## Abstract

Power generation from fossil fuels has long had a negative impact on the environment. Nowadays, a paradigm shift in power generation is being witnessed, with increasing investment in renewable energy sources. Despite this progress, efficient energy storage is still limited. Given this challenge, pumped storage technology can be one of the viable solutions. This involves storing gravitational energy by pumping water into a reservoir at a higher altitude, which is later converted into electrical energy using a turbine. This paper studies a pump hydro storage system (PHS) operation in water supply systems (WSSs), with the aim of minimizing operating costs and evaluating its effectiveness. Replacing conventional pumps with pump-as-turbines (PATs) provides a flexible and cost-effective approach. The proposed methodology aims to optimize the operation of these PATs considering dynamic energy prices. The developed computational model was applied to different operational scenarios and analyzed in terms of cost-effectiveness. The results show that the lower the average ratio between time-differentiated purchase and fixed sell energy tariffs, the greater the optimization potential of using PAT. In the WSS case study analyzed, energy cost reductions of 43.4–68.1% were achieved, demonstrating the effectiveness of PHS in WSS particularly for energy tariffs with large variations.

## HIGHLIGHTS

The management of a pumped storage system integrated into water supply systems is still little explored.

The integration of dynamic energy pricing with PAT operation represents an opportunity for water utilities to reduce their costs.

The computational model developed using optimization algorithms allows for efficient operation of PAT in WSSs.

## INTRODUCTION

*et al.*2018). This energy is consumed for collection, desalination, treatment, supply, and distribution. Figure 1 shows the energy consumption (in TWh) disaggregated by process.

Rapid industrialization and the exponential increase in population density are leading to a significant increase in water consumption and, consequently, an increase in energy consumption by WSS and, therefore, an increase in operating costs (Chhipi-Shrestha *et al.* 2017; Meng *et al.* 2019). It is estimated that by 2040, 60% of the world's population will live in metropolitan areas, leading to water scarcity situations (International Energy Agency 2016).

Worldwide, renewable energy sources have been the key to reduce CO_{2} emissions (Energy Agency 2014) in electricity generation. The most promising solutions are hydro, solar, and wind power. In the specific case of hydropower, it is currently the largest source of low-carbon electricity and is growing steadily, doubling by 2050. However, natural energy conversion technologies for electricity production, such as wind turbines or photovoltaic panels, are dependent on their primary energy source, wind, and solar radiation, respectively, which limits continuous production over long periods of time. Energy storage, such as pump hydro storage (PHS), is emerging as a solution to meet demand when production is affected by weather conditions or availability and provides an opportunity to decrease costs during periods of high demand.

*et al.*2022).

During periods of low demand and low electricity costs, water can be transported through the pumping system to the reservoir with the highest elevation. In times of peak electricity consumption, the potential and then mechanical energy in the water can be converted into electrical energy in a discharge process or by means of hydroelectric turbines connected to a generator (Bogenrieder 2006).

The incorporation of this technology into WSS is one of the most recent areas of research in the water sector. Existing water distribution tanks can be used as storage components for gravitational potential energy. The choice of this implementation does not jeopardize the population's consumption, since the turbined water is then pumped to the distribution tank without significant water losses.

Studies of PHS at a micro or medium scale, up to 100 kW (Olabi *et al.* 2021) for implementation in WSS, have emerged in a relevant way in recent years. Although the application of PHS in WSS allows the storage of gravitational potential energy for later recovery as electrical energy, it is necessary to define the number, volume, and size of storage depending on system demand, pump station location, pump size, and pressure requirements (Pasha *et al.* 2020). This integrated approach to storage energy and water supply can be a viable, long-term solution to the challenges of managing water and electricity resources.

The design variables of a tank include location, volume, and elevation as primary factors (Pasha *et al.* 2020). Pasha *et al*. developed a single-objective optimization model to optimize the dimensions of up to six water storage tanks in order to maximize hydroelectric energy production while reducing pumping energy consumed. While the total energy recovered relative to the total pumping energy is about 40% for all configurations, the specific energy recovered ranges from 0.116 to 0.121 kWh/m^{3}, demonstrating the potential use of water storage tanks as energy storage. The results show that hydropower production increases with the stored water up to a certain limit represented by constant water demand constraints with storage capacity. Small-scale PHS is also becoming a viable option for hydropower generation in small districts and remote areas, as demonstrated by Balkhair *et al.* for a case study in Pakistan (Balkhair & Rahman 2017), or by Arriaga (2010), who proposed the installation of a pump-as-turbine (PAT) for rural electrification in Lao People's Democratic Republic (Stefanizzi *et al.* 2020).

