Multi-person selection of the best wind turbine based on the multi-criteria integrated additive-multiplicative utility function.
Climate change and global warming are the most critical issues facing the world today (Hessami et al. 2011). World politicians of the highest rank speak that the energy production system is to be changed; otherwise, our planet will face catastrophic consequences. Green energy (wind, sun, water and other resources), which, for some time, has been considered to be only an enthusiastic invention, is getting more and more attractive for big business investments.
The current concerns about climate change relate strongly to past technological developments that have fundamentally changed the structure of the energy sector by making possible the diffusion of new and less costly technologies (Soderholm, Pettersson 2011). The rapid development of wind energy technology has made it to be the most promising alternative to conventional energy systems in recent years (Lee et al. 2009).
Wind energy is presented as one of the strategies for tackling global warming and accomplishing the Kyoto Protocol (Gamboa, Munda 2007). Recently, wind energy has started to be valued as the national wealth of each country just like the resources of organic fuel (oil, gas). These sources of energy, unlike organic fuel, are inexhaustible. Employing them ensures great ecological, social and political advantages, and in the nearest future, will undoubtedly bring economic benefits.
Over the past decade, many countries have invested heavily in wind power, and the current energy policies imply that there is a lot more investment to come in (Green, Vasilakos 2011). Most of the existing wind power plants are constructed on land while some countries (first of all in Europe) have started to invest into developing sea wind power parks. Offshore wind energy generation is the fastest growing source of renewable energy in the world (Singh et al. 2010).
1. Description of offshore wind power turbines
The problems of sustainable energy generation are complicated. Modern technologies should be defined applying a multiple criteria set. The criteria describing alternatives have different measurement units and optimization directions.
Martin et al. (2013) applied the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method for assessing the conceptual design process of floating offshore wind turbine support structures. Collu et al. (2012) investigated the design space of a floating support structure for an offshore vertical axis wind turbine. The alternatives are ranked based on the TOPSIS method. Lozano-Minguez et al. (2011) provided a systemic assessment of the selection of the most preferable, among different configurations, offshore support structures taking into consideration several criteria through TOPSIS for benchmarking candidate options. Lee et al. (2012) presented an integrated MCDM model incorporating Interpretive Structural Modelling (ISM), the Fuzzy Analytic Network Process (FANP) and the VIKOR method. Kaya and Kahraman (2010) applied an integrated fuzzy VIKOR and AHP method to determine the best renewable energy alternative for Istanbul. Van Haaren and Fthenakis (2011) proposed a spatial multi-criteria methodology implemented in New York State, and the results were compared with the locations of the existing wind turbine farms and based on multi-criteria analysis. Khan and Rehman (2012) presented study on the efficient design of wind farms in Saudi Arabia. The conducted analysis has been based on a fuzzy logic decision making approach.
While onshore wind is developing by leaps and bounds, in the meantime, offshore wind has also attracted people's attention in recent years. As generally known, wind energy is clean and inexpensive, but space for turbines is becoming scarce, which makes offshore wind an attractive choice (Leung, Yang 2012).
New investment in the capacity of offshore wind generation has shown a remarkable increase. The total offshore installed capacity in Europe has increased from under 50 MW in 2000 to about 1471MW by the end of 2010 thus translating to an average annual rate of growth in about 50% per year (Green, Vasilakos 2011).
Conducting the research and development of offshore wind power began in the '70s of the last century. After more than 30 years of progress, offshore wind power technology is becoming more and more mature and has entered the stage of large-scale development (Zhixin et al. 2009).
Europe has always been the leader in offshore wind technology. Looking back on the history of offshore wind, it is necessary to mention Denmark that is not only the second highest contributor to offshore wind in Europe but also a pioneer in this field. One should never forget that the United Kingdom is the leader in producing European wind energy.
Despite its growth, the current share of offshore capacity remains relatively low when compared to that operating onshore (only over 2% of total wind capacity for EU-27) (Green, Vasilakos 2011). It is expected that in 2020, European offshore wind power capacity could reach the one-third of electricity demand for Europe) (Zhixin et al. 2009).
