On the operational optimization of pump storage systems in water supply systems using PATs and time-differentiated energy prices

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 CO₂ 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.

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/m³, 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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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:

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

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.

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.

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

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 €.

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.

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

The authors declare there is no conflict.