Selection of the technologically most appropriate variant of the solar photovoltaic (PV) water supply system by using multicriteria methods PROMETHEE and GAIA
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Abstract
Nowadays, technical directors, operative engineers and managers in utility companies often meet with many variants of various types of water supply systems. Such a task is becoming complicated if solar photovoltaic (PV) energy is used as an energy source, due to its stochastic nature. This paper will present the use of the multicriteria methods PROMETHEE and GAIA for the case of technological criteria. The aim of the paper is finding a technologically most appropriate variant of the observed urban water supply system (UWSS), given that the resulting solution differs according to the size of certain parts. It should be noted that the observed UWSS consists of PV generator and inverter (subsystem PV), pump station (subsystem PS) and water reservoir (subsystem W). In addition, this paper explains the scientifically innovative and applicable methodology for sizing the UWSS driven by PV energy.
Keywords
Water supply Solar photovoltaic energy Variant PROMETHEE GAIAIntroduction
The usage of solar photovoltaic (PV) energy has special importance, not only in urban water supply systems, but also for the entire human population in the world when it comes to the distribution of energy from renewable sources in hardtoreach places (or remote areas). If a location has a sufficient quantity of water, it should be noted that electricity supply for its abstraction, further distribution and use can be a problem. PV energy is particularly suitable for energy supply for water supply systems in rural areas because there are locations where classical power network is not available or has limited availability. In this situation, especially in remote areas and on islands, PV energy solves this energy and water distribution problem. In doing so, the emphasis is not only on the use of PV energy, but also on improving the performance of pumping stations and reservoirs, as well as the remaining parts of the water supply system (for the most part that refers to pipelines). Nowadays, in addition to meeting the technological and economic criteria, it is necessary to meet other criteria, such as environmental, social, political and other. Among other procedures, multicriteria methods are used for the solution of such issues. In this case, multicriteria methods, i.e., PROMETHEE and GAIA methods, will be used only for technological criteria, due to the aim and scope of this paper.
Subsystem PV turns solar energy from the sun into electrical energy E_{el,PV} in the subsystem PV, which is used for water pumping into the water reservoir overcoming geodetic height H_{g}, i.e., manometric height H_{PS}. Solar energy is of stochastic nature in view of intensity and duration. Therefore, the role of water reservoir as a reservoir of water, i.e., energy, in conjunction with possible electric energy production from the subsystem PV, is crucial in providing the continuity and safety of water supply. Therefore, the system must be appropriately planned and sized, i.e., the methodology described in this paper must be applied. Given the scope and purpose of this paper, the detailed procedures and terms for dimensioning individual parts of the system will not be explained, but they can be found in Ðurin and Margeta (2014) and Ðurin (2014).
Methodology
Definition of the critical period method (CPM)
The difference between the previous ways of sizing of the water supply systems using the critical period method (CPM) is that instead of one critical period which relates to the maximum daily consumption of water, the CPM considers three critical periods. In the case of using PV energy for urban water supply system (UWSS), these critical periods are: critical period for sizing the subsystem PV (PV generator and inverter) \(t_{{{\text{Pel}}(i)}}^{*}\), critical period for sizing the subsystem PS (pumping station) \(t_{{{\text{PS}}(i)}}^{*}\) and critical period for sizing the subsystem W (water reservoir) \(t_{{{\text{W}}(i)}}^{*}\) (Ðurin 2014). This provides security and reliability of the operation of each subsystem, since the sizing is performed with respect to the critical period/periods of each subsystem. In so doing, CPM produces operating integrity and technological reliability of such type of the UWSS. In other words, if critical period(s), i.e., day (days), for every subsystem are satisfied with regards to the required power of PV system, the pump station capacity and power, and water reservoir volume, will also be satisfied in all other days in the years. As a matter of fact, there will be surplus of the produced energy, but this comes in favor with providing the technologic reliability of the system.
It is understood that adequate PV subsystem power P_{el,PV} is provided, with respect to the corresponding critical period \(t_{{{\text{Pel}}(i)}}^{*}\). Thus, in accordance with the rules of the profession, the capacity of the pumping station is determined that can pump the required quantity of water Q_{hour(t)} (m^{3}/h), which in fact represents the highest flow per hour during a typical year in the planning period.
Each of the three critical periods is determined with regard to a certain balancing period (periods) t_{b}, i.e., equalization periods of the required and pumped water or equalization periods of the required and produced energy. The shortest possible balancing period t_{b} is 1 day. When the balancing period t_{b} is longer, the solution is in principle safer, because longer balancing period reduces the impact of extreme low insolation E_{s} on the required power of the subsystem PV, P_{el,PV}. In addition, the system is more efficient with regard to the possibility of using solar radiation, since the sum of the total available solar insolation is greater when t_{b} is longer, because it eliminates the impact of extreme maximum individual daily duration and intensity of solar radiation. Also, possible failures, energy lacks or other interruptions are being diminished by extension of the balancing period. Therefore, the solution is safer and more rational in view of sizing the subsystem PV. This means that the required water amount can be pumped with a lower installed power of the subsystem PV, Ðurin and Margeta (2014).
Multicriteria methods PROMETHEE
The family of PROMETHEE methods were developed by Brans and Vincke (1985) to help a decisionmaker rank partially (PROMETHEE I) or completely (PROMETHEE II) a finite number of options which are evaluated on a common set of noncommensurable multiple criteria (Mutikanga et al. 2011). PROMETHEE is an outranking method for a finite set of alternative actions to be ranked and selected among criteria which are often conflicting. PROMETHEE is also a quite simple ranking method in conception and application compared to the other methods for multicriteria analysis (Brans et al. 1986). Alternatives are evaluated according to different criteria, which have to be maximized or minimized. Determination of the weights is an important step in most multicriteria methods. It is assumed that the decisionmaker is able to weigh the criteria appropriately, at least when the number of criteria is not too large (Macharis et al. 2004). For each criterion, the preference function translates the difference between the evaluations obtained by two alternatives into a preference degree ranging from zero to one. The alternatives evaluated will be generated as a function of the balancing period length (number of days) t_{b}.
 Output flow:$$\varPhi^{ + } (a) = \frac{1}{n  1}\sum\limits_{x \in A} \prod (a,x).$$(4)
 Input flow:$$\varPhi^{  } (a) = \frac{1}{n  1}\sum\limits_{x \in A} \prod (x,a).$$(5)

