# Optimization Strategy for Improving the Energy Efficiency of Irrigation Systems by Micro Hydropower: Practical Application

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods and Materials in the Optimization Strategy

#### 2.1. Methods

#### 2.2. Materials

#### Characterization of the Hydraulic Machine

^{3}/s; N is the rotational speed of the machine in rpm; and D is the impeller diameter in m.

- Selection of the operation parameters: different parameters must be defined. To establish a database of synthetic PATs (in this particular case 8893 different PATs were defined). The database was developed through characteristic curves that are shown in Figure 2 (Input 1) as well as changing the following parameters:
- Specific speed (n
_{s}): defined according to Equation (3):$${n}_{s}=N\frac{\sqrt{{P}_{R}}}{{H}_{R}^{1.25}}$$_{R}is the rated power (kW); H_{R}is the rated head (m w.c.); being ‘R’ the pump design point or the best efficiency condition.The range of specific speed oscillates between 14 and 79 rpm (m, kW). - Rotational speed (N): the range of the rotational speed oscillated between 510, 1020, 2040, 2400, and 2900 rpm.
- Impeller Diameter (D): the range of the defined impeller was between 0.04 and 0.6 m.
- Variation of the rotational speed: when the machine operates with a different rotation speed as a function of the flow, the coefficient ($\mathsf{\alpha}$) that is defined by Equation (4) can vary between 0.5 and 1.5.$$\mathsf{\alpha}=\frac{{N}_{t}}{{N}_{0}}$$

- To interpolate characteristic curves: when the specific speed is defined and the n
_{s}curve is not known, the values of head number (${\mathsf{\psi}}_{int}$) and efficiency (η_{int}) for each discharge number value (φ_{int}) are estimated by linear interpolation - To generate head and efficiency curves as a function of flow: when the characteristic numbers are defined for each diameter and rotational speed (N
_{0}) that are selected in step one, the head and efficiency curve are determined by Equations (5) to (7):$$Q={\mathsf{\phi}}_{int}N{D}^{3}$$$$H=\frac{{\mathsf{\psi}}_{int}{N}^{2}{D}^{2}}{g}$$$$\mathsf{\eta}={\mathsf{\eta}}_{int}\left({\mathsf{\phi}}_{int}\right)$$The polynomic equations are fitted to the obtained values (the maximum considered degree is four) through linear regression by Equations (8) and (9):$${H}_{\mathsf{\alpha}=1}=A{Q}^{4}+B{Q}^{3}+C{Q}^{2}+DQ+E$$$${\mathsf{\eta}}_{\mathsf{\alpha}=1}=F{Q}^{4}+G{Q}^{3}+H{Q}^{2}+IQ+J$$These curves can be used when the flow is between the interpolated range, where A, B, C, D and E are coefficients of the Q-H characteristic curve and F, G, H, I and J are coefficients of the efficiency curve. The flow limit of the turbine is defined by a minimum efficiency condition, which is proposed to be 0.3 for this case study. - To obtain runaway curve: the runaway curve is generated by second polynomic equation curve that contains the following points: coordinates origin and the minimum value obtained through Equation (8).
- To develop BEL/BEH: the best efficiency point is estimated for each rotational speed (α), adjusting by regression the curves defined by Equations (10) and (11):$${H}_{BEH}=H{Q}^{4}+I{Q}^{3}+J{Q}^{2}+KQ+L$$$${\mathsf{\eta}}_{BEL}=M{Q}^{4}+N{Q}^{3}+O{Q}^{2}+PQ+R$$