Despite many advantages, sea energy production presents plenty of challenges that should be overcome in order to ensure more successful development of sea wind power plants. First of all, the cost of constructing an offshore wind farm is 1.5-2 times greater than that of the onshore one, as towers, foundations, underwater cabling and installation offshore are more difficult and expensive (Offshore Wind Collaborative Organizing 2005). Since the offshore wind farm is far away from the shore, maintenance and repair are also more challenging due to difficulty in accessing the site. What is more, the need for crane vessels in repair makes it 5-10 times more expensive than onshore repair (Van Bussel, Zaaijer 2001).
The operation of wind power plants depends on two most important components: wind turbines and wind. A rotor of a wind turbine consists of blades and a rotor hub. The requirements set for the blades include the maximal diameter of the rotor and the height of its axe as well as aerodynamic efficiency to get as much energy from the wind as possible, low weight, simple production technology, sufficient resistance to mechanical loads and weather impact, durability (Gipe 2004).
Previous investigations have shown that for an efficient wind farm, operation distance between adjacent wind turbines should make 5-10 diameters of the rotor (Maeda et al. 2004). However, in the case of a possibility of positioning wind farms considering wind direction, a distance between wind power plants may be reduced (Markevi?ius et al. 2007).
Wind velocity is the most important parameter for evaluating wind energy resources. Any choice for designing wind turbines must be based on the average wind velocity at the selected site for constructing wind turbines
(Katinas et al. 2009).
The wind and its speed in the industry of wind power plants is the most important feature, because it determines where the wind power park is going to be located, what size it will have to fit and whether it is going to be constructed in this place at all. The amount of energy produced by a wind turbine during a long period of time may be calculated rather precisely because the average wind speed and direction at a certain place change insignificantly.
Regular measurements of wind velocities and directions have been performed in Lithuania since 1945. The measurements are performed typically at a height of 10 m above the ground level every 3 h. All readings are averages over the specified periods of time. Monthly and annual averages are also determined (Katinas et al. 2009).
An onshore wind farm can be typically utilized about 2000-3000 h per year while an offshore farm normally achieves a utilization rate of approximately 30004000 h annually. In addition, the environmental costs of offshore installations are overall lower than those typically experienced at onshore farms (Soderholm, Pettersson 2011).
Offshore winds are less turbulent (because the ocean is flat relative to onshore topography), and they tend to flow at higher speeds than onshore winds thus allowing turbines to produce more electricity. Because the energy produced from the wind is directly proportional to the cube of wind speed, increased wind speeds of only a few miles per hour can produce a significantly larger amount of electricity. For instance, a turbine at a site with an average wind speed of 26 km/h would produce 50% more electricity than that at a site with the same turbine and an average wind speed of 22 km/h (Kurian et al. 2009).
As regards big wind turbines, steel pipes narrowing towards the top are used for the tower, although other structures are also suitable for low power wind turbines.
In general, the support of the wind power plant at sea is influenced by (Structural Engineers Club 2014):
--wave and current loads;
--hydrodynamic and hydrostatic water pressure;
--fluctuations in temperature;
--forces on the top of the body that appear from the movement of the blades;
--other impacts of ships, rust, deposits, etc.
For designing wind power plants, one may not take into consideration some of the loads.
One of the most important features of offshore wind generators are the selection of foundations. The foundations of a tower are different when constructed in the sea and on land. Wind pressure forces act on the wind turbine. For example, if the diameter of the rotor of the wind turbine reaches 100 m, under the wind speed of 25 m/s, the air mass equal to 470 t/s goes through the rotor. The turbine tower itself has to stand wind pressure at wind speed equal to 50 m/s. Therefore, the resistance of the basement must meet high demands.
The price of constructing the basement of the wind power plant and the foundations themselves differ a lot depending on whether they are built in the sea or on land. For a typical onshore wind power station, the cost of foundations normally represents 4-6 percent of the total investment costs (Lemming et al. 2008). Offshore foundations constitute a significant fraction of the overall installed cost that varies between 15% and 40% (Houlsby, Byrne 2000). Higher costs can also be explained by the fact that, so far, no well-developed supply industry for installation work offshore has been offered, and that during recent years, offshore wind power industry has been forced to compete with more established fossil fuel industry for these installation services (Sovacool et al. 2008).
