![IP relation. Taken from Ref. [5].](https://www.researchgate.net/publication/317418100/figure/fig1/AS:505089795084288@1497434199548/IP-relation-Taken-from-Ref-5_Q320.jpg)
![Output flow. Taken from Ref. [5].](https://www.researchgate.net/publication/317418100/figure/fig2/AS:505089796173824@1497434199626/Output-flow-Taken-from-Ref-5_Q320.jpg)
![Input flow. Ibid 11, Ref. [5].](https://www.researchgate.net/publication/317418100/figure/fig3/AS:505089795923968@1497434199703/Input-flow-Ibid-11-Ref-5_Q320.jpg)
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Chapter 11
Multi-Criteria Decision-Making in the Implementation
of Renewable Energy Sources
Dejan Jovanovic and Ivan Pribicevic
Additional information is available at the end of the chapter
http://dx.doi.org/10.5772/67734
Abstract
The consideration of renewable energy sources as sources for the production of electricity,
demands an approach that would enable an analysis which comprehends various fac-
tors and stakeholders. The Preference Ranking Organization METHod for Enrichment
Evaluations (PROMETHEE), as a mathematical model for multi-criteria decision-making,
is one of the ideal methods used when it is necessary to rank scenarios according to spe-
cic criteria, depending on whom the ranking is applied. This chapter presents various
scenarios whose ranking is done according to dened criteria and weight coecients for
each of the stakeholders. This model recognized and accepted according to the theory of
decision-making could be used as a tool for so-called stakeholder value approach.
Keywords: renewable energy sources, PROMETHEE, the production of electricity,
stakeholder value, multi-criteria decision-making proces, National Renewable Energy
Action Plan (NAPOIE), mini hydros, biomass, wind, solar, geothermal energy
1. Introduction
The basis for this chapter was document which established the goals in usage of renewable
energy sources until 2020 (National Renewable Energy Action Plan of the Republic of Serbia
further on NAPOIE) [2], as well as the manner in which they are to be achieved. In addition,
it has the goal to enhance investments in the eld of renewable energy sources.
‘According to article 20 of the Treaty Establishing Energy Community (further on: UOEnZ),
the Republic of Serbia accepted the obligation to apply European Directives in the eld of
renewable energy sources (further on: OIE) —Directive 2001/77/EC on the promotion of the
use of energy from renewable sources and Directive 2003/30/EC on the promotion of the use
© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
of biofuels and other renewable fuels for transport. Those Directives were gradually replaced
since 2009, and in January 2012 abolished by the new Directive 2009/28/EC of the European
Parliament and the Council of the 23rd of April 2009 on the promotion of the use of energy
from renewable sources, amending and subsequently repealing Directives 2001/77/EC and
2003/30/EC CELEX No. 32009L0028’.1**
2 [3] the Republic of Serbia internationally
2].
Data given in Tables 1 and 2 were used as input data for this chapter.
Types of renewable energy sources taken in consideration in this chapter are as follows:
• Mini hydros (up to 10 MW).
• Wind energy.
• Solar energy.
• Biomass.
• Geothermal energy.
-
get values, that is, the amount of GWh expected to be produced from every renewable energy
-
lowing renewable energy sources: mini hydros, biomass, solar, wind and geothermal energy
(Table 3).
The goal is to verify the ranking sequence of renewable energy sources if only one of the listed
renewable energy sources would be delivering the total expected amount of GWh into the
system and to rank scenarios according to stakeholders3
renewable energy sources is identical for all stakeholders.
On the basis of ranking achieved this way, we may determine which type of renewable energy
source is the priority, depending on the stakeholder, and also whether the participation of all
A multi-criteria analysis will provide a clearly established sequence of renewable energy
sources for the stakeholders, and according to clearly established criteria. This sequence is
important for the establishing of priorities.
Beograd 2013 [2].
the Republic of Albania, Republic of Bulgaria, Bosnia and Herzegovina, Republic of Croatia, Former Yugoslav Republic
of Macedonia, Republic of Montenegro, Romania, Republic of Serbia and United Nations Interim Administration Mis-
R. Edward Freeman. The stakeholder theory is a theory of organizational management and business ethics that ad-
dresses morals and values in managing an organization [1].
