Optimal location selection for offshore wind-PV-seawater pumped storage power plant using a hybrid MCDM approach: A two-stage framework

Energy Conversion and Management 199 (2019) 112066

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Optimal location selection for offshore wind-PV-seawater pumped storage power plant using a hybrid MCDM approach: A two-stage framework

T

Yunna Wua,b, Ting Zhanga,b, , Chuanbo Xua,b, Buyuan Zhanga,b, Lingwenying Lic, Yiming Kea,b, Yudong Yana,b, Ruhang Xua,b ⁎

a

School of Economics and Management, North China Electric Power University, Beijing 102206, China Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Changping, Beijing 102206, China c Sichuan Branch of China Development Bank, China b

ARTICLE INFO

ABSTRACT

Keywords: Wind-PV-seawater pumped storage plant Site selection Offshore area TIFNs Entropy weight method TODIM

Constructing an economical wind-PV-seawater pumped storage (SPS) plant is crucial to promote the complementarity of wind and PV resources in time and space dimensions and to reduce energy abandonment caused by voltage instability. It is also beneficial to realizing long-time sustainable development objectives for offshore areas and even for the whole country. To select the optimal site of wind-PV-SPS power plants with massive difficulties lying in different attitudes of decision makers to loss risk, uncertainties of decision-making environment and various attributes of evaluation alternatives, a fuzzy multi criteria decision making based a twostage evaluation mode is proposed. Firstly, two sets of criteria systems, representing veto selection of regional resources and the conditions of sustainable development described by triangular intuitionistic fuzzy numbers (TIFNs), are established to ensure the scientificality and comprehensiveness of the evaluation process. Then, alternatives are preliminarily selected through veto identification. Afterwards, criteria weights of the second evaluation stage determined by the entropy method are incorporated within TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) to rank potential wind-PV-SPS objects. Finally, to validate the effectiveness of the proposed model, a case study in China is conducted and the calculation result shows that Qingtian Bay in Zhou Shan is the best.

1. Introduction Application of renewable energy, especially wind and solar power, has become an important way for energy conservation and emission reduction under the background of global low-carbon economy. Over the past five years, China has made great efforts in the construction of wind and solar power plants to improve the national energy system towards sustainable development and to prevent further deterioration of natural environment. However, with large-scale applications of wind and solar power, the intrinsic volatility and intermittent nature of energy itself have become more and more prominent, which leads to low power quality and large power abandonment, as shown in Fig. 1. Clearly, neither an independent solar system nor an independent wind system can provide continuous energy supply due to seasonal and cyclical changes in the amount of energy resource [1–3]. Fortunately, these bottlenecks can be settled by energy storage which has the advantages of complementing wind and PV resources in time and space dimensions [4], smoothing wind and solar power generation for

⁎

relieving abandoning power [5], participating in peak adjustment [6] and improving the reliability of electric side [7,8]. Therefore, wind-PVstorage, as a hybrid power system, has been highly valued and widely used [9]. The offshore area, which is far away from the power grid and is rich in natural resources, is of great significance to construct windPV-storage plants. On one hand, it can expand the construction of renewable energy and achieve regional self-production-consumption, which is more efficient and economical than the central power grid supply [10]. On the other hand, seawater, solar and wind resources are abundant in the offshore areas, so these regions can utilize the environmental-friendly and low cost seawater pumped method as a storage part to better meet the needs of sustainable development [11]. The International Renewable Energy Agency (IRENA) analyzed the effects of the energy transition by 2050 in a recent study for the G20, and found that over 80% of the world’s electricity would derive from renewable sources by that date. Solar and wind power would account for 52% of total electricity generation at that time point. According to the 13th Five-Year plan, China will strengthen the comprehensive

Corresponding author at: School of Economics and Management, North China Electric Power University, Beijing 102206, China. E-mail address: [email protected] (T. Zhang).

https://doi.org/10.1016/j.enconman.2019.112066 Received 1 January 2019; Received in revised form 9 September 2019; Accepted 11 September 2019 Available online 20 September 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

Energy Conversion and Management 199 (2019) 112066

Y. Wu, et al.

and complexity, site selection of wind-PV-SPS plant in offshore areas under the perspective of sustainable development has been rarely studied. Thus, this paper will study this topic from the perspective of sustainable development, which can expand the existing research field. Due to a great deal of uncertainties in wind-PV-SPS location selection, such as renewable energy resources, benefit estimation, policy changes, environment impacts and other unpredictable factors, it is ineluctable to value them through empirical rules or experts’ subjective experience on account of the complexity and dynamic of society environment. However, because of the ambiguity and limitation of human emotions, it is difficult for DMs to express their assessment via crisp values [30]. Fortunately, the fuzzy set theory introduced by Zadeh [31] combined with intuitionistic degrees, such as Intuitive Language Fuzzy Number, Two-Dimensional Semantics, Triangular Intuitionistic Fuzzy Numbers (TIFNs), Trapezoidal Intuitionistic Fuzzy Numbers (TrIFNs) and Probabilistic Interval Intuitionistic Fuzzy Numbers (PIIFNs), can fully describe the information under the uncertain, incomplete or ambiguous situations [32]. By comparison, the language fuzzy number is unsuitable for describing quantitative information, which will strengthen the fuzziness of the problem itself. Besides, with high complexity, TrIFNs and PIIFNs could over completely describe wind-PV-SPS information, which will increase the complicacy and difficulty of the calculation process [33]. Nevertheless, TIFNs have great application advantages lying in characterizing data in nonlinear terms [34], reflecting the fuzziness and uncertainty of decision information [35], preventing information loss and possessing a simpler calculation process for popularization and application than the other fuzzy numbers [36]. A TIFN on a scale of 0–1 such as < (0.67, 0.83, 1); 0.6, 0.3> represents that the evaluation value is between 0.67 and 1, and the most possible value is 0.83 with a maximum satisfaction degree 0.6, minimum dissatisfaction degree 0.3 and hesitation degree 0.1. A large number of literatures have used the combination of TIFNs and multi criteria decision making (MCDM) techniques to solve renewable energy decision-making problems [37–39]. The characteristics comparison of the widely used MCDM methods are shown in Table 1. Viewed from the characteristics of each method, it is clearly demonstrated that TODIM, as an improved method of cumulative prospect theory, has overcome the deficiencies of other methods, such as strong subjectivity, regardless of decision makers’ (DMs’) risk preference change and cumbersome calculations, etc. Moreover, with the advantages of effectively distinguishing different evaluation types and reducing the complexity degree of assessment process [28,37], a two-stage mode is utilized in this paper to formulate better decision making results. Therefore, this paper will select the optimal location of wind-PV-SPS plant via an extended fuzzy TODIM based the two-stage framework for taking full account of information fuzziness and DMs’ hesitation in the evaluation process. The contributions in this paper includes three holds. (i) The windPV-SPS plant site selection is firstly researched in this paper under the intuitionistic fuzzy environment based on DM’s loss preference. (ii) Two sets of criteria systems for veto selection in the first stage and MCDM evaluation in the second stage are firstly established. (iii) A comprehensive evaluation framework of two-stage mode with entropy based fuzzy TODIM is firstly established. In former site selection processes, the compensation of different criteria is often occurred but neglected. For wind-PV-SPS plants, compensation among several indicators will lead to ineffectiveness of the overall evaluation. For example, assume a place which is rich in wind resources but weak in PV resources, the wind resources will be used to make up for the lack of PV in classical MCDM process and make the site relatively superior. However, due to the lack of PV resources, it is impossible to build a wind-PV storage power station in this place in actual. Thus, this paper uses the veto selection as the first stage to exclude the places which cannot meet the basic requirements of capital construction. Subsequently, considering the loss preference of DMs and the uncertain environment, entropy based fuzzy TODIM is utilized to comprehensively sort the potential objects selected from the first stage.

Fig. 1. The statistics of wind and solar power abandoning.

application of diversified technologies of wind-PV-storage plants to build low-carbon, secure and efficient energy system. Besides, the plan of power industry points out that the proportion of non-fossil energy in China will reach 15% by 2020, while the wind power installation will reach 210 million to 250 million kW and the photovoltaic installation will reach 150 million kW estimated by experts. With such high expected shares of wind and solar power by 2020, the long-term energy storage becomes crucial to smooth supply fluctuations over days, weeks or months, which calls for storage technologies with low energy costs and emission rates such as pumped hydro systems [12]. Accordingly, establishing seawater pumped storage (SPS) stations can effectively solve the problems of the intermittent of wind and solar power, make full use of coastal resources and provide a new solution for power peaking in offshore areas [13]. Throughout the research in recent years, great breakthroughs have been made in the SPS field such as technology [14], economic feasibility [15], superiority analysis [16], etc. Moreover, a great deal of cases have been successfully built in Japan [17], Guadeloupe island [18] and so on. Considering the advantages and the wide applications of SPS plants, China has begun to follow the international pace as a country with more than 1800 km of coastline. According to a recent resource census result from National Energy Administration (NEA), there are more than 174 potential offshore SPS sites in China, and eight typical sites with relatively better construction conditions are further screened out. Scholars proposed that the combination of solar, wind and SPS power could provide a sustainable energy generation for offshore communities, and its energy costs would be lower than diesel power generation [19]. As a new kind of wind photovoltaic storage device, wind-PV-SPS plant is of great significance for the comprehensive planning of nature resources in offshore areas, which can not only reduce construction costs [20] but also improve overall energy efficiency [21,22]. Jurasz, Dąbek [23] simulated and optimized the operation of a large scale solar-wind hybrid with pumped-storage plant on a district level considering a simplified approach to incorporating grid-related costs. Moreover, the pumped reserve mode was proposed as the most economically feasible one compared with others in offshore area [24]. Besides, the technicaleconomic mode of wind powered pumped hydro storage was analyzed through a series of comprehensive mathematic evaluation methods [25]. Along with the extensive research on the technology and optimization of wind-PV-storage plants, site selection needs to be highly valued and deeply studied as the first step in the construction process. Daskalou, Karanastasi [26] selected and optimized wind and solar sites by the GIS method in the Prefecture of Thessaly. Yun-na, Yi-sheng [27] selected the wind-solar hybrid power station based on the ideal matterelement model. A series of restrictions have been identified in renewable energy site selection such as the wind speed, solar radiation and slope [28]. Besides, the type, size and site of energy storage system combined with solar and wind power were considered and analyzed in Homer [29]. Owing to the characteristics of great comprehensiveness 2

