# Impact of Hydraulic Variable Conditions in the Solution of Pumping Station Design through Sensitivity Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{max}). Finally, the fifth configuration (5. FSP and VSP with FC) operates in such a way that the PS meets the operational points of the network (Q, H).

## 2. Methodology

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

_{max}), the setpoint curve). The second stage identifies the feasible pump models and defines the overall number of pumps to satisfy the hydraulic conditions of the network. The efficiency curve of the pump, the head pumping curve, and the operating conditions of the network (Q, H) constraints the selection of pump model and the number of pumps. Conventional practice involves choosing a viable pump configuration by seeking out a pump model capable of supplying the highest demanded flow (Q

_{max}) and maximum pressure head (H

_{max}) within the system. Once the appropriate pump model is identified, the necessary quantity of pumps is determined by dividing the maximum required flow (Q

_{max}) by the flow rate of an individual pump (Q

_{b1}) that can generate the needed head (H

_{max}), given that the pumps are set up in a parallel arrangement. However, in some cases, first the number of pumps (b) is fixed. Then, the model is selected according to the ratio of the maximum flow to the number of pumps (Q

_{max}/b) and considering the maximum required head (H

_{max}). Finally, the third stage includes selection of a control system strategy for the PS according to the setpoint curve of the network.

#### 2.1. Required Data

#### 2.1.1. Demand Pattern

#### 2.1.2. PS Layout

_{1}, the length of the pump branches was represented by L

_{2}, and the suction and discharge main lengths were defined by L

_{3}.

#### 2.1.3. Setpoint Curve

#### 2.1.4. Pump Model

_{1}, and B in Equation (2). The pump efficiency curve is defined by the fixed parameters E and F in Equation (3). Both curves consider the rotational speed of the pump (N) and the number of pumps (b). The rotational speed of the pump is expressed as the ratio of the current rotational speed to the nominal rotational speed (α = N/N

_{0}).

_{a}) matches the electrical power utilized by the motor–pump assembly (P). This power encompasses both hydraulic power and the losses incurred during shaft transmission. Consequently, the overall pump assembly efficiency is established by the relation of hydraulic power to shaft power. This relation is defined by the following Equation (4):

_{1}, k

_{2}, k

_{3}are constant parameters, while η

_{v}

_{,0}is the maximum frequency drive efficiency. Finally, P

_{s}in Equation (6) is the consumed power of the PS, and Q

_{FSP}and Q

_{VSP}are the flow delivered by FSPs and VSPs, respectively.

#### 2.2. Approches of PS Design

#### 2.2.1. Classical Approach

#### 2.2.2. Approach Based on the AHP

- Size: The size of the PS is a function of the number of pumps installed and the length of the pipelines in the station (see Figure 1). A higher score is assigned to this sub-criterion if the installation area is small. In this way, the highest size is assigned a score of 0 and the smallest size is assigned a score of 1. Equations (8) and (9) are used to evaluate the size of the PS.

_{1}, L

_{2}, and L

_{3}are set proportionally to the nominal diameter of the pipes (ND

_{i}) by using a constant factor (f

_{i}). The sub-index i represents the type of length (L

_{1}, L

_{2}, or L

_{3}).

- 2.
- Flexibility: The flexibility of the PS is associated with the number of pumps installed, i.e., the higher the number of pumps installed, the larger the flexibility. A higher score is assigned if the number of pumps installed is large. The potential solution with the highest number of pumps (b) is assigned a score of 1 and the solution with the smallest number of pumps is assigned a score of 0.
- 3.
- Complexity of control: This sub-criterion is related to the complexity of operation of the control system. The smaller the number of control elements in the system, the less complex the control system is considered to be. The complexity of operation is evaluated with a numeric score from 0 to 1 (see Table 2), corresponding to the highest and lowest levels of complexity, respectively, for the control systems. The scores are obtained from pairwise comparisons of the different control system strategies based on the AHP.

- 4.
- Investment cost: This includes the costs of the pumps, pipes, fittings, and control elements, as well as their installation. The investment costs are annualized considering the life cycle of the elements and the annual interest rate, and they are represented by Equation (10). A higher score is assigned to this sub-criterion if the investment cost is small. In this way, the solution with the lowest investment cost is assigned a score of 1 while 0 goes to the solution with the highest investment cost.

_{Inv}represents the initial investment outlay for the PS, C

_{PS}signifies the cost per unit of each individual pump, b denotes the count of installed pumps, FA

_{PS}stands for the amortization factor of the pumps, C

_{pipe}represents the cost per unit length of the pipelines, L

_{T}indicates the overall pipeline length, and FA

_{pipe}accounts for the pipeline amortization factor. Furthermore, C

_{ACCi}corresponds to the cost per unit of minor station accessories such as valves and pipe connectors, while N

_{ACCi}refers to the quantity of each minor accessory within the station. FA

_{ACCI}represents the amortization factor for these minor accessories. Similarly, C

_{RMj}signifies the unit cost of each control component (such as pressure switches, flow meters, pressure transducers, PLC, and VFD), N

_{RMj}represents the number of units for each control element, and FA

_{RMj}stands for the amortization factor of the control system devices. The amortization factor is determined using Equation (11).

_{i}, which represents the factor for amortizing the components within the PS infrastructure; T

_{i}, denoting the yearly interest rate; and N

_{LC}, indicating the count of years that constitute the life cycle of the components within the PS.

- 5.
- Operational cost: This sub-criterion is related to the yearly cost (EUR) of energy consumed for operation of the PS, and it is calculated using Equation (12).

