 BðtÞ;

ð17cÞ i ¼ 1; 2; . . . ; m:

ð17dÞ

ming by allowing a higher type of fuzzy analysis [75]. 3.5. Pseudo-optimal interval type-2 fuzzy sets linear programming T2 fuzzy sets parameters exist in model (13). To obtain optimal results of IT2 fuzzy sets, the model can then be solved by finding an optimal fuzzy type reduction method to obtain one optimal a-cut

where A(t), B(t) and C(t) are sets of random parameters with a probability space T, t e T; X is a vector of decision variables. By applying the CCP approach into this model framework, the SMP model can be converted into a deterministic one [77]. A certain probability level pi e [0, 1] has been contained by coefficients of constraints. Thus, ~ ðtÞPi . CCP method can effectively reflect probability of b

Fig. 3. Inexact T2 fuzzy interval membership function with distance r.

80

L. Jin et al. / Applied Energy 138 (2015) 71–90

3.7. Pseudo-optimal inexact stochastic interval type-2 fuzzy sets linear programming Although the Pseudo-optimal Inexact Interval Type-2 Fuzzy Sets Linear Programming (PI-IT2FSLP) approach can deal with uncertainties with a higher type of fuzzy information existing in the right hand side of the constraints, it does not represent uncertainties when the coefficients have features of a stochastic nature with probability distribution information. The CCP method is an effective method to address probability distributions of B, however, it cannot handle imprecise information such as linguistic data. However, in issues of energy source management, many interval parameters also fluctuate with stochastic features [78], ~ of constraints. If the especially, parameters in the coefficient b DI-T2FSP can be presented as probabilistic distributions, thus the new characteristic of these coefficients can be defined as Pseudooptimal Inexact Stochastic Dual Interval T2 Fuzzy Sets Random Parameters (PIS-IT2FSRP). Fig. 4 shows features of PIS-IT2FSRP.



Min f ffi

3.8. Xiamen PIS-IT2FSLP energy modeling formulation Base on above optimal methods, this PIS-IT2FSLP will be formulated for planning energy systems of Xiamen City. The objective of PIS-IT2FSLP model is to minimize system cost and environmental pollution such as SO2 else under multiple uncertainties over 15 years of time. It contains two major parts, which are costs and profits. The detail of costs part includes energy supply, processing, conversion, relative facilities expansion and environmental pollution costs. In the other hand profit of this energy system is made by exporting energy products for example the extra-electricity output from energy conversion facilities. The environmental pollution costs mainly refer to running cost of environmental protection equipment and payment for emissions of air pollutants discharge. The model’s decision variable are included by production quantity of energy, import amount of energy sources, expansion of relative energy facilities and export amount of energies. The detail formation of PIS-IT2FSLP model are following:

 X3 X2  X3       PIMði; tÞ  IMPði; tÞ þ TPðk; tÞ  Cðk; tÞ þ Yðk; m; tÞ  XPðk; tÞ  CIðk; tÞ t¼1 k¼1 m¼1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} X3 X10 t¼1

i¼1

Total energy import costs

Energy processing and facility expansion costs

 X3 X10  X3     þ Eðj; tÞ  CEðj; tÞ þ Yðj; m; tÞ  XEðj; tÞ  CCEðj; tÞ t¼1 j¼1 m¼1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Energy conversion and facility expansion costs

h io X3 X9 X2 n       þ Eðj; tÞ  CVPðp; j; tÞ þ CPCðp; j; tÞ  PFEðp; j; tÞ  ð1  g ðp; j; tÞ Þ  CGRðj; tÞ t¼1 j¼7 p¼1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Environmental pollution costs



X3 X11





PEXði; tÞ  EXPði; tÞ t¼1 i¼1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð19aÞ

Total energy exports benefit

Thus, for better quantifying uncertainties in parameters of constraints, the CCP method is introduced into the PSD -IT2FSLP method within an LP framework leading to the PIS-IT2FSLP method, which can be described as follows: 

Max f ffi CðtÞ X  ~ ðtÞpi ; e b S:t: A ðtÞX  6 i 

ð18aÞ ð18bÞ

i

X P 0;  bi ðtÞpi

ð18cÞ 1

¼ F ðpi Þ;

pi 2 ½0; 1:

ð18dÞ

Objective function: S.t.: (1) Mass balance of coal

IMPð1; tÞ þ IMPð2; tÞ  EXPð1; tÞ  EXPð2; tÞ P DMð1; tÞ þ DMð2; tÞ

8t

ð19bÞ

IMPð1; tÞ þ IMPð2; tÞ  EXPð1; tÞ  EXPð2; tÞ Eð7; tÞ  CFEð1; 7; tÞ

8t

Fig. 4. Characteristics of pseudo-optimal inexact stochastic interval T2 fuzzy sets random parameters.

ð19cÞ

81

L. Jin et al. / Applied Energy 138 (2015) 71–90

(2) Mass balance of coke 

(14) Capacity of renewable energy constraint



IMPð3; tÞ  EXPð3; tÞ P DMð3; tÞ 8t "

3 X RPð1; tÞ þ Yð1; m; tÞ  XPð1; tÞ

ð19dÞ

#



REðj; tÞ þ

3 X   Yðj; m; tÞ  XEðj; tÞ RPCðj; tÞ

8j; t

ð19vÞ

m¼1

(15) Electricity mass balance constraint

m¼1

IMPð3; tÞ  EXPð3; tÞ

8t

ð19eÞ

IMPð4; tÞ  EXPð4; tÞ P DMð4; tÞ 8t " IMPð4; tÞ  EXPð4; tÞ RPð2Þ þ

ð19fÞ

3 X

# Yð2; m; tÞ  XPð2; tÞ

8t

(4) Mass balance of gasoline

IMPð5; tÞ  EXPð5; tÞ P DMð5; tÞ



8t

ð19hÞ

8t

ð19iÞ

IMPð7; tÞ  EXPð7; tÞ P DMð7; tÞ



8t

ð19jÞ

8t

ð19kÞ

8t

ð19lÞ

(8) Mass balance fuel oil

IMPð9; tÞ  EXPð9; tÞ P DMð9; tÞ

IMPð9; tÞ  EXPð9; tÞ Eð8; tÞ  CFEð9; 8; tÞ

8t

ð19mÞ

(9) Mass balance of Liquefied Natural Gas (LNG)

g tÞ  P DMð10; IMPð10; tÞ  EXPð10; tÞ f

8t

ð19nÞ

8t

ð19oÞ

IMPð10; tÞ  EXPð10; tÞ Eð9; tÞ  CFEð10; 9; tÞ

8t

ð19pÞ

(10) Power demand–supply balance 10 X  g tÞ  Eðj; tÞ e DMð11;