Literature has shown that the use of PATs can be considered a good alternative for energy recovery in WSS (Marchis *et al.* 2014). On the other hand, the main challenges in analyzing a PAT are: (1) selecting the appropriate PAT when the available recovered head as a function of flow over time is known but shows large amplitudes; (2) determining the PAT operating point considering the necessary flow rate (*Q*), head (*H*), and efficiency (*η*) when the pump is selected; and (3) estimating the characteristics, efficiency, and operating curves, which are rarely provided by the supplier (Sánchez *et al.* 2020). Several models have been proposed in the literature to estimate PAT performances (such as Barbarelli *et al.* 2016; Sánchez *et al.* 2020; Kanakoudis *et al.* 2022), many of which are dedicated to estimating the characteristics of best efficiency point (BEP) in turbine mode.

Using only commercial pump data, Barbarelli *et al.* developed a numerical method to estimate the performance of centrifugal pumps in turbine mode. Additionally, they used the same numerical method to compare the characteristic curves of six centrifugal pumps with a speed range from 9 to 65 rpm with those obtained experimentally (Barbarelli *et al.* 2017). Barbarelli *et al.* (2016) developed a method through experimental and numerical analysis to select a suitable PAT according to the site characteristics. When evaluating the efficiency at the operating point of the pumping station, the method they suggested modified the pump choice (Ebrahimi *et al.* 2021). Four centrifugal pumps were studied by Derakhshan and Nourbakhsh (Marchis *et al.* 2014) in both direct and reverse modes at speeds below 60 rpm. The results of their investigation showed that the decrease of the specific speed results in a lower head and discharge at the ratio turbine's BEP for identical pump values.

Several studies in the water sector apply optimization methodologies, particularly in the design of water networks, with the goal of minimizing construction costs (Hosseini *et al.* 2016; Mala-Jetmarova *et al.* 2018). However, this work focuses exclusively on the operational optimization of PATs applied to WSSs. The optimization methods used in the operational management of WSS can be generally divided into programming and heuristic methods (Vakilifard *et al.* 2018). In traditional WSS, two optimization approaches are often considered (Luna *et al.* 2019): an explicit approach considering the optimization of pump scheduling or an implicit approach based on the optimization of water levels in storage tanks. However, with the inclusion of PAT, the optimization of turbine operation mode must also be considered. Both approaches can be relatively successful depending on the case study.

On the first approach, Emmanouil *et al.* investigated the implementation of a PHS in the Connecticut (USA) network. The results showed that existing water supply reservoirs can become small-scale distributed PHS units based on a methodology for estimating storage potential that depends solely on daily water level measurements and the natural characteristics of each reservoir (Emmanouil *et al.* 2021). The study estimates that, under certain assumptions about the infrastructure of potential PHS units, an average of about 90–95 MWh/day could be stored for a year. In addition, implementing PHS units using existing reservoirs can save up to 30–50% of the cost of conventional PHS structures (Emmanouil *et al.* 2021). The proposals by Fang *et al.* consist of keeping the reservoir level as high as possible during off-peak periods and discharging the reservoir during the peak period. If a drop to the minimum operating level occurs, water is supplied to maintain this level until the end of the peak period (Nogueira Vilanova & Perrella Balestieri 2014). The use of water storage tanks can reduce the need to turn on the pump during periods when energy prices are economically disadvantageous, and this approach is more common when energy costs fluctuate throughout the day (Correia 2013; Lai *et al.* 2022). Savic *et al.* developed an optimization model where water distribution tanks and their physical and operational characteristics are taken into account as decision variables in an optimization problem (Vamakeridou-Lyroudia & Savic 2007).

More recently, the use of genetic algorithms to choose optimal levels in water tanks to manage pump operation according to changes in the cost of electricity throughout the day has proven successful in reducing WSS energy costs, significantly when increasing pumping during periods when electricity prices are below the average (Alvisi & Franchini 2016; Marchi *et al.* 2017). In these works, optimized tank levels have been shown to save around 20% of energy consumption when compared with the help of the usual stipulated fixed tank levels (Luna *et al.* 2019).

On the second optimization approach, concerning PATs, the formalization of an optimized control system that focuses on both the number of times it starts (in both pump and turbine systems), duration, and its connection to energy prices is desired (Nogueira Vilanova & Perrella Balestieri 2014). In PHS systems, this approach is critical for a proper PAT operation. PATs control can also be optimized to reduce the amount of electricity required for the WSS. However, research and discussion on the impact of PAT installation on the cost and energy savings of water networks have been conducted as if water systems were independent pieces of infrastructure (Moazeni & Khazaei 2021). Moreira and Ramos suggested taking into account pump characteristic curves to choose the BEP, with energy savings of up to 44% (Luna *et al.* 2019). Electricity tariffs must be taken into account, and predictive controls can be created to optimize the operating hours of the PATs and their duration of operation (Hieninger *et al.* 2021). Alternatively, the switch on and off times can also be optimized in terms of cost efficiency based on the filling level of the tanks. These methods have led to cost savings of from 12 to 30% (Hieninger *et al.* 2021).

To minimize WSS operating costs considering the implementation of a PAT, water utilities can take advantage of dynamic energy prices, pumping at more economically advantageous energy prices and turbining at more economically expensive energy prices, without jeopardizing water consumption.

