# Methodology for Pumping Station Design Based on Analytic Hierarchy Process (AHP)

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## Abstract

**:**

## 1. Introduction

_{max}, Q

_{max}). Next, the control mode of the PS is established. For example, several research studies have been carried out to optimize energy costs in PSs through mathematical pump scheduling models. The main mathematical methods applied to solve these problems are: linear programming [3], no lineal programming [4], dynamic programming [5]. These pump scheduling problems start from a fixed pump model, and a fixed number of pumps and consist of finding the optimal values of decision variable. In this case, the decision variables are the state of the pumps (on/off) at each time interval to minimize the power consumption of the PS. These methods were used to optimize different types of pumping systems: with one or several pumps, with or without storage tanks. One limitation of these methods is their computational efficiency, since they require high computation time to find the optimal solution. Other algorithms with better computational efficiency in solving pumping scheduling problems are genetic algorithms [6]. In addition, these algorithms could have other decision variables, such as the rotational speed of the pumps in each every time interval [7].

_{2}emissions analyzing different scenarios, such as installing a flow regulator valve and implementing VSPs in the PS. Alternatively, Walski and Creaco [18] compared the total annualized cost of PSs, including capital costs and operational costs for different pumping configurations including FSPs and VSPs. The capital costs were determined as described by Walski [19]. These configurations are analyzed with different scenarios of demand flow and total dynamic head required. Then, Diao et al. [20] analyzed the impacts that a design and operation of a water distribution system could have with different flow design scenarios, such as uniform demand pattern and spatial-variant pattern, and considering life cycle costs. Finally, Martin-Candilejo et al. [21] proposed a methodology to design a water supply system efficiently through optimizing construction and operation costs when there is a variation of the type of demand. This methodology was based on an equivalent flow rate and equivalent volume to optimize the computational calculation process.

## 2. Materials and Methods

#### 2.1. Problem Statement

_{max}) and the corresponding maximum head (H

_{max}). At this point, two different variables must be considered: model of the pump and number of them. The variation of the pump efficiency with flow and the different operating conditions conditioned both the pump model and the number of pumps.

_{max}) by the flow a single pump (Q

_{b}

_{1}), which would deliver at the maximum head H

_{max}. Hence, if the pump model is known, the design of the PS would be completely defined. However, there is no bi-univocal relationship between these two variables (model and number of pumps). In some situations, the number of pumps is initially fixed. In this latter case, there will be several models that can be installed in the PS. The selection will depend on other factors as expected efficiency, required automation, and other operating conditions. The method presented in this work is aimed to select the best combination of number of pumps and pump model according to different criteria. These criteria will be assessed using the AHP.

#### 2.2. Required Data for Pumping Station Design

- Iglesias-Rey et al. [34] proposed a basic scheme of a PS (Figure 1). This scheme includes a backup pump to guarantee the reliability of the PS. The scheme is defined by three characteristic lengths (L
_{1}, L_{2}and L_{3}). These lengths are considered proportional to the nominal diameter of the pipelines (DN_{i}) through a factor fn_{i}, as shown in Equation (1). It was also assumed that the diameter DN_{i}was calculated from the maximum required flow (Q_{max}) and a maximum design velocity of 2 m/s.$${L}_{i}=f{n}_{i}\xb7D{N}_{i}$$ - The setpoint curve represents the total dynamic head required (H
_{c}) for each required demand flow (Q) of the network to satisfy consumption nodes. This curve is defined as the total dynamic head needed by the pump station to supply the demand flow and maintaining the minimum pressure required at the critical consumption node of the network [12]. Usually, the setpoint curve can be written as in Equation (2):$${H}_{c}=\mathsf{\Delta}H+R\xb7{Q}^{c}$$

_{c}) and its corresponding demand (Q, H

_{c}).

- 3.
- Demand patterns correspond to the variation of consumed flow in a period (day hour, weekday, year season).
- 4.
- To select a pump, it is accepted that there is a list of available commercial pumps. Each pump model is defined by the best efficient point (BEP), that is, nominal rotational speed (N
_{0}), nominal flow (Q_{0}), nominal head (H_{0}), nominal efficiency (η_{0}) and the parameters used to describe the curves of the pump (H-Q and η-Q). Relationships among these variables are used as follows:$${H}_{b}={H}_{1}{\alpha}^{2}-{\alpha}^{\left(2-B\right)}A\xb7{\left(\frac{Q}{b}\right)}^{B}$$$$\eta =E\xb7\frac{Q}{\alpha \xb7b}-F\xb7{\left(\frac{Q}{\alpha \xb7b}\right)}^{2}$$$$\alpha =\frac{N}{{N}_{0}}$$$${P}_{T,t}={\displaystyle \sum}_{i=1}^{n}\frac{\gamma \xb7{Q}_{FSP,i}\xb7{H}_{b,i}}{{\eta}_{FSP,i}}+{\displaystyle \sum}_{j=1}^{m}\frac{\gamma \xb7{Q}_{VSP,j}\xb7{H}_{b,i}}{{\eta}_{VSP,j}}$$$${E}_{T}={\displaystyle \sum}_{i=1}^{{h}_{T}}{P}_{T,i}\xb7{h}_{i}$$

_{1}, A, B, E and F are coefficients that characterized the pump; the term b is the total number of pumps of the PS; and the term α is the relation between the current rotational speed (N) and the nominal rotation speed (N

_{0}). In Equation (6), the term P

_{T,i}is the total consumed power by the PS in every period t; $\gamma $ is the specific gravity of the water; Q

_{FSP,i}is the flow of every FSP; Q

_{VSP,j}is the flow of every VSP, H

_{b,i}the head of pump i; and n and m are the number of FSPs and VSPs, respectively. Finally, in Equation (7) the term E

_{T}is the total consumed energy by the PS in a day, h

_{t}is the period duration and h

_{T}represents the 24 h in a day.

- 5.
- Electric tariffs are managed by companies that provide energy service to the users. These tariffs could be different in a period of a day, year, season or could not have any kind of variation. This work contemplates three different electric tariff hours: peak hours, off-peak hours and plain hours, and two seasons: summer and winter.
- 6.
- In addition, every element of a PS, such as pumps, pipes, valves, control elements and other accessories has a database with its commercial costs including the installation costs.
- 7.
- Seven different modes of control systems have been used in this work based on two aspects. The PS may content FSP, VSP or a combination of both. Besides, measurements devices may supply readings for pressure only (pressure control, PC) or pressure and flow (flow control, FC) [32]. Table 1 described the required equipment of every control system. For a detailed description of these control systems, the reader can find t. The operational modes of these seven configurations of control system are detailed in Appendix A of this document.