8t

ð19qÞ

j¼1

DMð11;tÞðpÞ

6 DMð11; tÞðpÞ 6 kc l

DMð11;tÞðpÞ

8t

ð19rÞ

(11) Energy processing technologies constraint 

RPðkÞ þ

3 X



Yðk; m; tÞ  XPðk; tÞ TPðk; tÞ



8t; k

ð19sÞ

m¼1

(12) Peak load constraint for power demand 



IMPð11; tÞ  EXPð11; tÞ þ

10 X

3 X  REðj; tÞ þ Yðj; m; tÞ  XEðj; tÞ

j¼1

QPðtÞ

ðpi Þ

!



m¼1

8t

ð19tÞ

(13) Capacity of power generating 

½REðj; tÞ þ

3 X    Yðj; m; tÞ  XEðj; tÞ   hðj; tÞ  ½1  DLLðj; tÞ  m¼1

 4:1816  106 Eðj; tÞ



3 X Yðk; m; tÞ ¼ 1;

8j; t



3 X m¼1 

Yðj; m; tÞ ¼ 1;

ð19uÞ

ð19zÞ



IMPði; tÞ ; EXPði; tÞ ; Eðj; tÞ P 0 i ¼ 1; 2 . . . 11 j ¼ 1; 2 . . . 10;

(7) Mass balance of Liquefied Petroleum Gas (LPG)

IMPð8; tÞ  EXPð8; tÞ P DMð8; tÞ

ð19yÞ

(18) Binary and nonnegative constraints

m¼1



8t

Yðk; m; tÞ; Yðj; m; tÞ ¼ integer; Yðk; m; tÞ; Yðj; m; tÞ 2 ½0; 1

(6) Mass balance of kerosene

kc l

11 X 2 X   DMði; tÞ  PEDðp; i; tÞ e POLLM i¼1 p¼1

(5) Mass balance of diesel

IMPð6; tÞ  EXPð6; tÞ P DMð6; tÞ

ð19xÞ

j¼7 p¼1

þ



IMPð11; tÞ  EXPð11; tÞ þ

IMPði; tÞ 6 LIMði; tÞ 8i; t

9 X 2 X    Eðj; tÞ  PFEðp; j; tÞ  ð1  gðp; j; tÞ Þ

ð19gÞ

 c kc lDMð10;tÞ 6 DMð10; tÞ kl DMð10;tÞ

ð19wÞ

(17) Environmental condition constraint

m¼1



E ðj; tÞ 6 Emax ðj; tÞ 8j; t (16) Import energy constraint

(3) Mass balance of crude oil





t ¼ 1; 2; 3

The detailed nomenclatures of model (19) are listed in Appendix A, which includes the decision variables and model parameters. Obviously, the objective of model (19) is to minimize the relative costs of energy import, supply, consumption and environmental pollution. It involves kinds of energy sources, energy conversion facilities and expansion options for a long term energy planning under multiple uncertainties. The objective function of this model contains costs of import energy, costs of energy processing, costs of energy conversion, costs of environmental pollution and costs of various facilities expansion in Xiamen City. Constraints of model (19) is defined for relationship among decision variables, limited energy sources and environmental conditions. In details, inequations (19b)–(19k) indicates mass balance requirements. These constraints involve mass balance of raw coal, washing coal, coke, crude oil, coke, crude oil, gasoline, diesel, kerosene, LPG, fuel oil and LNG in which these all kinds of energy resources are used in this city. These constraints denote that total input of energy sources of Xiamen City should be equal to output of energy supplies. Constraint (19l) indicates power balance which mean supply power should meet the needs power volume of consumption units such as industries or municipal departments. However, this constraint can change during different seasons. It has multiple uncertainties since it fluctuates seasonally especially during the typhoon season, it drastic changed even just one day. Power supply also has a feature of probability level. It requires power supplies on a probability level to satisfy operation of Xiamen City. Therefore, this constraint has a typical characteristic with multiple uncertainties. Constraint (19m) denotes limitation of power processing technologies. Constraint (19n) indicates periodic capacity of processing technologies. The capacity of processing technologies changes yearly with expansion and depreciation of facilities. Constraint (19o) defines peak load of power supply. The installed gross capacity power volume of Xiamen City should be large than power peak load demand. Constraint (19p) denotes capacity of power generation. The total capacity of power volume should be included self-consumption and limitation of gross capacity of power generation. Eq. (19q) means periodic capacity of power generating. This constraints also changes because of expansion of facilities from time to time. Constraints (19r) and (19s) denote capacity of thermal power. These

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L. Jin et al. / Applied Energy 138 (2015) 71–90

two constraints also are changed by expansion of heating facility. Constraint (19t) represents capacity of renewable energy sources such as wind power, solar power and hydropower else. Renewable energy has limitation of self-development ability. Constraint (19u) denotes requirements of import energy. These requirements are composed by condition of transportation. In order to secure local energy consumption, the import energy amount should be more than local supply levels. Constraint (19v) presents environment demand. The total discharge pollutions suppose within the acceptance of environment regulations. Constraint (19w) denotes the binary and nonnegative numbers for rest of molding parameters such as expansion decisions. In this model (19) multiple facilities, multiple periods and multiple options of energy supply have be engaged to serve energy-environmental management. Therefore, model (19) can fully represents the distribution of energy consumption and allocation. 3.9. Solution method According to [43,63,79], fuzzy interval programming can be then solved by a robust two-step solution method. So this interval model can be transformed into two submodels. The first submodel which corresponds to f- as follows, k n X X Max f ¼ cj xj þ cj xþj 

j¼1

S:t:

ð20aÞ

j¼kþ1

k n X X  jaij jþ Signðaij Þxj þ jaij j Signðaij Þxþj 6 bi ; j¼1

j¼kþ1

i ¼ 1; 2; . . . m xj

P 0;

xþj P 0;

ð20bÞ

j ¼ 1; 2; . . . ; k

ð20cÞ

j ¼ k þ 1; k þ 2; . . . ; n

ð20dÞ

mn

1n



m1

n1

where a 2 fR g , c 2 fR g , b 2 fR g , x 2 fR g , and {R±} denote a set of interval numbers with lower and upper bounds. þ The results, x jopt ðj ¼ 1; 2; . . . ; kÞ and xjopt ðj ¼ k þ 1; k þ 2; ; . . . ; nÞ can be obtained for model (20). The second submodel f+ can be obtain as follows: þ