_{d}is the number of daily demand scenarios, d corresponds to each demand scenario, the duration of the time slot is represented by Δt, Pr

_{DP,d}is the probability of occurrence of every scenario, and TE is the electric tariff. The number 365 is used to obtain the number of days of occurrence for every demand scenario. The more economical the operational costs, the higher the rating given to this sub-criterion. Hence, the solution with the lowest operational cost is assigned a score of 1, while 0 goes to the solution with the highest operational cost.

- 6.
- Maintenance cost: This signifies the expenses associated with performing maintenance tasks within the PS in order to uphold its optimal state. The regularity and expenses of maintenance tasks for the PS components are derived from a database, which is used to calculate the yearly maintenance expenditures. This cost is represented by Equation (13). This sub-criterion receives a higher rating when the maintenance cost is low. In this way, the solution with the lowest maintenance cost has a score of 1, while the solution with the highest maintenance cost has a score of 0.

_{Maint}denotes the maintenance cost associated with the PS. C

_{APSi}represents the individual cost for maintenance tasks related to the pump. F

_{APi}signifies the yearly occurrence of maintenance activities linked to the pump. The variable ‘b’ corresponds to the count of pumps within the PS. C

_{pipe}stands for the individual cost pertaining to maintenance tasks related to the pipelines and is expressed in units of currency (EUR/m). F

_{pipe}represents the annual frequency at which pipeline maintenance is conducted. The parameter L

_{T}refers to the total extent of pipeline length. C

_{ACCj}signifies the individual cost for maintenance actions related to accessories within the PS, including valves and connectors. F

_{ACCj}represents the yearly frequency of maintenance for each accessory. N

_{ACCJ}represents the total quantity of units for each accessory. C

_{RM,j}refers to the unit cost associated with maintaining control elements within the PS, such as pressure switches, flow meters, pressure transducers, PLCs, and frequency inverters. F

_{RMk}indicates the annual frequency of maintenance for each control element, while N

_{RMj}represents the total quantity of units for each control element. It is important to note that the maintenance tasks and their frequency for the PS components are based on the guidelines provided by the manufacturer.

- 7.
- MEI: The minimum efficiency index (MEI) is a metric used to evaluate the energy efficiency of a pump. It is a standardized way to assess the efficiency of different pump models. A higher MEI value signifies better overall efficiency and suggests that the pump operates more efficiently across a range of flow rates. This index is established by EU regulation 547/2012 [28]. This regulation established an MEI of 0.7 as excellent, and an MEI below 0.4 as not acceptable. This sub-criterion is evaluated using a numeric scale from 0 to 1 with pairwise comparison of different MEI values based on the AHP. The obtained scores are detailed in Table 3:

- 8.
- CO
_{2}emission: This signifies the volume of CO_{2}generated by the PS during its functioning. It is calculated by multiplying the energy utilized by the PS with the emission factor EF determined by El Ministerio de la Transformación Ecológica y el Reto Demográfico [29]. This sub-criterion is evaluated in terms of Kg of CO_{2}in a year.

_{2}emission is low. As a result, the solution exhibiting the lowest CO

_{2}emission receives a score of 1, whereas the solution associated with the highest CO

_{2}emission is given a score of 0.

- 9.
- Performance of regulation: This performance (η
_{RS}) relates the required energy at the demand node of the network to the energy delivered by the PS and is defined as the ratio of the required head of the network (H_{c}) to the head pumping (H) (see Equation (15)). This sub-criterion receives a high score if the regulation’s performance is good. Consequently, a score of 1 is given to the solution exhibiting the best regulatory performance, whereas a score of 0 is attributed to the solution with the worst regulatory performance.

_{feasible pump models}× 5 control systems) are evaluated on the basis of the 9 subcriteria. The third stage reduces the possible solutions by identifying dominant and dominated solutions based on the 9 subcriteria. The dominant solutions are scored by using an average of each solution’s scores on every one of the 9 subcriteria weighted with their respective priority. Finally, the solution with the highest score is considered to be the ultimate solution for the PS.

#### 2.3. Sensitibity Analysis

_{m}), pipeline lengths of the PS layout (L

_{i}), hydraulic parameters of the setpoint curve (ΔH, R), electricity tariff prices (TE), and annual amortization interest rate (T

_{i}). The objective of the sensitivity analysis was to determine the operational limits of these network parameters without changing the final solution of PS design. Therefore, gradual increases and decreases in each of these network parameters were performed iteratively until the final solutions for the two PS design approaches changed. The increment and decrement intervals were considered to be 0.5%. Finally, this analysis allowed evaluation of the robustness and reliability of the pumping station designs based on the AHP method versus the classical design approach.

## 3. Case Study

_{m}= 25.00 L/s) and the parameters of the setpoint curve (ΔH, R, c).

_{1}= 20, N

_{2}= 40, and N

_{3}= 20. Finally, the maximum number of installed pumps (b

_{max}) allowed for the PS design was 10.

_{c}) from 0 to 1.

#### 3.1. Results

_{i}), by increasing and decreasing them with a step of 0.5% with respect to the original interest rate (T

_{i}) of the case study until the ultimate solution in every approach was different from the original case study, to determine the sensitivity of this data for selecting the ultimate solution in both approaches. The obtained results of this sensitivity analysis are shown in Table 6. The obtained results in Table 6 demonstrated that the ultimate solutions in both approaches were not sensitive to the interest rate (T

_{i}), even though the interest rate could change drastically +/−50% compared to the original interest rate. The only changes in the ultimate solutions for the two approaches produced by increasing or decreasing the interest rate were in the investment costs and LCC. The characteristics of the pump models in the ultimate solutions and the values for the other subcriteria in both approaches were identical to the original results of the case study.

