An Operative Framework for the Optimal Selection of Centrifugal Pumps As Turbines (PATs) in Water Distribution Networks (WDNs)

Abstract

The current significant increase in energy consumption has resulted in the need to develop and implement effective approaches for defining alternative and sustainable solutions to couple primary resources with supporting methods of energy generation. In the field of effective water distribution network (WDN) management, the suitability of combining pressure regulation with small-scale hydropower generation is attracting even more interest, given that it can possibly reduce water leakages, as well as produce attractive rates of renewable energy. Specifically, pumps as turbines (PATs) are widely considered a viable solution because they combine hydraulic benefits with affordable investment and management costs. Nevertheless, despite several approaches available in the literature for the optimal selection and management of PATs, choosing the most suitable device to be installed in the network is still a challenge, especially when electrical regulation is arranged to modulate the PAT rotational speed and optimize the produced energy. Several approaches in the literature provide interesting solutions for assessing the effectiveness of electrical regulation when a PAT is installed within a water network. However, most of them require specific knowledge of the PAT mechanical features or huge computational efforts and do not support swift PAT selection. To overcome this lack of tools, in this work, an operative framework for the preliminary assessment of the main features (the head drop and the produced power at the best efficiency point (BEP), the impeller diameter and the rotational speed) of a PAT is proposed, aimed at both maximizing the daily produced energy and performing challenging economic selection. Then, it is assessed by estimations of the corresponding payback period (PP) and the net present value (NPV).

1. Introduction

According to the latest reports on the status of worldwide energy, as a consequence of population growth, economic development and urbanization, energy consumption is predicted to grow by about 28% by 2040 [1], resulting in a pressing need for the proper assessment of potential energy, economic and environmental impacts of sustainable solutions (i.e., small-scale hydropower generation) on the water–energy–food nexus environment [2].

In the context of the current interest in the development of sustainable and economic, viable criteria for water distribution networks (WDNs), different approaches have been employed to limit energy consumption and foster optimal usage of the devices as required for energy purposes. Among them, meta-heuristic approaches have been widely applied for pipeline optimization [3,4], pump scheduling enhancement [5,6,7] and optimal calibration of forcing actions for the design of water systems [8,9].

With specific reference to the effective management of WDNs, given the huge amount of leakages experienced by such systems [10,11], pressure regulation through pressure-reducing valves (PRVs) has been extensively used as a viable solution to limit the loss of significant water volumes [12,13].

In this context, the suitability of coupling pressure regulation with small-scale hydropower generation is attracting even more interest worldwide, its implementation allowing the application of well-known technologies in order to achieve attractive efficiencies and payback periods (PPs) [14].

Specifically, the benefits of replacing PRVs with pumps as turbines (PATs) have been widely assessed, given their capability to achieve significant efficiency and reduce investment and maintenance costs, as well as the ease of their procurement and spare part gathering [15]. Indeed, compared with classic micro-turbines, PATs result in a viable, cheaper approach for hydropower generation in pressurized systems because they consist of commercial pumps that are rather cheap and that work by both inverting the flow direction and applying the motor as an electric generator. PAT applications allow the selection of the most suitable model from a wide range of devices available in the market, without requiring a customized system and, thus, expensive procurement and management costs [16]. This achieves attractive payback periods for small-scale hydropower generation in WDNs serving centers with a low–medium number of inhabitants, given the range of exploitable pressure and, thus, of generated head drop. Conversely, compared with classic micro-turbines, PATs show lower flexibility in managing the variable flow rate and head; however, they are improvable through the implementation of hydraulic (HR) [17] and/or electrical regulation (ER) [18].