a has a higher rank than b (aP(2)b) if Φ(a) > Φ(b);

a is indifferent to b (aI(2)b) if Φ(a) = Φ(b).
The PROMETHEE II defines the complete relation where all the action from A are fully ranked, noting that in this relation part of information is lost, due to the balancing effects between the output and the input flow, which results in a higher degree of abstraction (Mladineo 2009).
Multicriteria methods GAIA
Method Geometrical Analysis for Interactive Aid (GAIA) gives a geometric presentation of the results of PROMETHEE method, or methods PROMETHEE I and PROMETHEE II. The idea underlying this method is the reduction in a multidimensional problem to a twodimensional one to enable planar presentation. The dimension of multicriteria analysis is determined by the number of criteria (each criterion determines one of the vectors in such space), and if a geometric presentation is desired, the problem should be reduced to a twodimensional image (a possible threedimensional image would be confusing). In this reduction in dimension, a loss of information regarding the problem is inevitable. To minimize this loss as much as possible, the plane in which the geometrical presentation is given is determined by the two largest values typical for covariance matrix. GAIA provides data on the percentage of information given by such presentation. With the exception of an extremely unfavorable problem structure, the geometric presentation provides sufficiently high percentage of information for analyzing the problem. It is also possible to connect GAIA method with the method PROMETHEE II. PROMETHEE II requires that a certain weight W_{j} be allocated to each criterion and that the complete order in set A be defined. The weights can also be displayed in the (u, v) plane by using the socalled decision vectors which are aimed toward the highest ranking activities. In this way, by interactive changing of weights, it is possible to observe changes in rank, acquired by the method PROMETHEE II (Mladineo 2009). The importance of the decisionmaking criteria is geometrically represented with the vector length π, so that dominant criteria correspond to the vectors of greater absolute values. Summing the vectors that present the criteria leads to a summary vector whose direction and value describe the resulting action of the criteria. If the summary vector of criteria is of small absolute value in relation to the summary vector of another individual criterion, this indicates the conflict of criteria. It can be concluded that geometrical presentation of multicriteria analysis is a very powerful “tool” and provides substantial assistance with problems characterized by partially or totally conflicting criteria, which is unfortunately frequent in the decisionmaking processes (Mladineo 2009).

