# PEPSO: Reducing Electricity Usage and Associated Pollution Emissions of Water Pumps

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## Abstract

**:**

## 1. Introduction

_{2}/year-can be recovered from the system [6,7]. León-Celi, C et al. also used EPANET toolkit and two optimization algorithms to find the optimum flowrate distribution in water systems with multiple pump stations and minimize energy usage and potential leakage [8].

## 2. Literature Review

## 3. Tool Development and Methodology

#### 3.1. Transition from the First Version of PEPSO to the Second Version

#### 3.2. Introducing the New PEPSO

## 4. Experimental Demonstration

#### Design of Experiment

- ${P}_{P}:$ Penalty associated with water pressure violation at junctions
- ${P}_{T}:$ Penalty associated with water level violation at tanks
- $i:$ Time step index starts from the 1st time block and goes to the Ith time block
- $j:$ Junction index starts from the 1st junction and goes to the Jth junction
- $k:$ Tank index starts from the 1st tank and goes to the Kth tank
- $x:$ A power defined to increase the penalty by increasing the amount of violation. x = 1.5 is used.
- ${p}_{ij}:$ Water pressure of junction j at time block i
- ${p}_{jmax}:$ Maximum allowed water pressure of junction j
- ${p}_{jmin}:$ Minimum allowed water pressure of junction j
- ${h}_{ik}:$ Water level of tank k at time block i
- ${h}_{kmax}:$ Maximum allowed water level of tank k
- ${h}_{kmin}:$ Minimum allowed water level of tank k

_{2}that was employed in all optimization tests of this study [40]. Based on the hydraulic models, duration of an optimization run is 24 h with one-hour time step. The same set of values for parameters of optimization algorithm was used for all tests that are listed in Table 6. The crossover and mutation percentage define the portion of the population which should be selected for crossover and mutation steps respectively. The Crossover and mutation rate shows the portion of selected solution which should be modified during crossover and mutation steps.

_{2}emissions, and total penalty). The next scenario (S2) is defined to evaluate the effect of optimizing based on the electricity cost and CO

_{2}emissions, so it is just optimized based on penalties. This scenario is similar to the base scenario, but it uses the total penalty as the only optimization objective.

## 5. Results and Discussion

_{2}emissions of each solution is calculated before comparing the results. It is assumed that a long-run deficit or surplus water volume at the end of each day will be balanced by the change of operation in different hours of upcoming days. Therefore, the average electricity charge ($/kWh) and CO

_{2}emission factor (kg/MWh) were used to take into account the effect of this deficit or surplus water volume and calculate the net electricity cost and net CO

_{2}emissions.

_{2}emissions (kg) (middle) and total penalty (right) of all five scenarios of the Monroe WDS (top) and the Richmond skeletonized WDS (bottom) tests are displayed in bar charts in Figure 2. Each column shows the average result of five repeated tests and the error bar on top of it displays the SEM value. Except for columns that show high total penalty values, the SEMs of all the other results are relatively small. This shows the consistency in the outcome of PEPSO runs. Since penalty values are related to the amount of violation raised to the power of 1.5, it is expected to see that the moderate change in violation value results in a more severe change in penalty values.

_{2}emissions of the S1 scenario are less than S0. On average, the electricity cost and CO

_{2}emissions of S1 scenarios are 12.9% and 11.7% in Richmond tests and 1.7% and 1.7% in Monroe tests less than S0 results respectively. Since, in most cases, reducing energy usage decreases both the electricity cost and pollution emissions, optimizing based on all three objectives (S1) helps PEPSO to better explore the solution space. So, despite our theoretical expectation to see the minimum electricity cost in the result of the S0 scenario, in practice, the S1 scenario is more efficient at finding low energy consumption solutions in a limited amount of time.

_{2}emissions. However, in these solutions, pressure at a couple of junctions and water level at some tanks are below the desired level which increases the total penalty of these solutions. Although the violations in these cases are not beyond the acceptable range, from the optimizer perspective, these are dominated solutions when there is only one objective (total penalty). So, PEPSO does not choose the final solution from the second group. However, in the S1 scenario, when all three objectives are considered, a solution from the second group, which has some penalties but has a considerably lower electricity cost and CO

_{2}emissions, is reported as the optimum solution.