3

i). Transfers subjective assessment from decisionmakers into objective evaluation; ii). Fully considers the subjectivity in decisionmaking process;

i). High computational efficiency; ii). Considers both the best and worst alternatives in a simple mathematical form; iii). Ideal point doesn’t assume preference independence of attributes;

i). Trades off the maximum group utility of the “majority” and minimum personal regret of the “opponent” in fuzzy situations; ii). Be suitable for risk-preferred DMs; iii). Selects solutions from conflicting criteria;

i). ii). iii). iv).

i). Reflects gains and losses attitudes of DMs to the problem; ii). Can be used for qualitative and quantitative criteria; iii). More appeal to practitioners as there is no single criterion to optimize within constraints; iv). Easier and quicker solve because of no optimization tool in general; v). Easier to configure through changing weights or adding new criteria;

AHP (Analytic Hierarchy Process) [40–43]

TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) [37,44]

VIKOR (Vlse Kriterijumska Optimizacija I Kompromisno Resenje) [44–47]

ELECTRE (Elimination et Choice Translating Reality) [37,46,48]

TODIM (A portuguese acronym meaning interactive multi-criteria decision making method) [49,50]

Decreases compensation among criteria; Has flexible application; Has strong theoretical basis; Constructs preference degrees of real numbers by using valued outranking relations;

Advantages

Methods

Table 1 Characteristics comparison of typical MCDM method.

i). Failures to take into account the hesitation of DMs; ii). Only considers the minimum of individual regret; iii). The ranking result is only partial ranking of alternatives; iv). Attribute value gap ignorance and tedious in setting many subjective parameters; i). Doesn’t take criteria dependency and interaction; ii). Be very comprehensive for the evaluation of decision-making problems;

i). Failures to take into account the hesitation of DMs; ii). The decision-making environment is considered to be critical to its outcome;

i). Ignores the characteristics of data itself; ii). The result is heavily influenced by the size of expert group and the different academic backgrounds of the expert group members; iii). Expert knowledge has limitations; iv). Attributes are fully compensated by each other; i). Only suitable for cautious DMs with more profit and less risk; ii). Doesn’t consider the relative importance of greatest and shortest distances; iii). Normalization depends on the evaluation unit; iv). Inverse order problems are prone to occur; v). Attributes are compensated by each other;

Shortcomings

i). ii). iii). iv).

Portfolio allocation; Group decision-making; Best solution selection; Grade evaluation;

i). Problems sorting like progressive sorting; ii). Best solution selection; iii). Group decision-making;

i). Schemes ranking; ii). Decision-making in renewable energy; iii). Performance assessment; iv). Simulation and optimization; v). Multi-objective linear programming problems; i). Decision making; ii). Performance improvement; iii). Performance evaluation;

i). Subjective weights determination; ii). Optimal subjective scheme selection;

Application

i). Natural gas; Thermal power station units rank; ii). Investment choice of rooftop photovoltaic in city; iii). Emergency decision making; iv). Website quality; v). Renewable energy location selection;

i). Novel green supplier selection; ii). Selection of professional property management company; iii). Elective admission control; iv). Renewable energy site selection; v). Portfolio selection; i). Selection of a sustainable third-party reverse logics provider; ii). Autonomy teaching performance; iii). Renewable energy site selection; iv). Irrigation plans;

i). The optimum solution of working fluid selection; ii). Renewable energy optimization; iii). Spatial decision process with complex interdependencies among attributes;

i). Sustainable micro grid assessment; ii). Energy combination optimization design; iii). Power distribution system adjustments iv). Energy efficiency;

Field

Y. Wu, et al.

Energy Conversion and Management 199 (2019) 112066

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Table 2 Criteria involve in onshore wind farm site selection. Factors

Baseer, Rehman [51]

Baban and Parry [52]

Gorsevski, Cathcart [53]

Latinopoulos and Kechagia [54]

Höfer, Sunak [55]

Sánchez-Lozano, GarcíaCascales [56]

Sum

Dist. from roads Dist. From electricity grid Dist. from urban areas/ settlements Dist. from airports Dist. from places of interest Dist. to power lines Dist. to mast Wind energy potential/speed Electricity demand Slope of terrain Natural environments Avian habitat Water bodies Wetlands Land cover Forest areas Soil type Elevation Landscape architecture Impact on birds

√ √ √

√ √ √

√ √ √

√ √

√ √ √

√ √ √

6 5 6

√ √

√

√

√

√

√ √ √

√ √

4 4 1 1 6 1 5 3 2 2 2 4 4 2 1 1 1

√

√

√

√

√

√

√ √

√ √ √ √ √ √ √ √

√ √ √ √

√ √ √

√

√ √ √ √

√ √

√

√

The remainder of this paper is arranged as follows. Section 2 establishes a set of comprehensive wind-PV-SPS location selection criteria system. A series of basic methodology is introduced in Section 3. Then, in Section 4, a two-stage decision framework of wind-PV-SPS site selection is formulated. Subsequently, a case study from NEA in China is conducted and analyzed in Section 5. Finally, conclusions of the whole paper are drawn in Section 6.

summarized as shown in Table 4 since there are a lot of similarities between the two storage methods except that SPS plants have some superiorities over water pumped ones in saving lower reservoir construction and so on. From above summary we can see that distance from roads, distance from electricity grid, distance from urban areas and wind energy potential are the criteria with the highest number of occurrences. Through expert group discussion with a scale of seven who are specializing in energy, economy, environmental protection and other fields, the wind energy potential is selected as the veto criteria which has strong constraints on resources in different places. And the criteria for further evaluation under the perspective of sustainable development should be comprehensively considered with other renewable energy sources. As shown above, the solar irradiance and distance to the grid/village/main roads appear the most frequently. As a rigid choice condition, solar irradiance was selected through experts’ discussion.

2. Macro site selection criteria system Criteria system plays a crucial role in wind-PV-SPS plant site selection. For establishing a more comprehensive criteria system, we studied the literature on wind and solar site selection and summarized their selection criteria as shown in Tables 2 and 3. Nevertheless, due to there are few literature on SPS site selection, we studied the ones on pumped storage power stations and the site selection criteria were Table 3 Criteria involve in solar generation plant site selection. Factors

Wu, Geng [57]

Sánchez-Lozano, TeruelSolano [58]

Fang, Li [59]

Tahri, Hakdaoui [60]

Sánchez-Lozano, GarcíaCascales [61]

Zoghi, Ehsani [62]

Sum

Sunshine time Direct normal irradiance Water supply Orography Transportation conditions Grid/village/ma-in roads connected distance/location Land use rate Soil capacity Land orientation Elevation Ecological environment influence Average temperature Energy-saving benefit: standard coal Cost Pollutant emission reduction benefits Land slope Impact on the local economy Plot area Initial investment Local government support Policy support Public support

√ √ √

√

√ √

√

√

√ √ √

√

√

√

√

3 6 2 1 1 6

√

√

√

√

√ √ √

√

√

√

√

√ √ √ √ √ √ √ √ √ √

√ √ √ √ √

√

√

√ √

√

√ √

4

√ √ √

5 3 3 1 2 3 1 1 1 4 2 1 1 1 1 2

Energy Conversion and Management 199 (2019) 112066

Y. Wu, et al.

from the perspective of sustainable development. Through Delphi method and the rule of minority being subordinate to the majority, expert group selected the most appropriate nineteen criteria directly related to the commonly used and the sustainable development goals based on previous literature and their experience. The established criteria system is shown in Table 6, which can be arranged into four main parts: natural resources aspect, economic aspect, environment aspect and social aspect. The proposed criteria system can not only meet investors’ preference, but also have considered the sustainable development in China. Moreover, detailed explanations of the sub-criteria are shown in Appendix B. Finally, the whole scale of criteria system can be formulated as Fig. 3.