The attention of researchers and technicians working in the field of PAT technology has mainly been devoted to overcoming the lack of knowledge about their performance, as they are infrequently made available by manufacturers. Indeed, several authors carried out experimental and numerical analyses to develop predicting models suitable for different PAT devices. Among them, Derakhshan and Nourbakhsh [19] provided the results of a laboratory investigation to calibrate the numerical coefficients of both the head and the power characteristic curves of centrifugal, single-stage PATs in dimensionless terms with respect to PAT operations at the best efficiency point (BEP). A similar approach was then carried out by Pugliese et al. [20], aimed at extending the reliability of formulations from the literature to wider operative ranges, namely for a flow rate number ϕ_b (-) higher than 0.40 and specific speed in pump mode N_s of up to 60:

$${\varphi }_b=\frac{Q}{N\cdot D^3}$$

(1)

$$N_s=60N\cdot Q^{1/2}/H^{3/4}$$

(2)

where Q (m³/s) is the flow rate, N is the rotational speed (rps), D is the runner’s diameter (m) and H is the head (m).

Later, the same authors [21,22] extended the experimental assessment to both single-stage and multi-stage, vertical-axis, centrifugal PATs, finding a direct correlation between the substantial constancy of the characteristics at the BEP, regardless of the rotational speed N in the range 5–50 rps.

Given the cost and time demands of experimental investigations, an alternative approach requires the implementation of computational fluid dynamics (CFD) models [23,24] to simulate the turbo-machine performance, both reproducing the internal fluid dynamic behavior [25,26] and assessing the influence of the geometric features of the device on its performing features [27].

Dimensionless characteristic curves require the knowledge of PAT characteristics at the BEP when running in turbine mode. Thus, the flow rate Q_tb/Q_pb and the head ratio H_tp/H_pb at the BEP between turbine and pump mode can be set by using different models from the literature, where the subscripts t and p refer to turbine and pump mode, respectively. Among many analytic models from the literature, and extensively discussed by Pugliese et al. [22], the Yang et al. [28] equations (Equations (3) and (4)) are widely applied because they provide the best accuracy for both flow rate and head ratio estimation:

$$\frac{Q_{tb}}{Q_{pb}}=\frac{1.2}{{\eta }_{pb}{}^{0.55}}$$

(3)

$$\frac{H_{tb}}{H_{pb}}=\frac{1.2}{{\eta }_{pb}{}^{1.1}}$$

(4)

where η_pb (-) is the efficiency in pump mode at the BEP, calculated as follows:

$${\eta }_{pb}=\frac{\gamma \cdot Q\cdot H_{pb}}{P_{pb}}$$

(5)

where γ (N/m³) is the specific weight of water, and H_pb and P_pb are the head and the power in pump mode at the BEP, respectively.

As alternative approaches, Barbarelli et al. [29] developed a recursive framework to predict both the flow rate and the head ratios and the characteristic curves of centrifugal PATs, and Stefanizzi et al. [30] proposed an analytic model to assess the flow rate and the head ratios when varying the specific speed in direct mode N_s.

In the literature, a number of approaches also aimed to couple economic assessment and optimization procedures for the optimal selection and location of PATs or microturbines in WDNs [31,32,33]. Among them, Fecarotta and McNabola [34] implemented a novel optimization model to maximize the hydropower generation and the water savings related to leakage reduction, and Giugni et al. [35] developed a genetic algorithm code to evaluate the energy recovery by PATs in a district of the Naples (IT) network, observing interesting payback periods at the expense of suitable investment costs. Morani et al. [14] coupled a novel, mixed-integer, non-linear model and a global optimization solver for the optimal location and setting of PATs and PRVs in WDNs, observing the effectiveness of the proposed approach by comparing short computational efforts [36]. Fernandez Garcia et al. [37] investigated a methodological strategy for the optimal location of PATs, showing interesting results for branched and not-looped networks. Crespo Chacón et al. [38] presented a methodology for the optimal design of a PAT plant in Spain, remarking on the suitability of the proposed solution to both satisfy the hydraulic requirements and assure attractive energy production rates. Ebrahimi et al. [39] proposed an optimization approach to replace PRVs with PATs in WDNs, showing that ER can increase the overall performance of the recovery system; however, it needs greater investment and maintenance costs. Kandi et al. [40], by applying the same optimization procedure, remarked on the effectiveness of pressure regulation through PATs, especially during the hours of greater user consumption.

