Analysis of policy scenarios for achieving renewable energy sources targets: A fuzzy TOPSIS approach

Abstract

The growing need to tackle climate change and mitigate greenhouse gas emissions has led to strong interest in renewable energy sources and the setting of specific renewable energy sources targets in countries and regions within Europe. Recent political discussions have mainly revolved around the question of the most effective and efficient renewable energy sources target and how to achieve it. In this context, European and national policy makers have to address difficult issues: On the one hand, how to support the successful achievement of renewable energy targets in the short and medium term and in a time horizon up to 2030, and, on the other hand, how to share the efforts required among individual entities such as single European Member States or groups of European Member States. This paper presents a multi-criteria approach based on an extension of the Fuzzy Technique for Order Preference by Similarity to Ideal Solution for group decision support in order to evaluate alternative policy scenarios for achieving the 2030 renewable energy target. Different effort-sharing arrangements among Member States are evaluated to determine the optimal burden sharing of the common renewable energy target among countries. The results and conclusions obtained can help to reduce uncertainty in the field of energy and climate policy, and aid policy makers in designing effective policies based on the findings.

Keywords

Renewable energy sources energy policy decision support multi-criteria analysis fuzzy TOPSIS sensitivity analysis

Introduction

At present, the global energy system consists primarily of conventional energy sources such as oil, gas and coal, which together produce about 80% of global primary energy.¹ The transition to an energy system with a clean and sustainable production, transportation and use of energy involves a large number of social, economic, environmental, technical and political factors.^2,3 The growing need to tackle global environmental problems has led to the consolidation of interest in renewable energy sources (RES) since it is proven that the energy sector is the major cause of environmental pollution.⁴ At the same time, the increased use of RES also offers significant economic benefits by promoting investment and new projects, and contributes to direct and indirect job creation.^5,6

The need to formulate a more integrated energy policy to support renewable energy in Europe quickly became noticeable, and this promoted a new way of thinking about comprehensive and ambitious decisions on a country level.⁷ The basis for an energy sector based on renewables at the European Union (EU) level was created in 1997 with the adoption of the ‘White Paper for a Community Strategy and Action Plan’. The EU defined an overall target for renewable energy of 20% in 2020,⁸ while the ‘2030 Climate and Energy Policy Framework’, adopted in October 2014, defines a binding target of a 40% reduction of greenhouse gas emissions (GHG) until 2030 compared to 1990, a 27% share of RES in gross final energy demand and an indicative target of a 27% increase in energy efficiency compared to a ‘business‐as‐usual’ projection of the future energy demand.⁹ Contrary to the 2020 policy framework, the EU‐target for renewables will not be broken down into legally binding national targets. The EU is now on a path towards a low carbon economy by 2050, to ensure regulatory certainty and a sustainable energy future.¹⁰

This paper analyses alternative policy scenarios and evaluation criteria aiming at the optimal allocation among Members States (MSs) of the efforts needed to achieve the RES target of 27% of gross final energy consumption. To cope with the disparate preferences of decision-makers, as well as to manage the uncertainty that arises when solving decision problems, a methodological assessment framework is developed using the multi-criteria Fuzzy TOPSIS method, which is based on the principles of fuzzy logic. The results provide a clear picture of the preferred options and their interactions with the evaluation criteria, while the conclusions focus on the impacts of energy and climate policy on the existing energy sector, and how to encourage the use of RES.

Multi-criteria analysis is a proven method to merge and analyse all of the perspectives associated with decision-making processes.¹¹ It is a sound methodology, which has been applied internationally over the last decade to several strategic environmental and energy planning issues,^12–17 and has also been used to support countries in deploying RES effectively in order to achieve their energy and climate-related targets.^18,19 Multi-criteria analysis has often been used to support decisions in the energy sector and energy planning, because it can solve very complex energy management problems.^20–23

Decision-makers can use a fuzzy multi-criteria method when having to make a satisfactory decision in imprecise and multi-criteria situations. Fuzzy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method is used in this paper, since it is widely used to solve decision-making problems. It meets specific requirements when uncertain and imprecise knowledge as well as possibly vague preferences have to be considered.²⁴ Fuzzy TOPSIS allows fuzzy values to be used in the decision problem,²⁵ making it highly comprehensible to decision-makers facing multi-dimensional energy policy problems. It offers a realistic approach using linguistic assessment instead of numerical values, offering decision-makers the chance to express their preferences with linguistic variables.²⁶

Following this introductory section, the remainder of the paper is structured as follows: the Overview of the methodological approach section gives an overview of the method used to assess alternative policy scenarios for achieving the 2030 RES target. In the Problem formulation section, the alternative policy scenarios are elaborated and the evaluation criteria presented. In the Selection of the multiple-criteria decision-making (MCDM) method section, the main steps for implementing the fuzzy TOPSIS method are described and applied in the Application of the fuzzy TOPSIS method section. A sensitivity analysis is conducted in the Sensitivity analysis section to derive the final ranking of the alternative policy scenarios. In the Conclusions section, the main conclusions are summarised and key points are proposed for further research.

Overview of the methodological approach

The new governance system proposed by the EU together with the objectives for 2030 discusses the extent to which the MSs are free to determine their energy mix, national targets and legal framework, creating a fertile ground for cultivating the development of RES collectively.^27,28 However, the implications of such a governance mechanism and how it can guarantee compliance with the EU’s RES target of 27% of gross final energy consumption remain unclear.

