Integrated urban wastewater system operation: Performance evaluation and sewer network's operation implications

Humanity is facing three major global environmental crises: pollution, loss of biodiversity and climate change. A large portion of the pollution crisis, besides air and land pollution, is represented by the increasing quantity of pollutants in water sources (UNESCO et al. 2023). Water is the source of life on Earth, thus its quality impacts the environment and public health. The main cause of water pollution is represented by human activities that are producing large amounts of heavily polluted wastewater, having the potential to compromise the water sources. For this reason, managing wastewater is an important topic and is included in most of the organizations' agenda, such as the United Nations 2030 Agenda for Sustainable Development (UN General Assembly 2015). Moreover, national and international legislation provides stricter and stricter limits for the quantity of pollutants in the wastewater discharged into the natural recipients, providing frameworks to respect these limits. One example of such legislation is the European Union (EU) Water Framework Directive (European Parliament 2000) which establishes a unified approach to wastewater legislation aiming at protecting the environment and restoring water quality across the EU. Respecting these limits in a continuously developing civilization is a challenge and implies developing new technologies for wastewater management or improving the existing ones by increasing the operational efficiency of Sewer Networks (SNs) and Wastewater Treatment Plants (WWTPs). Moreover, like any other industrial facility, WWTPs are non-negligible sources of Greenhouse Gases (GHGs), such as nitrous oxide (N₂O), methane (CH₄) and carbon dioxide (CO₂) (Flores-Alsina et al. 2011), contributing to another major worldwide crisis: climate change. Thus, in the context in which it became imperative to reduce GHG emissions (Intergovernmental Panel on Climate Change 2006, 2019), the issue of managing wastewater should account for these emissions.

The wastewater management processes include collecting wastewater from human communities and industrial facilities throughout SNs and treating wastewater in WWTPs. The literature approaches the two subjects either separately (such as Vasiliev et al. (2024) or Du et al. (2022)) or in an integrated manner (such as Butler & Schutze (2005)) – Integrated Urban Wastewater Systems (IUWS). The primary objectives when increasing the efficiency of SNs are preventing overflowing into the environment, and, in instances when inevitable discharges occur during heavy pluviometric events (rain and storm), keeping a minimum concentration of pollutants in the wastewater released into the natural recipients. On the other hand, for WWTP, efficiency is ensured by maintaining the pollutants' concentrations in the plant's effluent below the limits stipulated by the prevailing legislation. In the case that the two IUWS subsystems are treated in an integrated manner, it is important to discern the implications that the SN operation has on the operational efficiency of the WWTP as the effluent of the SN serves as the influent for the WWTP. Increased flow rates originating from the SN, a consequence of control actions designed to minimize overflows, have the potential to overload the WWTP, giving rise to environmental repercussions downstream. Consequently, SN control strategies should consider their impact on the operational efficiency of the WWTP. This is a well-known problem (i.e., Harremoës et al. 1993). Although recent innovations, such as Membrane Bioreactors (MBRs), have partly addressed the problem of hydraulic loading, it has become evident with the introduction of other process technologies like Enhanced Biological Phosphorus Removal (EBPR), sensitivity to incoming wastewater quality, not just quantity, remains a challenge. A recent study discusses variations in wastewater quality and in-sewer processes during conveyance in sewer systems (Gao et al. 2023). Conversely, WWTP control strategies should consider their role in helping the SN, particularly when the SN is affected by substantial pluviometric events. More specifically, the WWTP control strategies should be able to deal with increased wastewater flow for short time periods, taking over some of the stress that the extreme weather events pose on the SN.