The longer a criterion axis in the GAIA plane, the more discriminating this criterion.

Criteria expressing similar preferences are represented by axes oriented in approximately the same direction.

Criteria expressing conflicting preferences are oriented in opposite directions.

Criteria that are not related to each other in terms of preferences are represented by orthogonal axes.

Similar alternatives are represented by points located close to each other.

Alternatives being good on a particular criterion are represented by points located in the direction of the corresponding criterion axis.
Case study
Obtained results and discussion
Length of balancing period in accordance with critical days
Balancing period t_{b} (days)  1  2  3  4  5 

Critical periods (days in year) \(t_{{{\text{Pel}}(i)}}^{*}\)  352  344–345  344–346  349–352  348–352 
Critical periods (days in year) \(t_{{{\text{W}}(i)}}^{*}\)  244  244–245  243–245  243–246  242–246 
Critical period (days in year) \(t_{{{\text{PS}}(i)}}^{*}\)  352  344–345  344–346  344–347  343–347 
Sizes of subsystems for different balancing periods
Balancing periods t_{b} (days)  Power \(P_{\text{el,PV}}^{*}\) (kW)  Volume \(V_{{}}^{*}\) (m^{3})  Power \(P_{\text{PS}}^{*}\) (kW) 

1  512.50  1100  106.00 
2  477.82  1178  119.47 
3  443.87  1271  111.39 
4  419.80  1415  105.10 
5  403.45  1513  99.71 
Results obtained by using the method PROMETHEE
Variant  Φ  Φ +  Φ − 

t_{b}= 2  0.2531  0.4304  0.1773 
t_{b}= 3  0.0066  0.2204  0.2138 
t_{b}= 1  − 0.0618  0.2764  0.3383 
t_{b}= 4  − 0.0655  0.2114  0.2769 
t_{b}= 5  − 0.1323  0.2547  0.3871 
It can be seen that Variant 2 (t_{b} = 2 days) is the most favorable given the value of the indicators, followed by variants 3, 1, 4 and 5. Variant 2 significantly stands out compared to the remaining variants, so that based on the above said, it is technologically the most appropriate variant.
Sensitivity analysis regarding impact of the change of criteria weights with ranks of the variants regarding balancing periods, with full rank due to Φ
w_{Pel,PV} = 0.5  w_{W} = 0.25  w_{PS} = 0.25  w_{Pel,PV} = 0.25  w_{W} = 0.5  w_{PS} = 0.25  w_{Pel,PV} = 0.25  w_{W} = 0.25  w_{PS} = 0.5 