Max f ¼

k n X X cþj xþj þ cþj xj j¼1

S:t:

Periods T=1

T=2

T=3

Import energy Raw coal Washed coal Coke Crude oil Gasoline Diesel Kerosene LPG Fuel oil Natural gas Electric power

[22.4, 23.9] [25.4, 30.3] [39.0, 54.9] [124.6, 130.6] [208.6, 241.7] [170.2, 191.7] [78.9, 104.5] [94.7, 130.5] [80.8, 112.3] [108.7, 123.3] [79.2, 87.5]

[31.4, 33.5] [35.6, 42.5] [54.7, 77.0] [174.8, 183.1] [292.6, 339.0] [238.7, 268.9] [110.7, 146.6] [132.8, 183.0] [113.3, 157.5] [152.5, 172.9] [84.0, 97.2]

[44.0, 47.0] [44.9, 59.6] [76.7, 108.0] [245.1, 256.8] [410.4, 475.5] [334.8, 377.1] [155.3, 205.6] [186.3, 256.7] [158.9, 220.9] [213.9, 242.5] [101.4, 107.2]

Export energy Gasoline Diesel Kerosene LPG Fuel oil Electric power

[210.0, 242.1] [173.3, 194.7] [80.9, 105.2] [95.1, 130.4] [81.9, 112.5] [117.3, 172.4]

[294.5, 343.8] [243.1, 273.1] [113.5, 147.5] [133.4, 182.9] [114.9, 157.9] [164.5, 241.8]

[430.1, 482.2] [341.0, 383.0] [159.2, 206.9] [187.1, 256.5] [161.2, 221.5] [230.7, 339.1]

uncertainties. The dual interval T2 FS method which combined dual interval analysis with the interval T2 FS method can deal with such complex multiple fuzzy uncertainties with a pseudo-optimal solution process. It highly increases the model’s ability to deal with the optimization process. More importantly, the stochastic method can increase the impact of the dual interval T2 FS method through the CCP technique with probability distribution information. It can deal with the fluctuations of a higher level fuzzy uncertainties. However, this new model does not reduce the complexity of the management process; instead, this new method allows DMs to more comprehensively measure uncertainties in management problems. It provides more specific solutions which reduce the influence of such stochastic fuzzy uncertainties as well as the relationships between complex uncertainties input and easily understood output. Consequently, this new approach can enlarge decision dimensions through those unique optimal techniques (see Tables 3-6).

ð21aÞ

j¼kþ1

4. Result analysis

k n X X þ jaij j Signðaij Þxþj þ jaij jþ Signðaij Þxj 6 bi ; j¼1

j¼kþ1

i ¼ 1; 2; . . . m (

)

X n

þ  Max xj P 0; j ¼ 1; 2; . . . ; n aij xj 6 bi ;

j¼1

ð21bÞ

8i

ð21cÞ

xþj P xjopt ;

j ¼ 1; 2; . . . ; k

ð21dÞ

xj

6

j ¼ k þ 1; k þ 2; . . . ; n

ð21eÞ

xþj xj

P 0;

j ¼ 1; 2; . . . ; k

ð21fÞ

P 0;

j ¼ k þ 1; k þ 2; . . . ; n

ð21gÞ

xþjopt ;

Table 3 Energy cost in different periods (106 RMB/PJ).

þ  For (15c), if a ij > 0; then xj ¼ xj ; otherwise, xj ¼ xj . Hence, þ ðj ¼ k þ 1; k þ 2; . . . ; nÞ and x ðj ¼ 1; 2; . . . ; kÞ can be obtained x jopt jopt

through model (21). Thus the final solution can be attained as 



þ

þ  x jopt ¼ ½xjopt ; xjopt  and f opt ¼ ½f opt ; f opt .

This PSD-IT2FSRP model improves upon the existing optimal methods by reflecting dual interval type-2 fuzzy uncertainties combined with stochastic random features. In this new approach, four optimization techniques are included the ILP, FILP, DILP, IT2FSLP and the SMP methods, all having been harmoniously incorporated into an optimal modeling framework. Each method has been indispensable improving the model’s capability in handling

The results of the PIS-IT2FSLP model indicate that coal-fired power would remain main energy supply source for Xiamen City over the next 15 years. However, it is suffering from the challenges of increasingly serious environmental requirements. The liquid natural gas power now plays an important role in the power system due to its competitive price and environmental friendliness. Liquid natural gas has become the second largest energy source to support the energy needs of this city. Details of the energy strategy for Xiamen City follows in this section. Since uncertain conditions exist in input of energy demands, interval solutions can be a good method to reflect flexible decisions for decision makers. 4.1. Energy solutions for Xiamen City Table 7 shows the solutions obtained through the PIS-IT2FSLP model, which includes the import and export energy strategies for Xiamen City over the next 15 years. For example, imported raw coal, washed coal and coke in period one would respectively be [67.4, 75.3], [0, 0] and [3.1, 5.2] PJ; imported crude oil, gasoline, diesel and kerosene in period one would respectively be [0, 0], [126.3, 139], [394.9] and [394.9] PJ; similarly, imported LPG, fuel oil, natural gas and electric power in period one would respectively

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L. Jin et al. / Applied Energy 138 (2015) 71–90 Table 4 Cost of power generation in different periods (106 RMB/PJ). Energy types

Periods

Hydropower

Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost Operate cost Capital cost

Pumped storage Wind power Photovoltaic power Waste generation Biomass power Coal-fired power Oil-fired power Natural gas power Tidal power

T=1

T=2

T=3

[68.11, 68.7] [17496, 21384] [61.88, 66.9] [4800, 5000] [118.3, 155.4] [7908, 9666] [562.5, 618.0] [18900, 23100] [125, 133.3] [12000, 13600] [100.0, 110.0] [4100, 4500] [14.7, 15.0] [4200, 5100] [18, 20] [5220, 5300] [12.4, 12.95] [4000, 4500] 150.0 [17496, 21384]

[67.3, 81.2] [14892, 18204] [61.88, 66.9] [4570, 5000] [112.7, 123.3] [7338, 7475] [423.5, 478.8] [16200, 19800] [111.1, 125] [10000, 12000] [150.0, 160.0] [4000, 4200] [11.8, 12.0] [4300, 5200] [18, 20] [5220, 5300] [12.4, 12.95] [4000, 4500] 138.9 [14892, 18204]