Table 4 Criteria involve in pumped hydro energy storage plant site selection. Factors

Connolly, Maclaughlin [63]

Area of the upper reservoir Land use Altitude Area of the lower reservoir Permeability Excavation Height between reservoirs Storage capacity Horizontal distance between areas Gradients Loan repayment period Assets liabilities ratio Payback period Financial internal rate return Flatness/maximum earth moved to make upper reservoir flat Proximity to Roads Proximity to Populated areas Flatness/maximum earth moved to make lower reservoir flat L/H Viability of Conduits Proximity to Electricity Grid Grid search interval for lower reservoir Temperature Rainfall Radial search interval for upper reservoir Sulfur dioxide emission reduction Wind Areas that cause damages Nitrogen oxide emission Carbon emission reduction Employment Economy improvement Disasters withstand Seismic Vertical search tolerance for ‘flatness’

√ √ √

Capilla, Carrión [64] √ √ √ √ √

√ √

√

√

√

√

√ √ √

√ √ √ √

√ √

√ √

√

Sum

1 1 2 1 2 1 2 1 1 1 1 1 1 1 1

3. Methodology 3.1. TIFNs theory In practical applications, uncertain environment and hesitation of DMs to the information of wind-PV-SPS project cannot be ignored since these factors will affect the sorting results to a great extent. For better selecting the location of wind-PV-SPS plant, this paper will utilize TIFNs to express uncertain information, so as to accurately express DMs’ opinions as in a real decision environment.

1 1 1 √ √

√ √

√ √

√

Wu, Liu [65]

2 2 1

Definition 1 ([37]). An intuitionistic fuzzy set (IFS) A over X is represented as:

A = {x , µA (x ), vA (x )| x

1 1 1 √

1

√ √ √ √ √

1 1 1 1 1 1 1 1 1

where µA (x ) means the membership degree of x in the IFS, in the same manner, vA (x ) represents the non-membership degree of x in the IFS. A (x ) is the intuitionistic index of hesitancy degree of A which can be calculated as A (x ) = 1 µA (x ) vA (x ) . The restrictions of Eq. (1) are as follows: (1) X is a nonempty set: 1, x X (2) 0 µA (x ) + vA (X ) 1, 0 A (x ) Definition 2 ([70]). Set a as a TIFN which is shown in Fig. 4

a = ( a, a, a¯);

x a

Restriction

Length-height ratio Average gross head Wind speed Solar irradiation

L/H < 10 [66] Average gross head > 70 m [67] Annual wind speed > 6 m/s at 50 m height [68] Annual global horizontal irradiation > 3.5 kWh/m2/day [69]

a,

(2)

µa

The membership a (x ) and non-membership µ a (x ) function are defined as Eqs. (3) and (4):

Table 5 Veto criteria system. Veto criteria

(1)

X}

a

(x ) =

a¯ a¯

a a

a

x + (x

a

a

a + (a¯ a¯

From the literature review we can see that some criteria appear frequently and have strong restrictions on resources, such as wind speed, the solar radiation, average gross head and length-height ratio. After experts’ consultation, these four factors can be considered as necessary conditions for measuring whether there are sufficient resources to build wind-PV-SPS plant, which can be called veto criteria as shown in Table 5. If the potential alternative sites can’t satisfy the requirement of the veto criteria, the ones will be excluded from alternatives. A detailed explanation of each veto criteria is given in Appendix A. Besides, the physical descriptions of the average gross head and length-height ratio are shown in Fig. 2. After screening the veto criteria system, a comprehensive evaluation criteria system should be constructed to better select wind-PV-SPS plant

a) µa

µa

x

a

(3)

x

a

x=a x ) µa

a
a

1 where 0

a¯

x < a or x > a¯

a

µ a (x ) =

a

a
0 a

x x=a

a x a a

(x )

a¯

x < a or x > a¯

1, 0

µ a (x )

1, 0

a

(x ) + µ a ( x )

is an in-

1, a , a, a¯ R. a (x ) tuitionistic fuzzy condition of an element x in a which can be calcuµ a (x ) . lated by a (x ) = 1 a (x ) Definition 3 ([71]). Let a , b be two TIFNs: a = ( a, a, a¯); a , µ a , 0 . Then some basic operations are showed b = ( b , b , b¯); b , µ b and as follows:

a + b = ( a + b , a + b , a¯ + b¯); a b = ( a b, ab, ab ¯ ¯); 5

a

b

, µa

a

b

µb

, µa

µb

(5) (6)

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Y. Wu, et al.

Length-height ratio (L/H < 10)

Upper reservoir

Average gross head (H > 70 m)

Seawater

Fig. 2. Description of average gross head and length-height ratio.

between positive feeling and negative feeling. There are two types criteria in this paper as cost criteria (the smaller, the better) and benefit criteria (the higher, the better), criteria standardization is essential so that the interference from different physical dimensions on the decision-making results can be eliminated. Thus, the normalization of the element x ij = (xij a , x ija , x ija¯ ); x ij , µ x ij

Table 6 Criteria of sustainable development based on investment preference. First-class criteria

Symbol

Sub-class criteria

Symbol

Natural resources aspect

C1

Effective wind hours Sunshine days Reservoir volume of SPS Installed capacity of SPS Distance to the grid Area

C11 C12 C13 C14 C15 C16

Static investment Operation & maintenance cost Dynamic payback period Financial internal rate of return

C21 C22 C23 C24

Average rainfall Seismic activity Ecological corrosion Carbon emission reduction

C31 C32 C33 C34

Electricity demand Local residents attitude Policy support Economy improvement Employment

C41 C42 C43 C44 C45

Economic aspect

C2

Environment aspect

C3

Social aspect

C4

= ( a , a , a¯ );

where

and

µa

(8)

Definition 4 ([71]). Let a , b be two TIFNs: a = ( a, a, a¯); a , µ a , b = ( b , b , b¯); b , µ b . The distance between a and b is calculated as follows:

d (a , b ) =

1 6

a

µa ) a

(1 +

b

+ |(1 +

a

µ a ) a¯

(1 +

b

h (a ) =

R (a¯i , ) =

6 + (a¯ i

ai )(

2 ai

+ (1

+ (1

xija x ija , + x ija x ija

xija x ija¯ , + xija x ija

x ija

xija

x ija

,

x ij ,

µ x ij

,

x ij ,

µ x ij

(11)

(12)

= max i (xija¯ ) and x ija = mini (xij a).

1 ( a + 4a + a¯)(1 12

µa +

a)

(13)

Definition 6 ([74]). Let ej be the entropy of attribute j

µ b ) b| µ ) b¯| b

) (1

(9)

) (1

µa i)

m

hij m

i=1

× ln

hij

i=1

hij m

ej

[0, 1 ]

hij

i=1

(14)

Definition 7. Let wj be the entropy weight of attribute j

µ a i )2 ) 2)

1 ln n

ej =

Definition 5 ([72]). Let ai = ( ai , ai , a¯ i ); a , µ a be TIFNs. Following ranking operator can utilized for ranking the TIFNs ai (i = 1, 2, ...,n) 2 ai

x ija

µ b ) b|

b

+ |(1 +

( ai + 4ai + a¯i ) + (

+ x ija

+ x ija xija , + x ija x ija

As a branch of thermodynamics, the entropy weight method has been widely applied in decision-making process which severs as a useful tool to handle information provided by the data from an objected view [73]. Hence, this paper will use entropy weight method to gain the weight of wind-PV-SPS site selection criteria. Before determining the weights of the attributes, it is ineluctable to defuzzify fuzzy numbers x ij to hij by Eq. (13).

respectively mean minimum and maximum operators.

(1 +

+ x ija

+ xija¯ x ija , + xija x ija

3.2. Entropy weight method based on TIFNs

a,

µa ) a

x ija

where

(7)

a

+ x ija

rij =

, µa

|(1 +

+ x ija

rij =

a

a = ( a, a, a¯); a

to rij = (rij a, rija, rija¯ ); rij , µrij can be showed in the Eq. (11) for cost criteria and Eq. (12) for benefit criteria [35]:

gj = 1 (10)

wj =

[0, 1] represents the DM’s attitude toward the degree of where [0, 1/2) means that the DM prefers uncertainty or uncertain; (1/2, 1] means the DM prefers certainty or negative feeling; = 1/2 means the decision maker is indifferent positive feeling;

ej

gj n i=1

gj

where wj 6

(15)

(16)

[0, 1] and

m j=1

wj = 1. The smaller of wj is, the smaller

Energy Conversion and Management 199 (2019) 112066

Y. Wu, et al.

Veto criteria system

Length height ratio < 10

Average gross head > 70 m

Wind speed > 6 m/s

Solar irradiation > 3.5 kW/m2/day

Comprehensive evaluation criteria system Assessment

Natural resources

Economy

Environment

Society

Effective wind hours (B)

Static investment (C)

Average rainfall (C)

Electricity demand (B)

Sunshine days (B)

Operation & maintenance cost (C)

Seismic activity (C)

Local residents attitude (B)

Reservoir volume of SPS (B)

Dynamic payback period (C)

Ecological corrosion (C)

Policy support (B)

Financial internal rate return (B)

Carbon emission reduction (B)

Economy improvement (B)

Installed capacity of SPS (B)

Employment (B)

Distance to the grid (C) Area (B)

Note:

B

represents benefit criteria and

C

represents cost criteria

Fig. 3. Whole scale of evaluation criteria system.

steps. Step 1. Determine relative attribute weight wjr for attribute aj to the reference attribute ar as follows:

wjr =

wr max{wj |j = 1, 2, …, m}

(17)

Step 2. Calculate the dominance degree of the alternative Tp relative to the alternative Tq as below: (rpj

m

rqj ) wjr

j =1

0

j (Tp, Tq ) =

Fig. 4. A TIFN.