The three main issues to be investigated are:

how the target will be shared among MSs

whether this goal will be binding or not and

whether it will be implemented in each MS or regionally.

Figure 1 illustrates the methodology applied to analyse the effectiveness of alternative policy scenarios to achieve the RES target in the EU for 2030 (Figure 1).

Figure 1.

Overview of the methodological approach.

The first step was to identify alternative policy scenarios that aim to achieve the EU’s renewable energy target by 2030 and successfully implement the agreed EU energy framework and the criteria for evaluating them. Subsequently, after an extensive literature review, the most appropriate Multi-Criteria Decision-Making (MCDM) method was selected for this specific problem. This MCDM method was applied to assess and classify the alternative policy scenarios from the most to the least preferable according to decision-makers’ preferences. This method enabled the alternatives to be evaluated, providing important insights into the most suitable policy scenario for achieving the EU’s RES target by 2030. A sensitivity analysis was also conducted in order to address the uncertainty that exists in every decision-making problem and because the indication of how sensitive one alternative is to one or more variable changes is of prime importance for decision-makers, and the final ranking of the alternative policy scenarios was then obtained.

Problem formulation

Alternative policy scenarios

First, alternative policy scenarios for allocating the 2030 RES target among MSs are defined. The selection is based on policies that have already been discussed, decided or are under discussion in the EU, while emphasis is placed on the structure of the alternatives. Second, the selected structures are assessed using the criteria set in the next section which must be met to ensure the proper application of the alternatives. The alternative policy scenarios and the criteria selected are based on research conducted within the framework of the Intelligent Energy for Europe Initiative ‘Towards2030-dialogue - Dialogue on a RES policy framework for 2030’.²⁹

Α₁ – Binding national RES targets. This option essentially follows the 2020 logic for sharing the effort among MSs. The EU RES target is broken down into MS targets according to a fixed formula, which could once again include a flat-rate component and a component depending on Gross Domestic Product (GDP) of the countries. The resulting MS targets are legally binding. Reporting procedures are equivalent to the current system, with MSs delivering National Renewable Energy Action Plans (NREAPs) for the time frame 2020–2030, followed by regular progress reports.

Α₂ – Binding national RES targets through pledging. The EU RES target is broken down into benchmark MS targets according to a fixed formula, for instance following the allocation logic of the 2020 target. MSs are free to accept this suggested benchmark or may pledge a higher or lower target, which is legally binding. MSs are then obliged to deliver a NREAP to the EC to illustrate how they will achieve their pledged target. If the MS pledges are not ambitious enough, their combined targets will not add up to the EU target, leaving a gap at EU level. This gap would have to be bridged by an EU instrument. Such a gap could be prevented by providing strong incentives for MSs to make ambitious pledges, for instance, through financial incentives or supercredits. There may be a different kind of incentive arising from how the EU gap is bridged.

Α₃ – Binding regional targets. MSs are grouped into regions. Groups are suggested by the EC, but MSs may act according to their own preferences. MSs who do not find attractive partners may choose to remain by themselves. The grouping process is effectively an opt‐in process, as only those MSs form groups who wish to do so. After the initial formation, the groups remain fixed. The EU RES target is allocated to MSs by a fixed formula. For those MSs forming regional groups, national targets are combined into a common regional target. The allocation formula could, for instance, include a flat-rate component and a GDP‐dependent component, as was the case for the 2020 targets. MSs are jointly responsible for achieving the target in the region they belong to. Here, it necessary to regulate the sequence of group formation and target allocation. If groups are formed first and targets allocated afterwards, then MSs are unlikely to commit to a group because they do not yet know the target. If targets are allocated first and groups are formed afterwards, then some MSs might not be willing to accept the allocation of national binding targets, before knowing whether they will find suitable partners, and what the cost implications are.

Α₄ – Indicative national RES targets. The EU RES target is broken down into MS targets according to a fixed formula. The allocation formula could, for instance, once again include a flat-rate component and a GDP‐dependent component, as was the case for the 2020 targets. However, the resulting MS targets are indicative, rather than legally binding. Even though the target is only indicative, it enables the Commission to monitor and encourage target achievement through ‘naming and shaming’. This may have no legal consequences, but is still a political tool. For this reason, some MSs may oppose even indicative targets on MS level.

Α₅ – Indicative national RES targets with incentives for overcommitment. The ambition level for each MS is allocated according to a fixed formula. Each MS formulates a NREAP in which it states how it intends to achieve the target. MSs have the possibility to indicate in their NREAP their willingness to achieve a higher target than the one allocated to them. In order to incentivise such voluntary overcommitment, ambitious MSs benefit from supercredits or from a redistribution of Emissions Trading System (ETS) allowances in their favour. Supercredits can be issue, for instance, to the amount pledged above the benchmark target, to the amount realised using certain technologies, or to the amount realised in cooperation with other MSs.

Α₆ – Indicative regional targets. Similar to the previous option, the ambition level for each MS is allocated according to a fixed formula. However, MSs are grouped into regions, merging their national targets into a regional one. Group formation follows the same principle as for the binding regional targets, i.e. groups are suggested by the Commission, but MSs may act according to their own preferences. MSs who do not find attractive partners may choose to remain alone. The grouping process is thus effectively an opt‐in process, as only those MSs who wish to form groups do so. After the initial formation, the groups remain fixed. Each regional group formulates a Regional Energy Action Plan (REAP) in which it states how it intends to achieve the indicative target. Regions have the possibility to indicate in their REAP their willingness to achieve a higher target than the one resulting from their combined targets. In order to incentivise such voluntary overcommitment, ambitious regions benefit from supercredits or from a redistribution of ETS allowances in their favour. As in option A₃, the sequence of group formation and target allocation needs to be defined.