[64.5, 75.7] [11592, 14172] [61.88, 66.9] [4350, 4670] [111.3, 125.0] [6900, 8436] [277.9, 333.2] [13500, 16500] [108.4, 116.7] [9750, 11250] [200.0, 210.0] [3500, 3950] [10.85, 11.1] [5000, 5600] [18, 20] [5220, 5300] [12.4, 12.95] [4000, 4500] [125, 133.4] [11592, 14172]

Table 5 Pollutant discharge coefficients (104 tonnes/PJ). Energy technology

Periods T=1

T=2

T=3

Coal-fired power

SO2 NOx

0.01689 0.04156

0.00970 0.03034

0.00664 0.02180

Oil-fired power

SO2 NOx

0.01441 0.03926

0.01441 0.03926

0.01441 0.03926

Natural gas power

SO2 NOx

0.00019 0.00788

0.00018 0.007328

0.00017 0.007191

Table 6 Maximum pollution discharge amount in Xiamen (104 tonnes). Period

T=1

T=2

T=3

Pollution discharge

[8.5, 9.1]

[6.6, 7.4]

[5.3, 6.1]

Table 7 Results of PIS-IT2FSLP for Xiamen City. Periods T=1

T=2

T=3

Import energy (PJ) Raw coal Washed coal Coke Crude oil Gasoline Diesel Kerosene LPG Fuel oil Natural gas Electric power

[67.4, 75.3] [0, 0] [3.1, 5.2] [0, 0] [126.3, 139] [394.9] [394.9] [394.9] [394.9] [177, 219.027] [394.9]

[84.1, 90] [0, 0] [6.5, 6.9] [0, 0] [177.1, 195] [621.5] [621.5] [621.5] [621.5] [261.03] [621.5]

[105, 117.3] [0, 0] [8.1, 9] [0, 0] [248.4, 273.5] [970] [970] [970] [970] [344, 345] [970]

Export energy (PJ) Diesel Kerosene LPG Fuel oil Electric power

[123.5, 148.2] [277.7, 288.4] [333.4, 340.5] [344.9, 389] [92.05, 224.06]

[305.3, 334.1] [483.2, 495.8] [574, 581.4] [617.3] [298.69, 418.69]

[601.6, 635.2] [806.8, 821.7] [929.9, 935.7] [966.9] [597.8, 732.27]

be [394.9], [394.9], [177, 219.027] and [394.9] PJ. These results conform to the current situation of Xiamen City, which relies heavily on imported energies. However, due to the difference of regional energy prices, export of energies also plays an important role in the development of Xiamen City. This means that the energy administration office can earn a profit by exporting energies to other cities more than enough energy to meet its consumption need. Thus, in period one, the export energy of diesel, kerosene, LPG, fuel oil and electric power would respectively be [123.5, 148.2], [277.7, 288.4], [333.4, 340.5], [344.9, 389] and [92.05, 224.06] PJ. Those interval numbers in Table 7 demonstrate that the amount of energies is sensitive to the uncertain working conditions of Xiamen City. Fig. 5 shows the optimized solutions of energy allocation by way of the low system cost. It clearly shows that diesel, kerosene, LPG, fuel oil and electric power would always be the five largest parts among all imported energies in the planning time periods. These four kinds of energies in period 1 would remain 394.9 PJ to support energy consumption. They increase significantly to 621.5 PJ in period 2 this is 1.5 times more than before to satisfy the requirements of city development. They rise to 970 PJ in the period 3. This is also 1.5 times more than the second period. Such an increase is due to the lack of energy resources in this city and require for an optimal strategy of energy planning. These amounts of energy would be filled by other cities, mostly from the city of Quan Zhou and Jiang Xi province, which have a largest oil and coal products supply system. However, those imported energies are not only used in Xiamen’s consumption of energy, but most of them are used for export. The export of diesel, kerosene, LPG, fuel oil and electric power in period 1 as mentioned above would be [123.5, 148.2], [277.7, 288.4], [333.4, 340.5], [344.9, 389] and [92.05, 224.06] PJ. By comparing the import and export amounts in the first period, the solutions of the allocation model indicates that more than 70% of kerosene is used for export, and more than 85% of LPG is also used for export. Additionally, 95% of the fuel oil is used for sold. The exported amounts of diesel, kerosene, LPG, fuel oil and electric power in the period 2 would be [305.3, 334.1], [483.2, 495.8], [574, 581.4], [617.3] and [298.69, 418.69] PJ; in the period 3, these four exported energies would be [601.6, 635.2], [806.8, 821.7], [929.9, 935.7], [966.9] and [597.8, 732.27] PJ. As in period 1, most of these energy sources are used for export purpose to make profits for Xiamen City in period 2 and 3. Imported washed

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L. Jin et al. / Applied Energy 138 (2015) 71–90 1100 1000 900 800 700 600 500 400 300 200 100 0 1

2

3

4

5

6

7

8

Lower bound (T=1)

Upper bound (T=1)

Lower bound (T=2)

Upper bound (T=2)

Upper bound (T=3)

Mean value(T=1)

Mean value(T=2)

Mean value(T=3)

9

10

11

Lower bound (T=3)

Fig. 5. Interval solutions of energy supply for Xiamen City.

coal would basically be used in a coking plant. However, there is no coking plant in Xiamen City because of the priority given to the tourist economy. Therefore, unlike other cities, there is no reservation for washed coal in Xiamen City during next 15 years. As with washed coal, there would no import of crude oil since the refinery factories are far from this city. With high penalty risk of environmental conditions, Xiamen City would directly import crude oil products, for example, gasoline, from nearby cities for consumption by private or engineering vehicles. However, as an eastern coastal city, there are no such resources appeared from this land or adjacent waters. Instead, the import gasoline would be [126.3, 139], [177.1, 195] and [248.4, 273.5] PJ corresponding to different time periods. It increases 2 times from period 1 to period 3. The dramatic increased usage of gasoline is commonly due to the number of private cars. Gasoline still plays a key role in the modern internal combustion engines, although there are many innovations such as bio-fuel, which is used as an alternative. However, with the development of internal combustion engine, natural gas is primarily used as energy for public transportation in Xiamen City. The transportation vehicles of Xiamen has gradually changed its dependence on gasoline. The traffic department of this city requires public transport vehicles including taxies and city buses to burn natural gas rather than gasoline, which could reduce harmful gas exhaust to the environment. Natural gas purchase would increase significantly to satisfy the end-user demands. Therefore, the import of natural gas in period 1 would be [177, 219.027] PJ; it would be [261.03] PJ in period 2; and it would increase to [344, 345] PJ in period 3. It increases 47% from period 1 to period 2, and, it increases 31% from period 2 to period 3. The increase of import of natural gas is caused by not only transportation or household demands, but is also primarily attributed to power generation capacities. The imported natural gas would be the first used for power production, in order to meet a low environmental standard in Xiamen. 4.2. Electricity structure and generation Fig. 6 represents the optimal solutions for Xiamen power generation structures. There are two different power generation scenarios that have been shown differently by a lower and an upper plan. For the lower cost level (Fig. 6a), in period 1, the ratio of electric generation of coal-fired power would take 32% of the whole market, while the ratio of the natural gas, waste generation power, pumped storage and hydropower would be 46%, 6%, 9% and 7%,

