# Energy Consumption Optimization in Irrigation Networks Supplied by a Standalone Direct Pumping Photovoltaic System

^{1}

^{2}

^{*}

## Abstract

**:**

^{5}times, the best result was an irrigation schedule which satisfied all the requirements, involving the installation of 651 solar panels and energy consumption of 428.74 kWh per day, to deliver water to orchards of different varieties of citrus fruit spread over 167.7 ha.

## 1. Introduction

^{3}[11].

^{−2}) into direct current; DC), a frequency converter (which converts the DC into alternating current; AC) and an asynchronous motor (which converts AC into shaft work moving the pump) [16,17].

^{®}code to assist with the EPAnet toolkit [32]. In every combination, the energy audit in irrigation networks [29] was calculated using a Matlab-based graphical user interface (GUI; UAEnergy) developed for students and practitioners which can be downloaded at “http://rua.ua.es/dspace/handle/10045/76947”.

## 2. Materials and Methods

#### 2.1. Net Power Transferred to the Water

^{−2}, ${I}_{STC}$ is the irradiance under standard conditions (1000 W m

^{−2}), PP is the peak power generated by the PV modules (in W), $\gamma $ is the performance decay coefficient due to the rising temperature of the cell, ${T}_{cell}$ is the cell temperature in the module and ${T}_{STC}$ is the cell temperature under standard test conditions (25 °C). It will be necessary to determine the minimum irradiation (${I}_{m}$), the threshold value (depending on the frequency inverter and also the PV peak power) which may range between 250–500 W m

^{−2}[34,35]. This value represents the daily irrigation period (i.e., the number of hours of irrigation).

#### 2.2. Water Demands and Network Sectoring

_{o}) and the type of crop, characterized by the crop coefficient (K

_{c}). This method is robust and valid, both for the irrigation network design stage and for selecting the irrigation program schedule (once the crops are growing). Some other methods, which calculate water requirements more accurately, are based on direct measurements of the soil water content or on plant water stress monitoring [37,38]. Their use would require physically having the irrigation network working, as sensors would need to be in place to obtain the data required (in other words, these methods can only be properly used in the irrigation schedule programming stage).

#### 2.3. Energy Audit in Irrigation Networks

_{n}(${t}_{p}$) is the energy supplied by reservoirs, E

_{p}$\left({t}_{p}\right)$ is the energy supplied by pumps, E

_{u}$\left({t}_{p}\right)$ is the energy delivered to the crops (through the water supplied), E

_{l}$\left({t}_{p}\right)$ is the energy lost through water losses, E

_{f}$\left({t}_{p}\right)$ is the energy dissipated by friction in pipes, E

_{v}$\left({t}_{p}\right)$ is the energy dissipated in valves, and ΔE

_{c}$\left({t}_{p}\right)$ is the energy that can be stored in a compensation tank which accumulates water during low consumption hours and releases it in peak hours.

#### 2.4. Network Management

_{p}$\left({t}_{p}\right)$) as some other parameters in the energy audit are also affected. To name a few, the relationship between energy dissipated by friction in pipes and flow is of a quadratic type, and the leakage depends (among some other factors) on the pressure levels (whose figures are directly linked to head losses and circulating flows along the network).

## 3. Optimization Problem

#### 3.1. Input Data

- Irradiance input data:
- ○
- β is the angle of inclination (radians) of the photovoltaic panels
- ○
- ${I}_{sc}$ is the solar constant (1367 W m
^{−2}) - ○
- ${I}_{STC}$ is the irradiance under standard conditions (1000 W m
^{−2}) - ○
- $d$ is the performance decay coefficient due to the rising temperature of the cell (0.004 °C
^{−1}) - ○
- H is the global irradiance on horizontal surface (kWh m
^{−2}) - ○
- ${T}_{STC}$ is the cell temperature under standard test conditions (25 °C)
- ○
- ${T}_{avg}$ is the monthly average temperature (°C)
- ○
- φ is the latitude angle (positive to the North) (radians)
- ○
- n is the day of the representative month
- ○
- ρ is the albedo (-)
- ○
- PP is the peak power generated by the PV modules (W)
- ○
- ${\eta}_{p}$ is the pump efficiency (-).
- ○
- ${\eta}_{am}$ is the asynchronous motor efficiency (-).
- ○
- ${\eta}_{fc}$ is the converter efficiency (-).

- Hydraulic input data:
- ○
- A calibrated water-pressurized network which represents the water delivery in crops. This file must represent the hydraulic features of the system and no errors should appear when running this model. Moreover, the water requirements of the network should be defined in the model and the segments (if any) should also be included in the model.
- ○
- Report time step for the case study (minutes)
- ○
- ${\left(\frac{P}{\gamma}\right)}_{threshold}$ (defined in Section 2.2) is the minimum pressure required by standards at any hydrant and any time (m.w.c.)
- ○
- ${T}_{irr}$ (defined in Section 2.2) is the irrigation time (minutes).
- ○
- ${T}_{min\_irr}$ is the minimum irrigation time (minutes), a value which shows that if a node is delivering water to crops, it should be doing it for a time at least equal to or higher than this value.