_{m}) in both approaches is illustrated in Table 7 and Table 8. The mean demand (Q

_{m}) of the original case study was incremented and decremented with a step of 1% until the ultimate solution in every PS design approach was different.

_{m_max,}Q

_{m_min}) in the first approach was 25.25 L/s and 24.25 L/s, respectively. The ultimate solution of the original case study was valid with a range of mean demand (Q

_{m}) from 24.25 L/s to 25.25 L/s with the same pump model and same control system strategy, as can observed in Table 7. A variation in the mean demand (Q

_{m}) of the case study generated different values in the subcriteria, especially for investment costs, operational costs, GHG emissions, and LCC in the ultimate solutions. However, the ultimate solution remained the same. In contrast, when the mean demand (Q

_{m}) was outside the range 24.25 L/s to 25.25 L/s, the ultimate solution of the first approach was different from the ultimate solution of the original case study, in terms of pump model, control system, and the values for the subcriteria.

_{m_,min}= 24.50 L/s and Q

_{m_max}= 25.50 L/s, respectively. The ultimate solution of the second approach in this range of mean demand (Q

_{m}= 24.50 L/s to 25.50 L/s) was the same as the ultimate solution of the original case study with the same pump model and control system strategy, but with different subcriteria values, as can observed in Table 8. For example, operational costs, GHG emission, and the LCC of the ultimate solution changed in accordance with mean demand (Q

_{m}). On the other hand, if the mean demand (Q

_{m}) of the WDN was outside of that range (24.50 L/s to 25.50 L/s), the ultimate solution of the second approach was different from the ultimate solution of the original case study, involving a different pump model and different values for the subcriteria.

_{max}< ΔH < ΔH

_{min}), the ultimate solutions were different from the ultimate solution of the original case study and featured different pump models, control system strategies, and values for the subcriteria, as reported in Table 9.

_{max}< ΔH < ΔH

_{min}), the ultimate solutions differed from the original case study. These divergent solutions involved different pump models, control system strategies, and distinct subcriteria values, as reported in Table 10.

_{max}, R

_{min}), using the first and second approaches, respectively. Additionally, these tables display the ultimate solutions obtained by each approach when scenarios with values of losses (R) exceeding the maximum and minimum limits of the range were considered.

^{−3}to 1.14 × 10

^{−3}. When losses (R) reached these maximum and minimum limits (R

_{max}, R

_{min}), the ultimate solutions of the first approach were the same as the ultimate solution with the original data of the WDN. In fact, these ultimate solutions yielded the same values for the subcriteria as the ultimate solution of the original case study, except for the subcriteria operational costs and GHG emissions and the LCC. The values of these subcriteria in the ultimate solution were in accordance with the losses in the WDN. On the contrary, when losses (R) reached values above or below the maximum and minimum of the permissible range (e.g., R

_{max}= 1.16 × 10

^{−3}and R

_{min}= 1.10 × 10

^{−3}), the ultimate solutions of the first approach were different from the ultimate solution in the original case study, including different pump models and different subcriteria values.

^{−3}to 1.16 × 10

^{−3}(wider than the range obtained for the first design approach). When the losses (R) fell within these upper and lower limits (0.80 × 10

^{−3}< R < 1.16 × 10

^{−3}), the ultimate solutions obtained using the second approach aligned with the ultimate solution derived from the original WDN data. In fact, the only differences between these ultimate solutions and the original ultimate solution were in the operational costs, GHG emission, and LCC. The values of these subcriteria for the ultimate solution were in accordance with the losses (R) in the WDN. Conversely, when the losses (R) exceeded or fell below the permissible range (for instance, with values of R = 1.16 × 10

^{−3}and R = 1.10 × 10

^{−3}), the ultimate solutions obtained using the second approach differed from the ultimate solution in the original case study, involving different pump models and consequently different subcriteria values.

_{min}= EUR 0.034) led to the same pump model and control system as the ultimate solution in the original case study. In this case, the change of the average annual electric tariff only affected the operational costs and LCC. However, when the electric tariff reached the maximum average annual electric tariff (TE

_{max}= EUR 0.17) in the first approach, the ultimate solution was different from the ultimate solution in the original case study, as it featured a different pump model and consequently different subcriteria values. In this case, the ultimate solution of the first approach was affected significantly when the electric tariff reached the maximum average annual tariff over the last 5 years.

_{min}= EUR 0.034 and TE

_{max}= EUR 0.17), resulted in the adoption of the same pump model and control system as the ultimate solution in the original case study. In the second approach, the alteration of the electric tariff did not affect the ultimate solution of the PS design. The electric tariff solely impacted the operational costs and LCC.

#### 3.2. Discussion

_{m}), the setpoint curve (e.g., static head (ΔH), losses (R)), and the electric tariff (TE). In addition, other variables influence PS design, such as the interest rate (T

_{i}) of the amortization factor. However, the effects that these variables have in PS design are different. Moreover, another important point is that these variables affect the outcome of PS design differently depending on the approach considered in the design. In this study, two approaches to PS design were considered. The first approach, the classic approach, was based on the minimization of LCC, while the second approach was based on the AHP and considered technical, economic, and environmental criteria. Therefore, a sensitivity analysis of the different meaningful variables of PS design was carried out for both design approaches. The most salient results of the sensitivity analyses performed on each PS design approach are discussed below.

_{i}) of amortization factor in both PS design approaches (see Table 6) showed that the ultimate solutions of both Ps design approaches were not sensitive to alteration of the interest rate (T

_{i}). The only effects produced in the ultimate solution in each design approach by a change in the interest rate (T

_{i}) were in the investment cost and the LCC as the interest rate (T

_{i}) varied. However, the ultimate solution for each approach was the same regardless of the interest rate (T

_{i}).