respectively. This should be an optimal energy structure of power generation for Xiamen City in the first 5 years. It clearly shows that the part of natural gas plays significantly increased due to the advantage of being environmentally clean and economically efficient. However, the coal-fired power would still be the second largest source among all other producers. The coal-fired power maintains such important role in the city energy structure because it is the largest and cheapest resource in China area. Meanwhile, the renewable energies of power generation are also very important. Total ratios of waste generation power, pumped storage power and hydropower would take up 22% occupation of whole energy market. By comparison with coal-fired power, the renewable energies share 68% occupation of power generation. It is an important sign, and illustrates that the local government is planning to use several kinds of suitable renewable energy to replace the fossil fuel energies. However, due to their high costs, renewable energies hardly became as a suitable energy sources. According to Fig. 6, in the second period, the lower bound of coal-fired power make up 30% occupation of the energy market. That is because the falling share of coal energy can be replaced by other clear energies. Meanwhile, the share of natural gas has been squeezed from 46% to 42% in period 2. The total parts of renewable energies have taken a 28% share of the market. It increases to a 6% share of energy market in Xiamen City. There are two more varieties of energy types. They are wind power and biomass power. However, each of the renewable energy sources including waste generation power, pumped storage, and hydropower would individually share a relatively low level of the energy market in large part because it is unable to highly utilize. In period 3, being a lower cost strategy, the provision of various type of power generation in the whole energy market would be, 25% of coal-fired power, 38% of natural gas power, 3% of biomass power, 4% of waste generation power, 2% of photovoltaic power (solar energy), 3% of wind power, 6% of pumped storage power, 5% of hydropower and 14% of tidal power. The total shares of renewable energy would be 37%, surpassing the share of coal-fired power. This means renewable energy would be the second largest type of power generation in period 3 for Xiamen City. However, this does not means all renewable energies are suitable for development in Xiamen. Oil-fired power is not appropriate in the development of this city because of its higher prices and air emission rate. Natural gas power at 38% of the market share ultimately led to its being the largest part of energy sources in this city. This phenomenon demonstrates that coal-fired power technology would not be the major type of energy for Xiamen. These

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L. Jin et al. / Applied Energy 138 (2015) 71–90 0%

0%

7%

6% 8%

Hydropower

9% 0% 0%

Hydropower

Pumped storage 4% 0%

Wind power

6% 46% 0%

Photovoltaic power

42%

Wind power Photovoltaic power

6%

Waste generaon

Waste generaon 4%

Biomass power

Biomass power

Coal-fired power

Coal-fired power

Oil-fired power

Oil-fired power

Natural gas power

32%

Pumped storage

Natural gas power

Tidal power

T=1

Tidal power

30%

0%

T=2

0% 5% 6%

14%

Hydropower

3% 2%

Pumped storage

4%

Wind power Photovoltaic power

3% Waste generaon Biomass power Coal-fired power Oil-fired power 25%

38%

Natural gas power Tidal power

0%

T=3

(a) 0%

6% 0%

8% Hydropower

9%

49%

Hydropower

8%

Pumped storage

0% 0%

4%

Wind power

0% 6%

42%

0%

Photovoltaic power

0%

Waste generaon

Coal-fired power

Oil-fired power

Oil-fired power 0%

Natural gas power 0%

Photovoltaic power

Biomass power

Coal-fired power

Natural gas power

T=2

Tidal power

T=1

Wind power

Waste generaon 4%

Biomass power 34%

Pumped storage

Tidal power

30% 0%

0%

0%

0%

0%

Hydropower

0%

Pumped storage

0% 39%

Wind power Photovoltaic power Waste generaon Biomass power Coal-fired power Oil-fired power

61%

Natural gas power 0%

T=3

Tidal power

(b) Fig. 6. (a) Lower bounds of Xiamen City’s energy structure in three different periods and (b) upper bounds of Xiamen City’s energy structure in three different periods.

results require that the energy structure of Xiamen City would be transformed by the strong demand of natural gas power and renewable energies in the next decade. If the city authorizes prefer a low cost and environmentally friendly energy strategy, coal-fired power should no longer be the only resource for Xiamen, and renewable energy should be the main development objective. It is the requirement of 12th Five-year emission plan under globalized environment requirements.

Fig. 6b shows an extensive mode of power generation for Xiamen City. It causes a relative higher cost for energy management. As the conversion type of power technology, coal-fired power would take 34% of the energy market in period 1, 30% in period 2, and 39% in period 3, respectively, which is mainly due to low cost. It decreases 9% of market share in period 2 partially caused by the strict environmental plan and the limitation of source import. Natural gas power generation dramatically increases its