_{1}) is higher than the maximum total dynamic head of the set-point curve (H

_{c,max}), the pump model is suitable for selection. Otherwise, the pump model is not viable, and it is discarded. Then, the total number of pumps (b

_{i}) of every viable pump model needed to satisfy the maximum demand flow (Q

_{max}) is defined. As a result, several alternatives with different pump models and number of pumps are selected for further evaluation using the AHP. The criteria used in the AHP are described in detail below.

#### 2.3. Definition of the Techno-Economical Criteria Used

#### 2.4. Methodology of Analytic Hierarchy Process (AHP)

_{i}) for the viable pump models. The criteria of technical and economic factors of the solutions generated by the pump models and different configuration of control modes are evaluated. After the assessment, all these alternatives can be classified in dominant and dominated solutions thorough Pareto front. The dominant solutions continue in this process, while the dominated solutions are discarded. The AHP method follows a hierarchy construction. It is established by the objective to reach criteria and sub-criteria for the PS and finally by the alternatives to evaluate. The judgments of the group of experts determine the importance weight of the criteria of technical and economic factors in the PS. Then, the dominated solutions are assessed using these weighted criteria. Finally, the most suitable pump model alternative is selected according to the obtained rating of the alternatives. The following flowchart (Figure 2) describes the process of the proposed methodology applying the AHP method.

_{c}× n

_{c}) is constructed, where n

_{c}is the total number of criteria. The criteria are placed in rows and columns of the matrix in order to form a pairwise comparison of the criteria. Hence, this matrix is formed by values of the comparisons of every criterion over another (a

_{ij}). The sub-terms i and j represent each criterion placed in rows and columns, respectively. These pairwise comparisons are reciprocal with each other. For example, the reciprocal pairwise comparison of a

_{ij}(a

_{ji}) is defined as the inverse, that is, 1/a

_{ij}. The priority vector of every criterion and sub-criterion is usually obtained through arithmetic mean with the values of pairwise criteria comparisons as defined by the AHP. In addition, this work proposes to consider the consistency of the comparison values of every group of experts to obtain the final importance weight of the criteria. Therefore, the final importance weight of the criteria is determined thorough a geometric weighting of the priority vector of the criteria with the consistency of the obtained comparison by the group of experts. These values are obtained in a dimensionless way by the following expressions.

_{ij}are pairwise comparisons of a criterion over another. In Equation (9), the terms Na

_{ij}are normalized values of a

_{ij}concerning the summation of values in each column matrix

_{.}Finally, the term C

_{i}in Equation (10) is the importance weight vector or priority of each criterion for each group of experts. The sub-index i represents every criterion for each group of experts and n

_{c}is the number of criteria.

_{c}× n

_{c}) done by the group of experts should be consistent. This matrix is consistent if it satisfies the following expression:

_{i}, the term ${\lambda}_{max}$ represents the maximum quotient between the relation of the final vector $\left(\overline{{V}_{i}}\right)$ and the importance weight vector of the criteria (C

_{i}).

_{c}× n

_{c}). The term CI measures the consistency of the comparisons done by the group of experts [23]. These terms of consistency are calculated by the following expressions:

_{i,j}) is obtained in the Equation (16), where the sub-index j represents every group of experts.

_{i,GM}is the geometric mean of the importance weight considering the consistency of every criterion. It is defined as the product of the importance weight considering the consistency of all group of experts with an exponent of the summation of the inverse of consistency ratio of all group of experts. The term n

_{e}is the number of groups of experts. Finally, the term CP

_{0,i}is the general importance weight or priority considering the consistency of every criterion.

_{i}) is obtained as the AHP method establishes in Equation (10). The sub-term i represents the type of regulation mode. The maximum value of the complexity priority (ca

_{i}) is the regulation mode with the least complexity of operating. Finally, i the rating of priority of every regulation mode is determined, as shown in the following expression.

_{i}) is obtained as the relation between the complexity assessment of every regulation mode and an established ideal value that is the maximum complexity priority of the regulation modes $C{c}_{i,\left(max\right)}$. This obtained rating could have values from 1 to 0, where 1 is the regulation mode with the best complexity assessment and 0 is the regulation mode with the worst complexity assessment. Table 2 shows a matrix of the pairwise comparations of the regulation modes, the complexity priority, and the rating of every regulation mode.

_{i,j}) is normalized concerning the maximum and minimum assessment of the alternatives in every sub-criterion (${A}_{i\left(\mathrm{max}\right),j},{A}_{i\left(\mathrm{min}\right),j})$, as is shown in Equation (20). The sub-index i expresses the alternative number and j expresses the criteria number (From C1 to C5). The assessment of the alternatives (A

_{i,j}) corresponds to the obtained values of the number of pumps, complexity, investment, operational and maintenance costs of the alternatives. The best assessment of the criteria (number of pumps, complexity, investment, operational and maintenance cost) is the lowest value of all alternatives. In contrast, the worst assessment of the criteria is the highest value of all alternatives. Then, the overall normalized assessment of every alternative (ONA

_{i}) is obtained through the product of the normalized assessment of the alternatives and the overall priority of every criterion, as shown in Equation (21).

_{i}) is the summation of the product of normalized assessment of every alternative for each criterion (NA

_{i,j}) with the priority of every criterion (C

_{j}); the sub-index j takes values from 1 to n

_{c}, where n

_{c}is the total number of criteria considered in the PS design (n

_{c}= 5).

_{i}) to finally determine the total rating of every alternative (TR

_{i}), as is described in the following expressions.

_{i}) in Equation (22) expresses the relation between the overall normalized assessment of each alternative (ONA

_{i}) and the summation of the normalized assessment of the total number of alternatives. The sub-index i is the number of the alternative that takes values from 1 to n and n is the total number of evaluated alternatives. Finally, the total rating of every alternative (TR

_{i}) is the relationship between the distributive priority of the overall normalized assessment of every alternative (PA

_{i}) and the maximum value of distributive priority of the overall normalized assessment of every alternative (PA

_{i,(max)}). The values obtained for OR

_{i}range from 1 to 0, where 1 is the best assessment of the alternative and 0 is the worst.

_{i}) is obtained, and finally, the pump model alternative with the best assessment is determined. In other words, the most suitable pump model alternative for a PS design, considering technical factors (number of pumps and complexity of the control system) and economic factors (investment, operational and maintenance costs), is obtained.

## 3. Case Studies

_{m}), the minimum flow (Q

_{min}), and maximum flow (Q

_{max}) of the different PSs are shown in Table 4.

## 4. Results

_{1}) is higher than the maximum required head pressure (H

_{max}). In contrast, the pump models that are not viable are eliminated. This process is the first selection filter. These viable pump models with the combination of different regulation modes generate several solutions. These solutions are evaluated with the different criteria of PS design: technical factors (number of pumps and complexity) and economic factors (investment, operational and maintenance costs), and go through the second selection filter the Pareto front. This second filter selection reduces, in a significant way, the number of solutions. Finally, the overall rating of these solutions according to the assessment of the criteria is obtained.