#### 2.3. Optimization Strategy

- The knowledge of the flow over time is the starting point in the optimization strategy. The flow can be known when the water manager has flowmeters in the pipes. However, the knowledge of the flow in all lines over time is almost impossible, and therefore, the flow has to be estimated in each line. In this sort of irrigation water distribution network, the flow depends on consumption flow patterns which must be determined as a function of the agronomist parameters. To estimate the consumption flow patterns, the used methodology considers the farmers’ habits and the characteristics of the network [39]. This methodology is able to estimate the flow over time in any line of the systems, depending on the network characteristics (Input 1) and the farmers’ habits (Input 2). The farmers’ habits are irrigation needs, irrigation duration, maximum days between irrigation and the irrigation volume. The knowledge of the farmers’ habits allows the determination of the opening or closing in consumption nodes over time. The state of the irrigation point determines the flow (Output 1) of the strategy. This output is an input for the next step: Input 3.
- The second stage stands on the calibration strategy. It uses key performance indicators (KPIFs) that are adapted from the traditional hydrological models (Input 4) [40]. The characterization of the goodness-of-fit is divided into very good, good, satisfactory, and unsatisfactory, depending on the KPIF values (Table 1). The comparison is developed with the registered flow data (Input 5) to determine the success of the fit. If the calibration is satisfactory, the energy balance (Step 3) can be done.
- The energy balance is able to discretize different energy terms (e.g., total, irrigation, friction) differentiating the terms for the available energy between the theoretically recoverable energy and theoretically non-recoverable energy, considering the minimum irrigation pressure at each consumption point (Input 6) [39]. The available energy enables us to determine the theoretical recovery coefficient at any line, hydrant or consumption point. In addition, the energy balance enables us to estimate the recovered head for each flow over time. Knowing these pairs of data (Q, H), the most suitable machine at each study point can be selected. The formula used to determine the annual balance of the network is defined by Equations (12) to (18):$${E}_{T}={E}_{FR}+{E}_{RI}+\text{}{E}_{TR}+{E}_{NTR}$$$${E}_{{T}_{i}}\left(\mathrm{kWh}\right)=\frac{9.81}{3600}{Q}_{i}\left({z}_{o}-{z}_{i}\right)\Delta t$$$${E}_{F{R}_{i}}\left(\mathrm{kWh}\right)=2.725\xb7{10}^{-3}{Q}_{i}\left({z}_{o}-\left({z}_{i}+{P}_{i}\right)\right)\Delta t$$$${E}_{R{I}_{i}}\left(\mathrm{kWh}\right)=2.725\xb7{10}^{-3}{Q}_{i}{P}_{min{I}_{i}}\Delta t$$$${E}_{T{R}_{i}}\left(\mathrm{kWh}\right)=2.725\xb7{10}^{-3}{Q}_{i}{H}_{i}\Delta t$$$${E}_{T{A}_{i}}\left(\mathrm{kWh}\right)=2.725\xb7{10}^{-3}{Q}_{i}\left({P}_{i}-{P}_{mi{n}_{i}}\right)\Delta t$$$${E}_{NT{R}_{i}}={E}_{T{A}_{i}}-{E}_{T{R}_{i}}$$
^{3}/s); ${z}_{i}$ is the geometry level above reference plane of the irrigation point, considering the reference datum level (m); ${z}_{\mathrm{o}}$ is the geometry level above the reference plane of the free water surface of the reservoir (m); ${P}_{i}$ is the service pressure in any point of the network when consumption exists (m w.c.); ${P}_{min{I}_{i}}$ is the minimum pressure of service of an irrigation point required to ensure the irrigation water evenly; and ${H}_{i}$ is the value of the head of an irrigation point, hydrant or line (m w.c.). This head is obtained as ${H}_{i}={P}_{i}-\mathrm{max}\left({P}_{mi{n}_{i}};{P}_{min{I}_{i}}\right)$; and $\Delta t$ is the time interval (s). - Knowing the flow (${Q}_{i}$) and recoverable head (${H}_{i}$) over time from the