1

(rpj

rqj ) wjr

difference between two attributes is the smaller the difference is, the smaller the weight is.

if rpj

rqj > 0

if rpj

rqj = 0

f rpj

rqj < 0

wjr

m j= 1

wjr

(18)

where is the risk aversion of the DMs to gain and loss which can be said that a higher of risk aversion will attain with a small value. Step 3. The overall dominance degree of each alternative Tp over each alternative Tq should be calculated by the following formula.

3.3. TODIM method in decision making As an extension of the prospect theory, TODIM method is a useful way to solve MCDM problems based on DMs’ subjective opinion through pairing comparisons between criteria. What’s more, this method can eliminate occasional inconsistencies calculated from these comparisons as well as make value judgment in oral scale [75]. The TODIM method utilized in this proposed model involves the following

m

(Tp, Tq) =

j (Tp, j=1

Tq)

(19)

Step 4. Calculate the global value of the alternative as follows:

7

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p

(Tp, Tq)

q=1

=

n

maxp

(Tp, Tq)

minp

n q= 1

minp

q=1

Table 7 The relationship between linguistic variables and intuitionistic fuzzy values.

(Tp, Tq) n

(Tp, Tq)

(20)

q= 1

Step 5. Rank all the alternatives based on the global values of alternatives. The bigger p is, the better alternative Tp is.

Linguistic variables

Intuitionistic fuzzy values

Very high High Medium Poor Very poor

(0.9, (0.8, (0.6, (0.3, (0.1,

0.1) 0.1) 0.3) 0.6) 0.9)

4. Decision framework of wind-PV-SPS plant site selection 4.1. Phase I – veto identification of alternative sites

m

jr

j =1

In this stage, the potential sites selected by experts should be screened by the veto criteria system which is measured by crisp numbers. Firstly, several possible sites of wind-PV-SPS power plant are selected in accordance with investors’ willingness, and the basic information of the potential sites can be gained by searching for satellite remote sensing data, wind solar resource maps, NEA web and other information sources. After that, screen the potential sites by veto identification to avoid site selection failure or project freeze. Finally, the alternatives that meet these basic resource requirements are identified.

j (Tp,

Bad

Fair

Good

Very good

0,

Tq) = 1

j=1

r

r

pj

qj

>0

if

r

pj

r

d (r pj, r qj ),

if

qj

r

qj

=0

jr

jr

r

pj

<0

(21)

And m

(Tp, Tq) =

j (Tp,

Tq)

j=1

(22)

where d (rpj, rqj ) represents the distance between rpj and rqj which can be calculated by Eq. (9). The process of the decision framework of wind-PV-SPS plant site selection has been proposed as Fig. 6. 5. A real case study

For reducing wind waste, increase renewable energy absorptive capacity and promote sustainable development in China, the optimal wind-PV-SPS plant location is selected via MCDM method. In general, traditional TODIM method is used to handle crisp numbers in MCDM problems. However, for adapting to fuzzy environment, it is indispensable to be improved. The procedure of selecting the optimal windPV-SPS location by fuzzy TODIM method can be summarized as the following steps. Step 1: Determine criteria value of each alternative. The criteria values are determined by TIFNs, which are formulated based on the seven semantic terms shown in Fig. 5 [76] and the relationship between the linguistic variables and the intuitionistic fuzzy values shown in Table 7 [35]. After that, an assessment matrix obtained from experts meeting can be derived. Step 2: Standardize above assessment matrix according Eqs. (11 and 12). Step 3: For comprehensively considering the influence of subjective and objective decisions, the entropy weight method is utilized to determine criteria weight. Step 4: Compare two fuzzy numbers on the ground of definition 5. Step 5: Rank the alternatives through TODIM method. Determine the dominance degree of the alternative Tp relative to the alternative Tq as below according to the extended TODIM method. And then, rank the optional alternatives and choose the best one. Very bad

if

m

4.2. Phase II – sustainable development decision framework for wind-PVSPS plant site selection

Extremely bad

d (r pj, r qj ), jr

In order to make full use of the large amount of resources in offshore area to achieve rapid energy development, NEA released eight potential SPS sites in China which are Tao Hua Island in Zhou Shan, Long Tan in Zhou Shan, Qingtian Bay in Zhou Shan, Tian Dengzhan in Taizhou, Fu Ying Island in Ning De, Nan'ao Island in Shan Tou, Wanshan Island in Zhu Hai and Shang Chuan island of Jiang Men with the basic elements in Table 8 [77], respectively. The locations are shown in Fig. 7. For long-term energy planning, above eight places denoted as A1, A2 , A3 , A 4 , A5 , A6 , A7 and A8 are considered to construct micro grids as windPV-SPS plant which can meet the needs of energy complementary. The eight alternatives should be firstly evaluated in the first stage. And then, the potential alternatives can be selected into the phrase II to further assess which sites are available to better meet energy sustainable development goals. 5.1. Phase I – Veto identification of alternative sites Firstly, the veto criteria data of the eight potential alternatives are collected through NASA ATMOSPHERIC SCIENCE DATA CENTA and NEA, as shown in Table 9. The best value of each criteria is signed with a grey background. Since the optimum length-height ratio is determined by water capacity, it is meaningless to make comparison between the data under this criterion. Then the contrast results to the standard are shown in Table 10. From the contrast result, we can see that A 4 , A5 and A6 can’t pass the veto identification. The symbol of “√” represent the alternatives satisfy the standard. Thus, these three alternatives are excluded from the veto identification, and the remaining five stations will enter the second evaluation stage.

Extremely good

5.2. Phase II-Sustainable development decision framework for wind-PVSPHS plant site selection 0

0.17

0.33

0.5

0.67

0.83

1

After the veto selection, collecting and processing the data of the selected alternatives on the sustainable development perspective is the

Fig. 5. Seven semantic terms and their intervals [57]. 8

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Fig. 6. The flowchart of the proposed mode.

first step. To get closer to the reality and computational simplicity, fuzzy set theory is utilized to determine the qualitative attributes. The quantitative data of C13, C14 and C21 were collected from the official website of NEA and further expressed into TIFNs for data unification. Due to the ambiguity of the effective hours, sunshine days, etc., TIFNs was used to describe these criteria by expert scoring referring to Fig. 5 and Table 7 based on experts’ experience and local resources data and further described in Table 11. Then, preliminary results are obtained. Firstly, the weight of the

criteria is determined by Eqs. (13–16). Subsequently, paired comparison is calculated by the operator of R (a¯i , ) through Eq. (10) with a as 0.5 here for assuming that DMs are risk neutral. After that, the distance between every two alternatives is calculated in the form of TIFNs through Eq. (9), and the results are shown in Table 12. After further treatment, the dominance and priority index of each alternative Ai over remaining alternative Aj under nineteen criteria can be determined by Eq. (21) and Eq. (22) with a parameter as 2.25 [78] for in line with the real situations. The dominance matrix under the 9

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weights of C11 (effective wind hours) and C12 (sunshine days) can lead to a significant rise in comprehensive dominance degree of A7 . Namely, A7 is sensitive to C11 and C12. Thus, it is feasible to improve criteria values of C11 and C12 to improve A7 when DMs consider these two criteria are more important. Conversely, the comprehensive dominance degree of A7 will show a downward trend when the weights of C13 (reservoir volume of SPS) and C14 (installed capacity of SPS) become larger. For other alternatives, the comprehensive dominance degree doesn’t change palpable with weight fluctuations. Hence, the alternatives except A7 are insensitive to weight changes of the criteria under the C1. Besides, the weight fluctuation will not alter the overall ranking results. In the view of economic sensitivity analysis shown in Fig. 9, the ranking result has no changes when the weights of criteria static investment, operation & maintenance cost, dynamic payback period and financial internal rate of return become 10%, 20% and 30% less and more alternation. But C21 (static investment) and C24 (financial internal rate return) are the sensitive criteria of A7 due to the decline in the comprehensive dominance degree when their weights fluctuate. Besides, A2 and A8 are sensitive to C23 (dynamic payback period), thus, the comprehensive dominance degree can be improved by reducing the importance degree or increasing the value of this criteria. For other alternatives, there is no obvious change due to weight fluctuations. The evaluation results are shown in Fig. 10 when the weight of subcriteria in the environmental aspect has 10%, 20% and 30% less or more wave. From the figure we can see that the alternatives values of sub-criteria under C3 are insensitive to weight fluctuation, thus, this mode in the aspect of environment has great stability. For social aspect as shown in Fig. 11, C42 (local residents), C43 (policy support), C44 (economy improvement) and C45 (employment) are the sensitive factors for A2 , A7 and A8 , respectively. But their impacts are slight. In detial, A7 shows an uptend when the weight of local residents become larger but downtend when economy improvement become more important. In addition, when increase the importance degree of policy support will enhance the overall level of A2 , so does employment which will also increase the domaince degree of A8 when its weight increases. However, there are minor impacts for other alternatives when weights are fluctuated. But no matter how the weights fluctuated, the overall ranking has never been changed. From above analysis, it can be concluded that A3 is always the first choice for wind-PV-SPS site selection no matter how the sub-criteria