Computer Simulation238
Type of renewable energy sources (MW) (GWh) Specic investment
costs* (€/kW)
Price according to planned installed
capacity until 2020 (millions €)
HE (over 10 MW) 250 1108 1819 454.8
MHE (up to 10 MW) 188 592 2795 525.5
Plants powered by wind energy 500 1000 1417 708.5
Plants powered by solar energy 10 13 2500 25.0
Biomass: power plants with combined
production
100 640 4522 452.2
Biogas (manure): power plants with
combined production
30 225 4006 120.2
Geothermal energy 1 7 4115 4.1
Waste 3 18 4147 12.4
Landll gas 10 50 2000 20.0
Total planned capacity 1092 3653 –2322.6
1 Full name “Law on Ratication of the Treaty Establishing Energy Community between the European Community and
the Republic of Albania, Republic of Bulgaria, Bosnia and Herzegovina, Republic of Croatia, Former Yugoslav Republic
of Macedonia, Republic of Montenegro, Romania, Republic of Serbia and United Nations Interim Administration Mission
on Kosovo in compliance with the Resolution 1244 of the UN Security Council” („Službeni glasnik RS”, no. 62/06 [2].
Table 2. Estimated nances for each of the technologies using renewable energy sources in the production of electricity
needed to complete the planned share in energy production from new capacities until 2020 in electric energy sector1.
Type of renewable energy sources (MW) Estimated work
hours (h)
(GWh) (ktoe) Participation (%)
HE (over 10 MW) 250 4430 1108 95 30.3
MHE (up to 10 MW) 188 3150 592 51 16.2
Wind energy 500 2000 1000 86 27.4
Solar energy 10 1300 13 1 0.4
Biomass: power plants with combined
production
100 6400 640 55 17.5
Biogas (manure): power plants with
combined production
30 7500 225 19 6.2
Geothermal energy 1 7000 7 1 0.2
Waste 3 6000 18 2 0.5
Landll gas 10 5000 50 4 1.4
Total planned capacity 1092 – 3653 314 100.0
1 Full name “Law on Ratication of the Treaty Establishing Energy Community between the European Community and
the Republic of Albania, Republic of Bulgaria, Bosnia and Herzegovina, Republic of Croatia, Former Yugoslav Republic
of Macedonia, Republic of Montenegro, Romania, Republic of Serbia and United Nations Interim Administration Mission
on Kosovo in compliance with the Resolution 1244 of the UN Security Council” („Službeni glasnik RS”, no. 62/06 [2].
Table 1. The production of electricity from renewable energy sources from new plants in 20201.
Multi-Criteria Decision-Making in the Implementation of Renewable Energy Sources
http://dx.doi.org/10.5772/67734
239
For solving this type of problems, one of the mathematical models that can be used is the one
developed by Jean-Pierre Brans in 1982, for a multi-criteria decision-making in a group of
alternatives described with several aributes.
2. Theoretical overview of the PROMETHEE
The Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE)4
is part of a group of methods for multi-criteria decision-making within a group of alternatives
described with several aributes, used as criteria. This method enables a comprehensive struc-
turing of quality and quantity criteria of dierent importance into a relation of partial organiza-
tion in a unique result (PROMETHEE II), on the basis of which alternatives can be ranked in
an absolute manner.
We will consider a multi-criteria problem:
Max
{
(
k
1 (a ) , … , k
k (a )
)
|
a ∈ A
}
, (1)
where A is a nite group of activities and ki = 1,…, k are usefulness criteria which should be maxi-
mized or fullled according to the principle ‘bigger is beer’ (this supposition enables a more
simple presentation of the method—in cases when some of the criteria are price criteria, they can
be transformed into usefulness criteria, or we can adjust the proceeding to those criteria as well).
The application of the PROMETHEE is characterized by two steps:
(1) constructing a preference relation within a group of alternatives A,
(2) using this relation to nd an answer to the problem (1.1).
In the rst step, a complex preference relation is formed (in order to stress the fact that this
relation is based on the consideration of more criteria, this relation is called outranking rela-
tion), based on the generalization of the notion of the criteria. A preference index is then dened
and a complex preference relation is obtained, which is shown in a graph representation. The
essence of this step is that the decision maker (stakeholder) must express his preference
4Theoretical overview of the PROMEHTEE method is described in brief according to the “Odlučivanje”, Milutin Čupić,
Milija Suknović, Fakultet organizacionih nauka, Beograd 2010. All general theoretical formulas, functions and graphs
are taken from Ref. [5].