energy balance (Output 2, that is Input 7), enables the selection of the hydraulic machine type (e.g., radial, axial) according to the frequency histogram of the power generated among other conditions. To develop a guaranteed estimation of the recovered energy, the head and efficiency curve as a function of flow should be known for different rotational speeds (Input 8). If this information is not provided by the manufacturer, experimental tests are recommended to obtain the efficiency variation depending on the flow and for different rotational speeds. However, if experimental tests cannot be carried out, the experimental curves are determined using the characteristic numbers (discharge and head number, Figure 1) to select a machine considering its specific speed [41] using the turbine that was described in the previous section (Figure 2).
- When the tests are carried or the characteristic curves are used, the modified classical affinity laws based on the variation of the specific parameters (discharge coefficient, q; head coefficient, h; and velocity coefficient, n) can be used [33,42]. These parameters are defined by Equations (19) to (21):$$h=\frac{H}{{H}_{0}}$$$$q=\frac{Q}{{Q}_{0}}$$$$n=\frac{N}{{N}_{0}}$$
^{3}/s when the rotational speed of the machine is N; and H_{0}and Q_{0}are head and flow, respectively, when the machine operates in its best efficiency point (BEP), for the rotational speed N_{0}.Based on modified classical similarity laws (when there are not experimental data), two new concepts (the best efficiency line, BEL and best head line, BEH) are proposed (Output 4). The BEL adapts the rotational speed as a function of the flow, adjusting the maximum efficiency at each time point and maximising the energy recovered. The BEH relates the best efficiency point for each rotational speed with the recovered head as a function of the flow [35]. The knowledge of the BEL and/or BEH (Input 9) makes possible the use of these curves to develop the optimization of the energy recovery on a water system through the variation of the rotational speed as a function of the flow. The classical laws are defined by Equations (22) to (24) [36]:$$\frac{{Q}_{1}}{{Q}_{0}}={\left(\frac{{D}_{1}}{{D}_{0}}\right)}^{3}\frac{{N}_{1}}{{N}_{0}}$$$$\frac{{H}_{1}}{{H}_{0}}={\left(\frac{{D}_{1}}{{D}_{0}}\right)}^{2}{\left(\frac{{N}_{1}}{{N}_{0}}\right)}^{2}$$$$\frac{{P}_{1}}{{P}_{0}}={\left(\frac{{D}_{1}}{{D}_{0}}\right)}^{2}{\left(\frac{{N}_{1}}{{N}_{0}}\right)}^{3}$$_{1}is the flow in the new conditions of the rotational speed in m^{3}/s; D_{1}is the diameter of the impeller in the new N status in m; D_{0}is the nominal diameter of the impeller in m; N_{1}is the new rotational speed in rpm; H_{1}is the head in the new N status in m w.c.; P_{1}is the shaft power for each N in kW; and P_{0}is the shaft power in the nominal condition in kW. - This new strategy to maximize the energy recovered was developed by using PATs or any type of turbine. The theoretically recovered energy and the economic feasibility indexes (Input 10), particularly the simple payback period are considered (PSR) [39]. This strategy makes use of a simulated annealing algorithm to carry out the optimization, selecting the best lines to install turbines as a function of the number of installed turbines in the water system. The optimization can be developed with two different functions: the first function only considers the recovered energy, while the second one analyses the ratio between recovered energy and PSR [35]. The final output results of the optimization strategy are the optimal number of machines to install in the network according to the objective function; the optimal rotational speed as a function of the flow; the real recovered energy; as well as the efficiency parameters to analyse the energy improvement in the network.

