# Optimal Selection and Operation of Pumps as Turbines for Maximizing Energy Recovery

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- Validation of the methodology proposed in Manservigi et al. [31]. The validation is performed by means of two sites that differ in both flow rate and head characteristics by strengthening the general validity of the proposed methodology;
- Validation by means of the experimental characteristic curves of a fleet of forty-five PATs so that the recovered energy is calculated by exploiting the entire operating range of each turbomachine. Thus, this paper differs from state-of-the-art studies, which usually present the validation of the respective methodologies by means of predicted PAT characteristic curves;
- Operation of each pair of PATs is finely scheduled to maximize the recovered energy (15 min step time). Instead, some studies assume that each PAT continuously operates over a longer time slot (e.g., night or day).

## 2. PAT Selection and Control

#### 2.1. PAT Selection

_{max}) and maximum head of the site (H

_{max}); (ii) mean flow rate (Q

_{mean}) and mean head of the site; and (iii) a fleet of pumps, among which the optimal PAT can be selected. For each pump of the fleet (i.e., N

_{P}in total), the flow rate and head at BEP (Q

_{BEP,P}, H

_{BEP,P}) are known, since they can be derived from pump catalogues or experimental data.

_{r,T}) and the minimum head of the PAT (H

_{r,T}) based on the BEP values of some PATs running in pump mode (i.e., Q

_{BEP,P}and H

_{BEP,P}).

_{rec}) would be null.

_{ratio}is the ratio of Q

_{BEP,P}to the mean flow rate of the site (Q

_{mean}). Similarly, H

_{ratio}is the ratio of H

_{BEP,P}to the mean head of the site (H

_{mean}).

_{ref}and H

_{ref}are the reference flow rate and reference head, respectively. Q

_{ref}is equal to 1.00, while H

_{ref}is equal to 0.95. Such reference values were derived in Manservigi et al. [31] by using the sixteen PAT–site matches considered in [8]. In [8], the Q

_{ref}of the best PAT–site matches was close to 1, while the H

_{ref}of the best PAT–site matches was in the range from 0.5 to 1.4 with a mean value of 0.95.

#### 2.2. PAT Control

_{r,T}). Thus, the entire flow rate passes through the bypass line, the PAT does not run, and consequently, the recovered energy is null.

_{PAT}) is lower than the head of the site [32], e.g., point B in Figure 2b. In this case, a throttle control is used [32], and the exceeding head of the site is dissipated. The unexploited head (ΔH

_{un}) is the difference between the head of the site and the PAT’s head (Equation (4)), while the PAT swallows for the entire flow rate made available by the hydraulic site. Due to throttle control, part of the hydraulic energy is unexploited (E

_{un,TC}) (Equation (4)).

_{PAT}is higher than H

_{site}, e.g., point C in Figure 2b. In such a case, a bypass control is performed: the PAT operates at the head of the site, and the exceeding flow rate is delivered through the bypass line. Thus, a part of the flow rate fraction is unexploited (ΔQ

_{un}) by wasting the hydraulic energy E

_{un,BC}(see Equation (5)).

_{rec}) is calculated by using the PAT’s power characteristic curve, which can be derived experimentally (as performed in this paper) or by applying one of the methodologies available in the literature. To this purpose, different approaches can be exploited, e.g., physics-based approaches (e.g., [36,37]), empirical models (e.g., [23,38,39]), black box models (e.g., [40,41]), CFD models (e.g., [39,42]) and entropy production analysis (e.g., [43]).

_{rec}can be estimated according to Equation (6).

## 3. Case Study

#### 3.1. Sites

_{site}) is roughly equal to 115 MWh/year (Site #1) and 101 MWh/year (Site #2); E

_{site}is calculated as the sum of the hydraulic energy of each site data, i.e., 0.25∙ρ∙g∙Q∙H. The coefficient 0.25 accounts for time granularity that is equal to 15 min.

#### 3.2. Pumps as Turbines

#### 3.3. Layout of Installation

## 4. Results

#### 4.1. Single PAT

#### 4.1.1. PAT Selection

_{r,T}) was higher than the maximum head of the site, meaning that the recovered energy would have been null (Figure 6b).

#### 4.1.2. PAT Operation

_{PAT}varies from 3.5% to 71.8% (i.e., the BEP). Although, in this paper, PAT #30 is allowed to explore its entire range of operation, η

_{PAT}is in the range from 71% to 71.8% in 30.5% of cases.