This paper focuses on the incorporation of a PHS system in WSS and has as its main objective the reduction of electricity costs in this type of system. The PHS operation is performed by activating pumps to store the water in the upper reservoir (with a higher elevation). However, this pumping should be done at the lowest possible energy cost, i.e., when the purchased energy tariff is economically most advantageous. In this water conservation, there is also a conservation of potential mechanical energy, which can be converted into electrical energy employing a turbine. This electrical energy can be sold to the grid and thus obtain a financial return that minimizes the cost of operating a WSS. The use of PATs can be a viable solution compared to individual turbines. PATs provide lower maintenance, repair, and acquisition costs with little negative environmental impact (Ramos *et al.* 2023).

The methodology used in this work focuses on developing a hydraulic modeling of a WSS together with optimization tools to economically efficiently operate the PAT. The methodology developed in this work is based on three main components: (1) a hydraulic simulator, (2) a converter, and (3) an optimizer, which is described in the following section. Also, the Methodology section proposes key performance indicators (KPIs) for the PHS efficiency in WSS. The Case Study section presents the model validation through a case study and several dynamic energy tariffs and economic analyses. The last section presents the conclusions of this paper.

## METHODOLOGY

### Hydraulic simulator

Water supply networks are characterized by interconnected hydraulic elements, including pipes, junctions, tanks, reservoirs, pumps, and valves. As mentioned before, this work focuses on replacing pumps with PATs for energy storage. When the PAT is used as a pump, the pump transfers mechanical energy from the shaft to the water, increasing the water pressure. The energy conversion involved in this process is from kinetic energy to pressure, which can then be converted to gravitational potential energy. The process is reversed when the PAT is used as a turbine, converting the potential energy of the water into kinetic energy that powers the PAT shaft. The most common solution is to couple the pump to a generator to produce electricity, but the torque available from the shaft can be used to drive any other machine.

*A*represents the area of the tank,

_{r}*dh*

_{level}/

*dt*is the variation of the water tank level over time,

*Q*is the pump flow rate, and

_{b}*Q*

_{cons}is the water demands. However, when integrating a PHS system, a reverse process occurs to recover energy whenever possible, when the PAT operates in turbine mode, the water flows through the PAT and the mass conservation equation must be written as:where

*Q*

_{turb}represents the flow rate through the PAT at the discharge of the system. These flows,

*Q*and

_{b}*Q*

_{t}_{urb}, are not equal due to the water demands and the water tank level at the loading and unloading instants in the PHS system.

*ρ*is the water density,

*g*is the gravitational acceleration,

*h*is the head of the PAT in pump mode, and

_{b}*η*is the efficiency of the PAT in pump mode.

_{b}*a*and

*b*are the coefficients of the hydraulic equation in pump mode. The equivalent equation is developed for multiple PATs running in parallel as follows:where

*n*

_{PAT}represents the number of PATs required for a given WSS.

*h*

_{turb}is the useful head, and

*η*

_{turb}is the efficiency of the PAT in turbine mode. The typical curve in turbine mode is a quadratic function, however ascending with respect to increasing flow rate, as follows:where

*a*

_{2}and

*b*

_{2}are the coefficients of the hydraulic equation in turbine mode, and the equivalent curve is represented as follows:and the energy balance condition in the operation of the PAT in turbine mode is given by:where

*h*

_{loss}is defined by a hydraulic equation as follows:where

*f*represents the friction factor, and

*L*and

*d*represent the pipe length and diameter, respectively.

The outputs of the hydraulic simulator are the evolution of the tank levels, the power in pump and turbine mode and the corresponding energy cost. These outputs are required to evaluate the value of the objective function and the constraints defined in the optimization model presented in the next subsection.

### Optimization model

In traditional WSS, the control of the pumps is based on the water tank level, i.e., when the water tank level reaches the stipulated operational minimum level, the pumps turn on and only stop when the water tank level reaches the required operational maximum (Coelho 2012). Most of the time this operation does not consider the variation in energy tariffs, which results in high operating costs for these systems.

Several types of optimization methods have been used to find optimal control of pump operation (Luna *et al.* 2019). Due to the nonlinear nature of the hydraulic equations, namely the pump and head loss curves, in this work, a nonlinear programming model was considered to determine the optimal operation of a WSS by the inclusion of a PHS. This methodology has the particularity of being parameterized and can be applied to any other water network with different input data. The optimization model developed aims to minimize costs while complying with the imposed constraints, in this case, the minimum and maximum operational levels of the tanks as well as the water demand needs. In this work, two distinct time-steps are defined as: (1) the hydraulic simulation time-step , (set to 6 min in the case study) and (2) the optimization time-steps *i*, in which the total planning period is divided. This optimization time-step corresponds to the time period of each control decision variable and to the corresponding given energy price.

### Decision variable

*i*. The decision variable is mathematically defined as a continuous variable

*x*∈ [−1, 1] representing the PAT relative operating time with respect to an optimization time-step , where

*x*< 0 represents the PAT relative operating time in turbine mode,

*x*= 0 represents the PAT not operating, and

*x*> 0 represents the PAT relative operating time in pump mode, as shown in Figure 3.