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L. Jin et al. / Applied Energy 138 (2015) 71–90

share of energy market. It would take 49% of the share of the market in period 1, 42% of the share of market in period 2 and 61% of the share of market in period 3. Its share decreased in the second period. Due largely to the extensive mode of energy management in the third period. Renewable energies would take 17% of share in period 1, 28% of share in period 2 and zero percent in period 3. It is indicated that renewable energy generation would be developed in period 2 to make up for the shortfall of other types of energy. Hydropower, pumped storage power, waste generation power, biomass power and photovoltaic power should be the major energies explored to correspond to the energy policy of Xiamen. Hydropower and pumped storage power would be the head renewable power technology of Xiamen City. Hydropower is wildly used in Xiamen because this city is close to offshore and it has plenty of water resources. However, it has been replaced by natural gas power because of the high cost of maintenance of renewable energy power. The main difference between low cost and high cost power production strategy, which are individually shown in Fig. 6a and b, is the attitude toward developing renewable energies. If the city managers choose to develop renewable energy for Xiamen City, the energy cost would be lower than to only use conversional energy types. Renewable energy is the key for achieving a suitable energy strategy of power generation. Conversely, if these authorities only develop the traditional power technologies, the energy cost would be much higher than the other way, which chooses renewable energy to generate power. Therefore, renewable energy is an essential characteristic needed to reduce environmental cost for Xiamen City. 4.3. Capacity expansion strategy If the current power generation capacity cannot meet the city’s consumption of energy, power facility expansion should be carried out to satisfy the municipal demand. Table 8 reflects binary solutions of capacity expansion patterns, which are solved by the PIS-IT2FSLP method. Considering the diversity of energy demands during the different periods, there are 3 options for the expansion pattern for each capacity facilities. However, decision makers face the difficult task in their choice of an appropriate way without wasting of existing resources in Xiamen. Consequently, the solutions of the PIS-IT2FSLP method can provide optimal expansion patterns for this a problem which indicates that these patterns would be unpredictable because capacity expansion may happen during each of periods. According to the PIS-IT2FSLP method, capacity of hydropower would be expanded by choosing the additional capacity of 0.2 GW in period 1. Meanwhile, capacity of relevant facilities such as pumped storage power, waste generation power, coal-fired power and natural gas power should be expanded to catch up municipal demands. However, the capacity of other facilities, for example wind power, photovoltaic power, biomass power, oil-fired power and tidal power, do not need expansion in period 1. The special facility of waste generation power should be expanded for the lower boundary solution. However, if given the upper boundary solutions, it is not necessary to expand in period 1. In period 2, the existing capacities cannot generate enough power to meet municipal users. Therefore, capacity expansion of relevant facilities should be considered. Based on an optimal planning method, the capacities of hydropower, pumped storage power, wind power, waste generation power, biomass power, coal-fired power and natural gas power would be expanded to meet the requirements of Xiamen City. Other facilities such as photovoltaic power, oil-fired power and tidal power do not need to expand whether choosing the upper or lower boundary energy solutions. In period 3, power generation cannot meet the Xiamen

Table 8 Binary solutions of capacity expansion for conversion technologies. Period

Option (GW)

T=1

T=2

T=3

Hydropower

0.1 0.15 0.2

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 0]

Pumped storage

0.1 0.15 0.2

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 0]

Wind power

0.15 0.2 0.25

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 0]

Photovoltaic power

0.3 0.4 0.6

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [1, 0]

Waste generation

0.05 0.1 0.15

[0, 0] [0, 0] [1, 0]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 0]

Biomass power

0.1 0.15 0.2

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 0]

Coal-fired power

0.4 0.6 0.8

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 1]

Oil-fired power

0.15 0.2 0.25

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [0, 0]

Natural gas power

0.6 1 1.3

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 1]

[0, 0] [0, 0] [1, 1]

Tidal power

0.1 0.15 0.2

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [0, 0]

[0, 0] [0, 0] [1, 0]

power consumption, and energy capacities would need to expand again to meet the development of city activities. Correspondingly, hydropower would be expanded another 0.2 GW; pumped storage power would be increased to 0.2 GW as well; wind power would need to expand by 0.25 GW; biomass power would be increased to 0.2 GW to meet demands; coal-fired power increased by a 0.8 GW expansion and natural gas power would need a 1.3 GW expansion to satisfy municipal development. These results clearly show that renewable energy facilities, for example waste generation, hydropower and others, still remain at a low level of expansion. However, expansion of these renewable energy capacities would largely reduce the energy cost for Xiamen. In other words, if authorities develop these renewable energy power sources, they could decrease energy bills for Xiamen City. Such expansions are significant for energy allocation under the environmental emission requirements. However, these expansions, based on their technologies, would not be changed. Therefore, by observing these expansion data, the reasons for the expansion of facility capacity are mainly due to environmental impact, cost of capacity and import power prices. Thus, by expanding the capacity of these facilities, the power generation would be sufficient to support development of Xiamen City from period 1 to period 3. 4.4. Energy system cost solutions Fig. 7 presents the results of the objective values associated with different pi levels. They are obtained through the PIS-IT2FSLP model. The objective of this model is to look for a minimization of energy systems cost under uncertainties. According to the different conditions of energy demand, the solutions of the objective function provide a lower and upper solution with different pi levels

L. Jin et al. / Applied Energy 138 (2015) 71–90 Lower cost

Average cost

Upper cost

1400000 1200000 1164507

1158740

1155741

1000000 800000 600000

657444.4

653733.4

651989.4

400000

87

City. This phenomenon demonstrates that, with the consideration of environmental pollutions, the behavior of reducing renewable energies would increase cost of energy management, though power export may help earn a little profit back. Currently, the energy structure of Xiamen has given priority to coal energy. However the emissions of coal energy causes serious air pollution. Therefore, the energy authority should gently increase development of renewable energy and thus, reduce the energy system cost of the energy system for Xiamen City.

200000 148237.7

148726.7

150381.7

Probability value (QP) is 20%

Probability value (QP) is 60%

Probability value (QP) is 20%

5. Discussion

0

Fig. 7. Energy system cost under various probability levels.

7000 5767

6000 5000

3711

4000 3000

2999

2000

1744

1000

489

1655

0 1 Rate of increase for lower bound

2 Rate of increase for mean value

Rate of increase for upper bound Fig. 8. Rate of increase for different boundaries.

to demonstrate the superiority of PIS-IT2FSLP model. The probability level of function indicates the chances of violation. The relationship between probability (pi level) and the function objective offers a compromise for risk of random events. Thus, the PIS-IT2FSLP model can provide useful solutions associated with probability levels. It can help energy administrators to choose a desired energy plan to achieve a suitable local energy strategy, which means a power generation strategy and capacity of facilities expansion under various uncertain conditions. Moreover, combined with pi levels, this method would find an optimal energy structure, whereas a higher probability level fits looser constrains. Thus, when p1 = 20%, the optimal solution is  f opt ¼ ð148237:7; 1155741Þ  106 RMB. A lower probability level presents a lower risk of violation for an energy system. However, this lower pi level would cause a narrow decision space. When the probability level is 60%, the optimal solution of the objective  function would be f opt ¼ ð148726:7; 1158740Þ  106 RMB. The higher pi level enlarges decision space for system management. When p3 = 20%, the system cost of the objective function would  be f opt ¼ ð150381:7; 1164507Þ  106 RMB. Obviously, the solutions of the PIS-IT2FSLP model are different with each pi level. Fig. 8 gives growth the rate for each of pi levels. It shows that when i of pi equal to 1, it has the largest growth rate. The growth rates of other functions are relatively smaller than the first one. This is because that for the first pi level (pi = 20%), more power would be output to reduce system cost. The second pi level (pi = 60%) decreases export power energy, and cuts off the generation of hydropower. These changes led to a higher system cost in the second level. The third pi level (pi = 20%) continues to reduce power export. In this level, the power output is smaller than the second level. The waste generation power has been reduced under the third pi level. These conditions result in higher costs for Xiamen