Α₇ – Binding national RES targets through free pledging. Under free pledging, MSs commit to a RES target they determine; no benchmark value is provided by the Commission. The self‐determined targets are legally binding but the sum of the national targets will probably be less than the EU target. One or more iterations can follow the first round, in order to negotiate higher targets with the MSs and close the EU gap. If, after repeated iterations and negotiations, a gap still remains, this part of the target is covered by an EU-level instrument. This instrument is financed from the EU budget, with MS contributions not related to how ambitious their target pledge was.

Α₈ – Binding regional RES targets through free pledging. Similar to the free pledging procedure for MSs, regions commit to a RES target determined by them; no benchmark value is provided by the EC. Regions are created following the same principle as for the binding regional targets, i.e. groups are suggested by the EC, but MSs may act according to their own preferences. MSs who do not find attractive partners may remain by themselves. The grouping process is thus effectively an opt‐in process, as only those MSs who wish to form groups do so. After the initial formation, the groups remain fixed. The self‐determined targets are legally binding for the regions. It can be expected that the sum of the national targets will be less than the EU target. In this case, one or more iterations can follow the first round to try and close the gap, similar to the previous scenario.

Α₉ – RES target on EU level. The target is set on EU level and financed entirely through a EU‐wide harmonised instrument. The possibility of correlating the financial burden for all EU electricity consumers with GDP should be considered. Also, it must be determined who will be considered (legally) responsible in case the target is not achieved, and clarified whether or not additional voluntary RES support frameworks will exist for those MSs who want them.

Criteria formulation

The methodology leads to specific criteria for evaluating alternative policy scenarios to achieve the EU RES target by 2030 through literature review, EC instructions and the decisions of the European Parliament (EP) about the allocation of GHG reduction efforts.^29–32 In this case, four criteria are selected to determine the best alternative (static efficiency, flexibility, applicability and political acceptability). The defined criteria will be used to evaluate all the alternatives, while adequately incorporating the diversity of policies, regulations and priorities of MSs, and remaining consistent with the perspective of energy policy decision-makers, the available infrastructure, financial capacity, regulators and network managers.

C₁ – Static efficiency. This refers to the total system costs incurred to achieve the 2030 target(s). Energy system costs vary with the amount, technology type, and geographical distribution of deployed RES. Burden-sharing arrangements among MSs affect the geographical distribution of RES installations.

C₂ – Flexibility. This refers to the degree of freedom a MS has to set its own focus in reducing GHG emissions, i.e. to concentrate on RES deployment, energy efficiency, or other measures. Many MSs have a strong interest in retaining flexibility to adapt targets to their national circumstances and preferences. This criterion is closely linked to political acceptability.

C₃ – Applicability. A meaningful target structure must be practicable in its implementation and measurable in its effects. This includes the possibility to identify a baseline, and clarity about which instruments can be applied to achieve the target and by whom.

C₄ – Political acceptability. This refers to whether a specific burden-sharing arrangement is politically attractive for MSs at a given time. Factors influencing political and social acceptability include the policy’s level of ambition and the associated costs for individual MSs, and how binding the commitments are.

Selection of the multiple-criteria decision-making method

In order to structure and solve decision problems that de facto involve multiple dimensions, researchers are often using Multiple-Criteria Decision-Making MCDM methods (also termed Multiple-Criteria Decision Analysis MCDA). Apart from their obvious ability to handle numerous criteria, these methods also enable the decision-maker to better understand the nature of the problem and prioritise the various criteria, and they promote decision-makers’ dynamic engagement with the process and facilitate collective decision-making.

MCDM is widely accepted for multi-dimensional studies through participatory and analytical tools.^33,34 Along with scenarios, participatory and multi-criteria analysis can assess different elements of policies, reflecting different views, goals and limitations.^35,36

Most real-world decision problems take place in a complex environment where conflicting systems of logic, uncertain and imprecise knowledge, and possibly vague preferences have to be considered. To handle such complexity, it is crucial to use specific tools, techniques, and concepts which allow the available information to be represented with the appropriate granularity. In particular, the fuzzy set theory is ideal for coping with these kinds of problems.

The fuzzy TOPSIS method

Under many conditions, crisp^a sets are inadequate to model real-life situations. A more realistic approach may be to use linguistic assessments instead of numerical values, so that the ratings and weights of the criteria in the problem are assessed by means of linguistic variables.^26,37–39 Considering the fuzziness in the decision data and group decision-making processes, linguistic variables are used to assess the weights of all criteria and the ratings of each alternative with respect to each criterion.