### Objective function

*T*), and the PAT operation time (

*x*) for the total planning period

*P*. This formulation can be described as follows:where

*i*represents the optimization time-step,

*n*

_{inc}represents the number of optimization time-step,

*T*

_{buy}is the energy purchase price, and

*T*

_{sell}is the energy sale price for the produced energy by the PAT.

### Constraints

**A**is the hydraulic system matrix (mass and energy balances),

**H**means the head, and

**F**represents the water demands. An additional constraint imposed in this methodology focuses on the water level in the storage tanks,

*h*

_{level}. In this way, and for reasons of operational safety, namely, to pressurize the supply network and avoid the risk of deflagration of the PAT, the minimum operational level,

*h*

_{min}, and maximum operational level,

*h*

_{max}, were defined as constraints. Therefore, the water tank level,

*h*

_{level}, should be between the minimum and maximum levels and is formulated as follows:

*g*

_{1,i}and

*g*

_{2i}, imposing that the water tank level should remain within a minimum (

*h*

_{min}) and a maximum (

*h*

_{max}) operational range for all time intervals over a day and can be mathematically formulated for any optimization time-step

*i*, with

*i*= 1, … ,

*n*

_{inc}, as follows:

*h*

_{level}) at the end of the day must be equal to or greater than the water tank level at the beginning of the day. This constraint can be written in the following mathematical form:where

*i*= 0 means the beginning of the day and

*i*= 24 is the last optimization interval for a

*n*

_{inc}= 24.

### Optimization problem formulation

**x**that minimizes the WSS operational energy costs over time, whose constraints are the minimum and maximum operating levels. The decision variable is the PAT operating time, and it can be pump or turbine depending on the value of the variable. Briefly, the problem is formulated mathematically as follows:

### Converter

*x*in its continuous form to a discrete variable designated

*s*that represents the state of the PAT. This state is defined by

*s*= {− 1,0,1}, where

*s*= −1 means ‘turn on’ the PAT in turbine mode,

*s*= 0 means PAT off, and

*s*= 1 means ‘turn on’ the PAT in pump mode. The mathematical equation referring to the converter is stated as follows:

### Computational model implementation

The optimization algorithm used is the Sequential Least Squares Quadratic Programming (SLSQP) (Minimize(Method = ’LSQP’) — SciPy V1 2023). This algorithm is usually used in the optimization of nonlinear problems with constraints. The gradient of the function is calculated using the finite difference method.

### Key performance indicators

As criteria for analyzing the economic profitability of a possible implementation of a PHS system in WSS, the following indicators were adopted:

Storage index,

*I*_{PHS};Average purchase tariff price;

Standard deviation over the purchase energy tariff;

Local ratio between the purchase tariff and the fixed sales tariff,

*R*_{C/V};Average ratio between the purchase tariff and the fixed sales tariff,

*R*_{C/V,average};Payback.

*I*

_{PHS}is the ratio between the turbine volume and the total available volume. Technically, the turbine volume,

*V*

_{turb}, represents a portion of the entire pumped volume,

*V*, if the

_{b}*h*

_{level}is equal at the beginning and at the end of the day. However, for the case where the continuity constraint is not employed, the difference between the level at the beginning of the day and the end of the day must then be equal to

*V*. In mathematical form, this indicator can be written as follows:

_{b}The average price and the standard deviation are useful indicators in evaluating the energy tariff for a given day. The average price represents the average hourly tariff prices over a 24-h interval. For this work, the OMIE spot energy market for Portugal and Spain was used as an example for the energy prices (Preço Horário Do Mercado Diário | OMIE 2023). The standard deviation measures the volatility of the tariffs throughout the day. It is assumed that the more tariff volatility, the more profitable the use of PHS can be.

*R*

_{C/V}, and the average ratio,

*R*

_{C/V,average}, are defined as the ratios between the purchase tariff and the fixed sales tariff. If the local ratio at a given time is equal to or greater than 1, the system should not pump but turbine. If it is less than 1, it is advantageous to pump. In the case of the average

*R*

_{C/V,average}, this indicates globally the ratio between the selling and buying tariffs for the 24 h of the day. This indicator illustrates the opportunity to turbine on a given day; lower values indicate a larger opportunity to take advantage of PHS. The

*R*

_{C/V}can be mathematically written as:where

*T*

_{buy}is the purchase tariff at a given time of day,

*j*, and

*T*

_{sell}is a fixed tariff for selling electricity throughout the day.

Note that these two ratios must be analyzed together for a complete and cohesive analysis.