_{m}) in approaches 1 and 2 (referred to in Table 7 and Table 8) demonstrated that the selection of the ultimate solution in both approaches was very sensitive to a fluctuation in the mean flow (Q

_{m}). The permitted flow range in the first design approach, where the ultimate solution of the original case study was not altered, was from 24.25 L/s to 25.25 L/s. Hence, the range of mean flow variations (ΔQ

_{m}) that would not affect the ultimate solution in the first approach was 1 L/s. Similarly, the range of the mean flow fluctuations (ΔQ

_{m}) in the second design approach that would not alter the ultimate solution of the original case study was 1 L/s, with a range from 24.5 L/s to 25.5 L/s. Therefore, both PS design approaches have the same sensitive to fluctuation in the mean flow (Q

_{m}) in the WDN.

^{−3}to 1.14 × 10

^{−3}, with an amplitude of 0.13 × 10

^{−3}. The second approach had a wider range, from 0.80 × 10

^{−3}to 1.16 × 10

^{−3}, with an interval of 0.36 × 10

^{−3}. The variation in losses (R) in the setpoint curve primarily impacted operational costs, GHG emissions, and LCC in the ultimate solution of the PS. The first approach solely considered LCC for ultimate solution selection, making it more susceptible to changes in losses (R) in the setpoint curve. Conversely, the second approach incorporated technical, economic, and environmental criteria using the AHP, resulting in a more robust solution when losses varied in the setpoint curve.

## 4. Conclusions

- The tolerance range for the variation in amortization interest rate was undefined because the amortization rate did not affect the selection of the ultimate solution in either PS design approach (see Table 8).
- Variations in the amortization interest rate impacted both pumping station design approaches in the same way. These mainly affected the investment costs and, consequently, the LCC in the final solutions of both approaches. However, the pump model of the ultimate solutions in both approaches remained unchanged.

_{m}):

- Variations in the mean flow (Q
_{m}) within the tolerance range (Q_{min}< Q_{m}_{<}Q_{max}) had an impact on operational costs, GHG emissions, and LCC, while maintaining the ultimate solution of the original case study in both approaches. - Fluctuations in the average flow rate outside the tolerance range generated significant effects on the selection of the final solution in both design approaches. In the first approach, with the flow variation outside the tolerance range, the final solution was changed mainly in the pump model and its flow capacity, while in the second approach, the final solution was changed in the pump model and its flow capacity, the number of pumps, and the control strategy.

- Fluctuations in static head (ΔH) and losses (R) had a greater impact on the first design approach compared to the second approach.
- Variations in static head (ΔH) and losses (R) within the tolerance range in the setpoint curve primarily impacted operational costs, greenhouse gas (GHG) emissions, and the LCC of the ultimate solutions in both design approaches. However, the first approach, which considered only LCC, was more susceptible to changes in losses, while the second approach, incorporating multi-criteria analysis including technical, economic, and environmental factors, was more robust facing variations in the variables of static head (ΔH) and losses (R).
- On the other hand, when the variations of the static head (ΔH) and losses (R) were outside the tolerance range, the main impact on the selected solutions in both approaches was a change in the pump model, with different flow and pumping head capacity, from that of the ultimate solution in the original case study.

- The sensitivity analysis revealed important differences between the two design approaches regarding the electric tariff (TE), as can be observed in Table 13. The tolerance range of the electric tariff (TE) of the first approach had a defined width, whereas the tolerance range (TE) in the second approach was undefined because variation in this variable did not affect its ultimate solution.
- The solution obtained in the first approach was affected by significant variations in the electric tariff, as they were considered in the present work. In contrast, the solution obtained in the second approach remained unaffected by changes in the electric tariff, even when the electric tariff (TE) had extreme variations.
- Changes in the electric tariff primarily impacted operational costs, but they had a significant impact only on the ultimate solution of the first approach, which relied solely on LCC. The second approach, considering technical, economic, and environmental aspects, based on the AHP, resulted in a more robust solution that remained unchanged despite variations in the annual electricity tariff (TE).