## 5. Discussion

_{,i,j}in Equation (24) is the deviation of the importance weigh of every criterion for each group of experts, the sub-terms i express the criteria number (From C1 to C5), and j expresses the group of experts, and the term $\widehat{{C}_{i}}$ is the overall importance weigh of every criterion. The term D

_{j}in Equation (25) is the deviation of the priority of each group of experts. This term represents the summation of the product of the deviation of the priority of every criterion with the overall priority of every criterion. The term D

_{j}represents the importance weight of the overall criteria for each group of experts concerning the overall importance weight.

_{i}) of 3% was assumed, and the cycle life (CL) of the equipment of PS is based on the fabricator, in order to determine the life cycle cost of the PS. The amortization factor (FA) is determined according to the Equation (26), and this factor is affected to the investment cost to annualize it.

_{max}, H

_{max}). The number of pumps of the model is obtained by the relation of maximum demand flow (Q

_{max}) and the flow that one pump (Q

_{b}

_{1}) of the selected model deliver at the maximum head required of the system (H

_{max}). Then, the number of pumps of every pump model was combined with all the different control mode obtaining several alternatives of solution. In every alternative is determined the life cycle cost, and finally, the best alternative is selected according to the minimum life cycle cost. The following Table 16 shows the best alternative of pump model (B28) with two FSP and VSP respectively, and with a flow control mode. This table describes the respective number of pumps, control mode, investment, operational and maintenance annual cost of the best pump model. The summary of these costs determines the cycle life cost of the most suitable alternative.

_{max}= 70 L/s) and minimum demand flow (Q

_{min}= 12.30 L/s) of the network. This relation gives as a result 6 unit-pumps. Then, the relationship of the maximum demand flow and the number of pumps (6 pumps) determines the supplied flow by each pump (Q

_{b}= 11.66 L/s). This flow and the required head of the maximum demand flow of the system (H

_{max}= 34.8 m) are the operational points to select the pump model with the best efficiency curve in the catalogue. In this case, the pump model selected is the model B27. Finally, the 6-unit pumps of the selected model are combined with different number of FSP and VSP and with every control mode configuration. These combinations determine several solutions. Then, the most suitable solution is selected according to the minimum cycle life cost of all alternatives. In Table 17 is appreciate the most suitable alternative of control of the model B27 and the different parameters of this model: the pump model, the number of pumps, the control mode, and the cycle life cost.

## 6. Conclusions

_{2}emission by the pumps and the performance of the regulation mode. In addition, it could be included an analysis of annual interest rates on the investment costs. Another future research is to apply new optimal methodologies in pumping control mode systems and compare them with the other configurations of control system that were analyzed in this work.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols | |

A_{i,j} | Assessment of the alternative for each criterion |

$\overline{{W}_{i}}$ | Criteria comparison matrix |

H1; A; B; E; F | Coefficients that characterized the pumping curve |

E | Consumed Energy of the pumping station |

c | Coefficient that characterized the set-point curve |

CI | Consistency Index |

Cc_{i} | Complexity priority of every regulation mode |

CR | Consistency ratio |

Q | Demand flow |

CD_{i,j} | Deviation of the importance weight of every criterion for each group of experts concerning the overall priority |

D_{j} | Deviation of the priority of every group of experts respect to the overall priority |

PA_{i} | Distributive priority of the overall normalized assessment of each alternative |

η; η_{0} | The efficiency of the pump; Nominal efficiency of the pumps |

R | Energy losses in the network |

$\overline{{V}_{i}}$ | Final vector of criteria comparison matrix with their importance weight |

L_{i} | Length of the pipelines |

C_{i} | Priority or importance weight of every criterion |

CP_{i} | Priority considering the consistency of every criterion |

λ_{max} | Maximum quotient between $\overline{{V}_{i}}$ and $\overline{{W}_{i}}$ |

H_{max} | Maximum total dynamic head |

Q_{man} | Maximum demand flow |

A_{i(max),j}; A_{i(max),j} | Maximum and minimum assessment values of the alternatives in each criterion |

PA_{i,max} | Maximum distributive priority of the overall normalized assessment of each alternative |

Q_{m} | Mean demand flow |

Q_{min} | Minimum demand flow |

fn_{i} | Multiplication factor for the length of the pipelines |

H_{0} | Nominal head of the pump |

DN_{i} | Nominal diameter of the pipelines |

Q_{0} | Nominal flow of the pump |

Na_{i,j} | Normalized values of the pairwise comparison |

NA_{i,j} | Normalized assessment of the alternatives for each criterion |

n_{c} | Number of criteria |

n_{e} | Number of groups of experts |

b | Number of pumps |

n | Number of FSPs |

m | Number of VSPs |

ONA_{i} | Overall normalized assessment of the alternative |

OR_{i} | Overall rating of the alternative |

a_{i,j} | Quantitative values of the pairwise comparison of the criteria |

RI | Random consistency index |

Rc_{i} | Rating of complexity priority of every regulation mode |

N; N_{0} | Rotational speed; Nominal rotational speed |

ΔH | Static head of the system |

CP_{i,GM} | The geometric mean of the priority considering the consistency of every criterion |

CP_{0,i} | The general priority considering the consistency of every criterion |

P_{T} | Total consumed power of a pump |

H | Total dynamic head |

## Abbreviations

AHP | Analytic hierarchy process |

FC | Flow control |

FSP | Fixed speed pump |

MEI | Minimum Efficiency Index |

PC | Pressure control |

PS | Pumping station |

VSP | Variable speed pump |

VFD | Variable frequency drive |

## Appendix A

#### Control System

**1.0—Without regulation:**This mode corresponds with the use of FSPs that are in operation all the time. In addition, the flow supplying by the PS is constant through time. This type of regulation does not have any king control device.

**2.1—Pressure Control with FSPs:**This control mode operates switching on/off FSPs and is based on measuring the total head of the system at the end of the PS with a pressure meter. This configuration works with a pressure switch that sends pressure signals to a system that orders the pumps to switch on/off. These signals correspond to starting head and stopping head for every FSPs. For example, if the PS is made up of three pumps, this regulation mode operates in the following way. The starting head of every FSP begins with determining the starting head of the last pump (i FSP), where i is the number of the FSP in operation. The intersection of the pumping curve of 2 FSP with the set-point curve determines the starting head of the last pump (H

_{Ai}). Then, setting a head step (for example, ΔH = 5 m), it is obtained the starting head of the other FSPs. In this way, the starting head of 2 FSP (H

_{A}

_{2}) is determined by (H

_{A}

_{2}= H

_{Ai}+ ΔH). The intersection between H

_{A}

_{2}and the pumping curve of 1 FSP is the starting point of the 2 FSP. On the other hand, the stopping heads begin with the last FSP (H

_{Pi}). This head is obtaining with the intersection of the flow of H

_{Ai}in the 2 FSP with the pumping curve of the i FSP. In order to determine the stopping head of 2 FSPs (H

_{P}

_{2}), we obtained the head (H

_{Pi}+ ΔH). The intersection of the flow of this head in 1 FSP with the pumping curve of the 2 FSP determines the stopping Head (H

_{P}

_{2}). The following Figure A1 shows a scheme of an example of this regulation mode with three FSPs. In general, the necessary pieces of equipment of this regulation mode are the pressure meters and pressure switches.