## CASE STUDY

*q*

_{VC}–

*q*

_{R}) (Manteigas

*et al.*2022) as shown in Figure 5. Regarding power equipment, the four pumps P are located at an elevation of 0 m and pump the water from the catchment to a tank downstream and to the consumption point designated R (upstream of the tank). The tank F has an area of 155 m

^{2}and a height of 9 m. This tank is at an elevation of 50 m in relation to the pump, and the water level inside the tank can vary between 2 (minimum operating level) and 8 m (maximum operating level) for safety reasons. The tank supplies the consumption points R and VC by gravity. The initial water tank level is 4 m. The pipes are made of cast iron, with a Fanning friction factor equal to

*f*= 0.02, with a diameter of 300 mm, and the length between P and R of the pipe is 3,500 m, the length between R and F is 6,000 m, and the length between P and F is 9,500 m.

*Q*

_{VC}and

*Q*

_{R}are the water demands flow rates in m

^{3}/h and

*t*is the time in h. As already mentioned, the European market is becoming more and more decentralized and consequently, there is larger volatility in electricity prices. To calculate the energy costs in this WSS, three tariffs were considered based on the spot Iberian market (OMIE) for Portugal. The days chosen for simulation and optimization of the operation were March 10, April 23, and May 30 of 2023, representing quite distinct patterns from each other. Figures 6–8 show the price variation according to the respective days. Regarding the price of selling electricity to the grid, in this work, a reference tariff of 100 €/MWh was considered based on the Portuguese regulated market.

On March 10 (Day A), it can be seen that the periods with high energy prices are between 07:00 and 13:00 and between 19:00 and 24:00. On the other hand, between 01:00 and 06:00 and between 14:00 and 18:00, energy prices are relatively low. The average tariff price on this day was 58.9 €/MWh and its standard deviation was 61.62%. According to these results, it is visible that the tariff price volatility was quite large and representative of the new energy paradigm in the Iberian market.

*R*

_{C/V}over the chosen day can be seen.

With the data in Figure 9, it is possible to obtain the average local ratio of 0.43. The local ratio between 7–10 and 20–22 is close to 1 and is above the *R*_{C/V,average}. During the rest of the day, the *R*_{C/V} is below the *R*_{C/V,average}, which may be economically advantageous to turbine. The *R*_{C/V,average} value equal to 0.43 indicates that this tariff can be advantageous, since the selling price of electricity is higher than the buying price during most of the day, meaning that there is an economic opportunity to turbine throughout the day.

*R*

_{C/V}, over April 23, is shown in Figure 10.

With the data in Figure 10, it is possible to obtain the average local ratio of 0.50. In this tariff, the *R*_{C/V} is lower than the *R*_{C/V,average}, particularly when the energy tariffs are equal or very close to 0 €/kWh. Therefore, in this interval, the operation of the PAT is expected to be in direct (pumping) mode. During the rest of the day, this no longer happens, the *R*_{C/V} is above the *R*_{C/V,average}, and it may be more economically advantageous to turbine or not operate. In this tariff, the *R*_{C/V,average} is also below 1, due to energy tariffs of 0 €/MWh in the middle of the afternoon.

*R*

_{C/V}, over the May 30 period is shown in Figure 11.

With the data in Figure 11, it is possible to obtain the average local ratio of 0.93. In this tariff, the *R*_{C/V} is very close to 1 throughout the day. This means that the PAT should pump only what is necessary to meet water demands. The *R*_{C/V,average} is almost 1 due to an almost constant tariff, which shows the low possibility of having an advantageous cost reduction per PHS. During the day, the possibility of using turbines is almost zero, as shown in the simulation results.

### Different scenarios

To study the operation of a PHS in WSS, three scenarios were defined for the case study. These are (1) Reference/baseline, (2) Optimized pump operation, and (3) Optimized PAT operation scenarios. The characteristics of each scenario can be described as follows:

Reference/baseline scenario: Comprises the case study without any changes, where the pumps are controlled according to the minimum (starting the pumps) and maximum (stopping the pumps) operation levels.

Optimized pump operation scenario: Includes the case study with optimized operation of the pumps according to the energy tariffs presented.

Optimized PAT operation scenario: Comprises the case study where pumps are replaced by PATs and their operation is optimized. The tank level constraints and water demands are kept similar to the reference case study, as well as the WSS characteristics.

*et al.*(2017) on a test bench in a controlled environment, and can be mathematically defined by:

## RESULTS AND DISCUSSION

### Reference scenario

*H*

_{min}) and turn off whenever the tank reaches its maximum level (

*H*

_{max}), without any consideration for the difference in energy prices throughout the day (Luna

*et al.*2019). Figures 14–16 show the control of the pumps according to this mode of operation and the associated cost.

The final costs reflected in this type of operation approach are €21.02, €42.73, and €79.81 for March 10, April 23, and May 30, respectively. As can be seen, the tank level always ends up equal to the level at the beginning of the day, 4 m, considering continuity constraint.

### Optimized pump operation scenario

As shown in Figure 17, in contrast to the reference scenario, the pumps are turned on and off in the early hours of the day. At 02:00, the pumps are turned on at a time when the energy tariff is low and they operate for 5 h and only turn on again at 12:00, also in a period of economically advantageous energy. These also turn off at 7:00, before the energy tariffs go up again, unlike the first scenario that turns off only at 8:00, operating for 1 h in a period of high prices.