The International Water Association (IWA), aiming at combining the relevant biological treatment models into a unified model that can describe the activated sludge treatment process, gave the scientific community a series of WWTP mathematical models, such as ASM1 (Henze et al. 1987) – modelling carbon and nitrogen removal, ASM2 (Gujer et al. 1995) – modelling, in addition to ASM1, the phosphorus removal, ASM2d (Henze et al. 1999) and ASM3 (Gujer et al. 1999). The development of WWTP control strategies required complex models encompassing the entire treatment system, capable of facilitating the comparisons among different control strategies. In this context, a series of benchmark models have been developed: BSM1 (Alex et al. 2008), BSM1-LT (Rosen et al. 2004) and BSM2 (Gernaey et al. 2014). Additionally, as WWTPs are a source of GHG emissions, models including these emissions have been developed. One such model has been considered in this paper, namely BSM2G (Flores-Alsina et al. 2011). Controlling the WWTP usually aims at maximizing the plant's efficiency by maintaining the effluent quality within the legal limits, while, at the same time, having a lower operational cost. The scientific community proposed, throughout the years, a series of control strategies for WWTPs ranging from a simple PID controller (as presented in the default strategies defined by BSM1 and BSM2) to more complex ones, such as event-triggered Model Predictive Control (Du et al. 2022), fuzzy logic techniques (Santín et al. 2023; Zhao et al. 2023) or adaptive PID controllers (Piotrowski et al. 2023).

Regarding the SN, the literature reports two types of models (Vasiliev et al. 2022a):

• 1. Flow models – based on the Saint-Venant equations (for example, the model presented in Joseph-Duran et al. (2013)).

• 2. Quality models – capable of modelling pollutants entering, moving through and exiting the SN. The quality models can be further split into:

• a. Stochastic quality models (data-driven, using various techniques such as multigene genetic programming (Safari & Danandeh Mehr 2018) or polynomial regressions (Najafzadeh et al. 2017)).

• b. Deterministic quality models (based on causality relationships). A reference deterministic quality model is BSMSewer (Saagi et al. 2016), an SN benchmark simulation model, which is also considered in this paper. It is composed of a catchment model and an SN model accounting for wastewater transport (flow and loads), pipes flushing and wastewater storage.

Regarding IUWS, the literature reveals a limited number of papers. The majority primarily concentrates on the modelling aspects of these integrated systems in terms of combining an SN model with a WWTP model. Sharma et al. (2012), aiming to investigate the effects of SN chemical dosage on WWTP efficiency, propose an IUWS model by combining the SeweX model (SN) with the ASM2d model (WWTP). Barbu et al. (2017a) propose an IUWS model by combining BSMSewer (SN) with BSM2 (WWTP) aiming at enhancing the understanding regarding the interactions between the two subsystems. Another integrated model is SYNOPSIS proposed by Butler & Schutze (2005). The authors implemented and tested a series of Real Time Control (RTC) strategies (a reference strategy, an optimal setpoint strategy, but also a hierarchical control approach) on the proposed model. Other approaches using RTC strategies for IUWS can be found in Seggelke et al. (2013), Lu et al. (2020) and Sun et al. (2020). One interesting approach is presented by Kroll et al. (2015), where the authors use an RTC control strategy for the SN in order to maintain the volume of overflow at a minimum value, while, at the same time, the SN effluent is limited at the WWTP maximum capacity, helping, this way, the efficiency of the plant.

However, as seen in Vasiliev et al. (2023), limiting the SN outflow to the maximum WWTP capacity does not always provide the best results with respect to the performances of both subsystems. Thus, this paper aims to define a way to evaluate the operational efficiency of the IUWS and study the implications of SN operation on the integrated system performance. Various control strategies are explored and their implications are studied. Firstly, a simple SN control is imposed (constant value for the SN outlet valve opening, while all the other SN valves and pumps are fully opened and running at 100%). Secondly, a previously developed SN Model Predictive Control (MPC) algorithm (Vasiliev et al. 2024) designed for reducing the environmental impact of SN and modified by constraining it in terms of SN outlet valve opening is used for reducing the environmental impact of the IUWS.