## 3. Results and Discussion

#### 3.1. Case Study Description

#### 3.2. Results of the Optimization

^{3}and 1978 h, respectively. For PAT1, the average flow and the average recovered head were 5.06 L/s and 26.05 m w.c., respectively, obtaining an average power of 1.04 kW and a total recovered energy of 2047 kWh/year. Figure 9c,d show the recoverable energy values which were available to be operated throughout the PAT2 and the PAT3. The operation points are also shown in these figures for both PATs. Hence, the same values of volumetric turbine flow, operation time, turbine flow, recovered head and power are also indicated in Figure 9c,d. Finally, when the global values were analysed, the total volumetric turbine flow was 53,420 m

^{3}, representing 98.71% of the volume throughout line 47. The minimum and the maximum turbine flow were 2.19 and 18.99 L/s, respectively. The total recovered energy was 2924 kWh/year, recovering 58.26% of the theoretical available energy of this line.

#### 3.3. Comparison of the Results of the Theoretical Energy Analysis, Fixed Rotational Speed, and BEL Strategy

_{R}

_{α=1}), the increase of the recovered energy varied between 140.88 and 183.79%. Therefore, the BEL strategy is one of the novelties introduced in this research, improving the energy recovery under all assumptions when the energy recovery was compared with values for the machine under nominal conditions.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

BEH | best efficiency head |

BEL | best efficiency line |

BEP | best efficiency point |

E | Nash-Sutcliffe coefficient |

E_{FR} | friction energy |

E_{R} | real recovered energy |

E_{RI} | energy required for irrigation |

E_{T} | total energy |

E_{TA} | theoretically available energy |

E_{TN} | theoretically energy necessary |

E_{TR} | theoretically recoverable energy |

E_{NTR} | theoretically non-recoverable energy |

KPIF | key performance indicators |

n | number of groups of turbines or PATs |

n_{s} | specific rotational speed |

PAT | pump as working turbine |

PBIAS | percent bias |

PSR | simple payback period |

RRSE | root relative square error |

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**Figure 7.**Database of turbines created by the turbine module based on the experiments and affinity laws.

**Table 1.**Classification of the goodness-of-fit (adapted from [40]).

Goodness-of-Fit | E | RRSE | PBIAS (%) |
---|---|---|---|

Very Good | E > 0.6 | 0.00 ≤ RRSE ≤ 0.50 | $PBIAS<\pm 10$ |

Good | 0.40 < E ≤ 0.60 | 0.50 < RRSE ≤ 0.60 | $\pm 10\le PBIAS<\pm 15$ |

Satisfactory | 0.20 < E ≤ 0.40 | 0.60 < RRSE ≤ 0.70 | $\pm 15\le PBIAS<\pm 25$ |

Unsatisfactory | E < 0.20 | RRSE > 0.70 | $PBIAS>\pm 25$ |

**Table 2.**Results of the maximization of the recovered energy (n is the number of pipes where the turbines are installed;

**n**in rpm (m, kW); D in mm; N in rpm; ${E}_{{R}_{BEL}}$ in MWh/year).

_{s}n | Lines in Which Turbines Are Allocated | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 38 | |||||||||||

2 | 22 | 38 | ||||||||||

3 | 22 | 38 | 59 | |||||||||

4 | 22 | 38 | 47 | 59 | ||||||||

5 | 5 | 22 | 38 | 47 | 59 | |||||||

6 | 5 | 22 | 38 | 47 | 58 | 59 | ||||||

7 | 5 | 22 | 38 | 47 | 58 | 59 | 70 | |||||

8 | 5 | 22 | 38 | 39 | 47 | 58 | 59 | 70 | ||||

9 | 2 | 10 | 22 | 39 | 43 | 47 | 58 | 59 | 70 | |||

10 | 2 | 10 | 22 | 39 | 43 | 47 | 58 | 59 | 70 | 85 | ||

n | Total${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | |||||||||||

1 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 35 114.3 2900 33.78 | 33.78 | |||||||||

2 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 35 133.8 2900 30.97 | 35 134.9 2900 11.59 | 42.55 | ||||||||

3 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 35 133.8 2900 30.97 | 35 134.9 2900 11.59 | 35 122.9 2900 3.56 | 46.11 | |||||||

4 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 35 133.8 2900 30.97 | 35 134.9 2900 11.59 | 29 90.5 2900 2.96 | 35 122.9 2900 3.56 | 49.08 | ||||||

5 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 44 175.7 2040 9.81 | 35 164.7 2900 24.16 | 35 134.9 2900 11.52 | 29 90.5 2900 2.96 | 35 122.9 2900 3.56 | 52.00 | |||||

6 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 44 175.7 2040 9.81 | 35 164.7 2900 24.16 | 35 134.9 2900 11.52 | 29 90.5 2900 2.96 | 35 100.6 2900 2.64 | 40 121.2 2900 3.52 | 54.60 | ||||