In the case of offshore wind power development, water depth considerably affects the economics of the wind power project when establishing the offshore foundations the type of which is dependent on water depth and soil conditions, etc. (Kim et al. 2013).
The main types of the foundations of wind power plants in the sea are discussed below:
--Gravity base structure (Fig. 1a) foundations are typically used at sites where the installation of piles in the underlying seabed is difficult, such as on a hard rock ledge in relatively shallow waters (Malhotra 2010). The maximum depth achieved applying this system can reach 10 m. Concrete is the only material used for producing it (Singh et al. 2010).
--Monopole (Fig. 1b) covers a simple design and consists of a steel pipe pile (Carey 2002). The diameter varies from 6 to 8 m. (Singh et al. 2010) and wall thickness as much as 150 mm (Carey 2002). Depth achieved by the monopole is in the range of 25 to 30 m. It is a steel tabular structure the manufacturing of which is simple and quick (Singh et al. 2010). Monopoles are flexible (Carey 2002).
--Tripod (Fig. 1c) has a structure that is considered to be relatively lightweight. Under the central steel column, which is below the turbine, there is a steel frame that transfers forces from the tower into three steel piles installed at each leg position to anchor the tripod to the seabed. The three piles are driven 1020 m into the seabed. The tripod can also be installed using suction buckets. The foundations of the tripod have good stability and overall stiffness. The tripod support structure is pre-assembled in an onshore construction yard. The entire structure is placed on a suitable vessel such as a barge and transported to the offshore location where it is slowly lowered onto the seabed ensuring it is entirely level. When the piles are at the required depth, a connection between the top of the pile and the pile sleeve is made by filling the annulus with grout or by means of a swaged connection (Four C Offshore 2013b).
--Jacket structures (Fig. 1d) contain many variants of the three or four-legged jacket/lattice structure typically consisting of corner piles interconnected with bracings with up to 2 m in diameter. These types of structures are considered well suited for sites with water depth ranging from 20 to 50 m. Proponents cite the advantages of the jacket structures and refer to low wave loads in comparison to monopoles (jacket structure is very stiff and the area facing wave movement is smaller than that of monopoles), which makes fabrication expertise is widely available in part due to Offshore Oil and Gas industry supply chain. Others cite disadvantages that embrace high initial construction costs, potentially higher maintenance costs and moderately difficult and expensive transportation (Four C Offshore 2013a).
--Floating platform (Fig. 1e) is the structure that must provide enough buoyancy to support the weight of the turbine and to restrain pitch, wave as well as roll motion within acceptable limits. Therefore, a classification system has been developed and divides all platforms into three general categories based on ballast, mooring lines and buoyancy (Singh et al. 2010).
2. Case study
The existing offshore wind farms offer important advantages for aquaculture plans, especially in terms of a lack of major physical constrains, e.g. navigation routes, submarine cables, marine protected areas. Moreover, enhanced current velocity, due to the presence of the piles and air fluxes of the turbines, may increase the environmental suitability of aquaculture plans in these areas. In addition, the transmission of localized depleted water masses or waste material towards near-shore zones can be avoided, excluding a potential impact close to the coast. On the other hand, other environmental constrains (e.g. temperature and variability of salinity, dissolved oxygen concentrations, phytoplankton dynamics) also need to be considered when planning aquaculture activities (Benassai et al. 2011).
Four alternatives to the development of the wind power park in the Baltic Sea near the Lithuanian coast could be considered. The main technical parameters and requirements as well as the preliminary price are provided in Table 1.
Alternative [A.sub.A] - Nordex N80 2.5 MW Wind Turbine (Clean Technology 2010). Nordex offers the N80 2.5 MW wind turbine. A three-bladed rotor incorporated in the wind turbine measures 80 m in diameter and offers a swept area of 5026 m2. The rotor operates at speeds ranging from 10.8 to 18.9 rpm and its maximum tolerable tip speed may reach 80 m/s.
Alternative [A.sub.B] - Vestas V90 3.0 MW Wind Turbine (Vestas 2013). The V90-3.0 MW[R] is designed to be low weight ensuring easy transportation and installation while reducing foundation costs thanks to its lower load. The nacelle is lighter because its gearbox has an integrated main bearing that eliminates the need for a traditional main shaft.
