# Energy Production by Means of Pumps As Turbines in Water Distribution Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Pump and PAT Performance

#### 2.1. Available Field Data from Literature

#### 2.2. Pump and PAT Performance Curves

_{p}(Ω,ϕ) = a

_{2p}(Ω)ϕ

^{2}+ a

_{1p}(Ω)ϕ + a

_{0p}(Ω)

_{PAT}(Ω,ϕ) = a

_{2PAT}(Ω)ϕ

^{2}+ a

_{1PAT}(Ω)ϕ + a

_{0PAT}(Ω)

_{Yk}, expressed in Equation (3), is adopted:

_{ki})

_{e}for a given turbomachine k (both in pump and PAT mode) to the corresponding simulated value (Y

_{ki})

_{s}, predicted by means of Equations (1) and (2).

_{Yk}are summarized in Figure 2. It can be noticed that, in general, RMSE

_{ψ}values are very good in both pump and PAT mode (they are in the range 0.5–2.6%). Moreover, RMSE

_{π}values in pump mode are even better (values in the range 0.2–1.6%). Otherwise, RMSE

_{π}values in PAT mode are considerably higher (values in the range 1.9–7.5%), and this also reflects on the values of RMSE

_{η}. However, the selected interpolating functions expressed in Equations (1) and (2) are considered satisfactory for the purpose of this paper, since they provide a physics-responding approach for simulating the behavior of pumps and PATs over the entire range of operation.

## 3. Field Data of Water Distribution Networks

#### 3.1. Water Distribution Networks

#### 3.2. WDN Field Data

## 4. Results

- (1)
- Assessment of the energy potential of otherwise-wasted hydraulic energy. The yearly producible electric energy is obtained by considering the actual PAT working point for each data set. The working point is set by acting on two valves, as outlined in Section 4.1;
- (2)
- Estimation of the conversion efficiency of energy recovery, for both the entire WDN (overall efficiency) and for the PAT alone (PAT efficiency).

#### 4.1. Producible Energy

- (1)
- availability of pump performance curves over the entire range of operation. In this paper, four pumps (#1 through #4) are evaluated;
- (2)
- estimation of PAT’s performance curves over the entire range of operation, as described in Section 2.2;
- (3)
- estimation of the producible electric power for each data set (i.e., for each time point), by considering that:
- If H
_{PAT}≤ H_{meas}, the producible electric power is calculated at Q_{meas}and H_{PAT}. This means that there is a reduction of H, so that ΔH_{un}= H_{meas}− H_{PAT}is unexploited. In other words, available head has to be dissipated; - If H
_{PAT}> H_{meas}, the producible electric power is calculated at Q_{thr}(lower than Q_{meas}) and H_{meas}. In fact, the volume flow rate flowing through the PAT has to be decreased, so that, in this case, ΔQ_{un}= Q_{meas}− Q_{thr}is unexploited;

- (4)
- calculation of the producible electric energy by multiplying the producible electric power by the sampling time of WDN data (in this paper, 15 min); and,
- (5)
- calculation of the producible electric energy over one year.

_{PAT}equal to H

_{meas}. This regulation strategy was also discussed and investigated in [20] (where it was identified as “hydraulic regulation”) and represents a feasible operation mode for WDNs. It is clear that the possibility of varying PAT’s rotational speed and consequently moving PAT’s characteristic curve in order to match, at each time point, the available head and flow rate, may increase the producible electric energy, but would require the use of an inverter and a more sophisticated regulation system.