_{2}emissions (2.2%). However, it should be considered that calculating undesirability is an additional computation load on the optimization process. On average, calculating and using the UI in the optimization process of the Monroe WDS increased the required time for the optimization run by 8.9%. Based on these results, we can say that calculating the UI increased the required time for 16,600 solution evaluations in an optimization run. However, the final result was more practical and of higher quality. Obtaining a final solution with the same level of quality without using the UI needs more iterations and solution evaluations that increase the length of the optimization process. We expected that using the UI, by quantifying positive and negative effects of pump statuses on hydraulic responses of the water network, adds some intelligence to the process of producing the next generation and makes possible more purposeful crossover, mutation and elitism steps. Although calculating the UI increases the computational load of each iteration, we expected to see that within the same number of iterations, using the UI can provide better results. The outcome of these tests showed promising results regarding the use of the UI. However, this area still needs further research. More studies on complicated networks with vast solution space can help to show and quantify the level of effectiveness of the UI. It is possible that, in the case of a complex system with multiple pumps and vast solution space, traditional blind crossover, mutation and elitism steps (without using UI) cannot find an acceptable solution within a reasonable number of iterations. Results of the S4 scenario showed that giving PEPSO the possibility to operate pumps without tank level constraints, on average, reduces the electricity cost and CO

_{2}emissions of the system by 24.0% and 27.2%.

_{2}emissions, it considerably increased the water level violation of tanks and water pressure violation at strategic junctions. In the S4 scenario, the pressure of junctions has some fluctuations that caused considerable low and high-pressure penalties. The water level penalty of tanks of the S4 scenario is four times more than for the S0 scenario. Comparing patterns of the water level in tanks (see Figure 3) and water pressure at junctions (see Figure 4) of the S4 and S0 scenarios can clearly show these differences.

_{2}emissions by 4.8% and 1.2% respectively. However, this increases the total penalty by 35.1%.

## 6. Conclusions

- Optimizing based on all three objectives (S1) reduces the CO
_{2}emissions of the Monroe and Richmond WDSs by 1.3–3.4%. Optimizing based on all three objectives at the same time is more effective than optimizing based on only the electricity cost or total penalty. - Optimizing based on just penalty (S2 scenario) reduced the total penalty on Monroe and Richmond WDSs by 10 and 5.8% respectively.
- Calculating the Undesirability Index helped PEPSO to find more practical optimized solutions with fewer EPANET warnings and less tank drainage. However, on average, the undesirability calculation increased the required optimization time by 8.9%. The effect of the UI on finding high-quality solutions for a complex system with vast solution space needs to be evaluated.
- In the S4 scenario, the Monroe WDS was optimized without tank level constraints. The water level penalty of tanks of the S4 scenario is more than four times the water level penalties of the base scenario (S0). Like the Monroe WDS, optimizing without tank level constraints reduced the electricity cost and CO
_{2}emissions of the Richmond WDS. However, it considerably increases the water level penalty of tanks (35.1%). Removing water level constraints increases both water level and water pressure penalties and led to impractical and unacceptable solutions. - The time-of-use electricity tariff forces PEPSO to shift 1.7% of energy consumption from on-peak hours to off-peak hours. Including the power demand charge in the electricity tariff also, on average, reduces the peak power demand of the Monroe WDS by 9.7%. In the Richmond test, using a flat rate energy consumption charge enables PEPSO to consume energy at the time of high demand. This eliminated the need to store more water during off-peak hours which was causing 1.5% energy losses. In addition, by this method, PEPSO reduced tank drainage by about 10%.
- PEPSO used a multi-objective optimization algorithm to optimize three objectives independent of each other and report the final Pareto frontier that can be used in system studies and research. However, for practical use, one of the solutions among the Pareto frontier should be selected for operation. This selection is made by considering user preference based on user-defined weighting factors and also by removing impractical solution from the Pareto frontier (e.g., a solution with zero energy usage but high penalties). Defining different weighting factors can change the selected solution. Weighting factors are dependent on geographical, social, economic, etc., characteristics of the water system, defined constraints and practical preferences of operators. This area needs to be studied further to create a guideline that can help users to define weighting factors in such a way that results in the selection of the most desirable solution from the Pareto frontier.
- In this study, the net electricity cost and net CO
_{2}emissions are calculated to take into account the effect of deficit or surplus water volume of tanks within the acceptable range. However, using the average electricity charge ($/kWh) and CO_{2}emission factor (kg/MWh) might not match real operation conditions. Therefore, we suggest running tests and simulations for a longer period (e.g., a week instead of 24 h) or using better calculation methods to take into account the effect of tank level changes at the end of simulation in a more accurate way.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Undesirability Index (UI) calculation algorithm of Pollutant Emission Pump Station Optimization (PEPSO) [34].

**Figure 2.**Electricity cost (left), CO

_{2}emissions (middle) and total penalty (right) results of five scenarios of Monroe WDS (top) and Richmond skeletonized WDS (bottom) tests.

**Figure 3.**Typical water level pattern in tanks of S0 (top left), S3 (top right) and S4 (bottom) scenarios of the Monroe WDS.

**Figure 4.**Typical water pressure pattern at junctions of S0 (left) and S4 (right) scenarios of the Monroe WDS.

**Table 1.**Summary of the detailed model of Monroe and Skeletonized model of Richmond water distribution systems (WDSs).