Weights combinations for the w_{Pel,PV}, w_{W} and w_{PS}  
t_{b} = 2; Φ= 0.2731  t_{b} = 5; Φ = 0.0918  t_{b} = 2; Φ = 0.4078  
t_{b} = 1; Φ= 0.1298  t_{b} = 2; Φ = 0.0783  t_{b} = 3; Φ = 0.0711  
t_{b} = 3; Φ = − 0.0325  t_{b} = 4; Φ = 0.0671  t_{b} = 1; Φ = − 0.0969  
t_{b} = 4; Φ= − 0.1444  t_{b} = 3; Φ = − 0.0188  t_{b} = 4; Φ = − 0.1191  
t_{b} = 5; Φ = − 0.2259  t_{b} = 1; Φ = − 0.2185  t_{b} = 5; Φ = − 0.2629 
The importance of the particular part of the subsystems was graded with size equal to 0.5, while the other two subsystems were graded by 0.25. Comparing with results from Table 3, i.e., with equal weights for all subsystems, it can be concluded that water reservoir has the biggest changes in order of particular alternatives, while for PV generator and inverter power and pump station power changes are not so drastic. Moreover, variant t_{b} = 2 is the best ranked for the other two mentioned subsystems (PV generator and inverter power and pump station power), despite changing of the weights.
Conclusions
Technological reliability of the water supply system, which is driven by solar photovoltaic energy, is provided by the application of critical period method and by taking into account that water reservoir is not only water storage, but also energy storage by the connection with PV generator. Sensitivity analysis has shown that the size of the water reservoir has important impact on the choice of the technologically reliable variant of the observed urban water supply system (UWSS). In other words, bigger size means bigger reliability of the UWSS. Possible failures, stochastic nature of insolation, energy lacks and other interruptions of the water supply which may appear are compensated with water reservoir. The safety of energy inflow, i.e., electric energy, may be raised by covering with energy from the existing electric grid, especially in the socalled peak period of the day (in the morning, noon and evening) and year (during summer/touristic season). It should be noted that every water supply system has internal source of energy, which could be used for this purpose. This can be implied by putting small hydropower turbines into the pipelines.
The paper shows that the issue of selecting the technologically most appropriate variant of the water supply systems, taking into consideration a number of criteria, can only be solved by using multicriteria methods PROMETHEE and GAIA. In any case, further research requires a more detailed and complex analysis of the problem. This includes the use of other multicriteria methods, expansion of input criteria, sensitivity analysis of the change in importance/weight of individual parameters and engaging a large number of experts from different fields in the expert group that defines and analyzes the multicriteria analysis. Sensitivity analysis warns that multicriteria analysis, even for the technological criteria respecting certain weights and through them importance of the particular criteria, is an assignment which requires great attention when defining. The presented terminology could be applied for the conventional water supply systems and also for water supply systems driven by other renewable energy sources, i.e., wind, biomass, etc.
Notes
References
 Brans JP, Vincke P (1985) A preference ranking organisation method: (the PROMETHEE method for multiple criteria decisionmaking). Manag Sci 31(6):647–656CrossRefGoogle Scholar
 Brans JP, Vincke Ph, Mareschal B (1986) How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 24(2):228–238CrossRefGoogle Scholar
 District of Columbia Water and Sewer Authority—About Drinking Water Quality in Washington, DC, USA. http://www.dcwater.com/drinking_water/about.cfm. Accessed on 10 Dec 2013
 Đurin B (2014) Sustainability of the urban water supply system operating. Ph.D. thesis (on Croatian), Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, CroatiaGoogle Scholar
 Đurin B, Margeta J (2014) Analysis of the possible use of solar photovoltaic energy in urban water supply systems. Water 6:1546–1561CrossRefGoogle Scholar
 Macharis C, Springael J, de Brucker K, Verbeke A (2004) PROMETHEE and AHP: the design of operational synergies in multi criteria analysis. Strengthening PROMETHEE with ideas of AHP. Eur J Oper Res 153:307–317CrossRefGoogle Scholar
 Mareschal B (2014) Manual for visual PROMETHEE academic edition 1.4. http://www.prometheegaia.net/academicedition.html. Accessed on 19 Feb 2014
 Margeta J (2010) Water supply: planning, design, management and water purification, 1st edn. Faculty of Civil Engineering and Architecture, University of Split, Split, Croatia (in Croatian) Google Scholar
 Mladineo N (2009) Support for performance and decisionmaking in civil engineering (manuscript for the internal use). Faculty of Civil Engineering and Architecture, University of Split, Split, Croatia (in Croatian) Google Scholar
 Mutikanga HE, Sharma SK, Vairavamoorthy K (2011) Multicriteria decision analysis: a strategic planning tool for water loss management. Water Resour Manag 25:3947–3969CrossRefGoogle Scholar
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