Multi-criteria decision-making methods with fuzzy numbers (Fuzzy MCDM) are also applied to evaluate the performance of a process.^40,41 They are suitable for approximate interval problems and can therefore be used to analyse quantitative and qualitative data.^42–44 Fuzzy multi-criteria methods are one possible approach to evaluate alternative decisions which involve subjective judgments and are made by a group of decision-makers. A pairwise comparison process is used to assist decision-makers with comparative judgments, while a linguistic evaluation method is used for absolute judgments.²⁴

One of the best known classical MCDM methods – the TOPSIS – was first developed by Hwang and Yoon⁴⁵ to solve a MCDM problem. It is based upon the idea that the chosen alternative should be at the shortest distance from the positive ideal solution (PIS) and the farthest distance from the negative ideal solution (NIS). In a TOPSIS process, the performance ratings and the weights of the criteria are given as crisp values.

The fuzzy TOPSIS method has been applied in many fields and performs well for decision-making among a selection of alternatives.^46–50 In addition, Fuzzy TOPSIS has been applied in several studies in the field of energy policy,^51–53 in the assessment of energy suppliers and RES options^54–56 and in the selection of locations for power plant construction.^57–59 To the best of our knowledge, however, this is the first fuzzy-TOPSIS-based MCDM technique developed for the selection of the optimal policy scenario for effective and efficient RES target achievement. In doing so, we attempt to extend the application domains of the fuzzy TOPSIS method.

Implementation steps of the selected method

A systematic approach to extend the TOPSIS to the fuzzy environment is proposed in this section for group decision-making under the conditions of the specific problem addressed in this paper. The basic steps of the proposed method are shown in Figure 2.

Step 1

Form a committee of decision-makers (DMs), and then identify the evaluation criteria.

Figure 2.

Overview of fuzzy TOPSIS basic steps.

There are a number of ‘group-based’ research techniques available to determine the views or perceptions of individuals in relation to specific topics. At the end of this step, a set of K decision-makers, and a set of n benefit criteria $C = {C_{1}, C_{2}, \dots, C_{n}}$ have been defined and described, which are then used to measure the alternatives.

Step 2

Choose the appropriate linguistic variables for the importance weights of the criteria and the linguistic ratings for alternatives with respect to the criteria.

The importance weight of each criterion can be obtained either directly by assigning a weight or indirectly by using pairwise comparisons.³⁹ Within this step, it is suggested that the decision-makers use the linguistic variables (depicted in Tables 1 and 2) to evaluate the importance of the criteria and rate alternatives with respect to various criteria.

Table 1.

Linguistic variables and fuzzy numbers.

Linguistic variables for the importance weight of each criterion		Linguistic variables for the ratings
Linguistic variables	Fuzzy number	Linguistic variables	Fuzzy number
Very low (VL)	(0.0, 0.0, 0.1)	Very poor (VP)	(0, 0, 1)
Low (L)	(0.0, 0.1, 0.3)	Poor (P)	(0, 1, 3)
Medium low (ML)	(0.1, 0.3, 0.5)	Medium poor (MP)	(1, 3, 5)
Medium (M)	(0.3, 0.5, 0.7)	Fair (F)	(3, 5, 7)
Medium high (MH)	(0.5, 0.7, 0.9)	Medium good (MG)	(5, 7, 9)
High (H)	(0.7, 0.9, 1.0)	Good (G)	(7, 9, 10)
Very high (VH)	(0.9, 1.0, 1.0)	Very good (VG)	(9, 10, 10)

Table 2.

Assignment of importance weight to criteria by the DMs.

Decision-Makers	Weights
Decision-Makers	C₁	C₂	C₃	C₄
D₁	MH	ML	VH	M
D₂	H	M	VH	ML
D₃	H	H	VH	M

Step 3

Aggregate the weights to obtain the aggregated fuzzy weight ${\tilde{w}}_{j}$ of criterion C_j, and pool the decision-makers’ opinions to get the aggregated fuzzy rating ${\tilde{x}}_{ij}$ of alternative A_j under criterion C_j.

The importance of each criterion and the rating of alternatives with respect to each criterion can be calculated as

{\tilde{x}}_{ij} = \frac{1}{K} [{\tilde{x}}_{ij}^{1} (+) {\tilde{x}}_{ij}^{2} (+) \dots {\tilde{x}}_{ij}^{K} (+)] {\tilde{w}}_{j} = \frac{1}{K} [{\tilde{w}}_{j}^{1} (+) {\tilde{w}}_{j}^{2} (+) \dots {\tilde{w}}_{j}^{K} (+)]

where

{\tilde{x}}_{ij}^{K}

and

{\tilde{w}}_{j}^{K}

are the rating and the importance weight of the

K^{th}

decision-maker.

Step 4

Construct the fuzzy decision matrix and the normalised fuzzy decision matrix.

As stated above, a fuzzy multi-criteria group decision-making problem can be concisely expressed in matrix format as

\tilde{D} = [{\tilde{x}}_{11} {\tilde{x}}_{12} \dots {\tilde{x}}_{1 n} {\tilde{x}}_{21} {\tilde{x}}_{22} {\tilde{x}}_{2 n} : : {\tilde{x}}_{m 1} {\tilde{x}}_{m 2} \dots {\tilde{x}}_{mn}] \tilde{W} = [{\overset{\land}{w}}_{1} w_{2} \dots {\tilde{w}}_{n}]

where

{\tilde{x}}_{ij}, \forall i, j

and

{\tilde{w}}_{j}, j = 1, 2, \dots, n

are linguistic variables. These linguistic variables can be described by triangular fuzzy numbers,

{\tilde{x}}_{ij} = (a_{ij}, b_{ij}, c_{ij})

and

{\tilde{w}}_{j} = (w_{j 1}, w_{j 2}, w_{j 3})

To avoid the complicated normalisation formula used in classical TOPSIS, linear scale transformation is used here to transform the various criteria scales into a comparable scale. This yields the normalised fuzzy decision matrix denoted by $\tilde{R}$ .