Table 8 Projects basic information [77]. Basic elements

Projects

4

Install capacity (10 kW) Reservoir volume (104 m3) Average gross head (m) Distance and height ratio Static investment (billion)

A1

A2

A3

A4

A5

A6

A7

A8

5 92 145 3 9.41

1 25 86 3.8 2.21

5 133 90 4.3 12.48

1 29 91 4 2.55

4.2 88 138 4.9 7.87

5 69 241 5.1 11.2

2 42 165 3 7.06

3 58 174 7.1 7.16

criteria C11 is shown in Table 13. The larger the dominance value, the better the vertical alternative is than the horizontal direction. Besides, the best dominance of each alternative is marked with grey background. According to Eq. (20), the final ranking result is A3 > A2 > A8 > A1 > A7 as shown in Table 14. Therefore, A3 namely the wind-PV-SPS plant site at Qingtian Bay in Zhou Shan is the optimal site. 5.3. Sensitivity analysis Through the model we proposed in this paper, ranking result can be formulated as A3 > A2 > A8 > A1 > A7 . However, DMs usually have different risk attitudes towards wind-PV-SPS plant site selection in actual situations. Besides, investors will emphatically focus on different evaluation criteria for wind-PV-SPS location selection in different regions. Hence, it is necessary to test the sensitivity of the ranking result based on diverse weights and values to exhibit the choice results from different DMs. Firstly, a sensitivity analysis based on the weight fluctuation in 10%, 20% and 30% less and more is performed. As shown in the recalculated ranking result, A3 is always the best place for wind-PV-SPS plant construction and the worst one of the five potential alternatives is always A7 . But there are slight waves in final comprehensive dominance. Namely, the proposed model is stable to weight changes in the ranking result but sensitive in certain alternatives. Incidentally, performing sensitive analysis can help provide corresponding improvements to each alternative for better ameliorating the potential alternatives. For the aspect of natural resources shown in Fig. 8, increasing the

Fig. 7. Projects distribution. 10

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Table 9 The collected real data.

Criteria

A1

A2

A3

A4

A5

A6

A7

A8

Length-height ratio

3

3.8

4.3

4

4.9

5.1

3

7.1

Average gross head

145

86

90

91

138

241

165

174

Wind speed (m/s)

6.85

6.72

6.78

5.31

4.44

3.70

6.02

6.14

Solar irradiation (kWh/m2 /day)

4.15

4.22

3.92

3.61

3.6

3.88

3.69

3.78

alternated as the values of changing from 0.5 to 2.5, which indicates that the DMs’ psychology will also have impact on the overall ranking result. Therefore, with the advantages of considering DMs’ risk loss attitudes by TODIM method, the ranking result A3 > A2 > A8 > A1 > A7 gained by proposed framework is accurate and reliable. In summary, expert group concludes that A3 is the optimal site among all alternatives in this case and the fuzzy TODIM method in the two-stage evaluation mode for determining the best location from multiple alternatives is stable and reliable.

Table 10 The contrast result. Criteria

Standard

A1

A2

A3

A4

A5

A6

A7

A8

Length-height ratio Average gross head Wind speed

L/H < 10 > 70 m Annual wind speed > 6 m/s at 50 m height Annual global horizontal irradiation > 3.5 kWh/m2/day

√ √ √

√ √ √

√ √ √

√ √ ×

√ √ ×

√ √ ×

√ √ √

√ √ √

√

√

√

√

√

√

√

√

Solar irradiation

5.4. Discussion weights change. And the proposed framework has great reliability and stability. Considering different attitudes of DMs may result in different ranking orders, this section will examine whether the decision-making result will correspondingly change when the loss attitudes of experts change for showing the robustness of the initial ranking. Let = 0.1, 0.5, 1, 1.5, 2, 2.5 respectively, the calculation results are shown in Table 15 and Fig. 12. CDD represents the comprehensive dominance degree and R means the ranking result and AL represents the potential alternatives. Besides, the best value of each is marked with fontweight. From the calculation result, A3 always remains the best. Besides, when increases steadily, A3 becomes much better in comprehensive dominance degree which suggests that the psychological behavior characteristics of DMs play an important role on the gap between alternatives. However, the sorting result of A2 and A8 have

Compared with previous literature, this paper breaks the blank of the research on offshore wind-PV-SPS plant location selection, and for the first time innovatively proposes a two-stage optimal wind-PV-SPS plant location selection framework. The research results are of great significance to the exploitation and utilization of the resources in coastal areas. Besides, different from the study of single wind or PV plant, the multi-energy joint research can comprehensively consider the complementary effects of different energy sources and effectively improve energy efficiency. In addition, compared with wind-PV hybrid location selection model, the wind-PV-SPS system can cope with the uncertainty of wind power and PV generation, improve power quality and lay a solid foundation for joining in energy internet in the future. In our previous study of single SPS plant location selection in China, A5 was the best place for SPS construction acquired by a comprehensive weighting method based fuzzy Vlsekriterijumska Optimizacija I

Table 11 Standardized decision matrix.

C11 C12 C13 C14 C15 C16 C21 C22 C23 C24 C31 C32 C33 C34 C41 C42 C43 C44 C45

A1

A2

A3

A7

A8

A+

A

(0.51, 0.75, 1); 0.6, 0.3 (0.34, 0.68, 1); 0.6, 0.3 (0.62, 0.62, 0.62); 0.9, 0.1 (1, 1, 1); 0.9, 0.1 (0.35, 0.5, 0.65); 0.8, 0.1 (0.35, 0.34, 0.68); 0.6, 0.3 (0.3, 0.3, 0.3); 0.8, 0.1 (0, 0.4, 0.64); 0.6, 0.3 (0.32, 0.66, 1); 0.3, 0.6 (0.25, 0.51, 0.75); 0.6, 0.3 (0.25, 0.49, 0.75); 0.6, 0.3 (0.24, 0.5, 0.76); 0.6, 0.3 (0, 0.20, 0.40); 0.6, 0.3 (0.09, 0.4, 0.69); 0.6, 0.3 (0, 0.34, 0.68); 0.6, 0.3 (0.25, 0.51, 0.81); 0.6, 0.3 (0.34, 0.68, 1); 0.6, 0.3 (0.45, 0.72, 1); 0.3, 0.6 (0.25, 0.51, 0.75); 0.6, 0.3

(0.4, 0.6, 0.78); 0.8, 0.1 (0.34, 0.68, 1); 0.8, 0.1 (0, 0, 0); 0.9, 0.1 (0, 0, 0); 0.9, 0.1 (0.24, 0.5, 0.76); 0.8, 0.1 (0.34, 0.68, 1); 0.8, 0.1 (1, 1, 1); 0.9, 0.1 (0.74, 0.9, 1); 0.8, 0.1 (0.32, 0.66, 1); 0.6, 0.3 (0, 0.25, 0.51); 0.6, 0.3 (0, 0.25, 0.49); 0.8, 0.1 (0.5, 0.76, 1); 0.6, 0.3 (0.6, 0.81, 1); 0.6, 0.3 (0, 0.25, 0.44); 0.8, 0.1 (0, 0.34, 0.68); 0.6, 0.3 (0.67, 0.84, 1); 0.6, 0.3 (0.34, 0.68, 1); 0.6, 0.3 (0, 0.17, 0.3); 0.3, 0.6 (0.25, 0.51, 0.75); 0.3, 0.6

(0.25, 0.51, 0.75); 0.6, 0.3 (0.34, 0.68, 1); 0.6, 0.3 (1, 1, 1); 0.9, 0.1 (1, 1, 1); 0.9, 0.1 (0.24, 0.5, 0.76); 0.8, 0.1 (0.34, 0.68, 1); 0.6, 0.3 (0, 0, 0); 0.9, 0.1 (0, 0.4, 0.81); 0.6, 0.3 (0.32, 0.66, 1); 0.6, 0.3 (0.51, 0.75, 1); 0.6, 0.3 (0.25, 0.49, 0.75); 0.8, 0.1 (0.24, 0.5, 0.76); 0.6, 0.3 (0.4, 0.6, 0.81); 0.6, 0.3 (0.4, 0.69, 1); 0.8, 0.1 (0.34, 0.69, 1); 0.8, 0.1 (0.51, 0.75, 1); 0.6, 0.3 (0.34, 0.68, 1); 0.8, 0.1 (0.45, 0.72, 1); 0.6, 0.3 (0.51, 0.75, 1); 0.6, 0.3

(0, 0.25, 0.51); 0.8, 0.1 (0, 0.34, 0.68); 0.8, 0.1 (0.16, 0.16, 0.16); 0.9, 0.1 (0.25, 0.25, 0.25); 0.9, 0.1 (0.5, 0.76, 1); 0.8, 0.1 (0.34, 0.68, 1); 0.6, 0.3 (0.53, 0.53, 0.53); 0.9, 0.1 (0, 0.4, 0.81); 0.6, 0.3 (0, 0.32, 0.66); 0.6, 0.3 (0, 0.25, 0.51); 0.3, 0.6 (0.49, 0.75, 1); 0.8, 0.1 (0, 0.24, 0.5); 0.6, 0.3 (0.4, 0.6, 0.81); 0.6, 0.3 (0.09, 0.4, 0.69); 0.6, 0.3 (0, 0.34, 0.68); 0.8, 0.1 (0, 0.25, 0.51); 0.6, 0.3 (0.34, 0.68, 1); 0.6, 0.3 (0.17, 0.45, 0.72); 0.3, 0.6 (0, 0.25, 0.51); 0.6, 0.3