_{i}), mean demand (Q

_{m}), static head (ΔH), losses (R) in the setpoint curve, and electric tariff (TE). On the other hand, the first design approach, which relied solely on LCC, was more susceptible to variations in these variables.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Leiby, V.M.; Burke, M.E. Energy Efficiency Best Practices for North American Drinking Water Utilities; WRF: Albany, NY, USA, 2011. [Google Scholar]
- Luna, T.; Ribau, J.; Figueiredo, D.; Alves, R. Improving energy efficiency in water supply systems with pump scheduling optimization. J. Clean. Prod.
**2019**, 213, 342–356. [Google Scholar] [CrossRef] - Makaremi, Y.; Haghighi, A.; Ghafouri, H.R. Optimization of Pump Scheduling Program in Water Supply Systems Using a Self-Adaptive NSGA-II; a Review of Theory to Real Application. Water Resour. Manag.
**2017**, 31, 1283–1304. [Google Scholar] [CrossRef] - Carpitella, S.; Brentan, B.; Montalvo, I.; Izquierdo, J.; Certa, A. Multi-criteria analysis applied to multi-objective optimal pump scheduling in water systems. Water Sci. Technol. Water Supply
**2019**, 19, 2338–2346. [Google Scholar] [CrossRef] - Martin-Candilejo, A.; Martin-Carrasco, F.J.; Santillán, D. How to select the number of active pumps during the operation of a pumping station: The convex hyperbola charts. Water
**2021**, 13, 1474. [Google Scholar] [CrossRef] - Wu, W.; Simpson, A.R.; Maier, H.R. Accounting for Greenhouse Gas Emissions in Multiobjective Genetic Algorithm Optimization of Water Distribution Systems. J. Water Resour. Plan. Manag.
**2010**, 136, 146–155. [Google Scholar] [CrossRef] - Torregrossa, D.; Capitanescu, F. Optimization models to save energy and enlarge the operational life of water pumping systems. J. Clean. Prod.
**2019**, 213, 89–98. [Google Scholar] [CrossRef] - Alandi, P.P.; Pérez, P.C.; Álvarez, J.F.O.; Hidalgo, M.M.; Martín-Benito, J.M.T. Pumping Selection and Regulation for Water-Distribution Networks. J. Irrig. Drain. Eng.
**2005**, 131, 273–281. [Google Scholar] [CrossRef] - Lamaddalena, N.; Khila, S. Efficiency-driven pumping station regulation in on-demand irrigation systems. Irrig. Sci.
**2013**, 31, 395–410. [Google Scholar] [CrossRef] - Karpenko, M.; Stosiak, M.; Šukevičius, Š.; Skačkauskas, P.; Urbanowicz, K.; Deptuła, A. Hydrodynamic Processes in Angular Fitting Connections of a Transport Machine’s Hydraulic Drive. Machines
**2023**, 11, 355. [Google Scholar] [CrossRef] - Olszewski, P. Genetic optimization and experimental verification of complex parallel pumping station with centrifugal pumps. Appl. Energy
**2016**, 178, 527–539. [Google Scholar] [CrossRef] - Cimorelli, L.; Covelli, C.; Molino, B.; Pianese, D. Optimal regulation of pumping station in water distribution networks using constant and variable speed pumps: A technical and economical comparison. Energies
**2020**, 13, 2530. [Google Scholar] [CrossRef] - Briceño-León, C.X.; Iglesias-Rey, P.L.; Martinez-Solano, F.J.; Mora-Melia, D.; Fuertes-Miquel, V.S. Use of fixed and variable speed pumps in water distribution networks with different control strategies. Water
**2021**, 13, 479. [Google Scholar] [CrossRef] - Deptuła, A.; Augustynowicz, A.; Stosiak, M.; Towarnicki, K.; Karpenko, M. The Concept of Using an Expert System and Multi-Valued Logic Trees to Assess the Energy Consumption of an Electric Car in Selected Driving Cycles. Energies
**2022**, 15, 4631. [Google Scholar] [CrossRef] - Saaty, T.L. Analytic Hierarchy Process; McGraw Hil: New York, NY, USA, 1980. [Google Scholar]
- Saaty, T.L. Decision making with the analytic hierarchy process. Int. J. Serv. Sci.
**2008**, 1, 83–98. [Google Scholar] [CrossRef] - Aşchilean, I.; Badea, G.; Giurca, I.; Naghiu, G.S.; Iloaie, F.G. Choosing the optimal technology to rehabilitate the pipes in water distribution systems using the AHP method. Energy Procedia
**2017**, 112, 19–26. [Google Scholar] [CrossRef] - Kurbatova, A.; Abu-Qdais, H.A. Using multi-criteria decision analysis to select waste to energy technology for a mega city: The case of Moscow. Sustainability
**2020**, 12, 9828. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef] - Briceño-León, C.X.; Iglesias-Rey, P.L.; Martínez-Solano, F.J.; Creaco, E. Integrating Demand Variability and Technical, Environmental, and Economic Criteria in Design of Pumping Stations Serving Closed Distribution Networks. J. Water Resour. Plan. Manag.
**2023**, 149, 04023002. [Google Scholar] [CrossRef] - Lee, C.; Tien, I. Sensitivity analysis of interdependency parameters using probabilistic system models. In Proceedings of the 13th International Conference on Applications of Statistics and Probability in Civil Engineering, Brussels, Belgium, 26–30 May 2019; pp. 1–13. [Google Scholar]
- Morosini, A.F.; Haghshenas, S.S.; Haghshenas, S.S.; Choi, D.Y.; Geem, Z.W. Sensitivity analysis for performance evaluation of a real water distribution system by a pressure driven analysis approach and artificial intelligence method. Water
**2021**, 13, 1116. [Google Scholar] [CrossRef] - Jensen, H.; Jerez, D. A Stochastic Framework for Reliability and Sensitivity Analysis of Large Scale Water Distribution Networks. Reliab. Eng. Syst. Saf.
**2018**, 176, 80–92. [Google Scholar] [CrossRef] - Walski, T.; Creaco, E. Selection of pumping configuration for closed water distribution systems. J. Water Resour. Plan. Manag.
**2016**, 142, 04016009. [Google Scholar] [CrossRef] - Sanks, R.L. Pumping Station Design, 2nd ed.; Butterworth-Heinemann: Woburn, MA, USA, 1998. [Google Scholar]
- Coelho, B.; Andrade-Campos, A.G. A new approach for the prediction of speed-adjusted pump efficiency curves. J. Hydraul. Res.
**2016**, 54, 586–593. [Google Scholar] [CrossRef] - Hydraulic Institute. Pump Life Cycle Costs: A Guide to LCC Analysis for Pumping Systems, 2nd ed.; Office of Energy Efficiency and Renewable Energy (EERE), Energy Efficiency Office, Advanced Manufacturing Office: Washington, DC, USA, 2001.
- The European Union Comission. Commission Regulation (EU) N0 547/2012. Off. J. Eur. Union
**2012**, 4, 178–183. [Google Scholar] - Oficina Española del Cambio Climático (OECC). Factores de Emisión Registro de Huella de Carbono, Compensacion y Proyectos de Absorción de Dióxido de Carbono; Ministerio para la Transición Ecológica y el Reto Demográfico España: Madrid, Spain, 2022.