7 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 44 175.7 2040 9.81 | 35 164.7 2900 24.16 | 35 134.9 2900 11.52 | 29 90.5 2900 2.96 | 35 100.6 2900 2.64 | 35 122.9 2900 3.56 | 24 77 2900 0.83 | 55.47 | |||

8 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 44 175.7 2040 9.81 | 35 164.7 2900 24.16 | 35 134.9 2900 11.52 | 24 60.4 2900 1.05 | 29 90.5 2900 2.96 | 35 100.6 2900 2.64 | 35 122.9 2900 3.56 | 24 77 2900 0.83 | 56.53 | ||

9 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 83 118.3 2900 8.27 | 35 243.7 1020 6.22 | 35 164.7 2900 20.38 | 24 77 2900 1.46 | 35 134.9 2900 10.73 | 29 90.5 2900 2.96 | 35 100.6 2900 2.64 | 35 122.9 2900 3.56 | 24 77 2900 0.83 | 57.04 | |

10 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 83 118.3 2900 8.27 | 35 243.7 1020 6.22 | 35 164.7 2900 20.38 | 24 77 2900 1.46 | 35 134.9 2900 10.73 | 29 90.5 2900 2.96 | 35 100.6 2900 2.64 | 35 122.9 2900 3.56 | 24 77 2900 0.83 | 26 71.5 2900 1.14 | 58.18 |

**Table 3.**Results of the maximization of the ratio between the recovered energy and PSR (n is the number of pipes where the turbines are installed;

**n**in rpm (m, kW); D in mm; N in rpm; ${E}_{{R}_{BEL}}$ in MWh/year).

_{s}n | Lines in Which Turbines Are Allocated | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 38 | 38 | ||||||||||

2 | 22 | 38 | 22 | |||||||||

3 | 5 | 22 | 38 | 5 | ||||||||

4 | 5 | 22 | 38 | 60 | 5 | |||||||

5 | 5 | 22 | 38 | 56 | 60 | 5 | ||||||

6 | 5 | 10 | 22 | 38 | 58 | 60 | 5 | |||||

7 | 5 | 10 | 22 | 27 | 38 | 58 | 60 | 5 | ||||

8 | 1 | 5 | 12 | 13 | 22 | 38 | 58 | 60 | 1 | |||

9 | 1 | 5 | 10 | 22 | 38 | 48 | 58 | 54 | 60 | 1 | ||

10 | 1 | 5 | 6 | 8 | 10 | 22 | 26 | 38 | 58 | 60 | 1 | |

n | Total${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | |||||||||||

1 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 24 93.5 2900 27.32 | 27.32 | |||||||||

2 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 32 89.1 2900 20.27 | 35 76 2400 7.39 | 27.66 | ||||||||

3 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 77 60 2400 5.21 | 35 81.5 2900 17.27 | 41 77.1 2400 8.66 | 31.14 | |||||||

4 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 77 60 2400 5.21 | 35 81.5 2900 17.27 | 41 77.1 2400 8.66 | 35 68.7 2040 2.03 | 33.16 | ||||||

5 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 77 60 2400 5.21 | 35 81.5 2900 17.27 | 41 77.1 2400 8.66 | 24 43.8 2900 0.24 | 35 68.7 2040 2.03 | 33.40 | |||||

6 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 65 62.4 2400 5.12 | 40 108.9 1020 3.60 | 41 76.2 2900 14.49 | 41 77.1 2400 8.74 | 40 53.6 2400 0.38 | 35 68.7 2040 2.03 | 34.35 | ||||

7 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 62 72.4 2040 5.57 | 40 108.9 1020 3.60 | 41 76.2 2900 14.49 | 41 107.4 510 0.30 | 40 63.3 2900 6.71 | 38 47.4 2900 0.34 | 35 68.7 2040 2.03 | 33.03 | |||

8 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 65 116.5 510 1.01 | 76 59.2 2400 4.94 | 40 108.9 1020 2.95 | 37 76.6 2040 0.20 | 41 76.2 2900 14.49 | 41 77.1 2400 8.60 | 34 49.2 2900 0.32 | 43 58.5 2400 1.88 | 34.38 | ||