\tilde{R} = [{\tilde{r}}_{ij}]_{mxn}

where

{\tilde{r}}_{ij} = (\frac{a_{ij}}{c_{j}^{*}}, \frac{b_{ij}}{c_{j}^{*}}, \frac{c_{ij}}{c_{j}^{*}}) and c_{j}^{*} = {max}_{i} c_{ij} benefitcriteria {\tilde{r}}_{ij} = (\frac{a_{j}^{-}}{c_{ij}}, \frac{a_{j}^{-}}{b_{ij}}, \frac{a_{j}^{-}}{a_{ij}}) and a_{j}^{-} = {min}_{i} a_{ij} costcriteria .

Step 5

Construct the weighted normalised fuzzy decision matrix.

Considering the varying importance of each criterion, the weighted normalised fuzzy decision matrix can be constructed as

\tilde{V} = [{\tilde{v}}_{ij}]_{mxn} i = 1, 2, \dots, m; j = 1, 2, \dots, n

where

{\tilde{u}}_{ij}

{\tilde{r}}_{ij} (.) {\tilde{w}}_{j}

Step 6

Determine FPIS and FNIS.

According to the weighted normalised fuzzy decision matrix, it is evident that the elements ${\tilde{u}}_{ij}, \forall i, j$ are normalised positive triangular fuzzy numbers and their ranges are in the closed interval [0, 1]. Then, the fuzzy positive-ideal solution (FPIS, A*) and the fuzzy negative-ideal (FNIS, A^-) solution can be defined as

A^{*} = ({\tilde{u}}_{1}^{*}, {\tilde{u}}_{2}^{*} \dots, {\tilde{u}}_{n}^{*}) where {\tilde{u}}_{j}^{*} = {max}_{i} {u_{ij 3}} i = 1, 2, \dots, m; j = 1, 2, \dots, n A^{-} = ({\tilde{u}}_{1}^{-}, {\tilde{u}}_{2}^{-} \dots, {\tilde{u}}_{n}^{-}) where {\tilde{u}}_{j}^{-} = {min}_{i} {u_{ij 1}} i = 1, 2, \dots, m; j = 1, 2, \dots, n

Step 7

Calculate the distance of each alternative from FPIS and FNIS.

The distance of each alternative from A* can be calculated as

d_{i}^{*} = \sum_{j = 1}^{n} d ({\tilde{u}}_{ij}, {\tilde{u}}_{j}^{*}), i = 1, 2, \dots, m

The distance of each alternative from A^- can be calculated as

d_{i}^{-} = \sum_{j = 1}^{n} d ({\tilde{u}}_{ij}, {\tilde{u}}_{j}^{-}), i = 1, 2, \dots, m

where

d (., .)

is the distance measurement between two fuzzy numbers.

For triangular fuzzy numbers, the distance between two fuzzy numbers m and n is expressed by

d (\tilde{m}, \tilde{n}) = \sqrt{\frac{1}{3} [(m_{1} - n_{1})^{2} + (m_{2} - n_{2})^{2} + (m_{3} - n_{3})^{2}]}

where

\tilde{m} = (m_{1}, m_{2}, m_{3})

και

\tilde{n} = (n_{1}, n_{2}, n_{3})

Step 8

Closeness coefficient and alternatives’ ranking.

The closeness coefficient ${CC}_{i}$ enabling the alternatives classification can be calculated as

{CC}_{i} = \frac{d_{i}^{-}}{d_{i}^{*} + d_{i}^{-}}, i = 1, 2, \dots m

The closeness coefficient ranges between (0, 1) and the alternative with the largest closeness coefficient is the ideal solution. In addition, the alternative defining the ideal solution is also the one with the shortest distance from the positive ideal solution FPIS and with the largest distance from the negative ideal solution FNIS. Thus, alternatives ranked in descending order are the result of applying this approach.⁶⁰

Application of the fuzzy TOPSIS method

Based on the above-mentioned steps, this research used a total of three decision-makers (DMs) D_r, r = {1, 2, 3}, four different criteria C_j, j = {1, 2, 3, 4}, and nine alternative policy scenarios A_i, i = 1, 2,…, 9 in respect to the EU decisions, regulations and directives. The criteria weights were assigned to the alternatives through paired comparisons for the evaluation of the different policy scenarios (Figure 3).

Figure 3.

Hierarchical structure for assessing alternative policy strategies at EU level.

Through the proposed extension of the Fuzzy TOPSIS for group decision-making, the linguistic variables are defined to evaluate the importance of the criteria and the ratings of alternatives with respect to these criteria. The linguistic variables can be converted into fuzzy numbers using a seven-point scale transformation for the importance weight of each criterion S = (VL, L, ML, M, MH, H, VH) and a seven-point scale transformation for rating the alternatives S = (VP, P, MP, F, MG, G, VG). Thus, the calibrated conversion scales were constructed that are used to evaluate nine alternatives for each of the four criteria.

Tables 1 and 2 show the weights of the criteria and the ratings of alternative actions for the evaluation criteria as they result from each decision-maker.

Based on the aforementioned scale, the experts assign an importance weight to each criterion and assess the alternative policy strategies at EU level for each of the criteria as depicted in Table 3.

