# Optimal Near Real-Time Control of Water Distribution System Operations

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Real-Time Scheduling Framework

#### 2.1.1. Water Demand Forecasting Model

_{i,t}) values for the dynamic analysis time steps (i.e., 60, 30, and 15 min) will vary within ±5% of the hourly base water demand (q

_{i}) values.

#### 2.1.2. Hydraulic Simulation Model

#### 2.1.3. Control-Based Optimization Model

#### 2.2. Study Methodology

#### 2.3. Demonstration

## 3. Results and Discussion

#### 3.1. Proposed Real-Time Scheduling Framework Performance

- In the real-time scheme, energy consumption reduction is achieved by having the operational speed of pumps and valves vary compared to the conservative baseline scenario operations of tanks and pumps, where the criterion for operating a pump is solely based on whether a tank has reached its minimum or maximum level. However, the range within which tank levels can vary remains similar in real-time, dynamic operations to make the scenarios more comparable. One practical reason for the energy reduction is associated with the reduction in the speed, and thus the energy, of the pumps, which sets the priority on energy conservation rather than filling up the tanks suboptimally using pumps running at higher speeds. However, there are other plausible factors contributing to energy conservation, such as dynamic controls of valve settings. According to Figure 2, some of the valves are strategically located, in that they can alter pressure zone boundaries, and thus the dynamic controls of their settings can contribute to the reduction in the overall system pressure and, hence, the less consumed energy;
- Because the objective in the real-time operation is energy conservation, the tank levels have to follow the optimization purpose, and the observation associated with it turns out to be more numbers of fill/draft trends compared to the baseline scenario;
- The number of pump switches is not a critical issue, as the pumps undergo speed variations rather than the operationally expensive fact of being “on” or “off”; this means that the pumps experience less friction, fewer constant on/off changes, and thus experience a higher lifespan in the long run.

#### 3.2. Sensitivity Analyses

#### 3.2.1. Actual Water Demand Variation

#### 3.2.2. Minimum Allowed Tank Levels

#### 3.3. Future Work and Limitations

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Layout of BWDS (adapted from [13]).

**Figure 3.**Modified water demand pattern for BWDS (adapted from [26]).

**Figure 4.**The two pump schedules over the operational horizon: (

**a**) baseline, (

**b**) 60 min, (

**c**) 30 min, and (

**d**) 15 min.

**Figure 5.**Pump energy profile over the 24 hour operation period: (

**a**) baseline, (

**b**) 60 min, (

**c**) 30 min, and (

**d**) 15 min.

**Figure 6.**Tank levels profile over the 24 hour operation period for (

**a**) baseline, (

**b**) 60 min, (

**c**) 30 min, and (

**d**) 15 min.

**Figure 7.**Variations of (

**a**) energy consumption, (

**b**) pump speed, and (

**c**) tank levels for sensitivity analysis of system water demand randomization within 15%.

Pump ID | Close When | Open When |
---|---|---|

Pump-1 | Tank-1 water level > 5.2 m | Tank-1 water level < 4 m |

Pump-2 | Tank-2 water level > 5.9 m | Tank-2 water level < 5 m |

Scheme | Avg. Cost (in USD 1000) | Avg. Saving % |
---|---|---|

Baseline | USD 962.27 | -- |

60 min | USD 798.52 | 17.1% |

30 min | USD 795.22 | 17.4% |

15 min | USD 791.61 | 17.8% |

**Table 3.**Sensitivity analysis results for actual water demand variations and minimum allowed tank level in conventional and dynamic time steps.

Parameter Variations | Hourly Energy Consumption Cost (Conventional) | Hourly Energy Consumption Cost (Real-Time) | ||||||
---|---|---|---|---|---|---|---|---|

60 min | 30 min | 15 min | ||||||

AC ^{2} | RS ^{3} | AC | RS | AC | RS | AC | RS | |

Baseline ^{1} | 962.71 | -- | 798.22 | -- | 795.22 | -- | 791.61 | -- |

Demand Variations within ±1% | -- | -- | 796.79 | 0.17% | 803.00 | −0.98% | 790.04 | 0.20% |

Demand Variations within ±15% | -- | -- | 819.37 | −2.64% | 821.80 | −3.34% | 823.02 | −3.97% |

Minimum Allowed Tank Level Variations minus 0.305 m | 835.02 | 13.3% | 793.74 | 0.56% | 791.62 | 0.45% | 786.30 | 0.67% |

Minimum Allowed Tank Level Variations plus 0.305 m | 1159.9 | −20.5% | 800.33 | −0.26% | 803.32 | −1.02% | 801.28 | −1.22% |

^{1}Actual baseline variation: within ±5% and baseline. Min: Tank-1 (4 m) and Tank-2 (5 m); initial: Tank-1 (4.6 m) and Tank-2 (5.4 m).

^{2}Average hourly cost over the 24 h operational horizon (in USD 1000).

^{3}Relative savings in percentage compared to the corresponding baseline value.

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**MDPI and ACS Style**

Bin Mahmoud, A.A.; Momeni, A.; Piratla, K.R.
Optimal Near Real-Time Control of Water Distribution System Operations. *Water* **2023**, *15*, 1280.
https://doi.org/10.3390/w15071280

**AMA Style**

Bin Mahmoud AA, Momeni A, Piratla KR.
Optimal Near Real-Time Control of Water Distribution System Operations. *Water*. 2023; 15(7):1280.
https://doi.org/10.3390/w15071280

**Chicago/Turabian Style**

Bin Mahmoud, Abdulrahman Abdulaziz, Ahmad Momeni, and Kalyan Ram Piratla.
2023. "Optimal Near Real-Time Control of Water Distribution System Operations" *Water* 15, no. 7: 1280.
https://doi.org/10.3390/w15071280