9 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 65 116.5 510 1.01 | 76 59.2 2400 4.94 | 40 108.9 1020 3.16 | 41 76.2 2900 14.49 | 40 72.2 2400 6.43 | 46 106.8 510 0.30 | 24 47.7 2400 0.16 | 46 106.8 510 0.06 | 43 58.5 2400 1.88 | 32.42 | |

10 | n_{s}DN${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | 65 116.5 510 1.01 | 69 70.6 2040 5.37 | 41 107.4 510 0.07 | 48 98.8 2040 0.15 | 39 108.9 1020 3.04 | 42 74.7 2900 13.79 | 46 106.8 510 0.27 | 40 63.3 2900 6.71 | 39 47.7 2900 0.35 | 43 58.5 2400 1.88 | 32.63 |

**Table 4.**Comparison between recovered energy for the maximization of the recovered energy (${E}_{{R}_{BEL}}{}_{}$, MWh/year; $PSR$, years; $\frac{{E}_{R}}{PS{R}_{R}}$, MWh; $\frac{{E}_{R}}{{E}_{TR}}$, %).

n | BEL Strategy | Theoretical | Fixed Rotational Speed ($\mathsf{\alpha}=1$) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | $\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}$ | $\frac{{\mathit{E}}_{\mathit{R}}}{\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}}$ | ${\mathit{E}}_{\mathit{T}\mathit{R}}$ | $\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{T}\mathit{R}}$ | $\frac{{\mathit{E}}_{\mathit{T}\mathit{R}}}{\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{T}\mathit{R}}}$ | $\frac{{\mathit{E}}_{\mathit{R}}}{{\mathit{E}}_{\mathit{T}\mathit{R}}}$ | ${\mathit{E}}_{\mathit{R}}$ | $\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}$ | $\frac{{\mathit{E}}_{\mathit{R}}}{\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}}$ | $\frac{{\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}{}_{}}{{\mathit{E}}_{{\mathit{R}}_{\alpha =1}}}$ | |

1 | 33.78 | 1.7 | 19.87 | 90.29 | 5.56 | 9.10 | 37.41 | 23.98 | 2.40 | 9.99 | 140.88 |

2 | 42.55 | 6.24 | 6.81 | 109.75 | 5.65 | 10.68 | 38.77 | 31.44 | 8.28 | 3.80 | 135.35 |

3 | 46.11 | 7.59 | 6.07 | 120.36 | 5.99 | 11.05 | 38.30 | 31.44 | 12.42 | 2.53 | 146.67 |

4 | 49.08 | 7.42 | 6.61 | 125.45 | 6.31 | 10.94 | 39.12 | 33.27 | 12.15 | 2.74 | 147.54 |

5 | 52.00 | 15.97 | 3.25 | 129.55 | 6.22 | 11.45 | 40.14 | 29.01 | 25.89 | 1.12 | 179.28 |

6 | 54.60 | 15.94 | 3.42 | 133.18 | 6.28 | 11.67 | 40.99 | 29.71 | 26.34 | 1.13 | 183.79 |

7 | 55.47 | 15.67 | 3.53 | 135.35 | 6.41 | 11.61 | 40.98 | 30.26 | 14.16 | 2.14 | 183.32 |

8 | 56.53 | 15.41 | 3.66 | 136.98 | 6.53 | 11.54 | 41.26 | 30.77 | 14.00 | 2.20 | 183.72 |

9 | 57.04 | 16.4 | 3.47 | 138.04 | 6.79 | 11.19 | 41.32 | 36.42 | 8.70 | 4.19 | 156.64 |

10 | 58.18 | 16.16 | 3.60 | 139.64 | 6.85 | 11.21 | 41.66 | 36.98 | 8.63 | 4.29 | 157.33 |

**Table 5.**Comparison between recovered energy for the maximization of the ratio between the recovered energy and simple payback period (${E}_{R}$, MWh/year; $PSR$, years; $\frac{{E}_{R}}{PS{R}_{R}}$, MWh; $\frac{{E}_{R}}{{E}_{TR}}$, %).