The difference in results between this scenario and the reference scenario is striking. It is visible that in the optimized pump operation scenario, the pumps keep the tank level at the minimum just to cope with the consumption due to the high energy price at the beginning of the day. When the tariffs are equal to 0 €/kWh, the pumps turn on and operate for 9 h. It should be noted that the number of times the pumps turn on and off is detrimental to the life of the equipment; however, the maximum pump starts was not considered as a constraint in this work. During this operation, the tank levels, *h*_{min} and *h*_{max}, were never reached.

At first sight, the cost reduction is not significant. However, there are differences in the running time of the pumps compared to the reference scenario. The pumps start off and do not switch on until 02:00. In the following five optimization intervals, the pumps operate all the time. However, they turn off before reaching *h*_{max} and turn on again when the tank level reaches *h*_{min}, and turn off again at the end of the day at 20:00.

### Optimized PAT operation scenario

With the results in Figure 20, the PATs start with the same operation as in the optimized pump operation scenario without any difference until 07:00. However, from this time, the PATs start to operate as turbines in the following four optimization intervals for 0.8, 0.45, 0.94, and 0.8 h, respectively. This operation was expected considering the *R*_{C/V} and *R*_{C/V,average}. In this interval of the day, the *R*_{C/V} is close to 1, which indicates that it is advantageous to turbine in a first analysis; however, it is the *R*_{C/V,average} of 0.43 that guarantees that it is advantageous to turbine in this interval, since the difference between buying and selling allows it throughout the day. At 11:00, the PATs start to operate as pumps for 8 h because it is necessary to guarantee water consumption and it is economically more advantageous to pump during this period. At the end of the day, the PATs work as turbines with operating times close to 0.5 h until the end of the day in each optimization interval. The *R*_{C/V} criterion also confirms this operation, as its value is greater than 1.

In this case, it is interesting to note that the PATs do not turn on at the beginning of the day. This fact is due to the need to ensure water consumption. An analysis of the ratio shows that this is the case, since turning on the turbine mode at the beginning of the day would be disadvantageous. In this example, the *R*_{C/V,average} is below 1, which implies that there would be no obstacle to turbine, since the purchase rates would be low throughout the day. However, in this specific type of tariff, where there is clearly an advantageous opportunity to pump at very low or near zero cost, the operation of the PATs as a pump is reserved as much as possible for such intervals. At the end of the day, the PATs operate as turbines where the price is high and it is advantageous to turbine (visible by the local ratio, *R*_{C/V} which is greater than 1).

With the model developed for May 30 (Day C), the optimization result for the operation of the PAT is as follows:

*R*

_{C/V,average}, with a value of 0.93 reveals that the price of selling energy is almost equal to the all-day energy tariffs. It can be concluded that the opportunity to turbine and then pump at a lower price is almost nil.

### Analysis of final costs

Tables 1–3 present the results of the various scenarios under analysis according to the tariffs of the respective days:

Scenario^{a}
. | Number of starts . | Flow rate (m^{3}/h). | Operation time (h) . | Final cost (€) . | Cost reduction (%) . | |||
---|---|---|---|---|---|---|---|---|

Pumping . | Turbine . | Pumping . | Turbine . | Pumping . | Turbine . | |||

1 | 2 | – | 181.7 | – | 13 | – | 21.02 | – |

2 | 4 | – | 181 | – | 12.5 | – | 12.70 | 39.5 |

3 | 2 | 7 | 180.3 | 69.2 | 14.5 | 3.5 | 11.90 | 43.4 |

Scenario^{a}
. | Number of starts . | Flow rate (m^{3}/h). | Operation time (h) . | Final cost (€) . | Cost reduction (%) . | |||
---|---|---|---|---|---|---|---|---|

Pumping . | Turbine . | Pumping . | Turbine . | Pumping . | Turbine . | |||

1 | 2 | – | 181.7 | – | 13 | – | 21.02 | – |

2 | 4 | – | 181 | – | 12.5 | – | 12.70 | 39.5 |

3 | 2 | 7 | 180.3 | 69.2 | 14.5 | 3.5 | 11.90 | 43.4 |

^{a}1: Reference scenario; 2: Optimized pump operation scenario; 3: Optimized PAT operation scenario.