Table 3.

Ratings of the alternatives by the DMs.

DM	Criteria	Alternatives
DM	Criteria	A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉
D₁	C₁	MP	MP	MG	P	F	MG	P	MG	VG
	C₂	P	F	MP	MG	MG	G	MG	MG	P
	C₃	VG	G	VP	G	G	P	MG	VP	P
	C₄	VP	MP	P	MP	MP	F	F	MP	F
D₂	C₁	F	F	MG	MP	F	G	MG	MG	G
	C₂	VP	MP	F	MP	MP	G	G	MG	P
	C₃	VG	G	MP	G	VG	P	F	P	MP
	C₄	P	F	P	F	G	F	MG	P	MP
D₃	C₁	MG	G	G	MP	F	MG	P	G	MG
	C₂	VP	MP	P	F	MG	G	G	G	P
	C₃	VG	G	MP	F	F	P	F	MP	VP
	C₄	VP	P	P	MP	F	F	F	F	F

The aggregated fuzzy decision matrix for the alternatives and the aggregated fuzzy weights W_j for the four criteria are depicted in Table 4.

Table 4.

Aggregated fuzzy decision matrix.

A_i	C₁	C₂	C₃	C₄
A₁	(3.00, 5.00, 7.00)	(0.00, 0.33, 1.67)	(9.00, 10.0, 10.0)	(0.00, 0.33, 1.67)
A₂	(3.67, 5.67, 7.33)	(1.67, 3.67, 5.67)	(7.00, 9.00, 10.0)	(1.33, 3.00, 5.00)
A₃	(5.67, 7.67, 9.33)	(1.33, 3.00, 5.00)	(0.67, 2.00, 3.67)	(0.00, 1.00, 3.00)
A₄	(0.67, 2.33, 4.33)	(3.00, 5.00, 7.00)	(5.67, 7.67, 9.00)	(1.67, 3.67, 5.67)
A₅	(3.00, 5.00, 7.00)	(3.67, 5.67, 7.67)	(6.33, 8.00, 9.00)	(3.67, 5.67, 7.33)
A₆	(5.67, 7.67, 9.33)	(7.00, 9.00, 10.0)	(0.00, 1.00, 3.00)	(3.00, 5.00, 7.00)
A₇	(1.67, 3.00, 5.00)	(6.33, 8.33, 9.67)	(3.67, 5.67, 7.67)	(3.67, 5.67, 7.67)
A₈	(5.67, 7.67, 9.33)	(5.67, 7.67, 9.33)	(0.33, 1.33, 3.00)	(1.33, 3.00, 5.00)
A₉	(7.00, 8.67, 9.67)	(0.00, 1.00, 3.00)	(0.33, 1.33, 3.00)	(2.33, 4.33, 6.33)
Fuzzy weights	(0.63, 0.83, 0.97)	(0.37, 0.57, 0.73)	(0.90, 1.00, 1.00)	(0.23, 0.43, 0.63)

According to step 4 in the previous section, the normalised fuzzy decision matrix is calculated for the nine alternatives. Based on step 5, the values of the normalised fuzzy decision matrix r_ij and the linguistic variables W_j obtained from Table 1 were used to calculate the weighted normalised fuzzy decision matrix.

The maximum (1.00) and minimum (0.00) values identified in the weighted normalised fuzzy decision matrix correspond to the fuzzy positive-ideal solution and the fuzzy negative-ideal solution, respectively, determined using equation (Α* και Α−). The distance of each alternative from the positive ideal solution FPIS, d(A_j, A*), and the negative ideal solution FNIS, d(A_j, A−), is presented in Tables 5 and 6.

Table 5.

Distances from the Positive Ideal Solution FPIS.

d(A_i, A*)	C₁	C₂	C₃	C₄	d⁺
d(A₁, A*)	0.594	0.954	0.110	0.950	2.608
d(A₂, A*)	0.551	0.785	0.221	0.807	2.365
d(A₃, A*)	0.414	0.815	0.801	0.905	2.935
d(A₄, A*)	0.790	0.717	0.319	0.777	2.603
d(A₅, A*)	0.594	0.684	0.280	0.685	2.242
d(A₆, A*)	0.414	0.537	0.876	0.711	2.538
d(A₇, A*)	0.729	0.564	0.480	0.680	2.452
d(A₈, A*)	0.414	0.591	0.853	0.807	2.665
d(A₉, A*)	0.346	0.913	0.853	0.744	2.855

Table 6.

Distances from the Negative Ideal Solution FNIS.

d(A_i, A−)	C₁	C₂	C₃	C₄	d-
d(A₁, A−)	0.488	0.071	0.941	0.080	1.581
d(A₂, A−)	0.527	0.271	0.858	0.259	1.914
d(A₃, A−)	0.694	0.235	0.244	0.147	1.320
d(A₄, A−)	0.277	0.344	0.743	0.297	1.662
d(A₅, A−)	0.488	0.382	0.769	0.401	2.040
d(A₆, A−)	0.694	0.537	0.183	0.375	1.789
d(A₇, A−)	0.331	0.510	0.582	0.415	1.838
d(A₈, A−)	0.694	0.483	0.190	0.259	1.627
d(A₉, A−)	0.753	0.131	0.190	0.336	1.411

Furthermore, using equation [fpis, fnis] and the application of the Euclidean distance of each alternative from Α* and Α−, the closeness coefficient is calculated, which enables the ranking of alternatives. As a result, the closeness coefficient can indicate which alternative policy scenario is the optimal one for EU MSs to achieve the common RES target for 2030 (Table 7).