**2.2—Flow Control with FSPs:**This control system operates only with FSPs and is based on measuring the flow at the end of the pumping station. The flow measured sends signals of switching on/off to the FSPs through a programmable logic controller (PLC). This device identifies the set values of starting and stopping of the FSPs to order every FSP to switch on/off. The intersection of the set-point curve and the pumping curve of the i FSPs in operation defines the operational range of flow for the PS with their respective head that is defined by the terms Q

_{i}and H

_{i}. These terms represent the limit flow and limit head of the i FSPs in operation. In this way, when the demand flow (Q) is in the range (0 < Q < Q

_{1}) is operating 1 FSP. When Q is in the range (Q

_{1}< Q < Q

_{2}), the 2 FSP starts to operate and when Q is in the last range (Q

_{2}< Q < Q

_{max}), the i FSP starts to operate. On the other hand, when the demand flow (Q) decreases, the i FSP stops when Q is near to the limits flow (Q

_{i}). In the following Figure A2, it can be visualized the scheme of this regulation mode with 3 FSPs in the pumping station. The required pieces of equipment of this regulation mode are flow meters and a PLC.

**3.1—Pressure Control with VSPs:**In this control mode, it is necessary to incorporate a variable frequency drive (VFD) in the pumps to allow the VSPs to change the rotational speed according to the demand flow (Q). This control mode consists of measuring the total head of the system at the end of the PS. A switched pressure sends the signals of starting and stopping of every VSP to a PLC concerning a fixed head value. Then, the PLC orders every pump to switch on/off and change the rotational speed (N) according to the flow and the set head value. The objective of this configuration is to maintain a fixed head in the PS, regardless of the demand flow over time. This fixed head value is defined by the total dynamic head of the set-point curve at the maximum demand flow (H

_{c,max}). The intersection of the fixed head (H

_{c,max}) with the pumping curve of the i VSPs determines the limit flows (Q

_{i}) of the operational ranges of the i VSPs in operation. For example, if the PS has 3 VSPs and when Q is in the range (0 < Q < Q

_{1}), 1 VSP pump operates with a correspondent rotational speed (N) to follow the fixed head. When Q is in the range (Q

_{1}< Q < Q

_{2}), 2 VSPs are in operation. One option is that the 2 VSPs operate at the same rotational speed (N) following the fixed head, and the other option is that 1 VSP operates at the nominal rotational speed (N

_{0}) and the other VSP operates at a rotational speed that follows the fixed head. When Q is in the rage (Q

_{2}< Q < Q

_{max}), 3 VSPs are in operation, where 3 VSPs could operate at the same rotational speed (N) following the fixed head. Another option is that 1 or 2 VSPs operate at the nominal rotational speed (N

_{0}) and the other VSPs operate at a correspondent rotational speed (N) following the fixed head. On the other hand, when Q decreases, the VSPs also decrease their rotational speed (N) following the fixed head and the i VSP switch off when Q is near to the limit flows (Q

_{i}) of the operational ranges. The following Figure A3 shows a scheme of this regulation mode with 3 VSPs in the pumping station. The requirement equipment of this regulation mode is the variable frequency drives (VFDs), the pressure meters, the PLC, and the pressure switch.

**3.2—Flow Control with VSPs:**Similarly, to control mode (3.1), it is necessary to add a VFD into the pumps to become VSPs, and could change their rotational speed concerning the requirements of the network. The objective of this control mode is that the operational points of the PS follow the set-point curve. It is based on measuring the flow and total head (Q, H) at the end of the PS. A pressure transducer sends the values of total head and flow to a PLC that orders to switch on/off or change the rotational speed of every pump concerning the values of (Q, H) of the set-point curve. The following Figure A4 shows an example of how this control mode operates. The intersection of the set-point curve and the pumping curve of the i pumps in operation determines the operational range of the flow in the PS. In the first range (0 < Q < Q

_{1}), 1 VSP operates at a rotational speed (N) following the set-point curve. In the second range (Q

_{1}< Q < Q

_{2}), 2 VSPs operate at the same rotational speed (N) following the set-point curve, or 1 VSPS operates at the nominal rotational speed (N

_{0}), and the other operates at a rotational speed (N), concerning the set-point curve. In the last range (Q

_{2}< Q < Q

_{max}), 3 VSPs operate at the same rotational speed (N) following the set-point curve. Another option could be that 1 or 2 VSPs operate at the nominal rotational speed (N

_{0}) and the other VSPs operate at a correspondent rotational speed (N) concerning the set-point curve. On the other hand, when Q decreases, the VSPs reduce their rotational speed following the set-point curve. When Q is near to the limit flows (Q

_{i}) of the operational flows, the i VSP switches off to supply the necessary flow (Q) concerning the demand flow. The required pieces of equipment of this regulation mode are flow and pressure meters, VFDs, pressure transducer, and the PLC.

**4.1—Pressure Control with FSPs and VSPs:**The objective of this regulation mode is that the pumping system maintains a fixed head value for every flow rate over time. This fixed head corresponds to the total maximum required head of the set-point curve (H

_{c,max}). The operational mode of this type of control is similar to control mode (3.1) (Figure A3). The only difference between the regulation mode 3.1 is that the PS is combined by FSPs and VSPs. In this way, when demand flow (Q) is in the range (0 < Q < Q

_{i}), only VSP is in operation with a rotational speed following the fixed head. When Q is in the range (Q

_{i}< Q < Q

_{max}), FSPs supply the flow correspondent to Q

_{i}and VSPs supply the difference of the demand flow (Q) and the limit flow (Q

_{i}) with their respective rotational speed to follow the fixed head. The VSPs are always in operation and FSPs are switched on/off concerning the demand flow.

**4.2—Flow Control with FSPs and VSPs:**This control mode aims for the PS to follow the set-point curve. The configuration and operational model are similar to the control mode (3.2) (Figure A4). The difference between this regulation mode with the control mode 3.1 is that it is combined FSPs and VSPs. In this way, VSPs supply small flows and FSPs supply great flows, where VSPs are always in operation. For example, VSPs supply the flow correspondent in the range (0 < Q < Q

_{i}) or the difference of the demand flow (Q) and the limit flow (Q

_{i}) with their respective rotational speed following the set-point curve. Meanwhile, FSPs supply the flow correspondent to the limit flows (Q

_{i}).