Saaty’s Scale | Proposed Scale | ||||
---|---|---|---|---|---|

NS | Ci | Cj | Ci | Cj | NS |

1 | 50.00% | 50.00% | 50.00% | 50.00% | 1.00 |

2 | 67.67% | 33.33% | 55.00% | 45.00% | 1.22 |

3 | 75.00% | 25.00% | 60.00% | 40.00% | 1.50 |

4 | 80.00% | 20.00% | 65.00% | 35.00% | 1.86 |

5 | 83.33% | 16.67% | 70.00% | 30.00% | 2.33 |

6 | 85.71% | 14.29% | 75.00% | 25.00% | 3.00 |

7 | 87.50% | 12.50% | 80.00% | 20.00% | 4.00 |

8 | 88.89% | 11.11% | 85.00% | 15.00% | 5.67 |

9 | 90.00% | 10.00% | 90.00% | 10.00% | 9.00 |

_{i}, C

_{j}: importance percentages (%). NS: numerical scale.

Control System Configuration | Complexity Level | Numeric Score |
---|---|---|

- 1.
- Without CS
| 1 | 1.00 |

- 2.
- FSP with PC
| 2 | 0.57 |

- 3.
- FSP with FC
| 3 | 0.32 |

- 4.
- FSP-VSP with PC
| 4 | 0.15 |

- 5.
- FSP-VSP with FC
| 5 | 0.07 |

MEI Index | Numeric Score |
---|---|

0.1 | 0.05 |

0.2 | 0.07 |

0.3 | 0.12 |

0.4 | 0.27 |

0.5 | 0.40 |

0.6 | 0.61 |

0.7 | 1.00 |

Data | Q_{m} (L/s) | ΔH (m) | R | c |

25.00 | 29.50 | 0.0109 | 1.95 | |

${H}_{c}=29.50+0.0109\times {Q}^{1.95}$ |

Approaches | First Approach | Second Approach | |
---|---|---|---|

Pump Characteristics | Pump Model | 32 | 64 |

Q_{0} (L/s) | 22.71 | 16.97 | |

H_{0} (m) | 61.06 | 61.52 | |

η_{max} (%) | 61% | 83% | |

Tec. Aspects | C1 (m^{2}) | 151.20 | 140.80 |

C2 | 0 FSP–3 VSP | 1 FSP–3 VSP | |

C3 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 5355.78 | 12,778.24 |

C5 (EUR/year) | 13,079.49 | 9460.92 | |

C6 (EUR/year) | 1193.21 | 1462.31 | |

Env. Aspects | C7 | 0.10 | 0.70 |

C8 Kg CO_{2} | 57,041.02 | 41,208.60 | |

C9 (%) | 100% | 100% | |

Life Cycle Cost (EUR/year) | 19,628.48 | 23,701.47 |

Approaches | Ti + 50% = 4.5% | Ti − 50% = 1.5% | Ti + 50% = 4.5% | Ti − 50% = 1.5% | |
---|---|---|---|---|---|

Approach 1 | Approach 1 | Approach 2 | Approach 2 | ||

Pump Characteristics | PumpModel | 32 | 32 | 64 | 64 |

Q_{0} (L/s) | 22.71 | 22.71 | 16.97 | 16.97 | |

H_{0} (m) | 61.06 | 61.06 | 61.52 | 61.52 | |

η_{max} (%) | 61% | 61% | 83% | 83% | |

Tec. Aspects | C1 (m^{2}) | 151.20 | 151.20 | 140.80 | 140.80 |

C2 | 0 FSP–3 VSP | 0 FSP–3 VSP | 1 FSP–3 VSP | 1 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 5876.52 | 4866.67 | 13,928.41 | 11,688.22 |

C5 (EUR/year) | 13,079.49 | 13,079.49 | 9460.92 | 9460.92 | |

C6 (EUR/year) | 1193.21 | 1137.46 | 1462.31 | 1462.31 | |

Env. Aspects | C7 | 0.10 | 0.10 | 0.70 | 0.70 |

C8 Kg CO_{2} | 57,041.02 | 57,041.02 | 41,208.60 | 41,208.60 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 20,197.24 | 19,187.39 | 24,851.63 | 22,611.45 |

**Table 7.**Sensitivity analysis with the mean flow in the PS design approach based on LCC minimization.

Approaches | Q_{m_max} = Q_{m} + 1%(25.25 L/s) | Q_{m} + 2%(25.5 L/s) | Q_{m_max} = Q_{m} − 3%(24.25 L/s) | Q_{m} − 4%(24.0 L/s) | |
---|---|---|---|---|---|

Approach 1 | Approach 1 | Approach 1 | Approach 1 | ||

Pump Characteristics | Pump Model | 32 | 33 | 32 | 31 |

Q_{0} (L/s) | 22.71 | 24.32 | 22.71 | 19.50 | |

H_{0} (m) | 61.06 | 78.73 | 61.06 | 50.43 | |

η_{max} (%) | 61% | 61% | 61% | 70% | |

Tec. Aspects | C1 (m^{2}) | 151.20 | 151.20 | 151.20 | 158.40 |

C2 | 0 FSP–3 VSP | 0 FSP–3 VSP | 1 FSP–2 VSP | 2 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 5355.78 | 6604.70 | 5152.23 | 6328.61 |

C5 (EUR/year) | 13,258.22 | 13,320.51 | 12,552.96 | 10,594.24 | |

C6 (EUR/year) | 1193.21 | 1193.21 | 1170.78 | 1739.98 | |

Env. Aspects | C7 | 0.10 | 0.11 | 0.10 | 0.10 |

C8 Kg CO_{2} | 57,814.90 | 58,075.52 | 54,760.90 | 46,194.04 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 19,807.21 | 21,118.41 | 18,875.97 | 18,662.84 |

**Table 8.**Sensitivity analysis with the mean flow in the PS design approach based on AHP with technical, economic, and environmental criteria.

