# Robust Optimal Booster Disinfectant Injection in Water Systems under Uncertainty

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## Abstract

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## 1. Introduction

## 2. Robust Optimization

#### 2.1. RO-A Short Tutorial

#### Box Uncertainty

## 3. Problem Formulation

#### 3.1. Optimal Booster Chlorination Problem

#### 3.1.1. Decision and Uncertain Variables

#### 3.1.2. Optimization Problem Formulation

#### 3.1.3. Water Quality Objective

#### 3.1.4. Robust Counterpart Formulation

## 4. Case Studies

#### 4.1. Network System 1

#### 4.2. Network System 2

## 5. Results and Discussion

#### 5.1. Network System 1

#### 5.2. Network System 2

#### 5.3. Sensitivity Analysis

#### 5.3.1. Effect of Varying the Desired Residual Chlorine Concentration ${C}_{0}$

#### 5.3.2. Effect of Residual Chlorine Regulation Limits

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Graphical representation of NET-1 example of EPANET, which was used as the first network in this study.

**Figure 4.**Fossolo network graphical layout, extracted from Bragalli et al., 2008 [35].

**Figure 5.**This figure depicts the four different combinations of three booster locations in network system 1 that were considered in the study.

**Figure 6.**The figure depicts the results obtained for network system 1 in all four cases mentioned in Figure 5. (

**a**) illustrates the trend of objective function values. (

**b**) graphs the total amount of chlorine mass injected into the system.

**Figure 7.**This figure depicts the three different combinations of the four booster locations in network system 2 (Fossolo network) that were considered in the study.

**Figure 8.**This figure depicts results obtained for network system 2 (Fossolo network) in all three cases mentioned in Figure 7. (

**a**) graphs the total amount of chlorine mass injected into the system. (

**b**) exhibits the relationship between the objective function values.

**Figure 9.**The graphs shown in the figure depict the variations in the amount of chlorine dosage as well as in the penalty functions with an increase in the Co value.

**Figure 10.**The graphs shown in the figure depict the variations in the amount of chlorine dosage as well as the penalty functions with changes in the safe region of the objective function.

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**MDPI and ACS Style**

Boindala, S.P.; Jaykrishnan, G.; Ostfeld, A.
Robust Optimal Booster Disinfectant Injection in Water Systems under Uncertainty. *Water* **2023**, *15*, 1777.
https://doi.org/10.3390/w15091777

**AMA Style**

Boindala SP, Jaykrishnan G, Ostfeld A.
Robust Optimal Booster Disinfectant Injection in Water Systems under Uncertainty. *Water*. 2023; 15(9):1777.
https://doi.org/10.3390/w15091777

**Chicago/Turabian Style**

Boindala, Sriman Pankaj, G. Jaykrishnan, and Avi Ostfeld.
2023. "Robust Optimal Booster Disinfectant Injection in Water Systems under Uncertainty" *Water* 15, no. 9: 1777.
https://doi.org/10.3390/w15091777