The MPC algorithm is an online optimal control strategy. Optimal control is a subfield of the control theory involving an optimization procedure for finding the control inputs’ combination that minimizes a given fitness function. Based on the moment when the optimization procedure is run, two types of optimal control can be distinguished: (1) offline optimal control – the optimization procedure is performed before the system starts operating and (2) online optimal control – the optimization procedure is performed during the operation of the system. The MPC algorithm falls into the second category. It implies predicting the future behaviour of the system over a certain time horizon (named prediction horizon) using a dynamic model of the system. At each time step, the optimization problem is solved resulting in the optimal control actions. The first control action is applied to the real system and the procedure is repeated for the next time step (Camacho & Bordons 2007).

The rest of the paper is structured in three more sections. The first one presents the structure of the IUWS, its influent, the performance indicators of both subsystems, a short presentation of the MPC algorithm and also a method to evaluate the operational efficiency of the integrated system in terms of environmental impact (pollutants discharged, but also GHG emitted) and operation cost. The next section is dedicated to the simulation results obtained with various SN control actions, while the last section presents the conclusions of this research including subsequent research directions.

The model has been previously developed in Vasiliev et al. (2022b) using the BSMSewer Software Package (Saagi et al. 2016) for testing optimal control strategies that aim to optimize the efficiency of the SN.

However, because of the model's complexity, its integration is computationally costly, so using this model in online optimal control strategies imposes a series of limitations related to the model's integration time. For this reason, in Vasiliev et al. (2024), a simplified version of this model has been implemented by removing from BSMSewer all the dynamics and states that were related to the pollutants' transport and storage. Basically, the resulting simplified model accounts only for the wastewater flow throughout the SN. Of course, this means losing information about pollutant concentrations, which will be regained during the control phase using the methodology proposed by Vasiliev et al. (2024).

The influent of the SN is composed of five influents related to the five collecting areas. Each of them is further split into two components: a domestic component and a pluviometric one. Moreover, the influent related to the 5th collecting area includes an additional industrial component. Each of the components is described by its flow and pollutant loads (COD_part – Particulate Chemical Oxygen Demand, COD_sol – Soluble Chemical Oxygen Demand, – ammonia and – phosphate).

For testing purposes, a 28-day influent has been generated in two variants: a forecasted influent and a disturbed one. The domestic component of the forecasted influent has been generated as described in Saagi et al. (2016): based on the area's population equivalent and average flow/loads per inhabitant adjusted with their daily, weekly and yearly variations. The pluviometric component is generated based on a weather forecast and the surface of the collecting area, while the industrial component considers the flow and loads specific to a mid-sized brewery (Ng 2006) with weekly and yearly variations. The disturbed influent is obtained from the forecasted one, by altering the flows of the components with random Gaussian distributed numbers.

For the WWTP, this paper considers the BSM2G model, which extends the BSM2 model by including GHG emissions. The plant layout is the same as the BSM2 one (Gernaey et al. 2014). Thus, it includes both wastewater treatment (a nitrification/denitrification scheme with five tanks – three aerated ones and two anoxic – and two clarifiers) and sludge treatment (composed of a sludge thickener, an anaerobic digestor with a dewatering unit and a storage tank).

The WWTP tanks are modelled using a modified version of ASM1. Thus, besides modelling organic compounds and nitrogen biological removal, the GHG emissions are estimated from various sources (Flores-Alsina et al. 2011):

• CO₂ resulting from the biomass respiration, BOD oxidation and the nitrification stage.

• N₂O generated by heterotrophic denitrification.

In addition to the GHG emissions related to biological treatment, other sources are considered (Flores-Alsina et al. 2011):

• CO₂ produced during anaerobic digestion.

• CO₂ produced by CH₄ combustion.

• CO₂ equivalent of the net power usage.

The WWTP model considered in this paper uses a simple PI controller for regulating the dissolved oxygen (DO) concentration in the 2nd aerated tank by manipulating the aeration flow in all aerated tanks (the strategy A1 defined by BSM2 (Gernaey et al. 2014)).