**Economic Factors:**This criterion is the cost that includes in a PS design: investment costs, maintenance costs and operational costs. This section describes the formulations to determine investment, maintenance costs and operational costs for each alternative of pump model.

**Investment Costs:**This intervenes in the cost of construction and installation of the infrastructure of the pumping station and the control pumping system. These costs are obtained from a database of the unit cost of installation of all the components in a PS design. Then, the product of the quantity of each element of the PS with their respective unit costs determines the total investment cost in a PS design.

_{Inv}is the investment cost of the PS expressed in annual form. The term C

_{PS}corresponds to the unit cost of every pump unit. This cost is obtained from a database of the commercial costs of the factories pump. The term b is the number of pumps in the PS. The term C

_{pipe}is the unit cost of installation of pipelines and L

_{T}is the total length of the pipelines. The term C

_{ACCi}is the unit cost of installation cost of each accessory of the pumping station. These accessories include valves, elbow or tee connectors. The term N

_{ACCi}is the number of units of these accessories in the PS. The cost of the pipes and minor accessories of the PS are obtained by mathematical expressions. The terms of these expressions are detailed in Table A1. The sub-term RM

_{j}corresponds to all equipment of the control system of the PS. This equipment could be pressure switch, flow meters, transducer pressure, PLC or VFD concerning the type of the control mode in the PS. The term C

_{RMj}is the unit cost of the installation of the equipment of the control system and the N

_{RMj}is the number of every device of the control mode. The costs of the PLC, transducer pressure and pressure switch are obtained from a database of the commercial cost provided by the factory. In contrast, the cost of the flow meter and the VFD are obtained by mathematical expression, and it is detailed in Table A1. This table shows the function cost of different elements of a PS, the function variable of every equipment and the constant parameters of the function costs.

Element | C_{(X)}(EUR) | X | C_{1} | C_{2} | C_{3} |
---|---|---|---|---|---|

Pipe | ${C}_{\left(X\right)}={C}_{1}+{C}_{2}\xb7ND+{C}_{3}\xb7N{D}^{2}$ | ND (mm) | 10.13 | 0.20 | 0.0005 |

Elbow connector | ${C}_{\left(X\right)}={c}_{1}{}^{{C}_{2}*ND}$ | ND (mm) | 29.17 | 0.01 | - |

Tee connector | ${C}_{\left(X\right)}={c}_{1}{}^{{C}_{2}*ND}$ | ND (mm) | 42.60 | 0.01 | - |

Section Valve | ${C}_{\left(X\right)}={C}_{1}+{C}_{2}\xb7ND+{C}_{3}\xb7N{D}^{2}$ | ND (mm) | 63.63 | 0.79 | 0.01 |

Check Valve | ${C}_{\left(X\right)}={C}_{1}+{C}_{2}\xb7ND+{C}_{3}\xb7N{D}^{2}$ | ND (mm) | 35.63 | −0.14 | 0.01 |

Flow meter | ${C}_{\left(X\right)}={C}_{1}+{C}_{2}\xb7{D}_{in}+{C}_{3}\xb7{D}_{in}{}^{2}$ | D_{in} (mm) | 885.70 | −9.22 | 0.06 |

Variable Frequency Drive | ${C}_{\left(X\right)}={C}_{1}+{C}_{2}\xb7P+{C}_{3}\xb7{P}^{2}$ | P (KW) | 168.19 | 116.08 | −0.60 |

_{(X)}is the function cost of the elements of the PS, x is the variable of every function cost. These variables could be: the nominal diameter (ND) or the internal diameter (D

_{in}) of these accessories, and the power (P) of the frequency drive. Finally, the terms C

_{1,}C

_{2}, and C

_{3}are constant parameters of every function cost.

**Maintenance Costs:**These costs are related to the maintenance activities of the infrastructure of the PS, control system, and their frequency of implementation. This cost is expressed in annual form, so the frequency of implementation is defined as the number of times to implement the maintenance activities in a year.

_{Maint}is the annual maintenance cost of the PS. The term CUA

_{PSi}is the unit cost of the maintenance activities of the pump and the sub-term i is every maintenance activity of the pump. The terms f

_{APi}and b are the annual frequency of maintenance and the number of pumps in the PS, respectively. The term CU

_{pipe}is the unit cost of the maintenance activity of the pipe. This cost is expressed in unit of length of the pipe (EUR/m). The terms f

_{pipe}and L

_{T}are the annual frequency of maintenance and the total length of the pipe, respectively. The term CU

_{ACCj}is related to the unit cost of the maintenance activity of the accessories in the PS and the sub-term j is every one of these accessories (valves, elbow, and tee connectors). The terms f

_{ACCj}and N

_{ACCj}are the annual frequency of maintenance and the number of units of these accessories, respectively. Finally, $C{U}_{R{M}_{j}}$ is the unit cost of maintenance of every equipment of the control mode in the PS. The sub-term k is every one of the equipment of the control mode (pressure switch, flow meter, transducer pressure, PLC, and VFD). The terms f

_{RMk}and N

_{RMk}are the annual frequency of maintenance and the number of units of these devices of control, respectively. It is important to mention that every maintenance activity of the PS and their frequency of implementation is based on the recommendation for the factory of these elements. The unit cost is obtained from a database of maintenance costs.

**Operational Cost:**This cost is associated with the consumption energy by the PS in a year. This work considered two types of consumption energy in a year: Summer and Winter. Besides, every season has different energy tariffs concerning the type of hours, which are: peak off-hours, rush hours and plain hours. The following expression determines the operational cost.

_{Op}is the operational cost of the PS in a year. The terms P

_{T,i}and P

_{T,j}corresponds to the consumed power of every hour in summer and winter, respectively. The terms h

_{i}and h

_{j}are the time interval in hours of summer and winter. C

_{E},i and C

_{E,j}are the energy tariffs of every hour in summer and winter. The sub-terms i and j refer to every hour of a day in summer and winter and the term h

_{T}represents the 24 h of the day.