(0.25, 0.51, 0.75); 0.8, 0.1 (0.34, 0.68, 1); 0.6, 0.3 (0.31, 0.31, 0.31); 0.8, 0.1 (0.5, 0.5, 0.5); 0.9, 0.1 (0, 0.24, 0.5); 0.8, 0.1 (0, 0.34, 0.68); 0.8, 0.1 (0.52, 0.52, 0.52); 0.9, 0.1 (0, 0.4, 0.81); 0.8, 0.1 (0, 0.32, 0.66); 0.6, 0.3 (0.25, 0.51, 0.75); 0.6, 0.3 (0.49, 0.75, 1); 0.8, 0.1 (0.24, 0.5, 0.76); 0.6, 0.3 (0, 0.2, 0.4); 0.8, 0.1 (0.09, 0.4, 0.69); 0.9, 0.1 (0, 0.34, 0.68); 0.8, 0.1 (0.51, 0.75, 1); 0.6, 0.3 (0, 0.34, 0.68); 0.8, 0.1 (0.45, 0.72, 1); 0.8, 0.1 (0.25, 0.51, 0.75); 0.6, 0.3

A1 A2 A1 A1 , A3 A7 A2 A2 A2 A2 , A3 A3 A7 , A8 A2 A2 A3 A3 A2 A3 A8 A3

A7 A7 A2 A2 A8 A8 A3 A1 A7 , A8 A7 A2 A7 A1 A2 A1 A7 A8 A2 A7

Where A+ represents the alternative with the best values for each criteria and A means the alternative with the lowest values for each criteria. 11

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Table 12 The distance between alternatives. Criteria

d (A1 , A2 )

d (A1 , A3 )

d (A1 , A7 )

d (A1 , A8 )

d (A2 , A3 )

d (A2 , A7 )

d (A2 , A8 )

d (A3 , A7 )

d (A3 , A8 )

d (A7 , A8 )

C11 C12 C13 C14 C15 C16 C21 C22 C23 C24 C31 C32 C33 C34 C41 C42 C43 C44 C45

0.015 0.135 0.558 0.900 0.060 0.276 0.646 0.522 0.198 0.162 0.112 0.164 0.392 0.055 0.000 0.204 0.000 0.194 0.151

0.162 0.000 0.342 0.000 0.060 0.145 0.254 0.036 0.198 0.162 0.100 0.000 0.261 0.336 0.351 0.149 0.135 0.217 0.162

0.273 0.149 0.417 0.675 0.215 0.145 0.221 0.036 0.071 0.238 0.311 0.164 0.261 0.000 0.068 0.175 0.000 0.097 0.162

0.061 0.000 0.299 0.450 0.215 0.144 0.212 0.117 0.071 0.000 0.311 0.000 0.040 0.098 0.068 0.149 0.149 0.361 0.000

0.177 0.135 0.900 0.900 0.000 0.135 0.900 0.486 0.000 0.323 0.211 0.164 0.131 0.392 0.351 0.055 0.135 0.411 0.312

0.288 0.283 0.142 0.225 0.215 0.135 0.425 0.486 0.217 0.076 0.423 0.328 0.131 0.055 0.068 0.378 0.000 0.097 0.057

0.076 0.135 0.260 0.450 0.215 0.283 0.434 0.405 0.217 0.400 0.211 0.164 0.000 0.336 0.283 0.323 0.135 0.314 0.323

0.111 0.149 0.758 0.675 0.215 0.000 0.475 0.000 0.217 0.400 0.211 0.164 0.000 0.336 0.283 0.323 0.135 0.314 0.323

0.100 0.000 0.640 0.450 0.215 0.149 0.466 0.081 0.217 0.162 0.211 0.000 0.221 0.238 0.283 0 0.283 0.144 0.162

0.211 0.149 0.118 0.225 0.429 0.149 0.009 0.081 0.000 0.238 0.000 0.164 0.221 0.098 0.000 0.323 0.149 0.458 0.162

Table 13 The dominance matrix under C11.

Table 14 Ranking of alternatives.

Kompromisno Resenje (VIKOR) model, followed by A6, A1 and A3, other alternatives need to be greatly improved before construction [43]. In this paper, the ranking result for wind-PV-SPS plant sites is A3 > A2 > A8 > A1 > A7 . Thus, according to the calculation results of this paper, the best choice for wind-PV-SPS plant construction should be A3, but when comprehensive analysis of the two studies’ calculation results, the optional alternatives A3 and A1 are superior in different aspects, A3 is better than A1 in integrated energy construction but less profitable in single SPS construction. Therefore, some measures can be taken to optimize the construction schemes in these two places to achieve overall and partial synchronization optimization of wind-PVSPS plant. For A3, although it is best in wind-PV-SPS plant construction, some measures for improving topography and reducing investment of SPS plant should be taken since it has some deficiencies in poor average gross head, large static investment and long payback period. Besides, for A1, due to the deficiency of the high degree of equipment corrosion in a single SPS construction, and the relatively high operation & maintenance cost and low electricity demand in a wind-PV-SPS plant construction, some measures such as improving seawater quality and expanding energy consumption fields should be implemented.

6. Conclusions With the outbreak of integrated energy system, wind-PV-SPS plant has been highly valued because of its superiority and special geographical requirements. As the first step of construction, location selection plays an important role in the whole life of wind-PV-SPS projects. Previous research on offshore wind-PV-storage was limited since they didn’t make full use of the abundant seawater resources and therefore an effective energy conversion form as wind-PV-SPS plant was neglected. Besides, there are still quite a few problems in the decisionmaking process in previous research, such as lack of systematic analysis, inadequate consideration of fuzzy environment and so on. Therefore, this paper firstly demonstrates the significance and advantages of building a complementary wind-PV-SPS plant in offshore area. Secondly, key factors affecting location selection of wind-PV-SPS plant from the perspective of sustainable development are identified via literature review and expert meeting. Then, a two-stage decision framework for wind-PV-SPS plant location selection is established based on the fuzzy TODIM method due to its scientific property and efficiency. Namely, the proposed decision framework can not only comprehensively consider the fuzziness of information and the loss attitudes of different DMs, but also analyze the preponderance among different evaluation objects under each criterion. 12

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Fig. 8. Sensitivity analysis results of the sub-criteria in natural resource aspect.

Fig. 9. Sensitivity analysis results of the sub-criteria in economic aspect.

13

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Fig. 10. Sensitivity analysis results of the sub-criteria in environment aspect.

Fig. 11. Sensitivity analysis results of the sub-criteria in social aspect.

14

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Table 15 Ranking orders with different .

economy improvement and employment which can help improve potential alternatives by optimizing the corresponding values. Besides, DMs can well understand and endorse the process of decision making, and the proposed decision framework can extend the study fields of wind-PV-SPS plant and overcome the deficiencies in previous studies. Due to the practical experience of authors, several limitations are existed in this paper. Firstly, although there is much break in SPS plant, further researches and practice combined with wind and solar plant are needed. Secondly, the experts meeting is difficult to be held since experts in difference fields are always in every corner of the world. If we could solve these problems in the future, the decision result would be more consistent with the reality. Declaration of Competing Interest

Fig. 12. Sensitivity analysis results in different

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

This merit helps government or project managers to analyze the advantages and disadvantages of all alternatives more practically, clearly and conveniently, and reduce the probability of decision-making errors. At last, a practical case study in China is conducted and Qingtian Bay in Zhou Shan is selected as the optimal site to build an integrated windPV-SPS power plant. The proposed mode represents great stability in the change of criteria weight and DMs’ risk preference through sensitivity analysis. Beyond that, several sensitive criteria are checked out such as effective wind hours, sunshine days, reservoir volume of SPS, installed capacity of SPS, static investment, dynamic payback period, financial internal rate of return, local residents attitude, policy support,

Acknowledgements This research is supported by the National Social Science Fund of China (19AGL027), the Fundamental Research Funds for the Central Universities (NO. 2018ZD14), the 2017 Special Project of Cultivation and Development of Innovation Base (NO. Z171100002217024) as well as the National Natural Science Foundation of China (Grant No. 71803046).

Appendix A Length-height ratio The length-height ratio is calculated through the horizontal distance between the upper reservoir and sea divided by vertical height, which directly affects the cost of the SPS station and the resistance of water supply. In general, length-height ratio less than 10 is better. Average gross head Average gross head refers to the water level difference between upstream and downstream of a hydropower station. Therefore, the greater the total pressure head, the higher the efficiency of SPS. In general, the value of it is larger than 70 m. Wind speed Wind speed is a strict restriction for building wind plant. From literature review, the wind speed condition for the construction of wind farms is larger than 6 m/s.