n | BEL Strategy | Theoretical | Fixed Rotational Speed ($\mathsf{\alpha}=1$) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}$ | $\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}$ | $\frac{{\mathit{E}}_{\mathit{R}}}{\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}}$ | ${\mathit{E}}_{\mathit{T}\mathit{R}}$ | $\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{T}\mathit{R}}$ | $\frac{{\mathit{E}}_{\mathit{T}\mathit{R}}}{\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{T}\mathit{R}}}$ | $\frac{{\mathit{E}}_{\mathit{R}}}{{\mathit{E}}_{\mathit{T}\mathit{R}}}$ | ${\mathit{E}}_{\mathit{R}}$ | $\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}$ | $\frac{{\mathit{E}}_{\mathit{R}}}{\mathit{P}\mathit{S}{\mathit{R}}_{\mathit{R}}}$ | $\frac{{\mathit{E}}_{{\mathit{R}}_{\mathit{B}\mathit{E}\mathit{L}}}{}_{}}{{\mathit{E}}_{{\mathit{R}}_{\alpha =1}}}$ | |

1 | 27.32 | 0.71 | 38.46 | 49.66 | 5.46 | 9.10 | 55.01 | 11.78 | 1.65 | 7.14 | 147.20 |

2 | 27.66 | 0.59 | 46.82 | 60.36 | 5.65 | 10.68 | 45.83 | 13.66 | 1.20 | 11.38 | 113.83 |

3 | 31.14 | 0.6 | 51.71 | 62.61 | 5.58 | 11.23 | 49.73 | 16.74 | 1.12 | 14.94 | 107.79 |

4 | 33.16 | 0.61 | 54.01 | 68.24 | 5.87 | 11.62 | 48.59 | 17.83 | 1.14 | 15.64 | 114.54 |

5 | 33.40 | 0.61 | 54.03 | 69.68 | 5.96 | 11.69 | 47.93 | 17.95 | 1.15 | 15.60 | 115.69 |

6 | 34.35 | 0.65 | 52.34 | 70.95 | 5.98 | 11.87 | 48.41 | 20.02 | 1.13 | 17.78 | 101.12 |

7 | 33.03 | 0.64 | 51.03 | 70.95 | 5.98 | 11.87 | 46.55 | 19.48 | 1.10 | 17.70 | 95.24 |

8 | 34.38 | 0.72 | 47.24 | 70.93 | 5.95 | 11.94 | 48.47 | 21.64 | 1.19 | 18.18 | 89.35 |

9 | 32.42 | 0.66 | 49.10 | 71.05 | 5.95 | 11.95 | 45.62 | 19.75 | 1.08 | 18.28 | 87.08 |

10 | 32.63 | 0.67 | 48.68 | 71.05 | 5.95 | 11.95 | 45.93 | 19.53 | 1.12 | 17.44 | 91.09 |

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## Share and Cite

**MDPI and ACS Style**

Pérez-Sánchez, M.; Sánchez-Romero, F.J.; Ramos, H.M.; López-Jiménez, P.A.
Optimization Strategy for Improving the Energy Efficiency of Irrigation Systems by Micro Hydropower: Practical Application. *Water* **2017**, *9*, 799.
https://doi.org/10.3390/w9100799

**AMA Style**

Pérez-Sánchez M, Sánchez-Romero FJ, Ramos HM, López-Jiménez PA.
Optimization Strategy for Improving the Energy Efficiency of Irrigation Systems by Micro Hydropower: Practical Application. *Water*. 2017; 9(10):799.
https://doi.org/10.3390/w9100799

**Chicago/Turabian Style**

Pérez-Sánchez, Modesto, Francisco Javier Sánchez-Romero, Helena M. Ramos, and P. Amparo López-Jiménez.
2017. "Optimization Strategy for Improving the Energy Efficiency of Irrigation Systems by Micro Hydropower: Practical Application" *Water* 9, no. 10: 799.
https://doi.org/10.3390/w9100799