Renewable energy type Mtoe
Hydro 0.80
Solar 0.60
Biomass 2.25
Wind 0.20
Geothermal energy 0.20
Table 3. Available potentials [4].
Computer Simulation240
between two alternatives (action and activity), according to every criterion, on the basis of
PROMETHEE II can be a tool for ‘Management philosophy that regards maximization of the
interests of its all stakeholders (customers, employees, shareholders and the community) as
its highest objective’.
-
maker can apply partial ranking (PROMETHEE I) or absolute ranking (PROMETHEE II) in
the group of alternatives.
In this chapter, the absolute ranking method PROMETHEE II was used.
2.1. PROMETHEE preference relation
Let k
alternatives:
k : A → R (2)
Let us assume that this is a usefulness criterion, that is, that alternatives (scenarios/models)
For every alternative a dA, k(a) a criterion value is calculated according to criterion k. When
two alternatives a, b dA are being compared, the result of that comparison is expressed as
a preference.
With preference function P
P : A × A →
[
0,1
]
(3)
the intensity of preference for alternative a in relation to alternative b is expressed, with the
following interpretation:
P (a, ba and b, that is, there is no preference of a over b,
P (a, b) ≈ 0 marks weak preference of a over b,
P (a, b) ≈ 1 marks strong preference of a over b,
P (a, b) = 1 marks strict preference of a over b.
P(a,b)= P(k(a)k(b))= P(d) (4)
P(dd =
k (ak (b) , if the functions should be maximized, that is, P (a, b) = P (k (ak (b)), that is, dk
(ak (b)) if the criterion is minimized (Table 4).
Multi-Criteria Decision-Making in the Implementation of Renewable Energy Sources
http://dx.doi.org/10.5772/67734
241
2.2. Multi-criteria preference index
Let us assume that the decision maker sets preference function Pi and weight ti; for every cri-
terion ki (i = 1, …,n) of the problem (2.2).
Criterion Denition Graph
Type 1. Common criterion
P(d ) =
{
0,
d = 0
1,
d ≠ 0
Type 2. Quasi criterion
P(d ) =
{
0,
d < m
1,
d ≥ m
Type 3. Criterion with a growing linear preference
P(d ) =
{
d
_
m
, d < m
1,
d ≥ m
Type 4. Linear criterion with an indierence area
P(d ) =
⎧
⎪
⎨
⎪
⎩
0, d ≤ m
1
_
2 , m < d ≤ n
1, d > n
Type 5. Criterion with preference levels
P(d ) =
⎧
⎪
⎨
⎪
⎩
0,
d ≤ m
d − m
_
n − m,
m ≤ d ≤ n
1,
d > n
Type 6. Gauss’ criterion P(d ) = 1 − exp
{
− d
2
_
2 σ
2
}
1Taken from Ref. [5].
Table 4. Types of functions in the application of the PROMETHEE1.
Computer Simulation242
Weight ti is the measure of relative importance of the criterion ki. If all criteria have the same
value for the decision maker, all weights are equal.
Multi-criteria preference index IP is dened as the medium of preference functions Pi:
IP(a, b ) =
∑
i=1
k t
i P
i (a, b )
_________
∑
i=1
k t
i
IP (a,b) represents intensity, that is, the strength of decision maker’s preference for activity a
over activity b, when all criteria are compared at the same time. It varies between values 0 and 1.
P (a, b) ≈ 0 marks weak preference of a over b for all criteria,
P (a, b) ≈ 1 marks strong preference of a over b for all criteria.
This can also be shown in a graph. Between two nodes (two activities) a and b there are two
arches with values IP(a, b) and IP(b, a). This relation is shown in Figure 1. There is no direct
connection between IP(a, b) and IP(b, a).
Output and input ow:
Input and output ows can be dened for every node (shown in Figure 2.)
(a) Output ow is the sum of values of output ows:
T
+ (a ) = ∑
x∈k
IP(a, x )
(b) Input ow is the sum of values of input ows (Figure 3):
T
− (a ) = ∑
x∈k
IP(a, x )
Figure 1. IP relation. Taken from Ref. [5].
Multi-Criteria Decision-Making in the Implementation of Renewable Energy Sources
http://dx.doi.org/10.5772/67734
243
3. Absolute ranking: PROMETHEE II
a PII b (a prefers b) if T(a) > T(b).