Approaches | Q_{m_max} = Q_{m} + 2%(25.50 L/s) | Q_{m} + 3%(25.75 L/s) | Q_{m_min} = Q_{m} − 2%(24.50 L/s) | Q_{m} − 3%(24.25 L/s) | |
---|---|---|---|---|---|

Approach 2 | Approach 2 | Approach 2 | Approach 2 | ||

Pump Characteristics | Pump Model | 64 | 33 | 64 | 44 |

Q_{0} (L/s) | 16.97 | 24.32 | 16.97 | 19.50 | |

H_{0} (m) | 61.52 | 78.73 | 61.52 | 50.43 | |

η_{max} (%) | 83% | 61% | 83% | 70% | |

Tec. Aspects | C1 (m^{2}) | 140.80 | 140.80 | 140.80 | 144.00 |

C2 | 1 FSP–3 VSP | 0 FSP–3 VSP | 1 FSP–3 VSP | 6 FSP–0 VSP | |

C3 | 5 | 5 | 5 | 3 | |

Eco. Aspects | C4 (EUR/year) | 12,778.24 | 8376.14 | 12,778.24 | 9542.55 |

C5 (EUR/year) | 9732.85 | 13,501.42 | 9193.33 | 14,782.81 | |

C6 (EUR/year) | 1462.31 | 1210.36 | 1462.31 | 1918.87 | |

Env. Aspects | C7 | 0.70 | 0.12 | 0.70 | 0.70 |

C8 Kg CO_{2} | 42,387.25 | 58,858.99 | 40,048.68 | 64,669.36 | |

C9 (%) | 100% | 100% | 100% | 71% | |

Life Cycle Cost (EUR/year) | 23,973.41 | 23,087.92 | 23,433.88 | 26,244.24 |

**Table 9.**Sensitivity analysis with the parameter (ΔH) of the setpoint curve for the first PS design approach.

Approaches | ΔH_{max} = ΔH + 5%(30.98 m) | ΔH + 6% (31.27 m) | ΔH_{min} = ΔH − 8%(27.14 m) | ΔH − 9% (26.85 m) | |
---|---|---|---|---|---|

Approach 1 | Approach 1 | Approach 1 | Approach 1 | ||

Pump Characteristics | Pump Model | 32 | 33 | 32 | 31 |

Q_{0} (L/s) | 22.71 | 24.32 | 22.71 | 19.50 | |

H_{0} (m) | 61.06 | 78.73 | 61.06 | 50.43 | |

η_{max} (%) | 61% | 61% | 61% | 70% | |

Tec. Aspects | C1 (m^{2}) | 151.20 | 151.20 | 151.20 | 158.40 |

C2 | 0 FSP–3 VSP | 0 FSP–3 VSP | 1 FSP–2 VSP | 2 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 5355.78 | 6604.70 | 5355.78 | 6328.61 |

C5 (EUR/year) | 13,549.89 | 13,494.90 | 12,334.95 | 10,471.42 | |

C6 (EUR/year) | 1193.21 | 1193.21 | 1193.21 | 1739.98 | |

Env. Aspects | C7 | 0.10 | 0.11 | 0.10 | 0.10 |

C8 Kg CO_{2} | 59,104.26 | 58,860.22 | 53,775.66 | 45,625.47 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 20,098.88 | 21,292.80 | 18,883.94 | 18,540.02 |

**Table 10.**Sensitivity analysis with the parameter (ΔH) of the setpoint curve for the second PS design approach.

Approaches | ΔH_{max} = ΔH + 7%(31.57 m) | ΔH + 8% (31.27 m) | ΔH_{min} = ΔH − 21%(23.31 m) | ΔH − 22% (23.01 m) | |
---|---|---|---|---|---|

Approach 2 | Approach 2 | Approach 2 | Approach 2 | ||

Pump Characteristics | Pump Model | 64 | 32 | 64 | 31 |

Q_{0} (L/s) | 16.97 | 22.71 | 16.97 | 19.35 | |

H_{0} (m) | 61.52 | 61.06 | 61.52 | 50.43 | |

η_{max} (%) | 83% | 61% | 83% | 70% | |

Tec. Aspects | C1 (m^{2}) | 140.80 | 140.80 | 140.80 | 140.80 |

C2 | 1 FSP–3 VSP | 1 FSP–3 VSP | 1 FSP–3 VSP | 1 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 12,778.24 | 6261.77 | 12,778.24 | 5447.80 |

C5 (EUR/year) | 9922.35 | 13,839.98 | 8092.24 | 9421.28 | |

C6 (EUR/year) | 1462.31 | 1462.31 | 1462.31 | 1462.31 | |

Env. Aspects | C7 | 0.70 | 0.10 | 0.70 | 0.19 |

C8 Kg CO_{2} | 43,226.87 | 60,376.79 | 35,223.68 | 41,029.30 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 24,162.90 | 21,564.06 | 22,814.32 | 16,331.39 |