In this study, the developed a pseudo-optimal interval T2 FSLP proposal integrates interval and stochastic programming. The PIS-IT2FSLP method uses a pre-defuzzification process to determine a result by means of an a-cut, and then generates a dual interval which is applied to optimize the energy system problem by means of classical methods with a stochastic characteristic. This method can effectively reflect higher level fuzzy uncertainties, which are presented as T2 fuzzy interval numbers, CCP and dual intervals related energy factors to be incorporated with a linear programming framework. The reasons for developing such specific optimal programming is due to individual differences and unknowable effects from seasonal fluctuations of energy demands in climate change. It led to the coefficients contained in T2 fuzzy lower and upper interval bounds correspondingly. Different from former crisp fuzzy intervals, a T2 dual interval reflects higher level uncertainties of boundaries and would be a more accurate response to uncertainties. If the T2 FS intervals are substituted by conventional interval fuzzy, this energy system can still find optimal results through Interval Fuzzy Linear Programming (IFLP). When the boundary of T2 FS is determined, the T2 FS would collapse into a normal fuzzy set. Consequently, this method could provide the same solutions of the IFLP in some special cases. However, if the problem has a T2 FS feature, conventional IFLP cannot fully describe such uncertainties leading to oversimplified results. Compared with IFLP, the T2 FS model has a characteristic to provide a measure of fuzzy uncertainty. Thus the former IFLP method does not give optimal solutions since it reduced the uncertainty level in fuzzy-fuzzy situations. The simple IFLP model can only tackle planning problems if parameters are fuzzy intervals. However, this is not a repudiation of the IFLP method. Rather it means the IFLP method is only suitable to the situation of small fuzzy interval bounds. If the fuzzy interval boundary is uncertain, the solutions of IFLP become unreliable. The conversional fuzzy set is just like a mean value which hardly reflects dispersion of an array. In comparison, this PISIT2FSLP method reflects those factors. In this programming, the right hand side parameters allow T2 FS freedom, responding to the volatility of energy data under special conditions. It is for example, similar to minimizing mean-squared errors. In reality, the PIS-IT2FSLP method may increase the cost of energy systems by its limited scope of fuzzy parameters. However, it corrects fuzzy linear programing, although it may sacrifice some profits for systems. Its solutions will be much more reliable, but may increase computing time. They could imply both pre and post-optimal analysis in order to obtain a suitable interpretation of higher fuzzy boundaries. Thus the results of the PIS-IT2FSLP method is reliable in real-world energy systems. At a higher level of interval fuzzy boundaries, the PIS-IT2FSLP method allows the parameters to contain a bidimensional space, which is an extension of interval fuzzy programming. It can tackle inexact planning problems with the features of both the interval fuzzy programming and interval T2 fuzzy programming. The dual interval analysis ensures the correctness of type reduction. In its solution process, a pre-defuzzification

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a cut has been selected. This is the reason that it is called pseudooptimal programming. This PIS-IT2FSLP applies to Xiamen energy allocation. Compared with a previous study of energy systems, it shows: (a) the PISIT2FSLP method can provide a good measurement of dispersion of conventional fuzzy set programming. It is similar to variance to measure mean value. It provides two dimensional decision spaces for fuzzy linear programming. In the other words, the PISIT2FSLP method can be treated as ‘‘a ruler’’ to represent fuzzy uncertainties in energy system management. Therefore, the results of this method are more reliable and narrow. Those features of the PIS-IT2FSLP method illustrate the advantages in fuzzy linear programming. However, for using the T2 FS method, the complex solution procedures will occur, and upper boundary of the object function is smaller than that in the normal interval fuzzy linear programming method. (b) The PIS-IT2FSLP method can better represent the fuzzy uncertain boundary. It can find an optimal solution by compromises between the objective function and the parameter uncertainties. It not only has the feature of T2 fuzzy sets, but also contains the stochastic specialty for linear programming which covers the shortage of fuzzy sets programming. The interval results of PIS-IT2FSLP provides multiple decision alternatives for energy authorities. Its binary-variable solutions provide useful information when the capacity of facilities should be expanded to satisfy municipal energy consumption. (c) The PIS-IT2FSLP method also effectively analyzes the relationship of the dual interval. It reflects interrelationships between conversional fuzzy sets and the T2 fuzzy set theory. It reduces the T2 fuzzy set into a computable method with CCP levels to represent the energy availability. Thus, it improves upon the existing interval fuzzy approaches for energy systems allocation, so that the strength of the energy planning process is enhanced. (d) The PIS-IT2FSLP method solves a real problem of energy planning for Xiamen City based on a minimization of cost strategy. The solutions of this method provide an optimal decision for the development of Xiamen City. It guides the allocation pattern of Xiamen energy, and it improves the energy utilization level. Thus, authorizes can adjust the current energy strategy to generate a lower cost pattern for coordinating the conflict of interests in the social market. However, there are several assumptions that have been made for the Xiamen PIS-IT2FSLP energy model. Based on these assumptions, the results of this energy model may have some limitations as a reference. For example, there are 11 kinds of energy types which have been considered for the PIS-IT2FSLP energy model; heat consumption has not been considered in this model since the south of China has no heating supply for society; and the facilities expansion options are based on assumptions of other cities. Thus, the options of capacity expansion may show inconsistencies due to the regional differences. Furthermore, the randomness of pollution and gasoline supply parameters are not considered in this study. As a consequence, the PIS-IT2FSLP energy model should enhance its practical applicability with more energy parameters and constraints. However, it is an impossible mission to collect all energy data for Xiamen City because one single decision of data of energy supply are extensive but without regularity, and they may be highly uncertain. However, further investigation of these input data could increase the applicability of the PIS-IT2FSLP energy model. Thus if local government would supply more accurate and timely data, this PIS-IT2FSLP energy model could produce more accurate results than current models. This study is a new attempt to develop a PIS-IT2FSLP energy model, and has been applied to energy system of Xiamen City. However, these is a large space for further improvement of this model. The PIS-IT2FSLP method can integrate the random a cuts