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Control System | Frequency Inverter | Pressure Switches | Pressure Transducer | Flowmeter | PLC | No. Regulation Equipment | |
---|---|---|---|---|---|---|---|

1.0 | Without regulation | 0 | |||||

2.1 | PC with FSPs | X | 1 | ||||

2.2 | FC with FSPs | X | X | 2 | |||

3.1 | PC with VSPs | X | X | X | 3 | ||

3.2 | FC with VSPs | X | X | X | X | 4 | |

4.1 | PC with FSPs and VSPs | X | X | X | 3 | ||

4.2 | FC with FSPs and VSPs | X | X | X | X | 4 |

Regulation Mode (i) | 1.0 | 2.1 | 2.2 | 3.1 | 3.2 | 4.1 | 4.2 | Complexity Assessment (Cc _{i}) | Rating (R_{i}) |
---|---|---|---|---|---|---|---|---|---|

1.0 | 1 | 3 | 5 | 7 | 9 | 7 | 9 | 0.43 | 1.00 |

2.1 | 1/3 | 1 | 3 | 5 | 7 | 5 | 7 | 0.24 | 0.57 |

2.2 | 1/5 | 1/3 | 1 | 3 | 5 | 3 | 5 | 0.14 | 0.32 |

3.1 | 1/7 | 1/5 | 1/3 | 1 | 3 | 1 | 3 | 0.07 | 0.15 |

3.2 | 1/9 | 1/7 | 1/5 | 1/3 | 1 | 1/3 | 1 | 0.03 | 0.07 |

4.1 | 1/7 | 1/5 | 1/3 | 1 | 3 | 1 | 3 | 0.07 | 0.15 |

4.2 | 1/9 | 1/7 | 1/5 | 1/3 | 1 | 1/3 | 1 | 0.03 | 0.07 |

Time Zones | |||||
---|---|---|---|---|---|

Summer Season | Winter Season | ||||

Type of Hours | Electric Tariff | From | To | From | To |

Off-peak hours | 0.069 | 0 | 8 | 0 | 8 |

Peak hours | 0.095 | 11 | 15 | 18 | 21 |

Plain hours | 0.088 | 9 | 10 | 8 | 18 |

16 | 23 | 21 | 23 |

TF-PS1 | TF-PS2 | CAT-PS2 | CAT-PS3 | |
---|---|---|---|---|

Q_{m} (l/s) | 35.00 | 24.44 | 18.00 | 37.00 |

Q_{min} (l/s) | 12.30 | 8.60 | 6.30 | 13.00 |

Q_{max} (l/s) | 70.00 | 48.88 | 36.00 | 74.00 |

Data | TF-PS1 | TF-PS2 | CAT-PS2 | CAT-PS3 |
---|---|---|---|---|

ΔH | 25.00 | 28.00 | 25.00 | 22.00 |

R | 0.0020 | 0.0059 | 0.0106 | 0.0015 |

Overall | Academic | Commercial | Constructor | Consultancy | Management | Operation | Direction | ||
---|---|---|---|---|---|---|---|---|---|

TF | Technical Factor | 0.33 | 0.38 | 0.09 | 0.25 | 0.34 | 0.36 | 0.70 | 0.48 |

EF | Economic Factor | 0.67 | 0.62 | 0.91 | 0.75 | 0.66 | 0.64 | 0.30 | 0.52 |

C1 | Number of pumps | 0.20 | 0.26 | 0.04 | 0.18 | 0.15 | 0.20 | 0.43 | 0.36 |

C2 | Control system complexity | 0.13 | 0.13 | 0.06 | 0.07 | 0.19 | 0.15 | 0.27 | 0.12 |

C3 | Investment Cost | 0.14 | 0.15 | 0.32 | 0.12 | 0.15 | 0.11 | 0.06 | 0.09 |

C4 | Operational Cost | 0.31 | 0.29 | 0.44 | 0.31 | 0.29 | 0.31 | 0.11 | 0.25 |

C5 | Maintenance Cost | 0.21 | 0.17 | 0.15 | 0.32 | 0.22 | 0.22 | 0.12 | 0.18 |

Viable Solutions | Pareto Front | ||||
---|---|---|---|---|---|

No. Models | No. Solutions | No. Models | No. Final Solutions | Reduction Rate Solutions | |

TF-PS1 | 43 | 471 | 12 | 49 | 89.60% |

TF-PS2 | 39 | 359 | 14 | 40 | 88.86% |

CAT-PS2 | 45 | 357 | 15 | 30 | 91.60% |

CAT-PS3 | 45 | 490 | 7 | 31 | 93.67% |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | ||||||
---|---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | |||

Hierarchy | ID Model | No. Pumps b _{i} | n_{i}FSP | m_{i} VSP | Complexity | Investment Cost (EUR) | Operational Cost (EUR/Year) | Maintenance Cost (EUR/Year) |

1 | B30 | 3 | 3 | 0 | 2.1 | EUR 77,091.61 | EUR 18,094.16 | EUR 1040.11 |

2 | B65 | 3 | 3 | 0 | 1.0 | EUR 100,767.32 | EUR 21,387.13 | EUR 1136.44 |

3 | B61 | 3 | 3 | 0 | 2.1 | EUR 109,645.45 | EUR 15,351.70 | EUR 1148.58 |

8 | B33 | 2 | 0 | 2 | 3.2 | EUR 76,896.63 | EUR 16,099.10 | EUR 1018.72 |

12 | B31 | 3 | 2 | 1 | 4.1 | EUR 81,049.03 | EUR 14,910.76 | EUR 1107.24 |

15 | B59 | 4 | 4 | 0 | 1.0 | EUR 120,430.57 | EUR 18,320.99 | EUR 1420.55 |

22 | B66 | 3 | 0 | 3 | 3.2 | EUR 126,266.96 | EUR 10,723.13 | EUR 1318.83 |

24 | B28 | 4 | 4 | 0 | 2.2 | EUR 98,748.70 | EUR 13,046.24 | EUR 1407.69 |

37 | B58 | 5 | 5 | 0 | 2.2 | EUR 145,699.82 | EUR 11,328.55 | EUR 1787.40 |

38 | B27 | 6 | 6 | 0 | 2.2 | EUR 134,865.79 | EUR 11,963.36 | EUR 1960.90 |

39 | B57 | 8 | 8 | 0 | 2.2 | EUR 205,690.01 | EUR 11,123.06 | EUR 2617.86 |

40 | B49 | 10 | 10 | 0 | 2.2 | EUR 243,678.07 | EUR 9936.37 | EUR 3178.36 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | |||||
---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | ||

Hierarchy | ID Model | Rating N. Pumps | Rating Complexity | Rating Investment Cost | Rating Operational Cost | Rating Maintenance Cost | Final Rating |

1 | B30 | 0.88 | 0.57 | 0.95 | 0.71 | 0.93 | 1.00 |

2 | B65 | 0.88 | 1.00 | 0.83 | 0.60 | 0.89 | 1.00 |

3 | B61 | 0.88 | 0.57 | 0.79 | 0.80 | 0.89 | 1.00 |

8 | B33 | 1.00 | 0.07 | 0.95 | 0.78 | 0.94 | 0.98 |

12 | B31 | 0.88 | 0.15 | 0.93 | 0.82 | 0.90 | 0.96 |

15 | B59 | 0.75 | 1.00 | 0.74 | 0.70 | 0.78 | 0.96 |

22 | B66 | 0.88 | 0.07 | 0.71 | 0.95 | 0.82 | 0.94 |

24 | B28 | 0.75 | 0.32 | 0.84 | 0.88 | 0.79 | 0.94 |

37 | B58 | 0.63 | 0.32 | 0.61 | 0.93 | 0.64 | 0.85 |

38 | B27 | 0.50 | 0.32 | 0.66 | 0.91 | 0.57 | 0.80 |

39 | B57 | 0.25 | 0.32 | 0.31 | 0.94 | 0.31 | 0.62 |

40 | B49 | 0.00 | 0.32 | 0.12 | 0.98 | 0.10 | 0.48 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | ||||||
---|---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | |||