-
mentioned mathematical model could be applied. Those comprehend:
Figure 2. ].
Figure 3. ].
Computer Simulation244
• stakeholders
• criteria
• weight coecients
• preference functions (for every criterion)
• suggested models.
Stakeholders considered in ranking are as follows:
• State (DR)
• Potential investors (PI)
• Local community (LZ).
3.1. Criteria
PRMOTHEE needs criteria to be dened, according to whom the ranking will be done.
Criteria used in this study are presented in Table 5.
These 10 criteria can be divided into two categories:
(1) Empirical criteria, based on the data taken from NAPOIE (K1, K2, K3, K5, K9 and K10).
(2) Description criteria (K4, K6, K7 and K8).
Weight coecients are calculated and given in Table 4.
Since each of the stakeholders treats each of those 10 criteria in a dierent manner, it is essen-
tial to dene weight coecients so that every criterion has a weight denition in relation to
the stakeholder. For each of the stakeholders, the criteria were sorted into three categories:
K1 Maximal usage of available potentials
K2 Price according to planned installed capacity
K3 Incentive purchase price
K4 Technology development
K5 Supply safeness, expected work hours
K6 Possibility of combined production of electric and thermal energy
K7 Contribution to local development and welfare
K8 Social acceptability and sustainability of other inuences on the environment
K9 Period of investment return
K10 Installed power
Table 5. Criteria for ranking scenarios.
Multi-Criteria Decision-Making in the Implementation of Renewable Energy Sources
http://dx.doi.org/10.5772/67734
245
• Very important,
• Important,
• Of lile importance.
An assessment of weight coecients was made on that basis, with values for K aributed on
the scale of 1–10, starting from the categorization of the criteria. A representation of weight
coecients is given in Table 6.
Preference functions. A preference function is aributed to every dened criterion. Common
functions according the PROMETHEE are presented in Table 4. For this chapter, the follow-
ing allocation was adopted:
• Type 1. A common function is aributed to K6. Type 1 function is used when there are only
two expected results, and it provides an obvious preference. Because of that it is aributed
to criterion K6, since the combined production of electric and thermal energy is either pos-
sible or impossible.
• Type 3. A growing linear preference function is aributed to K2, K3, K5, K9 and K10. Type
3 function is used when the dierence can be a constant value. The maximum value of dif-
ference is taken as decision threshold (m = dmax)
• Type 4. A function with preference levels is aributed to K1, K4, K7 and K8. Type 4 func-
tion is used for discrete value dierences and their outputs are discrete preferences 0, ½,
1 (m and n are decision thresholds). For criterion K1, assumed decision thresholds are m =
10% dmax, and n = 30% dmax, while for criteria K4, K7, K8 m = 1 and n = 2.
Weight coecient ti∑ti
State
k1; k5; k10 (8 + 9 + 10)/3 = 9 0.1636 Very important: 16.36%
k2; k3; k6; k7; k8 (3 + 4 + 5 + 6 + 7)/5 = 5 0.0909 Important: 9.09%
k4; k9 (1 + 2)/2 = 1.5 0.02727 Of lile importance: 2.72%
Investors
k2; k3; k4; k9 (7 + 8 + 9 + 10)/4 = 8.5 0.154545 Very important: 15.45%
k5; k6; k10 (4 + 5 + 6)/3 = 5 0.0909 Important: 9.09%
k1; k7; k8 (1 + 2 + 3)/3 = 2 0.03636 Of lile importance: 3.63%
Local community
k6; k7; k8 (8 + 9 + 10)/3 = 9 0.1636 Very important: 16.36%
k1; k5 (6 + 7)/2 = 6.5 0.11818 Important: 11.818%
k2; k3; k4; K9; K10 (1 + 2 + 3 + 4 + 5)/5 = 3 0.0545 Of lile importance: 5.45%
Table 6. Calculation of weight coecients.
Computer Simulation246
3.2. Suggested models
The following models (scenarios) were dened (Table 6):
• The rst model (A1) represents allocation A1. This allocation ts the goals planned until
2020 according to NAPOIE.
• The second model (A2) represents allocation A2, in which the needed energy from renew-
able energy sources would be produced in mini hydros.
• The third model (A3) represents allocation A3, in which the needed energy from renewable
energy sources would be produced from biomass.