This turbine delivers exceptional performance, high yield and can be supplied in a variety of hub heights (65105 m) to accommodate site-specific needs. The tower for offshore is designed site-specific and is furthermore protected with a special offshore coating to withstand a harsh environment.
Alternative [A.sub.C] - GE Energy 3.6 MW Wind Turbine (GE Energy 2008). Engineered for high-speed wind sites and harsh marine environment, the 3.6 MW machine features exceptionally robust marine design. The generator and gearbox are supported by elastomeric elements to minimize noise emissions.
Alternative [A.sub.D] - REpower M5 5.0 MW Wind Turbine (Wind Energy Solutions 2013). The REpower 5M has a rated power of 5 megawatt and a rotor of 126 metres in diameter. The 5M is one of the largest and most powerful wind turbines in the world. The 5M sets new standards of the economic viability of wind farms, especially in offshore installations.
In order to proceed with the successful application of multi-criteria analysis, it is essential, on the one hand, to determine and examine an adequate number of criteria that will give a representative and complete picture of investigated alternative scenarios, whereas on the other, to calibrate the criteria that will be examined according to their characteristics (Rousis et al. 2008).
In total, five individual criteria have been selected (Project POWER 2008):
--Nominal power of the wind turbine--depends on the type of the wind power plant to be constructed;
--Max power in the area--the park of power plants may be constructed very widely or vice versa. Each separate wind power plant has the required operation area. This way, we may assess power plants in a certain area;
--Amount of energy per year--how much energy do wind power plants park produce in reality?
--Investments--the price for developing wind power plants, construction from the idea of design to construction and commissioning. This criterion is crucial for constructing a park, since one wind power plant costs several millions, and the park is developed through many years and the total sum usually is very big;
--C[O.sub.2]--This is one of the most important criterions indicating why the park of wind power plants is constructed. The situation may vary in each country. Five possible alternative places for constructing
wind power plants in the Baltic Sea, near the Lithuanian coast (Fig. 2) can be marked. We will choose the most suitable wind power plant for each of such places in accordance with the criteria introduced above.
3. Systemized results
On the basis of the analyzed reports on constructing wind power plants in the sea, the basic calculation data matrices were done, which would help with doing calculations for choosing the type of wind power plants using multi-criteria calculation methods.
The basic details necessary for choosing a type of wind power plants in five construction sites are provided in Tables 2-6 (Project POWER 2008).
4. Determination of criteria weights
The decision has been made using the derived weight w of evaluative criteria (Saaty 1980). The experiments conducted by Saaty shows that most individuals cannot compare more than seven, plus/minus two criteria (Table 7).
The AHP initial pair-wise comparison matrix is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
Also, the consistency index and consistency ratio should be calculated (Saaty 1980).
Ten experts prepared different pair-wise comparison matrixes the examples of which are shown in Table 8.
The weights of the criteria of the fuzzy group have been established and presented in Table 9.
5. Calculation method
A multi-person decision-making problem is defined as a decision situation in which an alternative to the given problem should be chosen. WASPAS method for finding a solution to the problem has been selected. The initial information on the problem has been provided by different people or experts.
Zavadskas et al. (2012) proposed aggregating WSM (Weighted Sum Model) and WPM (Weighted Product Model) methods. WASPAS (Weighted Aggregates Sum Product Assessment) method was developed. The optimization of the weighted aggregated function has been suggested, which allows reaching the highest accuracy of measurement. Zavadskas et al. (2013) used WASPAS and MOORA (Multiple Objective Optimization on the basis of Ratio Analysis) as well as MULTIMOORA (MOORA plus Full Multiplicative Form) methods for the multiple criteria assessment of building designs.
Hashemkhani Zolfani et al. (2013) applied Stepwise Weight Assessment Ratio Analysis (SWARA) and WASPAS methods for evaluating shopping mall sites in Tehran.