Hierarchy | ID Model | No. Pumps b _{i} | n_{i}FSP | m_{i}VSP | Complexity | Investment Cost (EUR) | Operational Cost (EUR/Year) | Maintenance Cost (EUR/Year) |

1 | B32 | 2 | 0 | 2 | 3.2 | EUR 40,033.75 | EUR 11,033.00 | EUR 890.95 |

4 | B29 | 3 | 3 | 0 | 2.1 | EUR 36,392.86 | EUR 14,103.42 | EUR 1022.96 |

9 | B60 | 3 | 3 | 0 | 2.1 | EUR 60,626.74 | EUR 11,562.38 | EUR 1131.43 |

10 | B30 | 3 | 0 | 3 | 3.2 | EUR 45,312.38 | EUR 9220.70 | EUR 1193.21 |

11 | B31 | 3 | 0 | 3 | 3.2 | EUR 47,703.25 | EUR 9194.79 | EUR 1193.21 |

23 | B63 | 3 | 2 | 1 | 4.1 | EUR 77,860.25 | EUR 10,228.48 | EUR 1198.55 |

24 | B61 | 3 | 0 | 3 | 3.1 | EUR 85,229.43 | EUR 9529.86 | EUR 1243.41 |

26 | B52 | 4 | 4 | 0 | 1.0 | EUR 66,574.52 | EUR 16,032.72 | EUR 1388.39 |

28 | B59 | 4 | 4 | 0 | 2.2 | EUR 68,867.09 | EUR 9965.95 | EUR 1483.99 |

32 | B62 | 4 | 2 | 2 | 4.1 | EUR 84,374.22 | EUR 9472.57 | EUR 1490.08 |

36 | B51 | 5 | 5 | 0 | 1.0 | EUR 76,708.45 | EUR 15,975.26 | EUR 1655.77 |

37 | B58 | 5 | 5 | 0 | 2.2 | EUR 79,132.91 | EUR 9269.51 | EUR 1751.38 |

39 | B28 | 6 | 6 | 0 | 2.2 | EUR 60,527.23 | EUR 11,276.87 | EUR 1918.87 |

40 | B50 | 7 | 7 | 0 | 2.2 | EUR 87,848.31 | EUR 9047.27 | EUR 2303.30 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | |||||
---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | ||

Hierarchy | ID Model | Rating N. Pumps | Rating Complexity | Rating Investment Cost | Rating Operational Cost | Rating Maintenance Cost | Final Rating |

1 | B32 | 1.00 | 0.07 | 0.88 | 0.83 | 0.90 | 1.00 |

4 | B29 | 0.80 | 0.57 | 0.94 | 0.68 | 0.81 | 0.99 |

9 | B60 | 0.80 | 0.57 | 0.55 | 0.80 | 0.75 | 0.97 |

10 | B30 | 0.80 | 0.07 | 0.80 | 0.92 | 0.71 | 0.97 |

11 | B31 | 0.80 | 0.07 | 0.76 | 0.92 | 0.71 | 0.97 |

23 | B63 | 0.80 | 0.15 | 0.27 | 0.87 | 0.70 | 0.94 |

24 | B61 | 0.80 | 0.15 | 0.15 | 0.90 | 0.67 | 0.94 |

26 | B52 | 0.60 | 1.00 | 0.45 | 0.58 | 0.58 | 0.92 |

28 | B59 | 0.60 | 0.32 | 0.41 | 0.88 | 0.52 | 0.91 |

32 | B62 | 0.60 | 0.15 | 0.16 | 0.91 | 0.52 | 0.91 |

36 | B51 | 0.40 | 1.00 | 0.28 | 0.58 | 0.41 | 0.85 |

37 | B58 | 0.40 | 0.32 | 0.25 | 0.92 | 0.35 | 0.85 |

39 | B28 | 0.20 | 0.32 | 0.55 | 0.82 | 0.24 | 0.62 |

40 | B50 | 0.00 | 0.32 | 0.10 | 0.93 | 0.00 | 0.48 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | ||||||
---|---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | |||

Hierarchy | ID Model | No. Pumps b _{i} | n_{i}FSP | m_{i} VSP | Complexity | Investment Cost (EUR) | Operational Cost (EUR/Year) | Maintenance Cost (EUR/Year) |

1 | B29 | 2 | 2 | 0 | 2.1 | EUR 26,857.50 | EUR 8709.77 | EUR 737.07 |

2 | B33 | 1 | 0 | 1 | 3.2 | EUR 36,172.84 | EUR 7584.03 | EUR 601.57 |

3 | B60 | 2 | 2 | 0 | 2.1 | EUR 45,032.91 | EUR 7529.47 | EUR 845.53 |

8 | B30 | 2 | 0 | 2 | 3.2 | EUR 33,929.54 | EUR 6267.96 | EUR 890.95 |

11 | B31 | 2 | 0 | 2 | 3.1 | EUR 34,140.13 | EUR 7678.38 | EUR 832.69 |

14 | B61 | 2 | 0 | 2 | 3.1 | EUR 62,754.16 | EUR 6476.45 | EUR 941.16 |

15 | B28 | 3 | 3 | 0 | 2.2 | EUR 35,755.30 | EUR 8198.96 | EUR 1097.85 |

16 | B58 | 3 | 3 | 0 | 1.0 | EUR 52,068.90 | EUR 10,959.26 | EUR 1110.71 |

21 | B59 | 3 | 0 | 3 | 3.2 | EUR 66,803.39 | EUR 5229.30 | EUR 1293.10 |

22 | B62 | 3 | 0 | 3 | 3.1 | EUR 73,330.86 | EUR 6405.97 | EUR 1234.83 |

23 | B15 | 5 | 5 | 0 | 2.2 | EUR 43,682.33 | EUR 8035.18 | EUR 1642.91 |

24 | B50 | 5 | 5 | 0 | 2.2 | EUR 66,086.69 | EUR 6721.67 | EUR 1751.38 |

25 | B41 | 5 | 5 | 0 | 2.2 | EUR 64,990.43 | EUR 7054.42 | EUR 1751.38 |

26 | B40 | 6 | 6 | 0 | 2.2 | EUR 68,421.27 | EUR 6627.74 | EUR 2027.34 |

27 | B38 | 8 | 8 | 0 | 2.2 | EUR 80,856.08 | EUR 5918.28 | EUR 2455.36 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | |||||
---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | ||