Table 7.

Ranking of alternative policy scenarios using the closeness coefficient.

Ranking	A_i	Alternative policy scenarios	Closeness Coefficient
1	A₅	Indicative national RES targets with incentives for overcommitment	0.476
2	A₂	Binding national RES targets through pledging	0.447
3	A₇	Binding national RES targets through free pledging	0.428
4	A₆	Indicative regional targets	0.413
5	A₄	Indicative national RES targets	0.389
6	A₈	Binding regional RES targets through free pledging	0.379
7	A₁	Binding national RES targets	0.377
8	A₉	RES target on EU level	0.331
9	A₃	Binding regional targets	0.310

RES: renewable energy sources.

The resulting ranking (Table 7) is A₅ > A₂ > A₇ > A₆ > A₄ > A₈ > A₁ > A₉ > A₃ and indicates alternative A₅ ‘Indicative national RES targets with incentives for overcommitment’ as the best option since the closeness coefficient of alternative A5 is the nearest to 1 and the largest compared to the others.

Sensitivity analysis

Sensitivity analysis is one tool able to manage uncertainty in decision-making problems.⁶¹ It is a process that refers to a model’s variable input data within permissible limits and recognises the factors that influence the stability of the alternatives.⁶² It investigates how the output data are affected, qualitatively and quantitatively and, therefore, indicates the sensitivity of the overall decision to uncertainties in the model’s input values. This mechanism is used to increase the reliability and improve the outcomes of a particular model.⁶³ It helps to understand how the model variables react to input changes, and whether they are related to the data used to adapt the structure of the model, or to independent variables of the model.⁶⁴ The impossibility of managing all the possible combinations for each variable is a potential problem, but the number of elements extracted from the process is sufficient to assess the sensitivity through probabilistic assumptions.^65,66

The set of potential experiments that could be performed for a sensitivity analysis equals all the possible combinations of weights, so that each weighted criterion is consecutively assigned each value across the whole range of the chosen linguistic scale. Without loss of generality, 20 experiments were conducted for the sensitivity analysis, composed of 20 different combinations of the criteria weights.

The following table indicates how an increase or decrease of a criterion’s weight can change the ranking of each alternative. The ranking is represented by shades of blue. For a given experiment, a darker grey closeness coefficient is higher in the ranking than a lighter one (Table 8). The results of the sensitivity analysis are also presented graphically in Figure 4.

Table 8.

The closeness coefficient in each of the 20 sensitivity analyses.

Figure 4.

Results of the sensitivity analysis.

The experiments [10], [14], [16] and [17] indicate that the optimum alternative ‘A₅ – Indicative national RES targets with incentives for overcommitment’ shows little sensitivity to variations in the weight of the criterion ‘C₃ – Applicability’, making it stable in the most influential criterion. This does not occur for the policy scenario ‘Α₆ – Indicative regional targets’, which was first in the ranking for the reduced effect of criterion C₃ in experiment [14], but only seventh of the nine alternatives when increasing the weight of criterion C₃ in experiment [10]. The three most prevalent alternatives (A₅, A₇, A₆) seem to be consistent with changes in ‘C₂ – Flexibility’ and ‘C₄ – Political acceptability’, showing low sensitivity to them (experiments [9], [13] and [11], [15], respectively). Regarding the least preferable alternative (‘Α₃ – Binding regional targets’) is little influenced by changes in the criteria weights and is occupies mostly the last or second last rank. It ranks in fourth place among the nine scenarios only in experiment [8], which reveals the important effect of ‘C₁ – Static Efficiency’. Alternatives ‘Α₁ – Binding national RES targets’ and ‘Α₉ – RES target on EU level’ display similar behaviour; most of the time they occupy the three bottom places in the final ranking, but place first in experiments [10] and [8], respectively.

The final ranking, taking into account the result of the sensitivity analysis, is based on the average closeness coefficients of the sensitivity analyses. It is obvious that this final ranking is slightly different to the one obtained previously when the optimal case was considered. Indicatively, the alternative policy scenario ‘A₅ – Indicative national RES targets with incentives for overcommitment’ ranks first in more than half the experiments for the sensitivity analysis

A_{5} > A_{7} > A_{6} > A_{2} > A_{8} > A_{4} > A_{9} > A_{1} > A_{3}

Conclusions

This paper presents a multi-criteria approach based on an extended fuzzy TOPSIS for group decision-making. The approach is used to evaluate alternative policy scenarios for implementing the EU target of 27% RES in gross final energy consumption.

The proposed decision-making model is able to manage uncertainty, inaccuracy and the complexity of decisions as they emerge from different and conflicting criteria. Linguistic variables were used to evaluate the alternative scenarios and criteria and qualitative information was then transformed into quantitative data. The application of the Fuzzy TOPSIS method with more than one decision-maker has proven effective in identifying the optimal policy scenario for achieving the EU’s RES target by 2030.

The method developed here is based on Fuzzy TOPSIS and adapted to the specific topic of interest here: evaluating alternative policy scenarios to achieve the EU’s 2030 renewable energy target. The overall rankings for all possible alternatives were determined, and ultimately the policy scenario ‘A₅ – Indicative national RES targets with incentives for overcommitment’ was selected as the ideal solution. This policy scenario provides flexibility to MSs to adapt to national circumstances and plans.