Nevertheless, many models from the literature are mainly based on the use of either long, time-consuming simulation models or complex, recursive approaches, in some cases, requiring specific setting parameters of the geometric and technical properties of the selected PAT model. Thus, despite the contributions available in the literature, the preliminary, optimal selection of a PAT in WDNs still remains a challenging issue.

In this work, the authors aim to overcome the lack of tools available in the literature, presenting an operative approach to easily detect, from a dataset of pump models available in the market, the main features of PAT devices able to both assure effective pressure regulation and optimize daily energy generation. A simple and effective workflow for the optimal estimation of the main characteristic parameters of PATs is, thus, discussed to both maximize the daily energy production and assure a viable payback period (PP) and net present value (NPV) when a PAT is installed within a water district of a WDN and ER is used to modulate its rotational speed.

Section 2 introduces the proposed workflow with the related analytic approach, Section 3 discusses the results of the proposed procedure when applied to a simplified WDN and, in Section 4, the main outcomes of the model are given.

2. Materials and Methods

In this work, the authors propose an operative framework for the optimal selection of PATs in WDNs, aiming to select, from a database of models available in the market, the model with the characteristic parameters (flow rate Q, head H and runner’s diameter D) that can maximize energy production consistently within the hydraulic and technical constraints of the system.

The procedure was developed with the expectation of having to perform ER, namely having to install a frequency modulator to vary the electrical frequency and, thus, the PAT rotational speed in the range [N_min,…,N_max].

The framework was based on the following assumptions:

-

the PAT location is initially set at the inlet branch of the water district, given both the discharge pattern and the pressure range acting on the WDN;

-

the daily pattern of user demand and the related flow rate Q_i and excess pressure H_av,i are known for each i-th time step;

-

a database of characteristic parameters of pumps working in direct operation is available.

Starting from these assumptions, the selection framework contemplates the following steps. Given a j-th pump from the gathered database of commercially available PATs:

• The runner diameter D_j, the rotational speed N, the flow rate Q_pb,j and the head H_pb,j are obtained;
• Both the flow rate and the head ratios are estimated using Equations (3) and (4) from the Yang et al. [28] model, and Novara et al.’s [41] equation (Equation (6)) is applied to assess the efficiency at the BEP in PAT operation:

  $${\eta }_{tb}=0.89-\left(0.024/Q_{tb}^{0.41}\right)-0.076\cdot {\left[0.22+\ln \left(N_{st}/52.933\right)\right]}^2$$

  (6)

  where N_st is the specific speed of the PAT:

  $$N_{st}=\frac{N\cdot Q_{tb}^{1/2}}{H_{tb}^{3/4}}$$

  (7)
• The flow rate Q_tb,j, the head H_tb,j and the power P_tb,j at the BEP in PAT mode are calculated for the rotational speed ${\overline{N}}_j$;
• The flow rate number ϕ_b,j, the head number ψ_b,j and the power number π_b,j dimensionless parameters are given:

  $${\psi }_{b,j}=\frac{g\cdot H_{tb,j}}{{\overline{N}}_j^2\cdot D_j^2}$$

  (8)

  $${\pi }_{b,j}=\frac{P_{tb,j}}{\rho \cdot {\overline{N}}_j^3\cdot D_j^5}$$

  (9)

  where g is the acceleration of gravity (m/s²), and ρ is the water density (kg/m³). It is worth mentioning that, according to Pugliese et al. [20,21], for centrifugal PATs ϕ_b,j, ψ_b,j and π_b,j are constant when varying the rotational speed N;
• The characteristic curves ψ_i,j(ϕ_j) and π_i,j(ϕ_j) are derived by applying the predictive models from the literature. Namely, for horizontal-axis, centrifugal PATs, Equations (10) and (11) from Pugliese et al. [20] are used:

  $$\frac{{\psi }_{i,j}}{{\psi }_{b,j}}=1.0283{\left(\frac{{\phi }_{i,j}}{{\phi }_{b,j}}\right)}^2-0.5468\left(\frac{{\phi }_{i,j}}{{\phi }_{b,j}}\right)+0.5314$$