method for the defuzzification process, and it can obtain global optimal solutions under different a cuts levels. It can also combine the joint probability method to deal with multiple stochastic features for more complex applications. With these improvements, this energy model could be used as a highly efficient method to analyze energy patterns and reduce a major cost for city development. However, the major limitation of this method is due to its characteristic of linear assumption. Some relationships in energy systems cannot be expressed as linear features. So other nonlinear sophisticated methods should be utilized to tackle such uncertainties. In addition, the left hand side parameters show high uncertainty as well. However, only the right hand side parameters have been considered in this model. In this study, peak power generation and its demands just have been treated as a multiple uncertainties coefficient. However, these processes may affect the final results of energy planning in the real world. Thus to deal with the issues of PSD-IT2FSLP, it can be a further subject of study.

6. Conclusions The inexact interval T2 FS boundary linear method represents higher level fuzzy interval uncertainties in energy-environment systems. It can be separated as two reasonable intervals (low boundary and upper boundary) to evaluate the dispersion of fuzzy sets. By integrating interval T2 FS and the stochastic method interval fuzzy linear programming, the PIS-IT2FSLP energy model is formulated. The PIS-IT2FSLP method can deal with uncertain issues, which contain T2 FS boundaries in the right hands side of constrains with stochastic characteristics. Given the interval T2 FS concept of interval boundary, more details of interval fuzzy linear programming can be described. The developed method is applied to Xiamen City energy system with multiple uncertainties. Optimal solutions have been obtained for Xiamen energy system. With the binary and interval solutions, two options for energy decision making strategy have been given as references for energy management. These solutions indicate optimal input and output amounts of energy systems including resource allocation, power generation, renewable energy expansion schemes and environmental pollution requirements under a minimized system cost. The environmental emission and system benefit are given as reasonable tradeoffs. The lower system cost represents expansion of renewable energy development for Xiamen City. Considerately higher system costs indicates the results of extensive energy development. This method is able to test relations between profit necessities and environmental protection cost. Although this study is the first attempt in planning an energy system by using developed PISIT2FSLP model, the solutions strongly suggest that renewable energy resources are the key for Xiamen development. The city energy department should pay attention to their development. The result is an optimal energy strategy appropriate for this city. In the mean time, this method is applicable to other uncertain issues such as water resources management.

Acknowledgements This research was supported by the Program for Innovative Research Team (IRT1127), Xiamen Science Project (3502202133053), Fujian Educational Bureau Project (JA14242), the Natural Science and Engineering Research Council of Canada, and the MOE Key Project Program (311013). The writers are very grateful to the editor and the anonymous reviewers for their insightful comments and suggestions.

L. Jin et al. / Applied Energy 138 (2015) 71–90

Appendix A. List of symbols (1) Subscripts i = energy carriers, i = 1, 2, . . . , 11, raw coal, washed, coal, coke, crude oil, gasoline, diesel, kerosene, LPG, fuel oil, natural gas, electric power; t = time stages, t = 1, 2, 3; k = power processing technologies, k = 1, 2, coking, oil refining; j = power conversion technologies, j = 1, 2, . . . , 10, hydropower, pumped storage, wind power, photovoltaic power, waste generation, biomass power, coal-fired power, oil-fired power, natural gas power, tidal power; p = pollution type, p = 1, 2, SO2, NOx. (2) Decision variables IMP (i, t) = supply amount of transferred from nonlocal energy type i in period t, PJ; EXP (i, t) = supply amount of transferred out of local energy type i in period t, PJ; TP (k, t) = generation amount of energy processing technology k in period t, PJ; E (j, t) = electric generation amount of conversion technology type j in electric power plant in period t, PJ. (3) Parameters XP (k, t) = expansion capacity of energy processing technology k in period t, PJ; XE (j, t) = expansion capacity of conversion technology type j in electric power plant in period t, GW; PIM (i, t) = purchased cost of transferred from nonlocal energy type i in period t, 106 yuan/PJ; PEX (i, t) = selling cost of transferred out of local energy type i in period t, 106 yuan/PJ; C (k, t) = operating cost of energy processing technology k in period t, 106 yuan/PJ; CI (k, t) = investment cost of energy processing technology k in period t, 106 yuan/PJ; CE (j, t) = operating cost of conversion technology type j in electric power plant in period t, 106 yuan/PJ; CCE (j, t) = investment cost of conversion technology type j in electric power plant in period t, 106 yuan/GW; CVP (p, j, t) = operating cost of conversion technology type j of emission pollution type p in period t, 106 yuan/PJ; CPC (p, j, t) = environmental facilities cost of conversion technology type j for pollution type p in period t, 106 yuan/PJ; CGR (j, t) = financial subsidy of conversion technology type j in period t, 106 yuan/PJ; RP (k, t) = energy processing demand of processing technology type k in period t, PJ; SP (k, t) = the loss of processing technology type k in period t, PJ; RE (j, t) = electric demand for energy conversion technology type j in electric power plant in period t, GW; SE (j, t) = electric loss of energy conversion technology type j in electric power plant in period t, GW; CFE (i, j, t) = conversion factor of energy type i by conversion technology type j in electric power plant in period t, j = 7, 8, 9, GW; h (j, t) = electric generation hours of conversion technology type j in electric power plant in period t, h; DLL (j, t) = power factor of conversion technology type j in electric power plant in period t, %; TLL (t) = the loss rate of power transmission in period t, %;

89

g (p, j, t) = emission factor of conversion technology type j of emission pollution type p in period t, %; QP (t) = power peak demand in period t, GW; DM (i, t) = demand of energy carriers i in period t, PJ; RPC (j, t) = bound of conversion technology type j in period t, GW; LIM (i, t) = maximum transport capacity of energy carriers i in period t, PJ; PFE (p, j, t) = emission efficiency of conversion technology type j of emission pollution type p in period t, 104 t/PJ; PED (p, i, t) = emission demand of energy carriers i for emission pollution type p in period t, 104 t/PJ; POLLM (t) = allowed amount of pollution in period t, 104 t.

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