Thus, it was proven that indicative targets are more attractive than binding ones, especially to less ambitious MSs. This specific scenario also features incentives for higher commitment such as supercredits that can be applied, for instance, to the amount pledged above the benchmark target, to the amount realised using certain technologies, or to the amount realised in cooperation with other MSs.

The scenario ranked second is ‘A₇ – Binding national RES targets through free pledging’. The binding target creates certainty for investors, lowering the necessary support levels. In addition, this alternative provides a clear division of responsibilities which helps to implement corrective measures in case the target is missed. MSs are free to accept any indicative benchmark suggested by the EU Commission or pledge a higher or lower target, which they have to accept as legally binding.

In contrast, the alternatives ‘A₁ – Binding national RES targets’ and ‘A₃ – Binding regional targets’ were shown to be less effective in achieving the common RES 2030 target. The application of scenario ‘A₁ – Binding national RES targets’ is limited since this top‐down allocation of a binding RES target offers minimum flexibility to MSs, both with regard to sectors (RES vs. other abatement measures) and geographically.

Finally, the ‘A₃ – Binding regional targets’ has limited applicability and is unclear who is held legally responsible in case the regional target is missed. This ambiguity in combination with the fact that powerful and ambitious MSs may be deterred by the idea of taking responsibility for less ambitious MSs results in this alternative being ranked last.

To sum up, the Fuzzy TOPSIS method developed here helps decision-makers to draw conclusions about the effectiveness of alternative strategies aiming to achieve to achieve the EU’s RES 2030 target (i.e. 27% RES share in gross final energy consumption). In this paper, a group of three decision-makers stated their preferences and rated the importance of the four criteria and the performance of the nine alternative policy scenarios. The developed approach provides added value to multiple criteria policy decision-making and can be easily applied to a larger number of DMs as well as to other similar problems.

In order to further improve the decision model, more criteria could be used to perform a more thorough analysis of the available options. Alternatively, instead of increasing the number of criteria to conduct more sensitivity analyses, random combinations of the weights of the performance criteria could ensure more impartial conclusions.

The proposed decision model could trigger a revised set of alternative policy scenarios and criteria for further analysis and planning of appropriate targets. These new policy scenarios could illustrate and capture the perspective of each MS concerning its alignment with RES targets for the period beyond 2030 and towards 2050.

Footnotes

Acknowledgements

The authors wish to thank S Steinhilber, A Held and M Ragwitz for their valuable contributions with regard to identifying alternative policy scenarios to achieve the 2030 European Renewable Energy target, which are presented in Towards2030-dialogue deliverable ‘Identification and qualitative analysis of target setting options’, April 2015. Their work in this respect was invaluable for this research. The contents of the paper are the sole responsibility of its authors and do not necessary reflect the views of the EC. The authors would further like to thank the anonymous reviewers for their helpful comments as well as Gillian Bowman-Köhler for the English check of this paper.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The current paper was primarily based on the research conducted within the framework of the project ‘Dialogue on a RES policy framework for 2030 (Towards2030-dialogue’ (project number: IEE/13/826/SI2.674882), supported by the Intelligent Energy Europe programme.

Note

Aikaterini Papapostolou is an Electrical and Computer Engineer of the National Technical University of Athens (NTUA). She is currently a PhD candidate in the Management & Decision Support Systems Laboratory of School of Electrical and Computer Engineering in the NTUA. Her scientific interests fall into the areas of energy-environmental and climate policy and planning and decision support systems. Her research focuses on the assessment of Renewable Energy Sources (RES) cooperation between Europe and its neighbouring countries using multiple criteria decision support methods. Ms Papapostolou has been involved in a number of research and consultancy projects related to energy efficiency, renewables and sustainable development.

Charikleia Karakosta is a Chemical Engineer and works as a Research Associate at the Management & Decision Support Systems Laboratory of the National Technical University of Athens (NTUA), as well as at the University of Piraeus Research Centre (UPRC). She has participated in several national and EU research and consultancy projects in the fields of energy-environmental and climate policy, energy planning and management, technology transfer and decision support. She holds a PhD in Decision Support Systems for the Promotion of the Effective Technology Transfer within the frame of Climate Change from the School of Electrical and Computer Engineering and MSc in Energy Production and Management by NTUA. She has more 115 scientific publications in international journals with reviewers, announcements in international conferences and chapters in books (SCOPUS h-index 12, 339 citations). For her work, she has received awards by the Alexander S Onassis Public Benefit Foundation, the State Scholarship Foundation (IKY) and the NTUA.

Haris Doukas is an Assistant Professor in the School of Electrical & Computer Engineering, NTUA. Dr Doukas is a mechanical engineer (Aristotle University of Thessaloniki – AUTH, 2003), holding a PhD degree on the decision support systems for the sustainable energy sector’s operation (National Technical University of Athens – NTUA, 2009). His areas of expertise include the development of models and decision support systems for energy and climate policy. In these fields, he has more than 75 scientific publications in international journals and numerous announcements in international conferences, chapters in books etc. For his work, Dr Doukas has received awards by the State Scholarship Foundation (IKY), the NTUA, the AUTH, the Technical Chamber of Greece (TCG) and the Hellenic Operational Research Society (HELORS).

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