  (10)

  $$\frac{{\pi }_{i,j}}{{\pi }_{b,j}}=4.0\cdot {10}^{-3}{\left(\frac{{\phi }_{i,j}}{{\phi }_{b,j}}\right)}^3+1.386{\left(\frac{{\phi }_{i,j}}{{\phi }_{b,j}}\right)}^2-0.390\left(\frac{{\phi }_{i,j}}{{\phi }_{b,j}}\right)$$

  (11)
• To initialize the procedure (z = 1), given the flow rate Q_i, the maximum rotational speed N_i,j ^z=1 = N_max is set, and the flow rate number φ_i,j^z=1 with z = 1…S* and S* is the number of iterations needed to reach the convergence;
• The head number ψ_i,j ^z=1 and the head drop H_t,i,j ^z=1 are estimated using Equations (10) and (11), respectively (Figure 1);
• If H_t,i,j^z=1 > H_t,av,i, then the rotational speed N_i,j^z+1 is lowered to an allowable value. Else, if H_t,i,j^z=1 ≤ H_t,av,i, the power number π_i,j^k=1 and the power P_t,i,j^z=1 are derived from Equation (11) and Equation (9), respectively;
• By varying the rotational speed N in the range [N_min,…, N_max], for each N, the power number π_i,j is assessed using Equation (11) and the related power P_ti,j using Equation (9) in order to find out the maximum value P_tmax_,i,j achieved for the fixed Q_i at varying N. The rotational speed N^*_i,j related to P_tmax_,i,j, maximizing the produced power for the fixed flow rate Q_i and the j-th pump model (Figure 2);
• If P_t,I,jz=1 = P_tmax_,i,j, the fixed rotational speed N_i^z=1 = N_max is the N^*_i,j, maximizing the produced power P_t,i,j. Else, the N_i,j^z+1 is reduced in the next iteration;
• If N*_i,j ≥ N_max or N*_i,j ≤ N_min, then the N_max or N_min values are set, respectively, to maximize the power P_t,i,j in the allowable range of rotational speed N. Conversely, for N_min < N*_i,j < N_max, the φ_i^z+1 is calculated as a function of N*_i,j;
• If the second condition at step 11 is valid, the head number ψ_i,j^z+1 and the head drop H_t,i,j^z+1 are obtained by Equations (10) and (8), respectively;
• For the optimal N*_i,j, the overall PAT efficiency η_ti,j is calculated as:

  $${\eta }_{ti,j}=\frac{P_{ti,j}}{\gamma \cdot Q_i\cdot H_{ti,j}}$$

  (12)
• If η_ti,j ≥ $\overline{{\eta }_t}$ (minimum threshold of allowable efficiency for PAT operations), the next i + 1-th time step is considered, else the PAT model is rejected;
• By performing the abovementioned steps 5–14 for each i-th time step, the maximum daily energy E_d,j generated by the j-th pump model is estimated as:

  $$E_d{}_{,j}={\displaystyle \sum _{i=1}^M{P}_t{}_{\max i,j}\cdot \Delta t_i}$$

  (13)

  where M is the number of time steps, and ∆t_i the time step duration;
• By repeating steps 1–15 for each available j-th pump model, the pump model able to maximize Equation (13) is selected as the most suitable one.