**Table 11.**Sensitivity analysis with the losses (R) of the setpoint curve in the first PS design approach.

Approaches | R_{max} = R + 5%(0.0114) | R + 6% (0.0116) | R_{min} = R − 7%(0.0101) | R − 8% (0.0100) | |
---|---|---|---|---|---|

Approach 1 | Approach 1 | Approach 1 | Approach 1 | ||

Pump Characteristics | Pump Model | 32 | 33 | 32 | 31 |

Q_{0} (L/s) | 22.71 | 24.32 | 22.71 | 19.35 | |

H_{0} (m) | 61.06 | 78.73 | 61.06 | 50.43 | |

η_{max} (%) | 61% | 61% | 61% | 70% | |

Tec. Aspects | C1 (m^{2}) | 151.20 | 151.20 | 151.20 | 158.40 |

C2 | 0 FSP–3 VSP | 0 FSP–3 VSP | 1 FSP–2 VSP | 2 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 5355.78 | 6604.70 | 5355.78 | 6328.61 |

C5 (EUR/year) | 13,233.72 | 13,139.54 | 12,864.50 | 10,990.73 | |

C6 (EUR/year) | 1193.21 | 1193.21 | 1193.21 | 1739.98 | |

Env. Aspects | C7 | 0.10 | 0.11 | 0.10 | 0.10 |

C8 Kg CO_{2} | 57,707.91 | 57,290.64 | 56,111.42 | 47,912.66 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 19,782.71 | 20,937.44 | 19,413.48 | 19,059.32 |

**Table 12.**Sensitivity analysis with the losses (R) of the setpoint curve in the second PS design approach.

Approaches | R_{max} = R + 6%(0.0116) | R + 7% (0.0117) | R_{min} = R − 19%(0.0088) | R − 20% (0.0087) | |
---|---|---|---|---|---|

Approach 2 | Approach 2 | Approach 2 | Approach 2 | ||

Pump Characteristics | Pump Model | 64 | 32 | 64 | 31 |

Q_{0} (L/s) | 16.97 | 22.71 | 16.97 | 19.35 | |

H_{0} (m) | 61.52 | 61.06 | 61.52 | 50.43 | |

η_{max} (%) | 83% | 61% | 83% | 70% | |

Tec. Aspects | C1 (m^{2}) | 140.80 | 140.80 | 140.80 | 140.80 |

C2 | 1 FSP–3 VSP | 1 FSP–3 VSP | 1 FSP–3 VSP | 1 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 12,778.24 | 6261.77 | 12,778.24 | 5447.80 |

C5 (EUR/year) | 9595.57 | 13,301.39 | 9035.25 | 10,640.50 | |

C6 (EUR/year) | 1462.31 | 1462.31 | 1462.31 | 1462.31 | |

Env. Aspects | C7 | 0.70 | 0.10 | 0.70 | 0.19 |

C8 Kg CO_{2} | 41,790.42 | 58,000.73 | 39,369.32 | 46,400.27 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 23,836.13 | 21,025.46 | 23,757.32 | 17,550.61 |

Approaches | TE_{max} = EUR 0.17 | TE_{min} = EUR 0.034 | TE_{max} = EUR 0.17 | TE_{min} = EUR 0.034 | |
---|---|---|---|---|---|

Approach 1 | Approach 1 | Approach 2 | Approach 2 | ||

Pump Characteristics | Pump Model | 31 | 32 | 64 | 64 |

Q_{0} (L/s) | 19.35 | 22.71 | 16.97 | 16.97 | |

H_{0} (m) | 50.43 | 61.06 | 61.52 | 61.52 | |

η_{max} (%) | 70% | 61% | 83% | 83% | |

Tec. Aspects | C1 (m^{2}) | 140.80 | 151.20 | 140.80 | 140.80 |

C2 | 1 FSP–3 VSP | 0 FSP–3 VSP | 1 FSP–3 VSP | 1 FSP–3 VSP | |

C3 | 5 | 5 | 5 | 5 | |

Eco. Aspects | C4 (EUR/year) | 12,778.24 | 5355.78 | 12,778.24 | 12,778.24 |

C5 (EUR/year) | 3875.56 | 5357.86 | 19,377.78 | 9460.92 | |

C6 (EUR/year) | 1462.31 | 1193.21 | 1462.31 | 1397.98 | |

Env. Aspects | C7 | 0.70 | 0.10 | 0.70 | 0.70 |

C8 Kg CO_{2} | 41,208.60 | 57,041.02 | 41,208.60 | 41,208.60 | |

C9 (%) | 100% | 100% | 100% | 100% | |

Life Cycle Cost (EUR/year) | 11,906.85 | 33,233.21 | 33,618.33 | 18,116.11 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Briceño-León, C.X.; Iglesias-Rey, P.L.; Martinez-Solano, F.J.; Creaco, E.
Impact of Hydraulic Variable Conditions in the Solution of Pumping Station Design through Sensitivity Analysis. *Water* **2023**, *15*, 3067.
https://doi.org/10.3390/w15173067

**AMA Style**

Briceño-León CX, Iglesias-Rey PL, Martinez-Solano FJ, Creaco E.
Impact of Hydraulic Variable Conditions in the Solution of Pumping Station Design through Sensitivity Analysis. *Water*. 2023; 15(17):3067.
https://doi.org/10.3390/w15173067

**Chicago/Turabian Style**

Briceño-León, Christian X., Pedro L. Iglesias-Rey, F. Javier Martinez-Solano, and Enrico Creaco.
2023. "Impact of Hydraulic Variable Conditions in the Solution of Pumping Station Design through Sensitivity Analysis" *Water* 15, no. 17: 3067.
https://doi.org/10.3390/w15173067