• The fourth model (A4) represents allocation A4, in which the needed energy from renew-
able energy sources would be produced by the Sun.
• The fth model (A5) represents allocation A5, in which the needed energy from renewable
energy sources would be produced by the wind.
• The sixth model (A6) represents allocation A6, in which the needed energy from renewable
energy sources would be produced from geothermal potentials.
N.B.: It is VERY important to point out here that, according to available potentials, as shown
in Table 7 (data taken from the document ‘Politika Republike Srbije u oblasti OIE’), each of the
renewable energy sources listed (mini hydros, biomass, solar, wind and geothermal energy)
can deliver 2252 GWh of energy independently (Table 8 presents coneversion of available
resources presented in Table 7 from Mtoe to GWh), which represents the remainder from the
total of 3360 GWh, diminished by the amount delivered by hydro potentials >10 MW. The rst
model A1 of this chapter was given illustratively as the goal which was set to be reached and
will be used in further researches as a continuation of this chapter.
Scenaria are treated according to the dened criteria. Values of criteria for each scenaria are
calculated and presetned in Table 9.
A1 A2 A3 A4 A5 A6
GWh GWh GWh GWh GWh GWh
Hydro potential
>10 MW 1108 1108 1108 1108 1108 1108
<10 MW 592 2252 0000
Biomass 640 02252 000
Solar 13 0 0 2252 0 0
Wind 1000 0 0 0 2252 0
Geothermal 700002252
Total 3360
Table 7. Scenarios A1–A6.
Multi-Criteria Decision-Making in the Implementation of Renewable Energy Sources
http://dx.doi.org/10.5772/67734
247
4. Mathematical model
Criterion K4: Technology development
Technologies in laboratory and research phases (laboratory) 1
Technologies in pilot programs (pilot) 2
Technologies demanding further improvements to enhance their eciency (further
improvement)
3
Commercially ready technologies with a reliable place in the overall local market (com_loc) 4
Commercially ready technologies with a reliable place in the supranational and European
market (com_EU)
5
Criterion K7: Contribution to local development
Without any inuence on local economy (none) 1
Weak inuence on local economy(weak) 2
Moderate inuence on local economy (only a small number of permanent workplaces)
(moderate)
3
Moderate to large inuence on local economy (opening new workplaces and chains of
companies in energy production sector)
4
Very large inuence on local economy (strong incentive to local growth, creation of small
industrial regions on wider areas)
5
Type of renewable energy sources Mtoe GWh
Hydro 0.8 9304
Biomass 2.25 26,167
Solar 0.6 6978
Wind 0.2 2326
Geothermal energy 0.2 2326
Table 8. Available potentials of renewable energy sources.
K1 (%) K2 (€) K3 K4 K5 K6 K7 K8 K9 K10
A1 PLAN 43.00 1,356,627,968 9.87 4 3564 1 3 4 6.1 799
A2 Hydro potential <10 MW 24.20 1,998,203,175 9.89 5 3150 0 2 4 9.0 715
A3 Biomass 8.61 1,591,178,750 10.74 4 6400 1 4 4 6.6 352
A4 Solar 32.27 4,330,769,231 18.45 3 1300 0 1 3 10.4 1732
A5 Wind 96.82 1,595,542,000 9.20 4 2000 0 1 3 7.7 1126
A6 Geothermal 96.82 1,323,854,286 8.30 4 7000 1 2 57.1 322
Table 9. Scenarios according to K criteria values.