The SN effluent is composed of the five variables defined by BSMSewer, while the BSM2G influent contains 21 variables, a coupling unit is required between the two systems. The coupling unit makes the conversion of these variables by using a modified version of the BSMsewer to ASM2d variables conversion defined by Saagi et al. (2016), as presented in Vasiliev et al. (2023).

In BSMSewer 10 performance indicators are defined for assessing the performance of SN control strategies (Saagi et al. 2016). Each of them can be calculated globally for the entire SN or individually for each of the storage tanks. This paper considers and analyses only two of them: V_ovf (the total volume of discharged wastewater during overflow events – measured in m³/year) and OQI (the quality index of the discharged wastewater during overflow events – measured in kg − polluting units/day). In the case of the simplified model, as it accounts only for the water flow throughout the network, only V_ovf can be computed.

BSM2G extends the BSM2 WWTP performance indicators set by including some indicators related to GHG emissions (Flores-Alsina et al. 2011). From the whole indicators set of BSM2G, this paper considers and analyses only three of them: EQI (the Effluent Quality Index – measured in kg − polluting units/day), OCI (the Operational Cost Index) and GHG_total (the total WWTP GHG emissions – measured in kg CO_2e/day).

The base case is defined as the case when no control is considered for the SN (all valves are fully open and all pumps are running at maximum capacity). The values of the performance indicators in the base case can be seen in Table 1.

Of course, there is a need for a truly integrated indicator definition, and this requires some extra research that is beyond the scope of this paper. Specifically, the definition of integrated operational cost index and integrated GHG emissions of the SN and WWTP is needed.

A first version of SN control is proposed by Vasiliev et al. (2024). In the mentioned paper, a MPC approach to control the SN in order to minimize its environmental impact is considered. Because it has been observed in simulations that only controlling the outputs of TK₃, TK₄ and TK₅ can lead to an improvement of the SN performances, the proposed MPC algorithm is searching for the optimal controls of just these three tanks, while for the other tanks, the outlet valves are fully open and the outlet pumps are running at full capacity.

Thus, in Vasiliev et al. (2024) the three essential elements of the MPC are defined as follows:

• • The dynamic model of the system – the simplified model described in Section 2.1.1.

• • The definition of the fitness function J – three versions were implemented and compared:

• • o the first is defined as the global volume of overflow;

  • o the second is defined as the sum of the tank volumes of overflow weighted with some values computed offline accounting for the medium loads of each of the storage tanks;

  • o the third is defined in the same way as the previous one but having an additional penalty term to account for the remaining free space in the SN at the end of the prediction horizon.

• • The optimization algorithm – Particle Swarm Optimization algorithm has been considered for computing the optimal control actions with the following characteristics:

• • o 20 particles in the swarm;

  • o algorithm stopping when 100 iterations are reached or when there were 30 consecutive iterations with no improvements or the fitness function value reached 0.

These quality indexes are calculated before running the control algorithm based on pollutant measurements in key points of the SN using the methodology proposed by Vasiliev et al. (2024). This approach is necessary for compensating the lost information given by the model simplification.

The statistical analysis of the best results obtained by Vasiliev et al. (2024) showed an average reduction of 52% of V_ovf and an average reduction of 50% of OQI compared to the base case. The small standard deviations of both performance indicators proved the reliability of the proposed MPC algorithm.

Table 2 presents the scaled average values of the IUWS performance indicators obtained when connecting the SN model controlled by the previously mentioned MPC algorithm to the WWTP model described in Section 2.1.2. As expected, using the MPC algorithm has an effect only on SN performances, while the effect on the WWTP performances is negligible.