For each pump, a cost–benefit analysis is performed, aiming to both assess the PP and the NPV of the investment. Specifically, the model of Novara et al. [31] is applied to estimate the combined investment cost of radial PAT and generator C_PAT+gen (€) when varying the pair poles from 1 to 3:

$$\begin{array}{l}for \mathrm{pair} \mathrm{poles}=1 C_{PAT+gen}(€)=11,913.91\cdot Q_{tb}\cdot H_{tb}^{1/2}+1289.92\\ for \mathrm{pair} \mathrm{poles}=2 C_{PAT+gen}(€)=12,717.29\cdot Q_{tb}\cdot H_{tb}^{1/2}+1038.44\\ for \mathrm{pair} \mathrm{poles}=3 C_{PAT+gen}(€)=15,797.72\cdot Q_{tb}\cdot H_{tb}^{1/2}+1147.92\end{array}$$

(14)

The rest of the project costs for electrical and technical equipment (including the frequency modulator procurement and installation) C_eq (€) were set equal to 300% of C_PAT+gen [42], and the yearly maintenance costs C_main (€/year) were considered equal to 5% of C_PAT+gen [41]. The total costs are, thus, estimated as:

$$C_{tot}=C_{PAT+gen}+C_{eq}+d\cdot C_{main}$$

(15)

where d is the operational lifetime set, consistent with recent studies [32,34], as equal to 10 years.

According to recent studies in the literature based on statistical analysis in European countries [32,34] and working for the sake of security by limiting the revenues deriving from the energy production, the energy sales to the national grid are assumed equal to 0.10 €/kWh, and the annual income of the water savings related to reduction of excess pressure is calculated using Equation (16):

$$W_y^s=c_w\cdot {\displaystyle \sum _{i=1}^M\alpha \cdot H_{ti}^{\beta }}\cdot \Delta t_i$$

(16)

where c_w is set equal to 0.30 €/m³ [32], β is the leakage exponent set equal to 1.18 [43] and α is the leakage coefficient obtained from the following:

$$\alpha =c\cdot {\displaystyle \sum _{f=1}^{F_f}0.5\cdot L_f}$$

(17)

where c = 0.0001 L/(s∙m^1+β), and F_f is the set of pipes with length L_f linked to the node [34].

The PP is estimated as the ratio between the total cost C_tot and the sum of the annual revenues from energy sales E_p and the annual income for water savings W_p. The NPV of the investment is, thus, calculated as:

$$NPV=-C_{tot}+{\displaystyle \sum _{d=1}^{D^{*}}\frac{E_p+W_p}{{\left(1+\lambda \right)}^d}}$$

(18)

where d and λ are the operational lifetime and the discount rate set as 10 years and 0.05, respectively.

3. Results and Discussion

The proposed framework was tested on a simplified WDN district serving 10,000 inhabitants with an average flow rate Q_tm = 23.1 L/s and a maximum flow rate Q_t,max = 33.3 L/s. The daily demand plotted in Figure 3 was set [35] for simulations.

The available head H_tav at each hourly time step was estimated considering a pressure set point at the delivery point of 30 m. Three scenarios were tested by varying the available head H_tav as follows to assess the reliability of the approach when increasing the exploitable head: “low” scenario (a) with mean H_tav = 19 m; “medium” scenario (b) with mean H_tav = 29 m; and “high” scenario (c) with mean H_tav = 59 m.

In the following Figure 4, the hourly flow rate Q_t and the available head H_tav for the three tested cases are plotted.

A database of 200 single-stage, centrifugal PATs was gathered from nine pump manufacturers, covering a wide range of operations, as summarized in the following

Table 1. Database of single-stage, centrifugal PATs.

PATs nr.	Manufacturers	Impeller Diameter D Range	Pump Flow Rate at BEP Qpb Range	Pump Head at BEP Hpb Range	Pump Rotational Speed N Range	Pump Efficiency at BEP ηpb Range
[-]	[-]	[m]	[L/s]	[m]	[rps]	[-]
200	9	0.135–0.550	26.5–136.7	15.0–142.7	48.33–58.33	0.67–0.88

.