Scenario^{a}
. | Number of starts . | Flow rate (m^{3}/h). | Operation time (h) . | Final cost (€) . | Cost reduction (%) . | |||
---|---|---|---|---|---|---|---|---|

Pumping . | Turbine . | Pumping . | Turbine . | Pumping . | Turbine . | |||

1 | 2 | – | 181.7 | – | 13 | – | 42.73 | – |

2 | 3 | – | 182.8 | – | 12.75 | – | 16.66 | 61 |

3 | 9 | 1 | 182.3 | 66.6 | 13.75 | 2.85 | 13.63 | 68.1 |

Scenario^{a}
. | Number of starts . | Flow rate (m^{3}/h). | Operation time (h) . | Final cost (€) . | Cost reduction (%) . | |||
---|---|---|---|---|---|---|---|---|

Pumping . | Turbine . | Pumping . | Turbine . | Pumping . | Turbine . | |||

1 | 2 | – | 181.7 | – | 13 | – | 42.73 | – |

2 | 3 | – | 182.8 | – | 12.75 | – | 16.66 | 61 |

3 | 9 | 1 | 182.3 | 66.6 | 13.75 | 2.85 | 13.63 | 68.1 |

^{a}1: Reference scenario; 2: Optimized pump operation scenario; 3: Optimized PAT operation scenario.

Scenario^{a}
. | Number of starts . | Flow rate (m^{3}/h). | Operation time (h) . | Final cost (€) . | Cost reduction (%) . | |||
---|---|---|---|---|---|---|---|---|

Pumping . | Turbine . | Pumping . | Turbine . | Pumping . | Turbine . | |||

1 | 2 | – | 181.7 | – | 13 | – | 79.81 | – |

2 | 6 | – | 182.3 | – | 13 | – | 77.97 | 2.3 |

3 | 6 | 0 | 182.3 | 0 | 14 | 0 | 78.00 | 0 |

Scenario^{a}
. | Number of starts . | Flow rate (m^{3}/h). | Operation time (h) . | Final cost (€) . | Cost reduction (%) . | |||
---|---|---|---|---|---|---|---|---|

Pumping . | Turbine . | Pumping . | Turbine . | Pumping . | Turbine . | |||

1 | 2 | – | 181.7 | – | 13 | – | 79.81 | – |

2 | 6 | – | 182.3 | – | 13 | – | 77.97 | 2.3 |

3 | 6 | 0 | 182.3 | 0 | 14 | 0 | 78.00 | 0 |

^{a}1: Reference scenario; 2: Optimized pump operation scenario; 3: Optimized PAT operation scenario.

The reference scenario illustrates a traditional operation of the pumps in the WSS, making it the most expensive of all the others with a cost of 21.02 €. This is explained by the fact that the operation of the pumps does not take into account the cost of energy tariffs throughout the day. By optimizing the operation of the pumps with energy tariffs in the Iberian market, the cost is significantly reduced to 12.70 €, which corresponds to a reduction of approximately 39.50%. However, the pumps tend to turn on more frequently due to the tariff variations represented by the corresponding daily tariff.

By implementing a PHS system in the same case study, it is possible to achieve a more profitable operation. Through the methodology presented in this work with the implementation of PHS, the total cost is 11.90 €, which is a reduction of about 43.4% compared to the reference scenario. The cost reduction between the optimized pump operation scenario and the optimized PAT operation scenario is approximately 6.3%.

Regarding the tariff for April 23, 2023, the traditional operation has an initial cost of 42.73 €. By optimizing the pump operation, the reduction was around 26.07 €, which corresponds to a relative reduction of 61% as illustrated in Table 2. By replacing the pump with a PAT, the reduction was even more significant, amounting to 29.10 €, a reduction representing a decrease of approximately 68% compared to the reference scenario and an additional 18% compared to the optimized pump operation scenario.

May 30, 2023 (Day C) presents almost no cost reduction, either on a pump optimization basis or even by PAT. Therefore, on a day with low tariffs volatility, the cost reduction is practically negligible. In the optimized pump scenario, the reduction does not reach 2 € compared to the reference scenario. The influence of a PHS system is practically zero compared to the optimized pump scenario, demonstrating that the chance of taking advantage of a PHS system in low volatile tariffs may be nonexistent.

### Key performance indicators

Table 4 lists the *I*_{PHS}, the average price, standard deviation, and *R*_{C/V,average} values per scenario in the corresponding energy tariff. In the presented methodology, *I*_{PHS} represents the amount of volume that is used to turbine over the total available volume. With the average values *Q _{b}*,

*Q*

_{turb},

*t*,

_{b}*t*

_{turb}, it is possible to determine the average

*I*

_{PHS}for each day.

Indicator . | March 10, 2023 . | April 23, 2023 . | May 30, 2023 . |
---|---|---|---|

PHS index (%) | 9 | 8 | 0 |

Average price (€/MWh) | 58.6 | 69.0 | 93.0 |

Standard deviation (%) | 61.62 | 62.09 | 14.5 |

R_{C/V,average} | 0.43 | 0.5 | 0.93 |

Indicator . | March 10, 2023 . | April 23, 2023 . | May 30, 2023 . |
---|---|---|---|

PHS index (%) | 9 | 8 | 0 |

Average price (€/MWh) | 58.6 | 69.0 | 93.0 |

Standard deviation (%) | 61.62 | 62.09 | 14.5 |

R_{C/V,average} | 0.43 | 0.5 | 0.93 |

On March 10 (Day A), with a high volatility of hourly tariffs with an average price rounding to 60 €/MWh, for the PAT operation scenario, the *I*_{PHS} was 9%, which means that 9% of *V _{b}* was stored to be turbined later. According to Day B, the same evaluation, on April 23, in the scenario with optimized PAT with an average price of 70 €/MWh and nearly the same standard deviation, only 8% of the available volume was used to be turbined. On May 30, in the optimized PAT scenario, the operation of the PAT in reverse mode does not exist. Consequently, the percentage of the turbine volume is 0%, which means that all the

*V*was used to meet water consumption and has never been used to recover energy.