Table 2

The scaled values of the performance indicators when SN is controlled by MPC

Performance indicator .	Scaled value .
	0.4773
	0.4961
	0.9643
	0.9976
	1.0024
	0.8457

Performance indicator .	Scaled value .
	0.4773
	0.4961
	0.9643
	0.9976
	1.0024
	0.8457

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As it has been mentioned before, the implemented MPC algorithm considers computing only the optimal control values for the outlet valve of three of the storage tanks (TK₃, TK₄ and TK₅) as their manipulation was the only way to improve the SN performances. In the ‘Results and Discussion’ section of this paper, the effect of constraining the MPC in terms of SN outlet valve opening will be explored. Consequently, a modification of this control algorithm is imposed. More specifically, the control actions of SN tanks 1–6 will be subject to optimization. This change will imply analyzing the resulting data from a statistical point of view to prove that the modified MPC is maintaining its reliability.

For studying the implications of SN operation on the integrated system performance, two sets of results were generated in simulation:

• The first set of results considers that the only control applied to the SN is the outlet valve opening, while all the other valves and pumps are opened and running at 100%.

• The second set of results considers that the MPC algorithm proposed by Vasiliev et al. (2024) is constrained in terms of SN outlet valve opening, with the changes imposed and presented at the end of Section 2.3.

All simulations were performed over a period of 28 days, using the disturbed influent as the influent of the IUWS. Knowing that the WWTP requires a stabilization period after start-up, the initial state of the WWTP model has been set such that the actual simulation will start after the stabilization period (Gernaey et al. 2014). This assures a consistent starting point for each simulation.

As mentioned before, the first set of results considers that all SN valves and pumps are opened and running at 100%, except the outlet valve which is kept at a constant value U_TK7 ∈ [0, 1]. For analyzing the implications of U_TK7 on the IUWS performances, multiple simulations have been performed for various values of U_TK7 and the performance indicators described in Section 2.2 were computed.

As observed, a value of U_TK7 > 0.8 has no effect on the SN performances compared to the base case. Lowering U_TK7 to 0.7 results in increasing the volume of overflow and the overflow quality index by 8%. Lowering U_TK7 more will lead to a further increase of the two performance indicators, with U_TK7 < 0.65 having a dramatic effect (over 100% increase).

On the other hand, Figure 2(b) shows the change in the WWTP performance indicators for each constant value of the SN outlet valve opening.

All WWTP performance indicators are improving when lower values of U_TK7 are considered, as there is less wastewater directed to the treatment plant. It can be observed that decreases as U_TK7 increases, with small improvements for U_TK7 > 0.7 and more consistently decreased values below this limit. remains unchanged until U_TK7 reaches 0.7, then starts decreasing as the SN outlet valve closes more. has a 1% increase while U_TK7 lowers from 1 to 0.5, followed by a constant improvement for U_TK7 < 0.5.

Consequently, it can be stated that U_TK7 has strong effects on the performances of both subsystems. However, these effects are in antithesis, thus setting a constant value of U_TK7 to get an improved performance of one subsystem will provide worse performance of the other one. Moreover, combining the effects, it has been observed that the best improvement of the IUWS performances (⁠ and I(λ) for practical λ values) is marginal (under 2%), much lower than the case when the SN outlet valve was kept fully open, while, at the same time, the SN was controlled by an MPC algorithm (see Table 2). Therefore, more control capacity at the SN level is needed.

The second set of results was obtained by considering a control strategy applied to the SN. The control strategy is the MPC algorithm defined by Vasiliev et al. (2024) and described in Section 2.3. A constraint regarding the opening of the SN outlet valve has been integrated into the algorithm. Consequently, the modifications of the MPC that were described at the end of Materials and Methods have been imposed. The following assumptions were made:

• The model required by MPC – the SN simplified model; the forecasted influent has been used as the input.

• The process – the integrated model composed of the SN model implemented in BSMSewer coupled to the BSM2G model; the disturbed influent has been used as the input.