Computer Simulation248
Criterion K8: social acceptability and sustainability of other inuences on the environment
Most inhabitants are against any installations, regardless of their surroundings (no) 1
Inhabitants’ opinion is split (split) 2
Most inhabitants accept installations, since they are far from inhabited areas and have no visible
damaging eects (vis-res)
3
Most inhabitants accept installations, since they are far from inhabited areas, regardless of
whether there is a visual contact (res)
4
Most inhabitants are pro installations (OK) 5
Mathematical model representation for the state as a stakeholder
State Min Min Min Max Max Max Max Max Min Max
K1% K2 € K3 K4 K5 K6 K7 K8 K9 K10
A2 Hydro potential
<10 MW
0.2420 1,998,203,175 9.89 5 3150 0 2 4 9.0 715
A3 Biomass 0.0861 1,591,178,750 10.74 4 6400 1 4 4 6.6 352
A4 Solar 0.3227 4,330,769,231 18.45 3 1300 0 1 3 10.4 1732
A5 Wind 0.9682 1,595,542,000 9.20 4 2000 0 1 3 7.7 1126
A6 Geothermal 0.9682 1,323,854,286 8.30 4 7000 1 2 57.1 322
d(a2,ai)Hydro potential
<10 MW
Dierentiation d: dierence between scenario a2 and other suggested scenarios
0.0000 0 0.00 0 0 0 0 0 0.0 0
Biomass −0.1559 −407,024,425 0.85 1−3250 −1 −2 0−2.4 363
Solar 0.0807 233,266,056 8.56 21850 0 1 1 1.4 −1017
Wind 0.7262 −402,661,175 −0.69 11150 011−1.3 −411
Geothermal 0.7262 −674,348,889 −1.60 1−3850 −1 0−1 −1.9 393
P(a2,ai)Hydro potential
<10 MW
Preference function P: scenario a2 versus other suggested scenarios
0 0 0 0 0 0 0 0 0 0
a3 Biomass 0 0 0.099299 0.5 0 0 0 0 0 0.923
a4 Solar 0 1 1 1 1 0 0.5 0.5 1 0
a5Wind 1 0 0 0.5 0.62 00.5 0.5 0 0
a6Geothermal 1 0 0 0.5 0 0 0 0 0 1
Ti 0.1636 0.0909 0.0909 0.02727 0.1636 0.0909 0.0909 0.0909 0.02727 0.1636
d(a3,ai)Hydro potential
<10 MW
Dierentiation d: dierence between scenario a3 and other suggested scenarios
0.1559 407,024,425 −0.85 −1 3250 1 2 0 2.4 −363
Biomass 0.0000 0 0.00 0 0 0 0 0 0.0 0
Solar 0.2366 2,739,590,481 7.71 1 5100 1 3 1 3.8 −1380
Multi-Criteria Decision-Making in the Implementation of Renewable Energy Sources
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d(a3,ai)Hydro potential
<10 MW
Dierentiation d: dierence between scenario a3 and other suggested scenarios
0.1559 407,024,425 −0.85 −1 3250 1 2 0 2.4 −363
Wind 0.8821 4,363,250 −1.54 0 4400 1 3 1 1.1 −774
Geothermal 0.8821 −267,324,464 −2.45 0−600 0 2 −1 0.5 30
P(a3,ai)Hydro potential
<10 MW
Preference function P: scenario a3 versus other suggested scenarios
0.5 0.148 0 0 0.637 1 1 0 0.63 0
a3 Biomass 0 0 0 0 0 0 0 0 0 0
a4 Solar 0.5 1 1 0.5 1 1 1 0.5 1 0
a5Wind 1 0.0016 0 0 0.862 1 1 0.5 0.289 0
a6Geothermal 1 0 0 0 0 0 1 0 0.131 1
ti 0.1636 0.0909 0.0909 0.02727 0.1636 0.0909 0.0909 0.0909 0.02727 0.1636
d(a4,ai)Hydro
potential<10 MW
Dierentiation d: dierence between scenario a4 and other suggested scenarios
−0.0807 −2,332,566,056 −8.56 −2 −1850 0−1 −1 −1.4 1017
Biomass −0.2366 −2,739,590,481 −7.71 −1 −5100 −1 −3 −1 −3.8 1380