Dejus and Antucheviciene (2013) suggested employing Multiple Criteria Decision Making (MCDM) technique for assessing and selecting appropriate solutions to occupational safety and proposed formulating considered alternatives from typical solutions to ensuring their quality and then applying the entropy method for determining relative significance to evaluation criteria. Finally, WASPAS method for ranking alternatives has been used.
Staniunas et al. (2013) referred to multi-criteria decision making method WASPAS and to the scenarios evaluating the modernization of multi-dwelling houses.
Siozinyte and Antucheviciene (2013) presented a model for improving daylight in the reconstructed building and simultaneously analysing the process of saving the features of vernacular architecture, which is based on WASPAS method.
Chakraborty and Zavadskas (2014) explored WASPAS method as an effective MCDM tool while solving eight manufacturing decision making problems. The method has been observed to find out the capability of accurately ranking alternatives in all considered selection problems.
Normally, information can be represented by any of the following three preference structures (Herrera et al. 2001):
--As a preference ordering alternatives. In this case, alternatives are ordered from the best to worst without any other additional information;
--As a utility function. In this case, an expert gives a real valuation (a physical or monetary value) on each alternative, i.e. the function that associates each alternative with a real number. This indicates the performance of that alternative according to that point of view;
--As a preference relation. This is the most usual case because most procedures for decision-making problems are based on a pair comparison in the sense that processes are linked to some degree of the credibility of the preference of any alternative over another.
The description of WASPAS method is presented below.
First, the initial decision-making matrix is formed. Next, a step - initial decision-making matrix is normalized as:
[[bar.x].sub.ij] = [x.sub.ij]/[max.sub.i] [x.sub.ij] (3)
for criteria that must be maximized, and:
[[bar.x].sub.ij] =- [min.sub.i] [x.sub.ij]/[x.sub.ij] (4)
for criteria that must be minimized.
Some multi-criteria utility functions are additive and some are multiplicative. Therefore, a proposal to integrate both additive and multiplicative utility functions to one has been made. For this reason, the applied function is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
[lambda] is used 0.5.
6. Summary of calculations
Following the calculations done employing WASPAS method (Table 10), it has been determined that the best option of assessing the types of wind power plants situated in different possible places of construction is the 4th one, which is Repower M5 5.0 MW Wind Turbine (Fig. 3).
Considering the suggested options, this is the most powerful (5 MW) wind power plant having the biggest rotor of 126 m in diameter and the average height of 100 m.
Due to its modular structure and logistical flexibility, the 5 M is suitable for onshore and offshore installation. The offshore version is specifically designed for withstanding extreme environmental conditions. This includes, for example, the redundancy of key components to guarantee maximum availability, effective protection against corrosion and a permanent monitoring system (Wind energy solutions 2013).
Recently, wind energy has become more and more valued. Although most of the constructed wind power plants have been constructed on land, those erected in the sea are taking the lead nowadays.
The construction sequence of the wind turbine should be as follows: [A.sub.D] [??] [A.sub.C] [??] [A.sub.B] [??] [A.sub.A].
Although investments in the production of wind energy in the sea are much bigger and construction is incomparably more complicated than investments and construction on land, the possibilities of payoff are significantly higher because the wind in the sea is much stronger.
Calculations have been done applying WASPAS method and show that the best type of the wind power plant suitable for all options is REpower M5 5.0 MW Wind Turbine.
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Vygantas BAGOCIUS (a, b), Edmundas Kazimieras ZAVADSKAS (a), Zenonas TURSKIS (a)
(a) Department of Construction Technology and Management, Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania
(b) Civil Engineering Department, Klaipeda University, Bijunu g. 17, 91225 Klaipeda Received 17 Oct 2013; accepted 24 Apr 2014
Corresponding author: Edmundas Kazimieras Zavadskas
Vygantas BAGOCIUS. PhD student at the Department of Construction Technology and Management of Vilnius Gediminas Technical University, Vilnius, Lithuania. Master of Construction Engineering, Kaipeda University, 2010. Research interests: building technologies, construction management, multiple criteria analysis and decision-making theories.