Hierarchy | ID Model | Rating N. Pumps | Rating Complexity | Rating Investment Cost | Rating Operational Cost | Rating Maintenance Cost | Final Rating |

1 | B29 | 0.86 | 0.57 | 1.00 | 0.76 | 0.88 | 1.00 |

2 | B33 | 1.00 | 0.07 | 0.86 | 0.84 | 0.94 | 1.00 |

3 | B60 | 0.86 | 0.57 | 0.73 | 0.84 | 0.83 | 1.00 |

8 | B30 | 0.86 | 0.07 | 0.90 | 0.93 | 0.81 | 0.98 |

11 | B31 | 0.86 | 0.15 | 0.89 | 0.83 | 0.84 | 0.97 |

14 | B61 | 0.86 | 0.15 | 0.48 | 0.92 | 0.79 | 0.96 |

15 | B28 | 0.71 | 0.32 | 0.87 | 0.80 | 0.72 | 0.96 |

16 | B58 | 0.71 | 1.00 | 0.63 | 0.61 | 0.72 | 0.96 |

21 | B59 | 0.71 | 0.07 | 0.42 | 1.00 | 0.64 | 0.94 |

22 | B62 | 0.71 | 0.15 | 0.32 | 0.92 | 0.66 | 0.94 |

23 | B15 | 0.43 | 0.32 | 0.75 | 0.81 | 0.49 | 0.94 |

24 | B50 | 0.43 | 0.32 | 0.43 | 0.90 | 0.44 | 0.94 |

25 | B41 | 0.43 | 0.32 | 0.45 | 0.88 | 0.44 | 0.93 |

26 | B40 | 0.29 | 0.32 | 0.40 | 0.91 | 0.32 | 0.92 |

27 | B38 | 0.00 | 0.32 | 0.22 | 0.95 | 0.13 | 0.92 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | ||||||
---|---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | |||

Hierarchy | ID Model | No. Pumps b _{i} | n_{i}FSP | m_{i} VSP | Complexity | Investment Cost (EUR) | Operational Cost (EUR/Year) | Maintenance Cost (EUR/Year) |

1 | B28 | 3 | 3 | 0 | 1.0 | EUR 76,003.47 | EUR 18,694.99 | EUR 1036.55 |

7 | B33 | 2 | 0 | 2 | 3.1 | EUR 78,954.39 | EUR 18,257.10 | EUR 973.32 |

10 | B27 | 4 | 4 | 0 | 1.0 | EUR 92,400.92 | EUR 18,663.93 | EUR 1312.08 |

12 | B61 | 3 | 0 | 3 | 3.1 | EUR 125,959.65 | EUR 11,041.80 | EUR 1269.14 |

14 | B59 | 4 | 4 | 0 | 1.0 | EUR 120,430.57 | EUR 18,564.49 | EUR 1420.55 |

20 | B58 | 5 | 5 | 0 | 2.2 | EUR 145,699.82 | EUR 11,276.69 | EUR 1787.40 |

24 | B49 | 7 | 7 | 0 | 1.0 | EUR 173,427.47 | EUR 16,154.81 | EUR 2255.73 |

Priory Weight of Factors | Technical Factors (0.33) | Economic Factors (0.67) | |||||
---|---|---|---|---|---|---|---|

Priority Weight of Criteria | C1 (0.20) | C2 (0.13) | C3 (0.14) | C4 (0.31) | C5 (0.21) | ||

Hierarchy | ID Model | Rating N. Pumps | Rating Complexity | Rating Investment Cost | Rating Operational Cost | Rating Maintenance Cost | Final Rating |

1 | B28 | 0.80 | 1.00 | 0.97 | 0.68 | 0.90 | 1.00 |

7 | B33 | 1.00 | 0.15 | 0.94 | 0.69 | 0.94 | 0.98 |

10 | B27 | 0.60 | 1.00 | 0.83 | 0.68 | 0.73 | 0.97 |

12 | B61 | 0.80 | 0.15 | 0.56 | 0.92 | 0.76 | 0.96 |

14 | B59 | 0.60 | 1.00 | 0.60 | 0.68 | 0.67 | 0.96 |

20 | B58 | 0.40 | 0.32 | 0.39 | 0.91 | 0.45 | 0.94 |

24 | B49 | 0.00 | 1.00 | 0.17 | 0.76 | 0.16 | 0.94 |

**Table 16.**Obtained results in (TF-PS1) in the first alternative of conventional design (analyzing life cycle costs).

Hierarchy | ID Model | b_{i} N° Pumps | n_{i} FSP | m_{i} VSP | Control Mode | Investment Cost (EUR/Year) | Operational Cost (EUR/Year) | Maintenance Cost (EUR/Year) | Total Cost (EUR/Year) |
---|---|---|---|---|---|---|---|---|---|

1 | B28 | 4 | 2 | 2 | 4.2 | EUR 7021.77 | EUR 10,259.15 | EUR 1472.04 | EUR 18,754.75 |

**Table 17.**Obtained results in (TF-PS1) in the second alternative of conventional design (fixing the number of pumps).

Design Method | ID Model | b_{i} | n_{i} FSP | m_{i} VSP | Control Mode | Investment Cost (EUR/Year) | Operational Cost (EUR/Year) | Maintenance Cost (EUR/Year) | Cycle Life Cost (EUR/Year) |
---|---|---|---|---|---|---|---|---|---|

Cycle Life Cost | B27 | 6 | 2 | 4 | 4.2 | EUR 8741.36 | EUR 10,707.82 | EUR 2025.25 | EUR 21,474.43 |

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**MDPI and ACS Style**

Briceño-León, C.X.; Sanchez-Ferrer, D.S.; Iglesias-Rey, P.L.; Martinez-Solano, F.J.; Mora-Melia, D.
Methodology for Pumping Station Design Based on Analytic Hierarchy Process (AHP). *Water* **2021**, *13*, 2886.
https://doi.org/10.3390/w13202886

**AMA Style**

Briceño-León CX, Sanchez-Ferrer DS, Iglesias-Rey PL, Martinez-Solano FJ, Mora-Melia D.
Methodology for Pumping Station Design Based on Analytic Hierarchy Process (AHP). *Water*. 2021; 13(20):2886.
https://doi.org/10.3390/w13202886

**Chicago/Turabian Style**

Briceño-León, Christian X., Diana S. Sanchez-Ferrer, Pedro L. Iglesias-Rey, F. Javier Martinez-Solano, and Daniel Mora-Melia.
2021. "Methodology for Pumping Station Design Based on Analytic Hierarchy Process (AHP)" *Water* 13, no. 20: 2886.
https://doi.org/10.3390/w13202886