Solar 0.0000 0 0.00 0 0 0 0 0 0.0 0
Wind 0.6455 −2,735,227,231 −9.25 −1 −700 0 0 0 −2.7 606
Geothermal 0.6455 −3,006,914,945 −10.16 −1 −5700 −1 −1 −2 −3.3 1410
P(a4,ai)Hydro potential
<10 MW
Preference function P: scenario a4 versus other suggested scenarios
0 0 0 0 0 0 0 0 0 0.721
a3 Biomass 0 0 0 0 0 0 0 0 0 0.978
a4 Solar 0 0 0 0 0 0 0 0 0 0
a5Wind 1 0 0 0 0 0 0 0 0 0.43
a6Geothermal 1t 0 0 0 0 0 0 0 0 1
ti 0.1636 0.0909 0.0909 0.02727 0.1636 0.0909 0.0909 0.0909 0.02727 0.1636
d(a5,ai)Hydro potential
<10 MW
Dierentiation d: dierence between scenario a5 and other suggested scenarios
−0.7262 402,661,175 0.69 −1 −1150 0−1 −1 1.3 411
Biomass −0.8821 −4,363,250 1.54 0−4400 −1 −3 −1 −1.1 774
Solar −0.6455 2,735,227,231 9.25 1 700 0 0 0 2.7 −606
Wind 0.0000 0 0.00 0 0 0 0 0 0.0 0
Geothermal 0.0000 −271,687,714 −0.90 0−5000 −1 −1 −2 −0.6 804
Computer Simulation250
P(a3,ai)Hydro potential
<10 MW
Preference function P – scenario a5 versus other suggested scenarios
0 0.147 0.075 0 0 0 0 0 0.481 0.51 a3
Biomass 0 0 0.166 0 0 0 0 0 0 0.962 a4 Solar
0 1 1 0.5 1 0 0 0 1 0 a5Wind 0
0 0 0 0 0 0 0 0 0 a6Geothermal 0 0
0 0 0 0 0 0 0 1 ti 0.1636 0.0909 0.0909
0.02727 0.1636 0.0909 0.0909 0.0909 0.02727 0.1636
d(a6,ai)Hydro potential
<10 MW
Dierentiation d – dierence between scenario a6 and other suggested scenarios
−0.7262 674,348,889 1.60 −1 3850 1 0 1 1.9 −393
Biomass −0.8821 267,324,464 2.45 0600 0−2 1−0.5 −30
Solar −0.6455 3,006,914,945 10.16 15700 1 1 2 3.3 −1410
Wind 0.0000 271,687,714 0.90 0 5000 1 1 2 0.6 −804
Geothermal 0.0000 0 0.00 0 0 0 0 0 0.0 0
P(a6,ai)Hydro potential
<10 MW
Preference function P – scenario a6 versus other suggested scenarios
0 0.224 0.157 00.675 1 0 0.5 0.576 0
a3 Biomass 0 0.089 0.241 0 0.105 0 0 0.5 0 0
a4 Solar 0 1 1 0.5 110.5 1 1 0
a5Wind 0 0.09 0.088 0 0.877 1 0.5 1 0.182 0
a6Geothermal 0 0 0 0 0 0 0 0 0 0
ti 0.1636 0.0909 0.0909 0.02727 0.1636 0.0909 0.0909 0.0909 0.02727 0.1636
IP(a2,a3) IP(a2,a4) IP(a2,a5) IP(a2,a6)
0.1736 0.49084 0.369567 0.340835
IP(a3,a2) IP(a3,a4) IP(a3,a5) IP(a3,a6)
0.398447 0.695355 0.5399 0.421672
IP(a4,a2) IP(a4,a3) IP(a4,a5) IP(a4,a6)
0.117956 0.160001 0.233948 0.3272
IP(a5, a2) IP(a5,a3) IP(a5,a4) IP(a5,a6)
0.116733 0.172473 0.386305 0.1636
IP(a6,a2) IP(a6,a3) IP(a6,a4) IP(a6,a5)
0.29712 0.92625 0.613555 0.391871
N.B.: IP = (ai,as), i,s = 2,3,4,5,6; IP = ∑tjPj(ai,as).
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a2a3a4a5a6 T+ T
a2 0 0.1736 0.49084 0.369567 0.340835 0.343711 0.111147
a3 0.398447 0 0.695355 0.5399 0.421672 0.513844 0.364169
a40.117956 0.160001 0 0.233948 0.3272 0.209776 −0.33674
a5 0.116733 0.172473 0.386305 00.1636 0.209778 −0.17404
a60.29712 0.092625 0.613555 0.391871 0 0.348793 0.035466
T− 0.232564 0.149675 0.546514 0.383822 0.313327
The results for State are shown in Figure 4.
The same approach could be usd for detailed calculation for the investors and local commu-
nity as stakeholders.