#### 4.2. Pair of PATs in Parallel

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

D | diameter |

E | energy |

g | gravitational acceleration |

H | head |

N | rotational speed |

P | power |

PSI | PAT–site index |

Q | flow rate |

t | time |

η | efficiency |

ρ | density |

Subscripts | |

BEP | best efficiency point |

max | maximum value |

mean | mean value |

P | pump mode |

r | runaway condition |

rec | recovered |

ref | reference value |

T | turbine mode |

un | unexploited |

Acronyms | |

BC | Bypass Control |

BEP | Best Efficiency Point |

PAT | Pump As Turbine |

PRV | Pressure Reducing Valve |

PSI | PAT–Site Index |

TC | Throttle Control |

## Appendix A

PUMP | PAT | ||||||
---|---|---|---|---|---|---|---|

PAT # | D [m] | N [rpm] | Q_{BEP} [L/s] | H_{BEP} [m] | Q_{BEP} [L/s] | H_{BEP} [m] | Ref. |

1 | 0.160 | 600 | 2.96 | 1.36 | 5.01 | 3.80 | [45] |

2 | 0.160 | 900 | 3.98 | 2.95 | 5.99 | 5.51 | [45] |

3 | 0.125 | 600 | 2.86 | 0.96 | 7.04 | 4.62 | [45] |

4 | 0.160 | 1200 | 4.33 | 5.65 | 7.08 | 8.45 | [45] |

5 | 0.160 | 1500 | 5.95 | 8.04 | 9.07 | 13.22 | [45] |

6 | 0.200 | 1450 | 5.87 | 11.51 | 9.60 | 25.14 | [23] |

7 | 0.250 | 1450 | 6.76 | 19.57 | 9.63 | 37.17 | [23] |

8 | 0.125 | 1200 | 5.03 | 2.90 | 9.13 | 7.60 | [45] |

9 | 0.125 | 900 | 3.98 | 1.70 | 7.99 | 5.86 | [45] |

10 | 0.160 | 1800 | 6.97 | 11.53 | 11.02 | 19.47 | [45] |

11 | 0.315 | 1450 | 7.54 | 31.38 | 14.10 | 110.64 | [23] |

12 | 0.125 | 1800 | 5.97 | 7.18 | 11.05 | 11.66 | [45] |

13 | 0.160 | 2100 | 8.00 | 15.66 | 13.09 | 27.06 | [45] |

14 | 0.160 | 2400 | 9.97 | 19.48 | 15.00 | 35.38 | [45] |

15 | 0.125 | 600 | 5.49 | 0.76 | 9.02 | 1.39 | [45] |

16 | 0.125 | 1500 | 5.98 | 4.55 | 10.05 | 9.33 | [45] |

17 | 0.160 | 2700 | 10.96 | 24.92 | 16.02 | 41.14 | [45] |

18 | 0.125 | 2400 | 7.99 | 12.20 | 15.00 | 20.80 | [45] |

19 | 0.125 | 2100 | 7.02 | 9.40 | 13.10 | 15.92 | [45] |

20 | 0.335 | 1450 | 7.99 | 31.29 | 13.71 | 99.54 | [23] |

21 | 0.125 | 2700 | 9.00 | 15.34 | 16.03 | 23.99 | [45] |

22 | 0.125 | 900 | 7.96 | 1.64 | 13.98 | 3.20 | [45] |

23 | 0.160 | 1450 | 9.72 | 8.55 | 15.27 | 13.10 | [23] |

24 | 0.250 | 1450 | 18.58 | 17.97 | 23.01 | 32.66 | [23] |

25 | 0.125 | 1200 | 11.00 | 2.84 | 18.10 | 5.38 | [45] |

26 | 0.125 | 1500 | 13.86 | 4.28 | 21.95 | 7.72 | [45] |

27 | 0.125 | 1800 | 16.61 | 6.13 | 25.95 | 10.97 | [45] |

28 | 0.200 | 1450 | 23.28 | 12.07 | 31.25 | 17.56 | [23] |

29 | 0.125 | 2100 | 19.00 | 8.38 | 29.90 | 14.48 | [45] |

30 | 0.250 | 1450 | 26.77 | 19.70 | 33.15 | 30.15 | [23] |

31 | 0.220 | 1450 | 24.15 | 14.54 | 32.70 | 19.25 | [23] |

32 | 0.193 | 1450 | 14.00 | 10.00 | 21.00 | 14.70 | [38] |

33 | 0.125 | 2400 | 21.79 | 10.79 | 33.99 | 18.61 | [45] |

34 | 0.125 | 2700 | 24.47 | 13.68 | 39.23 | 24.69 | [45] |

35 | 0.269 | 1450 | 40.25 | 22.26 | 45.82 | 24.40 | [44] |