The procedure herein proposed was applied to assess the potential energy recovery of the system and detect the characteristics of the most suitable PAT models. At each time step, given the ER, the PATs worked at suitable efficiency η_t, with none lower than 0.58. It is worth mentioning that, given the variation of PAT rotational speed N through the frequency modulator, the whole set of models from the collected dataset was potentially suitable for this purpose. Some of them (e.g., those providing excess head drop H_t at any time steps) were temporarily shut off in order to satisfy the hydraulic constraints of the network and to always ensure an exploited head H_t that is not higher than the available H_av.

In Figure 5, the payback period PP (year) when varying the daily energy E_d (kWh/day) is plotted for each case study.

Figure 5 shows that the higher the exploitable head, the higher the daily energy production. Indeed, even the worst PAT models were able to achieve energy production of a few tens of kwh per day in each case study, at the expense of a long PP of up to 70 years. Conversely, for the best PAT models that were capable of assuring a PP shorter than 10 years, when the exploitable head H_tav was increased, the daily energy production E_d moved from a maximum of about 40 kWh/day for case (a) to about 100 kWh/day for case (b), reaching more than 130 kWh/day for case (c).

Specifically, for case (a), the most effective PAT models had a mean flow rate at the BEP in direct operations Q_pb = 50 L/s and head H_pb = 45 m. For case (b), the most suitable models showed a slightly lower flow rate at the BEP Q_pb = 41 L/s and higher head H_pb = 63 m, and, in case (c), the flow rate was comparable to case (a), but the head increased up to H_pb = 79 m. In the last case, the PAT’s capability to exploit the head was, in many cases, lower than the actual available head H_av, revealing the suitability of multi-stage PATs when greater heads are exploitable.

In terms of economic suitability, in the following Figure 5, the NPV is plotted against the varying daily energy production E_d for the three case studies. As expected, the actual suitability of applying PATs for small-scale hydropower generation was observed for the models capable of reaching attractive levels of energy production, thus, assuring a short PP. Specifically, in scenario (a), this was observed for PATs with an NPV greater than EUR 10,000, corresponding to a PP shorter than 5 years. Nevertheless, among the PAT models capable of producing more than 40 kWh/day with a PP < 10 years, those with a PP longer than 8 years presented a negative NPV, thus, resulting in very few attractive solutions. In scenario (b), PATs with E_d > 80 kWh/day returned a NPV greater than EUR 35,000 and a PP shorter than 4 years, whereas, in scenario (c), PATs assuring E_d > 110 kWh/day gave a NPV higher than EUR 60,000 and a PP not longer than 3 years.

In Figure 6, it is worth noting that the higher the available head H_av, the more regular the correlation between the daily produced energy E_d and the NPV. Indeed, scenario (a) returned a scattered region of allowable operation, whereas scenarios (b) and (c) showed a more regular trend, which was essentially linear in scenario (c) where the maximum exploitable head was available.

The PAT models able to maximize the daily produced power for each case study are reported in the following

Table 2. Parameters of the PATs producing the maximum daily energy production for (a) low available head H_av, (b) medium available head H_av and (c) high available head H_av.

Scenario	Runner Diameter D Range	Pump Flow Rate at BEP Qpb Range	Pump Head at BEP Hpb Range	Pump Rotational Speed N Range	Pump Efficiency at BEP ηpb Range	Daily Energy Production Ed	Payback Period	Net Present Value
	[m]	[L/s]	[m]	[rps]	[-]	[kWh/day]	[year]	[€]
a “Low”	0.160	45.1	32.0	48.33	0.84	48.05	4.50	13,927
b “Medium”	0.203	38.9	51.5	48.33	0.83	100.60	2.02	58,581
c “High”	0.329	50.8	128.0	48.33	0.75	135.14	2.50	76,728

.