As observed, lowering the value of U_TK7 leads to SN performing worse, but also to a more efficient WWTP operation. Under this scenario, U_TK7 can be lowered to as much as 0.65 without having any significant negative impact on the SN performance. Moreover, further lowering to as much as 0.35 leads to just a small increase in the performance indicator, which could be compensated by the efficiency gained by the WWTP. Setting U_TK7 constraint below 0.35 leads to a high decrease in the SN performance. On the other hand, in the case of WWTP, while a value of U_TK7 over 0.7 leads to insignificant performance improvements, lowering it below this limit provides consistent decrease of all analyzed performance indicators: EQI, OCI and GHG_total.

Interesting results can be seen when analyzing DQI, a measure of the total pollutants discharged by the IUWS into the environment. Using a value above 0.7 for U_TK7 leads only to small improvements of DQI. Lowering U_TK7 more comes with an improvement of this performance indicator, with a ‘plateau’ value of approximately 0.5 (a reduction of approximately 50% in the total pollutants discharged into the environment) for U_TK7 ∈ [0.3 0.55], and consistent worsening below this interval.

Moreover, the small values of the standard deviations obtained for each constraint value and for each performance indicator demonstrate that the MPC algorithm keeps its reliability when constrained.

If the only objective of operating the IUWS is to minimize the quantity of pollutants discharged into the environment, a value of U_TK7 in the plateau range of DQI would be the best solution. Specifically, using U_TK7 = 0.35 will lead to the optimum reduction of pollutants of about 52%. Additionally, this solution also provides a 20% reduction of OCI and 25% reduction of GHG_total.

As the factor λ is kept above 0.4, the optimum value of U_TK7 remains at 0.35. For λ < 0.4, the best value of the constraint starts decreasing, as the importance of the total quantity of pollutants decreases and the importance of operational cost and GHG emissions increases.

The Fuzzy block has one input (SN outlet tank free space – described by the membership functions presented in Figure 7(b)) and one output (U_TK7 described by the membership functions presented in Figure 7(c)). The membership functions of the inputs and outputs were determined throughout a trial-and-error process. The rules that ensure the characteristics described in Figure 7(d) are:

• IF UTK7_FREE_SPACE IS LOW THEN UTK7 IS HIGH

• IF UTK7_FREE_SPACE IS MEDIUM THEN UTK7 IS MEDIUM

• IF UTK7_FREE_SPACE IS HIGH THEN UTK7 IS LOW

Using this fuzzy block to compute the SN outlet valve constraint leads to the results presented in Table 3.

Table 3

The scaled values of the performance indicators when SN is controlled by the constrained MPC and the constraint is computed by the fuzzy block

Performance indicator .	Scaled values when the constraint is constant (UTK7 = 0.35) .				Scaled values when the constraint is computed by the fuzzy block .
	MIN .	MEAN .	MAX .	STD .	MIN .	MEAN .	MAX .	STD .
	0.65	0.67	0.73	0.0312	0.54	0.59	0.69	0.0408
	0.67	0.71	0.78	0.0357	0.62	0.67	0.80	0.0638
	0.39	0.40	0.41	0.0067	0.37	0.38	0.39	0.0050
	0.81	0.81	0.83	0.0063	0.80	0.80	0.81	0.0050
	0.76	0.77	0.78	0.0066	0.74	0.75	0.76	0.0062
	0.46	0.48	0.50	0.0108	0.44	0.45	0.49	0.0173

Performance indicator .	Scaled values when the constraint is constant (UTK7 = 0.35) .				Scaled values when the constraint is computed by the fuzzy block .
	MIN .	MEAN .	MAX .	STD .	MIN .	MEAN .	MAX .	STD .
	0.65	0.67	0.73	0.0312	0.54	0.59	0.69	0.0408
	0.67	0.71	0.78	0.0357	0.62	0.67	0.80	0.0638
	0.39	0.40	0.41	0.0067	0.37	0.38	0.39	0.0050
	0.81	0.81	0.83	0.0063	0.80	0.80	0.81	0.0050
	0.76	0.77	0.78	0.0066	0.74	0.75	0.76	0.0062
	0.46	0.48	0.50	0.0108	0.44	0.45	0.49	0.0173

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It is observed that there is a persistent 2–3% improvement no matter the value of λ.