15

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Solar irradiation PV station is a kind of power generation system which converts solar irradiation energy into electric energy directly. Thus, it has high requirements for solar irradiation as annual global horizontal irradiation > 3.5 kW/m2/day. Appendix B 2.1. Natural resources aspect

• Effective wind hours (C11). The ability of energy production can be directly reflected by the effective wind hours as the accumulative hours of effective wind per year. • Sunshine days (C12). As a wind-PV-SPS plant, solar energy production can be dominated by the sunshine days in one year. • Reservoir volume of SPS (C13). Reservoir volume refers to the volume of water that can be stored in a reservoir at a certain level. Because of the large demand for power regulation, larger reservoir volume is more profitable for construction. • Installed capacity of SPS (C14). Installed capacity refers to the sum of the rated power of a SPS plant. It is one of the main indicators to characterize the construction scale and power production capacity of a SPS plant. • Distance to the grid (C15). As a hub, the grid plays a role in distributing electricity to demand [79]. Therefore, in order to replenish multiple •

power generations when power generation is insufficient or connect redundant electricity to the grid, the site should be as close as possible to the grid. Area (C16). It is necessary to have enough area for the construction of wind-PV-SPS plant.

2.2. Economic aspect

• Static investment (C21). Static investment includes total expenditure occurred in establishing a plant including the equipment, labor, installation, infrastructure and commissioning cost. • Operation & maintenance cost (C22). Operations and maintenance cost consist of the plant running cost including salaries of the employees, cost • •

of the parts or spares required for scheduled maintenance purposes etc. The operations and maintenance cost of renewable energy plants are lower than it in fossil fuel-fired power plants, but it is still very significant. Dynamic payback period (C23). The payback period of an energy project refers to the period of time required for returning on an investment to repay the sum of the original investment. Financial internal rate of return (C24). The financial internal rate of return is a dynamic index reflecting the actual rate of return of a project [80]. Generally, when the financial internal rate of return is larger than or equal to the benchmark rate of return, the project is feasible.

2.3. Environment aspect

• Average rainfall (C31). Much rainfall would lead to the splash of seawater and the corrosion of surrounding equipment which will not only cause damage to the environment around but also increase the cost of equipment maintenance. • Seismic activity (C32). SPS is installed in the offshore area, and it is very sensitive to crustal activity. Thus, SPS station need to be built in the places where earthquakes occur less frequently. • Ecological corrosion (C33). In general, the leakage and splash of seawater will cause pollution to the environment around the power station. In order to protect the ecological environment, ecological corrosion is subject to strict restrictions. • Carbon emission reduction (C34). Low carbon development is the most popular in the world for current serious environment pollution. As one of the important criteria to reflect environment improvement, carbon emission has been studied by a lot of scholars.

2.4. Social aspect

• Electricity demand (C41). Local demand can determine the power self-consumption ability. The more of self-consumption is, the better sites are. • Local residents’ attitude (C42). In order to ensure social stability, the attitude of local residents is significant to the entire construction. Through online surveys and investigation, expert group gives an evaluation rating described by TIFNs to the attitudes of the local people in each place. • Policy support (C43). Renewable energy policy support is often changing. And after the policy changes, the service capacity of wind-PV-SPS plant may change, which will affect the normal operation of power station. Therefore, a gainable and stable policy environment is very important. • Economy improvement (C44). The construction of the SPS station is essentially to promote the economic improvement so as to increase national comprehensive strength [81]. • Employment (C45). The employment can reflect the employment level of labor force [37]. The more employees in a certain period or fewer unemployed people, the higher the employment rate, conversely, the lower.

Appendix C Table 16.

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Table 16 Symbol list. Symbology Type

Number

Symbol

Description

Abbreviation

1 2 3

AHP DM ELECTRE

4

IRENA

5 6 7

MCDM NEA PIIFNs

8 9

SPS TOPSIS

10

TIFNs

11

TrIFNs

Analytic Hierarchy Process Decision maker Elimination et Choice Translating Reality The International Renewable Energy Agency Multi criteria decision making National Energy Administration Probabilistic Interval Intuitionistic Fuzzy Numbers Seawater pumped storage Technique for Order Preference by Similarity to an Ideal Solution Triangular Intuitionistic Fuzzy Numbers Trapezoidal Intuitionistic Fuzzy Numbers

1 2 3 4 5

A a b d (a , b ) ej

Formula parameter

6 7 8

An intuitionistic fuzzy set A TIFN A TIFN Distance between two TIFNs The entropy of attribute j

A defuzzification value of a TIFN Ranking operator of TIFNs A TIFN

9

h (a ) R (a¯i , ) rij Tp Tq

An alternative

11

An alternative

wj

The entropy weight of attribute j

10 12

wjr

The relative attribute weight A TIFN

14

x ij xija

15

The offline of x ij

xija

16

The middle of x ij

xija¯

17

The upper limit of x ij

+ x ija

The maximum value of xija

18

x ija

The minimum value of xija

22 24 23

vA (x ) a (x ) A (x )

25

µa (x )

13

19 20 21

p

26

µA (x )

27

j (Tp, Tq )

28

(Tp, Tq)

The DMs’ attitude toward uncertain Risk aversion of DMs The global value of an alternative Non-membership degree in IFS Membership degree in TIFN Intuitionistic index of hesitancy degree of A Non-membership degree in TIFN Membership degree in IFS

The dominance degree of two alternatives Overall dominance degree of an alternative over other alternatives

energy resources. Energy Convers Manage 2014;78:297–305. [9] Sezer N, Koç M. Development and performance assessment of a new integrated solar, wind, and osmotic power system for multigeneration, based on thermodynamic principles. Energy Convers Manage 2019;188:94–111. [10] Ray PK, Mohanty SR, Kishor N. Proportional–integral controller based small-signal analysis of hybrid distributed generation systems. Energy Convers Manage 2011;52(4):1943–54. [11] Portero U, Velázquez S, Carta JA. Sizing of a wind-hydro system using a reversible hydraulic facility with seawater. A case study in the Canary Islands. Energy Convers Manage 2015;106:1251–63. [12] Kanakasabapathy P, Swarup KS. Bidding strategy for pumped-storage plant in poolbased electricity market. Energy Convers Manage 2010;51(3):572–9. [13] Segurado R, et al. Optimization of a wind powered desalination and pumped hydro storage system. Appl Energy 2016;177:487–99. [14] Mclean E, Kearney D. An evaluation of seawater pumped hydro storage for regulating the export of renewable energy to the national grid ☆. Energy Procedia 2014;46(46):152–60. [15] Yazdani S, Deymi-Dashtebayaz M, Salimipour E. Comprehensive comparison on the ecological performance and environmental sustainability of three energy storage systems employed for a wind farm by using an emergy analysis. Energy Convers Manage 2019;191:1–11.

References [1] Sarkar T, et al. Optimal design and implementation of solar PV-wind-biogas-VRFB storage integrated smart hybrid microgrid for ensuring zero loss of power supply probability. Energy Convers Manage 2019;191:102–18. [2] Ji W, et al. Thermodynamic analysis of a novel hybrid wind-solar-compressed air energy storage system. Energy Convers Manage 2017;142:176–87. [3] Singaravel MR, Daniel SA. Studies on battery storage requirement of PV fed winddriven induction generators. Energy Convers Manage 2013;67:34–43. [4] Kusakana K. Optimal scheduling for distributed hybrid system with pumped hydro storage. Energy Convers Manage 2016;111:253–60. [5] Weibel S, Madlener R. Cost-effective design of ringwall storage hybrid power plants: a real options analysis. Energy Convers Manage 2015;103:871–85. [6] Elma O, Selamogullari US. A comparative sizing analysis of a renewable energy supplied stand-alone house considering both demand side and source side dynamics. Appl Energy 2012;96:400–8. [7] Bizon N, Oproescu M, Raceanu M. Efficient energy control strategies for a standalone renewable/fuel cell hybrid power source. Energy Convers Manage 2015;90:93–110. [8] Zhang L, Gari N, Hmurcik LV. Energy management in a microgrid with distributed