Table 2 shows that, moving from low to high available head, the proposed selection resulted in an increase in both the impeller diameter D and the head H_pb, whereas the nominal rotational speed N was always equal to 48.33 rps. Comparing scenarios (b) and (c), it is worth mentioning that, although the PP of scenario (c) was slightly longer than in scenario (b), significant benefits were detected for the NPV, with an increase of about 31%, despite the fact that efficiency at the BEP η_pb was 8% lower.

Considering an operational lifetime of PAT equipment of longer than 10 years, namely, of 20 to 30 years, a constant increase of PP was observed for each PAT and scenario, equal to 11% and 22%, respectively. This was due to the increase of the maintenance costs given by the longer period of operations (Figure 7).

Conversely, the lifetime extension resulted in a beneficial increase of the NPV, which varied with each PAT and scenario. Specifically, in scenario (a), PAT models providing a PP < 5 years for an operational lifetime of 10 years returned an average increase of NPV of 125% and 195% at 20 and 30 years, corresponding to an NPV of EUR 33,700 and EUR 44,200, respectively. For scenario (b), the average increase of NPV was equal to 104% and 164% and, in absolute terms, of EUR 68,800 and EUR 88,400, respectively. Lastly, in scenario (c), the NPV increased by 101% and 160% at 20 and 30 years, namely, by EUR 80,800 and EUR 103,300, respectively.

The lower relative increase of NPV observed in scenarios (b) and (c) compared to that observed in scenario (a) was due to the fact that, in the latter, an attractive NPV was derived even at an operational lifetime of 10 years (Figure 8). This limited the margin for improvement when extending the duration of operations. Indeed, in absolute terms, the greater the exploitable pressure, the higher the NPV increase.

4. Conclusions

The pursuit of optimizing the small-scale hydropower generation in WDNs requires the implementation of operative approaches for the optimal selection and management of PATs in the system. With this aim, the framework proposed in this work is intended to be a suitable approach for the preliminary detection of the main PAT features when the electrical regulation of the system is provided, capable of optimizing the energy production, as well as achieving attractive payback periods and net present values.

The proposed procedure was tested on a simplified network, and we observed the main outcomes when varying the available head from about 20 m to 60 m. It is worth noting that coupling the technical performances of the PATs with cost–benefit analysis is a viable solution because it allows the assessment of the performance capability of the devices along with capital returns. Specifically, the results showed that, given the daily flow pattern when a limited exploitable head is available, no direct correlation between the daily energy production and both the net present value and the payback period is detectable, meaning that devices, although showing attractive energy capability, provide low NPV and, thus, long payback periods. When increasing the available head, a better correlation was observed, revealing attractive net present values and payback periods shorter than 3 years when the daily energy production is greater than 110 kWh/day.

For scenario (c), with high available heads, the use of multi-stage PATs is recommended in order to exploit greater heads and, thus, assure both higher hydropower generation and better pressure regulation.

By increasing the operational lifetime of the PAT equipment beyond the 10 years suggested by several authors in the literature, a constant extension of PP was observed, equal to 11% and 22% for 20 and 30 years, respectively. Conversely, significant improvements in NPV were detected for each PAT and scenario, revealing the strength of this parameter to assess the effectiveness of the studied configuration.

The current work can, thus, be used as the first step of an ongoing study devoted to developing simple procedures for the optimal selection of PATs in WDNs. The main limitation of this work is that it relied on the assumption that the location of PAT was initially set in the main branch of a water district. Thus, future assessments will provide evidence of how to improve the selection when a PAT is installed on a branch belonging to the looped configuration of the network and what happens when more PATs are deployed. Moreover, the next steps will assess the reliability of the proposed approach to further pump models running in reverse mode (e.g., multi-stage devices).

Lastly, to extend this application, we plan to analyze the comparison of hydropower potential and economic viability of the network when hydraulic regulation, no regulation or a combination of electrical and hydraulic regulation of the PAT is applied.