Item | Monroe | Richmond Skeletonized |
---|---|---|

No. of Fixed Speed Pumps | 11 | 7 |

No. of Variable Speed Pumps | 2 | 0 |

No. of Pump Stations | 2 | 6 |

No. of Tanks | 3 | 6 |

No. of Water Sources | 1 | 2 |

No. of Pipes | 1945 | 44 |

No. of Junctions | 1531 | 41 |

Total Length of Pipes (km) | 450 | 22.69 |

Pipe Size Range (mm) | 50–910 | 76–300 |

Total Demand (m^{3}/day) | 36,500 | 3921 |

Storage volume (m^{3}) | 3974 | 2598 |

Storage to Daily Demand Ratio | 11/100 | 66/100 |

Range of Power of Pumps (kW) | 36–220 | 3–60 |

Max. Static Water Head (m) | 60 | 199 |

Demand Pattern Duration (hr) | 24 | 24 |

Demand Pattern Time Step (hr) | 1 | 1 |

Min and Max. Demand Multiplier | 0.67–1.19 | 0.39–1.53 |

Test Case | Strategic Junction ID | Min. Water Pressure (psi) | Max. Water Pressure (psi) |
---|---|---|---|

Monroe | J-6 | 42 | 52 |

J-27 | 32 | 46 | |

J-131 | 28 | 42 | |

J-514 | 42 | 56 | |

Richmond | 42 | 20 | 140 |

1302 | 0 | 100 | |

10 | 0 | 100 | |

312 | 0 | 100 | |

325 | 0 | 100 | |

701 | 0 | 100 | |

745 | 20 | 100 | |

249 | 20 | 100 | |

753 | 20 | 100 | |

637 | 20 | 140 |

Test Case | Tank ID | Min. Water Level (m) | Max. Water Level (m) |
---|---|---|---|

Monroe | T-2 | 1.56 | 8.12 |

T-3 | 1.41 | 7.28 | |

T-5 | 1.78 | 8.66 | |

Richmond | A | 0.30 | 1.70 |

B | 0.50 | 2.86 | |

C | 0.32 | 1.79 | |

D | 0.55 | 3.10 | |

E | 0.44 | 2.29 | |

F | 0.33 | 1.86 |

Pump Station | On-Peak Rate ($/kWh) | Off-Peak Rate ($/kWh) |
---|---|---|

A | 0.0679 | 0.0241 |

B | 0.0754 | 0.0241 |

C | 0.1234 | 0.0246 |

D | 0.0987 | 0.0246 |

E | 0.1122 | 0.0246 |

F | 0.1194 | 0.0244 |

**Table 5.**Emission factors of CO

_{2}obtained from the Locational Emission Estimation Methodology (LEEM) server.

Time | CO_{2} Emission Factor (kg/MWh) | Time | CO_{2} Emission Factor (kg/MWh) |
---|---|---|---|

00:00 | 767.771 | 12:00 | 662.793 |

01:00 | 738.324 | 13:00 | 630.703 |

02:00 | 702.904 | 14:00 | 630.531 |

03:00 | 702.904 | 15:00 | 628.591 |

04:00 | 702.904 | 16:00 | 628.882 |

05:00 | 767.771 | 17:00 | 666.549 |

06:00 | 781.469 | 18:00 | 693.607 |

07:00 | 808.212 | 19:00 | 665.274 |

08:00 | 764.333 | 20:00 | 730.766 |

09:00 | 719.768 | 21:00 | 790.628 |

10:00 | 719.768 | 22:00 | 808.212 |

11:00 | 695.334 | 23:00 | 780.477 |

Parameter | Value |
---|---|

Max. No. of Solution Evaluations | 16,600 |

Population Size | 100 |

Percentage of Elite Solution | 20% |

Crossover Percentage | 50% |

Crossover Rate | 50% |

Mutation Percentage | 5% |

Mutation Rate | 10% |

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**MDPI and ACS Style**

Sadatiyan A., S.M.; Miller, C.J.
PEPSO: Reducing Electricity Usage and Associated Pollution Emissions of Water Pumps. *Water* **2017**, *9*, 640.
https://doi.org/10.3390/w9090640

**AMA Style**

Sadatiyan A. SM, Miller CJ.
PEPSO: Reducing Electricity Usage and Associated Pollution Emissions of Water Pumps. *Water*. 2017; 9(9):640.
https://doi.org/10.3390/w9090640

**Chicago/Turabian Style**

Sadatiyan A., S. Mohsen, and Carol J. Miller.
2017. "PEPSO: Reducing Electricity Usage and Associated Pollution Emissions of Water Pumps" *Water* 9, no. 9: 640.
https://doi.org/10.3390/w9090640