_{b}It can be seen in Table 4 as well, that the *R*_{C/V,average} is increasing from 0.43 on Day A to 0.50 on Day B and reaches Day C with a value of 0.93, and consequently, the *I*_{PHS} decreased from Day A to Day C.

According to the results obtained on the revenue in the optimized PAT scenario compared to the reference scenario for the tariffs evaluated, these should be considered during the investment plan for the implementation of a PHS system in a WSS.

As mentioned, the optimized PAT operation scenario was implemented with 4 KSB 65-40-315 PATs. The value of these is approximately 6,550 € per unit on the foreign market (KSB Etanorm 065-040-315 | SuperPump 2023) for a total initial investment of 26,200 €. Considering this value twice of the purchase of the equivalent pumps, the additional investment of PAT would be 13,100 €.

## CONCLUSIONS

Research in the water sector has recently focused on the possibility of installing a PHS system as a cost-saving alternative to WSS. The idea of storing energy during periods of low energy cost and recovering it during periods of high tariffs can be a hypothesis to minimize the operating costs of a WSS.

This work focused on the operational optimization of a PAT installed in a water supply network from the perspective of dynamic energy tariffs. The methodology developed was applied to a case study of a simple water supply network, and three different operating scenarios were analyzed. The first scenario analyzed was in the situation of optimized pump operation. It was achieving cost reductions on March 10 and April 23, about 39.50 and 61%, respectively. With the replacement of the pumps with PAT, the cost reductions were even more beneficial, about 43.4 and 68%. This is explained by the volatility of the energy tariffs during the day. The analysis of the *R*_{C/V,average}, 0.43 and 0.50, with the local *R*_{C/V} ratios, was consistent with the results obtained. However, May 30 clearly showed that low volatility is associated with low cost reduction, no more than 2.3%, even with PAT. *R*_{C/V,average} is equal to 0.93, very close to 1, which is a negative indicator. It should be highlighted that the indicator ratios are conclusive. In gross value, April 23 is clearly the most significant with a reduction of 29.10 € in terms of reduction. The factors that define this solution are the following: a high percentage standard deviation, an *R*_{C/V,average}, and namely free mid-afternoon supply. With this combined cost and ratio analysis, the PHS incorporated into the WSS on March 10 (Day A) and April 23 (Day B) proved to be a very attractive alternative, as indicated by the high relative reductions. In all scenarios, the optimization was completed with the tank level ending at the same level as it started, equivalent to 4 m. As it was possible to demonstrate, the *I*_{PHS} on March 10 and April 23 was 9 and 8%, respectively, which means that only a small part of the *V _{b}* was stored to be turbined later.

The main high-level findings are the following:

The results demonstrate that the installation of PHS in WSSs is cost-effective for heterogeneous dynamic tariffs, with paybacks lower than 5 years.

Water utilities can take advantage of dynamic energy prices by pumping at more economically advantageous energy prices and turbining at more economically expensive energy prices without jeopardizing water consumption. However, the results show that these benefits cannot be realized on days when the tariff does not have a large price amplitude.

The cost-effectiveness of PHS in WSS is well evaluated by the KPI suggested here.

The effectiveness of PHS is only achieved with the use of a decision support system, which includes simulation and optimization techniques.

However, the methodology developed has some limitations, such as the limited applicability of using PATs in water supply networks whose *R*_{C/V} is close to 1, and the conclusions drawn from this work apply only to branched supply networks. Therefore, the conclusions should not be extended to meshed supply networks. Future research should further investigate the performance of WSS with PATs in more complex water networks, explore the operational control of PATs under dynamic selling energy prices, similar to the purchasing energy prices considered in this work, and use and compare other optimization algorithms in the optimizer component with the one used in this work.

In summary, the implementation of a PHS system can be beneficial in the new energy paradigm according to Mercado Ibérico de Electricidade (MIBEL) tariffs, with significant reductions on days with very volatile tariffs. It is also important to emphasize that when designing the size of the tanks, it would be interesting to study their best topographical position for a possible future inclusion of a PHS system.

## ACKNOWLEDGEMENTS

This work was supported by the Regional Operational Program of the Center Region (CENTRO2020) within project I-RETIS-WATER (CENTRO-01-0247-FEDER-069857) and UIDB/00481/2020 through the European Social Fund, the European Regional Development Fund, and the COMPETE 2020 Programs.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Improved Planning of Energy Recovery in Water Systems Using a New Analytic Approach to PAT Performance Curves*. ii. https://doi.org/10.3390/w12020468