Edmundas Kazimieras ZAVADSKAS. PhD, DSc, h.c.multi. Prof., Head of the Department of Construction Technology and Management at Vilnius Gediminas Technical University, Lithuania. Senior Research Fellow at the Research Institute of Internet and Intelligent Technologies. A member of Lithuanian and several foreign Academies of Sciences. Doctore Honoris Causa from Poznan, Saint-Petersburg and Kiev universities. The Honorary International Chair Professor in the National Taipei University of Technology. A member of international organizations; a member of steering and programme committees at many international conferences; a member of editorial boards of several research journals; the author and co-author of more than 400 papers and a number of monographs in Lithuanian, English, German and Russian. Editor-in-Chief of journals Technological and Economic Development of Economy and Journal of Civil Engineering and Management. Research interests: building technology and management, decision-making theory, automation in design and decision support systems.
Zenonas TURSKIS. Prof. Dr of Technical Sciences, Senior Research Fellow at the Laboratory of Construction Technology and Management, Vilnius Gediminas Technical University. Research interests: building technology and management, decision-making theory, computer-aided automation in design, expert systems.
Table 1. The main parameters of wind power plants Manufacturer Nordex Vestas GE Turbine Model Nordex N80 Vestas V90 GE 3.6 sl Rated Power kW 2500 3000 3600 Rotor Diameter m 80 90 104 Hub Height m 100 105 100 Swept Area [m.sup.2] 5026 6362 8495 Price [euro] 3000000 3600000 4320000 Turbine Area [km.sup.2] 0.448 0.567 0.757 Manufacturer REpower Turbine Model REpower M5 Rated Power 5000 Rotor Diameter 126 Hub Height 100 Swept Area 12469 Price 6000000 Turbine Area 1.111 Table 2. [L.sub.1] alternative [L.sub.1] Manufacturer Nordex Vestas Turbine model Nordex N80 Vestas V90 Rated power MW 2.5 3.0 Max capacity MW 100 96 Net energy [10.sup.3]MWh 356.4 360.2 for sale Capital costs [10.sup.6][euro] 358.969 341.100 C[O.sub.2] 103 t 223.10 225.50 [L.sub.1] Manufacturer GE REpower Turbine model GE 3.6 sl REpower M5 Rated power 3.6 5.0 Max capacity 86.4 80 Net energy 334.0 327.7 for sale Capital costs 314.184 290.447 C[O.sub.2] 209.05 205.13 Table 3. [L.sub.2] alternative [L.sub.2] Manufacturer Nordex Vestas GE Turbine model Nordex N80 Vestas V90 GE 3.6 sl Rated power MW 2.5 3.0 3.6 Max capacity MW 185 174 158.4 Net energy [10.sup.3]MWh 553.2 551.0 515.4 for sale Capital costs [10.sup.6][euro] 466.923 427.553 384.003 C[O.sub.2] 103 t 346.32 344.95 322.61 [L.sub.2] Manufacturer REpower Turbine model REpower M5 Rated power 5.0 Max capacity 150 Net energy 519.3 for sale Capital costs 348.567 C[O.sub.2] 325.06 Table 4. [L.sub.3] alternative [L.sub.3] Manufacturer Nordex Vestas Turbine model Nordex N80 Vestas V90 Rated power MW 2.5 3.0 Max capacity MW 95 90 Net energy for sale [10.sup.3]MWh 310.2 310.1 Capital costs [10.sup.6][euro] 259.662 240.048 C[O.sub.2] [10.sup.3] t 194.2 194.1 [L.sub.3] Manufacturer GE REpower Turbine model GE 3.6 sl REpower M5 Rated power 3.6 5.0 Max capacity 79.2 75 Net energy for sale 280.7 282.4 Capital costs 210.979 192.561 C[O.sub.2] 175.7 