For the investors as stakeholders:
Determination of preference index
IP(a2,a3) IP(a2,a4) IP(a2,a5) IP(a2,a6)
0.1611 0.590895 0.272998 0.359078
IP(a3,a2) IP(a3,a4) IP(a3,a5) IP(a3,a6)
0.377197 0.640883 0.402209 0.33841
IP(a4,a2) IP(a4,a3) IP(a4,a5) IP(a4,a6)
0.195746 0.206178 0.21615 0.281805
IP(a5,a2) IP(a5,a3) IP(a5,a4) IP(a5,a6)
0.143413 0.087446 0.477263 0.245445
IP(a6,a2) IP(a6,a3) IP(a6,a4) IP(a6,a5)
0.294074 0.041479 0.622703 0.267196
N.B.: IP = (ai, as), i, s = 2,3,4,5,6; IP= ∑tjPj(ai,as).
a2a3a4a5a6 T+ T
a2 0 0.1611 0.590895 0.272998 0.359078 0.346018 0.09341
a3 0.377197 0 0.640883 0.402209 0.33841 0.439675 0.315624
a40.195746 0.206178 00.21615 0.281805 0.22497 −0.35797
a50.143413 0.087446 0.477263 00.245445 0.238392 −0.05125
Figure 4. Chart representation of ranking results for the state as a stakeholder.
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a2a3a4a5a6 T+ T
a60.294074 0.041479 0.622703 0.267196 00.306363 0.000179
T- 0.2526075 0.124051 0.582936 0.289638 0.306185
The reuslts for investors are shown in Figure 5.
For the local community as a stakeholder:
Determination of preference index
IP(a2,a3) IP(a2,a4) IP(a2,a5) IP(a2,a6)
0.082911 0.393418 0.316357 0.19993
IP(a3,a2) IP(a3,a4) IP(a3,a5) IP(a3,a6)
0.436219 0.670658 0.553205 0.34342
IP(a4,a2) IP(a4,a3) IP(a4,a5) IP(a4,a6)
0.039295 0.053301 0.141615 0.17268
IP(a5,a2) IP(a5,a3) IP(a5,a4) IP(a5,a6)
0.066109 0.061476 0.202568 0.0545
IP(a6,a2) IP(a6,a3) IP(a6,a4) IP(a6,a5)
0.305534 0.10103 0.611568 0.438984
IP = (ai, as), i,s = 2,3,4,5,6; IP= ∑tjPj(ai, as).
a2a3a4a5a6 T+ T
a2 0 0.082911 0.393418 0.316357 0.19993 0.248154 0.036365
a30.436219 00.670658 0.553205 0.34342 0.500876 0.426196
a40.039295 0.053301 00.141615 0.17268 0.101723 −0.36783
a5 0.066109 0.061476 0.202568 00.0545 0.096163 −0.26638
a6 0.305534 0.10103 0.611568 0.438984 0 0.364279 0.171647
T− 0.211789 0.0746795 0.469553 0.36254 0.192633
The results for community are shown in Figure 6.
Figure 6. Chart representation of ranking results for the local community as a stakeholder.
Figure 5. Chart representation of ranking results for the investors as stakeholders.
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5. Chart representation of results
After applying the PROMETHEE, as a tool for stakeholder value approach, and after the rank-
ing, we can reach following conclusions on the basis of results obtained:
The results obtained and shown in the charts indicate, in fact, that, according to dened cri-
teria and weight coecients, the sequence of types of renewable energy sources is absolutely
identical regardless of the stakeholder. The sequence of priorities in the application of renew-
able energy sources for the production of electricity goes as follows:
(1) Biomass
(2) Mini hydros
(3) Geothermal
(4) Wind energy
(5) Solar energy
Further activities of all stakeholders should be given to mini hydros and biomass, since they
have the best relation toward the aforementioned criteria.
According to presented model, potentials of all the mentioned types of renewable energy
sources are capable for achieving its goals, with the limitation that wind and geothermal
energy would have, according to such a premise, a 96.82% usage, which is not a convenient
circumstance, while biomass would have an 8.61% usage and mini hydros 24.20%.
The general conclusion is that the state as a stakeholder should focus its activities regarding
the production of electricity from renewable energy sources on biomass and mini hydros,
since, according to listed hypotheses, dened criteria and the application of the mathematical
model, they proved to be the best solution. The same goes for investors and local community
as stakeholders.
Methodology use in this chapter is taken into account the criteria and stakeholders which
where possible to use according to the ocial available data. The nal number of stakolders
and criteria are endless and just make calculation model more comprehensive.
Author details
Dejan Jovanovic1* and Ivan Pribicevic2
*Address all correspondence to: deki.jovanovic@gmail.com
1 JP Zavod za udzbenike, Belgrade, Serbia
2 TMS CEE d.o.o Beograd, Belgrade, Serbia
Computer Simulation254
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