#### 4.2. Conversion Efficiency

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Abbreviations

a | performance curve coefficient |

D | pump nominal diameter, m |

g | gravitational acceleration, m/s^{2} |

H | head drop, m |

k | label of pump/PAT |

n | rotational speed, rps |

N | number of pump/PAT experimental data |

P | power, W |

PAT | Pump As Turbine |

PRV | Pressure Reducing Valve |

Q | volume flow rate, m^{3}/s |

RMSE | root mean square error |

WDN | water distribution network |

Y | non-dimensional performance parameter (ψ, π, η) |

η | efficiency |

ϕ | non-dimensional volume flow rate defined as Q/(nD^{3}) |

π | non-dimensional power defined as P/(ρn^{3}D^{5}) |

ρ | density, kg/m^{3} |

ψ | non-dimensional head defined as gH/(n^{2}D^{2}) |

ω | angular velocity, rad/s |

Ω | specific speed defined as ωQ^{0.5}/(gH)^{0.75} |

Subscripts and superscripts | |

1,2,3,4 | label of pump/PAT |

av | average |

BEP | best efficiency point |

e | experimental |

meas | measured |

p | pump |

PAT | pump as turbine |

s | simulated |

thr | throttle |

un | unexploited |

Y | non-dimensional parameter |

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**Figure 1.**(

**a**) Non-dimensional head vs. non-dimensional volume flow rate; (

**b**) Non-dimensional power vs. non-dimensional volume flow rate; and, (

**c**) Efficiency vs. non-dimensional volume flow rate (symbols: experimental data reported in [11]; lines: interpolation curves).

**Figure 2.**RMSE

_{Yk}values for (

**a**) non-dimensional head; (

**b**) non-dimensional power and (

**c**) efficiency.

**Figure 4.**Available head drop vs. volume flow rate (measured values). (

**a**) WDN A and B; (

**b**) WDN C and D.

**Figure 7.**Unexploited flow rate and head drop for (

**a**) WDN A and PAT #1; (

**b**) WDN B and PAT #2; (

**c**) WDN C and PAT #4 and (

**d**) WDN D and PAT #4.

**Table 1.**Pump characteristics at Best Efficiency Point (BEP) [11].

Pump | Ω | Q, (10^{−3} m^{3}/s) | η, (%) | H, (m) | P, (W) |
---|---|---|---|---|---|

#1 | 1.53 | 8.0 | 64.5 | 24.9 | 3044 |

#2 | 2.41 | 24.8 | 75.7 | 22.1 | 7114 |

#3 | 3.94 | 62.2 | 86.3 | 21.1 | 14,926 |

#4 | 5.82 | 107.7 | 86.8 | 18.3 | 22,288 |

**Table 2.**Pump and pumps used as turbines (PAT) operating range reported in [11].

Pump | Q, (10^{−3} m^{3}/s) | H, (m) | P, (W) | η, (%) |

#1 | 0.0–12.7 | 15.3–29.2 | 1559–2525 | 40.1–64.5 |

#2 | 0.0–43.9 | 10.9–24.7 | 4084–9504 | 30.0–75.7 |

#3 | 0.0–94.4 | 12.5–25.5 | 8465–18,860 | 30.3–86.3 |

#4 | 0.0–148.3 | 12.4–23.1 | 14,405–24,800 | 30.0–86.8 |

PAT | Q, (10^{−3} m^{3}/s) | H, (m) | P, (W) | η, (%) |

#1 | 10.4–18.3 | 27.0–67.7 | 668–4752 | 24.8–63.1 |

#2 | 19.5–43.5 | 19.8–50.8 | 817–15,296 | 25.1–71.6 |

#3 | 31.5–95.9 | 15.4–38.7 | 0–26,582 | 0.0–74.7 |

#4 | 55.2–129.3 | 12.1–27.1 | 0–25,468 | 0.0–78.3 |

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**MDPI and ACS Style**

Venturini, M.; Alvisi, S.; Simani, S.; Manservigi, L.
Energy Production by Means of Pumps As Turbines in Water Distribution Networks. *Energies* **2017**, *10*, 1666.
https://doi.org/10.3390/en10101666

**AMA Style**

Venturini M, Alvisi S, Simani S, Manservigi L.
Energy Production by Means of Pumps As Turbines in Water Distribution Networks. *Energies*. 2017; 10(10):1666.
https://doi.org/10.3390/en10101666

**Chicago/Turabian Style**

Venturini, Mauro, Stefano Alvisi, Silvio Simani, and Lucrezia Manservigi.
2017. "Energy Production by Means of Pumps As Turbines in Water Distribution Networks" *Energies* 10, no. 10: 1666.
https://doi.org/10.3390/en10101666