176.8 Table 5. [L.sub.4] alternative [L.sub.4] Manufacturer Nordex Vestas GE Turbine model Nordex N80 Vestas V90 GE 3.6 sl Rated power MW 2.5 3 3.6 Max capacity MW 267.5 255 226.8 Net energy [10.sup.3]MWh 753.1 762.7 696.8 for sale Capital costs [10.sup.6][euro] 632.161 582.605 507.556 C[O.sub.2] [10.sup.3] t 471.4 477.5 436.2 [L.sub.4] Manufacturer REpower Turbine model REpower M5 Rated power 5 Max capacity 215 Net energy 703.9 for sale Capital costs 457.27 C[O.sub.2] 440.6 Table 6. [L.sub.5] alternative [L.sub.5] Manufacturer Nordex Vestas GE Turbine model Nordex N80 Vestas V90 GE 3.6 sl Rated power MW 2.5 3 3.6 Max capacity MW 675 639 576 Net energy [10.sup.3]MWh 2438.1 2428.2 2255.7 for sale Capital costs [10.sup.6][euro] 1596.71 1462.0126 1290.07 [CO.sub.2] [10.sup3] t 1526.3 1520 1412.1 [L.sub.5] Manufacturer REpower Turbine model REpower M5 Rated power 5 Max capacity 545 Net energy 2262.1 for sale Capital costs 1160.311 [CO.sub.2] 1416.1 Table 7. Nine-point scale of a pairwise comparison (Saaty 1980) Intensity of Definition importance 1 Criteria i and j are of equal importance 3 Criterion i is moderately more important than criterion j 5 Criterion i is strongly more important than criterion j 7 Criterion i is very strongly or demonstrably more important than criterion j 9 Criterion i is extremely more important than criterion /j 2, 4, 6, 8 Compromise values between two adjacent judgments Reciprocals If activity i has one of the nonzero numbers nonzero assigned to it when compared with activity j, then, j has the reciprocal value when compared with i Table 8. Pair-wise comparisons considering criteria [X.sub.1] [X.sub.2] [X.sub.3] [X.sub.4] [X.sub.5] [X.sub.1] 1 4 0.167 1 6 [X.sub.2] 0.25 1 0.2 0.333 4 [X.sub.3] 6 5 1 1 5 [X.sub.4] 1 3 1 1 6 [X.sub.5] 0.167 0.25 0.2 0.667 1 Products [w.sub.1] [X.sub.1] 1.32 0.195 [X.sub.2] 0.582 0.086 [X.sub.3] 2.724 0.403 [X.sub.4] 1.783 0.264 [X.sub.5] 0.354 0.052 Table 9. Criterion weights Exp. 1 Exp. 2 Exp. 3 Exp. 4 Exp. 5 Exp. 6 [X.sub.1] 0.195 0.261 0.240 0.086 0.171 0.087 [X.sub.2] 0.086 0.207 0.292 0.330 0.271 0.191 [X.sub.3] 0.403 0.089 0.158 0.196 0.194 0.300 [X.sub.4] 0.264 0.390 0.162 0.345 0.207 0.366 [X.sub.5] 0.052 0.054 0.148 0.043 0.158 0.056 Exp. 7 Exp. 8 Exp. 9 Exp. 10 Average [X.sub.1] 0.162 0.088 0.181 0.112 0.158 [X.sub.2] 0.202 0.170 0.154 0.162 0.206 [X.sub.3] 0.343 0.385 0.308 0.394 0.277 [X.sub.4] 0.254 0.304 0.315 0.290 0.290 [X.sub.5] 0.039 0.054 0.043 0.043 0.069 Table 10. Solution results [L.sub.1] [L.sub.2] Alternative Alternative [K.sub.i] Rank [K.sub.i] Rank [A.sub.A] 0.8463 4 0.8311 4 [A.sub.B] 0.8733 3 0.8595 3 [A.sub.C] 0.8816 2 0.8786 2 [A.sub.D] 0.932 1 0.942 1 [L.sub.3] [L.sub.4] Alternative Alternative [K.sub.i] Rank [K.sub.i] Rank [A.sub.A] 0.8278 4 0.8204 4 [A.sub.B] 0.8558 3 0.8525 3 [A.sub.C] 0.868 2 0.9002 2 [A.sub.D] 0.9295 1 0.9359 1 [L.sub.5] Alternative [K.sub.i] Rank [A.sub.A] 0.8246 4 [A.sub.B] 0.8538 3 [A.sub.C] 0.8739 2 [A.sub.D] 0.9386 1
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|Author:||Bagocius, Vygantas; Zavadskas, Edmundas Kazimieras; Turskis, Zenonas|
|Publication:||Journal of Civil Engineering and Management|
|Date:||Aug 1, 2014|
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