Of course, the solution presented in this paper can be scaled to other IUWS configurations by following the steps: (1) develop and validate a model of the SN in the BSMSewer Software Package; obtain the simplified version according to the procedure presented in Vasiliev et al. (2024); (2) develop and validate a model of the WWTP using the modified version of ASM1 (Flores-Alsina et al. 2011); (3) determine the values of the two weights involved in computing DQI based on the severity of discharges from each of the subsystems; (4) prepare an influent scenario for the IUWS such as it takes into account various conditions; (5) scale the MPC algorithm to the SN configuration and perform hyper-parameter tuning as presented in Vasiliev et al. (2024), while considering the aspects related to the computational effort of the algorithm; (6) find the best value for the U_TK7 constraint, using the above presented methodology; (7) use fuzzy techniques to further improve the results.

This paper proposes a method to evaluate the performance of IUWS operation in term of performance indicators of both subsystems, by defining a DQI, a measure of the total pollutants discharged into the environment by both subsystems and an integrated performance indicator considering, besides the quantity of pollutants discharged, the operational cost and the greenhouse emissions of the WWTP. Based on the proposed method, a study of the effects of SN operation on the IUWS performances is conducted, the results being compared with a base case. The effects were studied in two cases. In the first case, only the SN outlet valve was controlled, by keeping it at a constant opening, U_TK7. In the second case, a previously developed MPC algorithm aiming at minimizing the environmental impact of the SN overflows has been modified by constraining it in terms of the SN outlet valve opening.

The results obtained in the first case showed that, for the considered IUWS, modifying the SN outlet valve opening has a strong effect on both subsystems' performances. However, the effects are opposed. Thus, closing the outlet valve below a certain limit led to improved performances of the WWTP, as it has less wastewater to treat and degrading performances for the SN, as its probability to overflow increases. Combining the effects, in absence of any other SN control actions, they cancel, resulting in just a marginal improvement of the IUWS performances (under 2%), much less than the case when the SN is controlled by an unconstrained MPC, with the outlet valve fully open. Therefore, more control capacity at SN level is needed.

In the second configuration, improvements of both subsystems were obtained for a quite wide range of connecting valve opening, unlocking a win-win region, as shown by the DQI: a plateau for U_TK7 ∈ [0.3 0.55] where the total quantity of pollutants discharged by the integrated system is reduced by 50%. The improvements when keeping the valve opening in this plateau are confirmed by analyzing the integrated performance indicator. Moreover, the additional improvement of the IUWS performances (2–3%) can be achieved by considering the SN outlet valve constraint to vary in time depending on the free space in the SN outlet storage tanks.

In subsequent research, the authors intend to define an integrated operational cost index, as well as integrated GHG emissions and use them for updating I(λ) into a truly integrated index. Moreover, more improvements of the IUWS performances should be possible if the optimal value of U_TK7 gets determined at each MPC step based on the state of the SN and the WWTP. Besides this, in future work, the authors want to extend the research presented in this paper by considering the impact of climate change-related aspects (such as extreme meteorological events or climate variability) on the IUWS performances. Additionally, the effects that operating the SN has on the IUWS long-term performances will be studied.

This work received support from the Catalan Government under Project 2022 SGR 197 and by the Spanish Government under MICINN projects PID2019-105434RB-C33 and TED2021-806 129134B-I00 co-funded with the European Union ERDF funds.

All relevant data are available from an online repository or repositories: http://doi.org/10.17605/OSF.IO/92Z8D.

The authors declare there is no conflict.