17

Energy Conversion and Management 199 (2019) 112066

Y. Wu, et al.

2019;124:341–8. [50] Gomes LFAM, et al. Criteria interactions in multiple criteria decision aiding: a Choquet formulation for the TODIM method. Procedia Comput Sci 2013;17:324–31. [51] Baseer MA, et al. GIS-based site suitability analysis for wind farm development in Saudi Arabia. Energy 2017;141. [52] Baban SM, Parry T. Developing and applying a GIS-assisted approach to locating wind farms in the UK. Renew Energy 2001;24(1):59–71. [53] Gorsevski PV, et al. A group-based spatial decision support system for wind farm site selection in Northwest Ohio. Energy Policy 2013;55(249):374–85. [54] Latinopoulos D, Kechagia K. A GIS-based multi-criteria evaluation for wind farm site selection. A regional scale application in Greece. Renew Energy 2015;78:550–60. [55] Höfer T, et al. Wind farm siting using a spatial Analytic Hierarchy Process approach: a case study of the Städteregion Aachen. Appl Energy 2016;163:222–43. [56] Sánchez-Lozano JM, García-Cascales MS, Lamata MT. GIS-based onshore wind farm site selection using Fuzzy Multi-Criteria Decision Making methods. Evaluating the case of Southeastern Spain. Appl Energy 2016;171:86–102. [57] Wu Y, et al. Decision framework of solar thermal power plant site selection based on linguistic Choquet operator. Appl Energy 2014;136(C):303–11. [58] Sánchez-Lozano JM, et al. Geographical Information Systems (GIS) and MultiCriteria Decision Making (MCDM) methods for the evaluation of solar farms locations: case study in south-eastern Spain. Renew Sustain Energy Rev 2013;24(10):544–56. [59] Fang H, Li J, Song W. Sustainable site selection for photovoltaic power plant: an integrated approach based on prospect theory. Energy Convers Manage 2018;174:755–68. [60] Tahri M, Hakdaoui M, Maanan M. The evaluation of solar farm locations applying Geographic Information System and Multi-Criteria Decision-Making methods: case study in southern Morocco. Renew Sustain Energy Rev 2015;51(10):1354–62. [61] Sánchez-Lozano JM, García-Cascales MS, Lamata MT. Comparative TOPSISELECTRE TRI methods for optimal sites for photovoltaic solar farms. Case study in Spain. J Clean Prod 2016;127:387–98. [62] Zoghi M, et al. Optimization solar site selection by fuzzy logic model and weighted linear combination method in arid and semi-arid region: a case study Isfahan-IRAN. Renew Sustain Energy Rev 2017;68:986–96. [63] Connolly D, Maclaughlin S, Leahy M. Development of a computer program to locate potential sites for pumped hydroelectric energy storage. Energy 2010;35(1):375–81. [64] Capilla JAJ, Carrión JA, Alameda-Hernandez E. Optimal site selection for upper reservoirs in pump-back systems, using geographical information systems and multicriteria analysis. Renew Energy 2016;86:429–40. [65] Wu Y, et al. An extended VIKOR-based approach for pumped hydro energy storage plant site selection with heterogeneous information. Information 2017;8(3):106. [66] http://www.360doc.com/content/14/0107/19/12109864_343393501.shtml. [67] https://baike.so.com/doc/4962114-5184200.html. [68] Anwarzai MA, Nagasaka K. Utility-scale implementable potential of wind and solar energies for Afghanistan using GIS multi-criteria decision analysis. Renew Sustain Energy Rev 2017;71:150–60. [69] USEPA (United State Environmental Protection Agency), Screening Sites for Solar PV Potential. [70] Wan SP, Wang QY, Dong JY. The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers. Elsevier Science Publishers B. V; 2013. p. 65–77. [71] Wan SP, et al. Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision making. Comput Ind Eng 2016;93(C):286–301. [72] Li D-F. A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput Math Appl 2010;60(6):1557–70. [73] Li Y, Shan Y, Liu P. An extended TODIM method for group decision making with the interval intuitionistic fuzzy sets. Math Probl Eng 2015;2015. [74] Xianguang G. Application of improved entropy method in evaluation of economic result. Syst Eng-Theory Prac 1998:12. [75] Chen R-H, Lin Y, Tseng M-L. Multicriteria analysis of sustainable development indicators in the construction minerals industry in China. Resour Policy 2015;46:123–33. [76] Wu Y, et al. Decision framework of solar thermal power plant site selection based on linguistic Choquet operator. Appl Energy 2014;136:303–11. [77] NEA, The Results of Resource Census of Seawater Pumped Storage Power Station Released by National Energy Administration http://www.2017-04/05/contengov. cn/xinwen/t_5183621.htm; 2017(68). [78] Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertainty 1992;5(4):297–323. [79] Capilla JAJ, Carrión JA, Alameda-Hernandez E. Optimal site selection for upper reservoirs in pump-back systems, using geographical information systems and multicriteria analysis. Renew Energy 2015;86:429–40. [80] Magni CA. Investment, financing and the role of ROA and WACC in value creation. Eur J Oper Res 2015;244(3):855–66. [81] Deane JP, Gallachóir BPÓ, Mckeogh EJ. Techno-economic review of existing and new pumped hydro energy storage plant. Renew Sustain Energy Rev 2010;14(4):1293–302.

[16] Fujihara T, Imano H, Oshima KJASoCE. Development of Pump Turbine for seawater Pumped-Storage Power Plant. 2013. 47(5): p. 199–202. [17] Hiratsuka A, Arai T, Yoshimura T. Seawater pumped-storage power plant in Okinawa island, Japan. Eng Geol 1993;35(3):237–46. [18] Bridier L, David M, Lauret P. Optimal design of a storage system coupled with intermittent renewables. Renew Energy 2014;67(4):2–9. [19] Ma T, et al. Optimal design of an autonomous solar–wind-pumped storage power supply system. Appl Energy 2015;160:728–36. [20] Malysz P, Sirouspour S, Emadi A. An optimal energy storage control strategy for grid-connected microgrids. IEEE Trans Smart Grid 2014;5(4):1785–96. [21] Das DC, Roy A, Sinha N. GA based frequency controller for solar thermal–diesel–wind hybrid energy generation/energy storage system. Int J Electr Power Energy Syst 2012;43(1):262–79. [22] Geem ZW. Size optimization for a hybrid photovoltaic–wind energy system. Int J Electr Power Energy Syst 2012;42(1):448–51. [23] Jurasz J, et al. Large scale complementary solar and wind energy sources coupled with pumped-storage hydroelectricity for Lower Silesia (Poland). Energy 2018;161:183–92. [24] Morabito A, et al. Set-up of a pump as turbine use in micro-pumped hydro energy storage: a case of study in Froyennes Belgium. Journal of Physics: Conference Series. IOP Publishing; 2017. [25] Bueno C, Carta J. Technical–economic analysis of wind-powered pumped hydrostorage systems. Part I: model development. Solar Energy 2005;78(3):382–95. [26] Daskalou O, et al. GIS-based approach for optimal siting and sizing of renewables considering techno-environmental constraints and the stochastic nature of meteorological inputs. EGU general assembly conference abstracts. 2016. [27] Yun-na W, et al. Macro-site selection of wind/solar hybrid power station based on Ideal Matter-Element Model. Int J Electr Power Energy Syst 2013;50:76–84. [28] Sánchez-Lozano JM, García-Cascales M, Lamata M. Identification and selection of potential sites for onshore wind farms development in Region of Murcia, Spain. Energy 2014;73:311–24. [29] Rangel CAS, et al. Methodology for ESS-type selection and optimal energy management in distribution system with DG considering reverse flow limitations and cost penalties. IET Gener Transm Distrib 2017;12(5):1164–70. [30] Yuan J, et al. Linguistic hesitant fuzzy multi-criterion decision-making for renewable energy: a case study in Jilin. J Clean Prod 2018;172:3201–14. [31] Zadeh LA. FUZZY SETS. Inf Control 1965;8(3):338–53. [32] Han Y, et al. Energy management and optimization modeling based on a novel fuzzy extreme learning machine: case study of complex petrochemical industries. Energy Convers Manage 2018;165:163–71. [33] Wu Y, et al. An extended TODIM-PROMETHEE method for waste-to-energy plant site selection based on sustainability perspective. Energy 2018;156:1–16. [34] Fetanat A, Khorasaninejad E. A novel hybrid MCDM approach for offshore wind farm site selection: a case study of Iran. Ocean Coast Manage 2015;109:17–28. [35] Dong J, Wan S. A new method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers. Kybernetes 2016;45(1):158–80. [36] Wu Y, et al. Study of decision framework of wind farm project plan selection under intuitionistic fuzzy set and fuzzy measure environment. Energy Convers Manage 2014;87:274–84. [37] Wu Y, et al. Study of decision framework of offshore wind power station site selection based on ELECTRE-III under intuitionistic fuzzy environment: a case of China. Energy Convers Manage 2016;113:66–81. [38] Peng H-G, et al. Investment risk evaluation for new energy resources: an integrated decision support model based on regret theory and ELECTRE III. Energy Convers Manage 2019;183:332–48. [39] Taylan O, Kaya D, Demirbas A. An integrated multi attribute decision model for energy efficiency processes in petrochemical industry applying fuzzy set theory. Energy Convers Manage 2016;117:501–12. [40] Jovanović B, Filipović J, Bakić V. Prioritization of manufacturing sectors in Serbia for energy management improvement–AHP method. Energy Convers Manage 2015;98:225–35. [41] Saaty RW. The analytic hierarchy process—what it is and how it is used. Math Model 1987;9(3–5):161–76. [42] Kumar A, et al. Integrated assessment of a sustainable microgrid for a remote village in hilly region. Energy Convers Manage 2019;180:442–72. [43] Wu Y, et al. Location selection of seawater pumped hydro storage station in China based on multi-attribute decision making. Renew Energy 2019;139:410–25. [44] Zhang N, Wei G. Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl Math Model 2013;37(7):4938–47. [45] Opricovic S, Tzeng G-H. Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 2004;156(2):445–55. [46] Zhang L, et al. Renewable energy project performance evaluation using a hybrid multi-criteria decision-making approach: case study in Fujian, China. J Clean Prod 2019;206:1123–37. [47] Liang D, et al. Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry. Appl Soft Comput 2019. [48] Brans J-P, Vincke P, Mareschal B. How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 1986;24(2):228–38. [49] Alali F, Tolga AC. Portfolio allocation with the TODIM method. Expert Syst Appl

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