36 | 0.219 | 1450 | 41.68 | 13.78 | 50.33 | 17.29 | [44] |

37 | 0.160 | 1450 | 41.98 | 7.91 | 48.44 | 10.04 | [23] |

38 | 0.200 | 1450 | 41.68 | 12.96 | 50.00 | 18.83 | [23] |

39 | 0.185 | 1450 | 41.62 | 7.72 | 59.83 | 12.93 | [44] |

40 | 0.200 | 1450 | 70.04 | 13.99 | 76.09 | 11.22 | [23] |

41 | 0.400 | 800 | 60.21 | 17.59 | 76.18 | 22.11 | [34] |

42 | 0.400 | 1000 | 75.14 | 26.90 | 96.60 | 34.71 | [34] |

43 | 0.224 | 1050 | 72.36 | 5.41 | 94.39 | 8.42 | [44] |

44 | 0.400 | 1200 | 102.12 | 36.21 | 98.70 | 44.13 | [34] |

45 | 0.400 | 1520 | 129.79 | 56.90 | 107.07 | 57.30 | [34] |

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**Figure 2.**Layout of the installation of a single PAT and a bypass line (

**a**); throttle and bypass control (

**b**).

**Figure 8.**Operation of PAT #40 (

**a**); share of recovered and wasted energy at Site #1 (

**b**); share of PAT’s operation (PAT #40) (

**c**); efficiency of PAT #40 (

**d**).

**Figure 9.**Operation of PAT #37 (

**a**); share of recovered and wasted energy at Site #2 (

**b**); share of PAT’s operation (PAT#30) (

**c**); efficiency of PAT #30 (

**d**).

**Figure 11.**Operation of PATs #40 and #36 (

**a**); share of recovered and wasted energy at Site #1 (

**b**); share of PAT’s operation (PATs #40 and #36) (

**c**); efficiency of PATs #40 and #36 (

**d**).

**Figure 12.**Operation of PATs #30 and #17 (

**a**); share of recovered and wasted energy at Site #2 (

**b**); share of PAT’s operation (PATs #30 and #17) (

**c**); efficiency of PATs #30 and #17 (

**d**).

Q_{mean} [L/s] | Q_{max} [L/s] | H_{mean} [m] | H_{max} [m] | E_{site} [MWh/Year] | |
---|---|---|---|---|---|

Site #1 | 117 | 303 | 12 | 16 | 115 |

Site #2 | 28 | 75 | 46 | 66 | 101 |

Best PAT | E_{rec} [kWh] | E_{rec}/E_{site} [%] | |
---|---|---|---|

Site #1 | #40 | 51,341 | 44.8% |

Site #2 | #30 | 40,575 | 40.3% |

Best Pair of PAT | E_{rec} [kWh] | E_{rec}/E_{site} [%] | |
---|---|---|---|

Site #1 | #40, #36 | 53,695 | 46.9% |

Site #2 | #30, #17 | 49,605 | 49.3% |

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## Share and Cite

**MDPI and ACS Style**

Manservigi, L.; Venturini, M.; Losi, E.; Castorino, G.A.M.
Optimal Selection and Operation of Pumps as Turbines for Maximizing Energy Recovery. *Water* **2023**, *15*, 4123.
https://doi.org/10.3390/w15234123

**AMA Style**

Manservigi L, Venturini M, Losi E, Castorino GAM.
Optimal Selection and Operation of Pumps as Turbines for Maximizing Energy Recovery. *Water*. 2023; 15(23):4123.
https://doi.org/10.3390/w15234123

**Chicago/Turabian Style**

Manservigi, Lucrezia, Mauro Venturini, Enzo Losi, and Giulia Anna Maria Castorino.
2023. "Optimal Selection and Operation of Pumps as Turbines for Maximizing Energy Recovery" *Water* 15, no. 23: 4123.
https://doi.org/10.3390/w15234123