#### 3.2. Optimization Parameters

#### 3.3. Calculation Process

**Step****1**- The first stage in the calculation is focused on calculating the monthly energy available per PV system. The unitary energy available is computed (Section 2.1, Appendix A).
**Step****2**- The second stage involves calculating the shaft work required by the pumps in the network (Section 2.3) for every segment combination Equation (5). Moreover, the m potential cases (DPMs) are calculated with the aforementioned restrictions:
- volume delivery should be constant
- the minimum pressure at every node and at every time should always be equal to or higher than the minimum pressure required by standards
- every time a segment is delivering water, the electro-valves have to be opened for a period longer than the minimum irrigation time.

**Step****3**- For the m combination, and at every i time step, the number of solar panels is calculated as:$${N}_{mod}^{\ast}=\mathrm{min}\left(\mathrm{max}\left\{ceil\left[{\left(\frac{{E}_{req-i}}{{E}_{av-i}}\right)}_{m}\right]\right\}\right)$$

## 4. Numerical Example

^{2}per tree. The total length of the network is 4.05 km. The pipe material is PVC, the pipe roughness for the aged pipes is 0.02 mm (a common value in water irrigation networks; [42]), and the minimum service pressure required is ${\left(\frac{P}{\gamma}\right)}_{threshold}$ = 25 m of water column. The irrigation networks were grouped into five segments which were determined based on the criterion of uniformity of pressure (and consequently flow) at each subunit. The water demands for the consumption of each segment were 79.7, 84.4, 85.4, 85.3 and 84 L/s for sectors 1, 2, 3, 4 and 5, respectively. All the subunits were equipped with drippers (4 L/h per emitter) and six emitters were required to irrigate every tree. The irrigation management system (current state; Case 0) is based on central system scheduled delivery and the total irrigation time (${T}_{irr}$) varies with regard to every month considered. The monthly water demands were calculated with the meteorological information recovered in the irrigation area and the reference crop evapotranspiration was calculated using the Penman-Monteith method from the last 13 years (from 2005–2017). Regional recommendations [43] were followed to calibrate crop coefficients (K

_{c}), and finally, the monthly average water needs varied from 0.31 L/m

^{2}in January to 3.4 L/m

^{2}in July. The irrigation time values are depicted in Table 2.

#### 4.1. Irradiation Curves

#### 4.2. Energy Requirements for Every Segment Combination

#### 4.3. Combinations Performed

^{53}(a very high value even for automated calculations). Some restrictions reduce this number of combinations, that is:

#### 4.4. Results for the DPM Combinations

^{5}potential combinations meeting the restrictions above were created. For each combination, the $ceil\left[{\left(\frac{{E}_{req-i}}{{E}_{av-i}}\right)}_{m}\right]$ for the 54 time steps was calculated in order to know the number of solar panels required at every instant of the day to satisfy the i water demand. Of course, the maximum of these values results in the number of PVs necessary to satisfy water demand in these combinations. So, the number of solar panels for each of the 10

^{5}potential combinations (a row vector of size (1, 1 × 10

^{5}) containing the panels required) was calculated. Among these, 60 combinations reached the minimum value of 651 solar panels (which returns the number of the modulus (${N}_{mod}^{\ast}$) obtained at the m* combination.

#### 4.5. Comparison between Scenarios

^{3}(which takes into account that natural energy remains constant as the water level in the reservoir). On the one hand, the pumping system is more energy-hungry in Case 0 than in the case of operations with solar panels, Case 1. This is due to the fact that the irrigation time is much longer 16.8 (Case 0) vs 9 h (Case 1). On the other hand, this shorter irrigation time involves greater flow rates and accordingly, higher friction losses. Finally, useful energy is lower in Case 1 than in Case 0 (maintaining the pressure above standards at every node and every hour of the day; Table 5). This decrease shows better network operating efficiency as overpressure is avoided (with the benefits inherent to reduced pressure) while reducing the energy consumption in pumps (522.66 − 428.74 = 93.92 kWh/day).

## 5. Conclusions

^{®}code has also been written to assist practitioners when dimensioning the PV array sets and another GUI (UAenergy) was also used for the energy audit calculations in networks.

^{6}potential candidates). This meant that an ad-hoc algorithm needed to be performed to create the 10

^{5}candidates (satisfying the requirements). It is noted that only 60 out of the 10

^{5}candidates involved 651 solar panels and the candidate with the lowest energy consumption was 428.74 kWh per day.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Irradiance Calculation

^{2}) on the location where the system is to be installed. In this work, hourly irradiance has been calculated using monthly average irradiation (kWh/m

^{2}) obtained from meteorological data. Hourly irradiance can be estimated by applying a series of transformations to irradiation data [33].

_{s}), both in radians:

Month | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

n | 17 | 47 | 75 | 105 | 135 | 162 | 198 | 228 | 258 | 288 | 318 | 344 |

^{2}) incident on a horizontal plane can be calculated:

^{2}).

^{2}) are given by:

Time | W/m^{2} | Time | W/m^{2} | Time | W/m^{2} | Time | W/m^{2} |
---|---|---|---|---|---|---|---|

4.75 | 0.02 | 8.5 | 151.29 | 12.25 | 250.70 | 16 | 126.75 |

5 | 2.57 | 8.75 | 163.18 | 12.5 | 248.92 | 16.25 | 114.31 |

5.25 | 5.17 | 9 | 174.70 | 12.75 | 245.96 | 16.5 | 101.88 |

5.5 | 12.52 | 9.25 | 185.73 | 13 | 241.86 | 16.75 | 89.55 |

5.75 | 22.11 | 9.5 | 196.18 | 13.25 | 236.66 | 17 | 77.42 |

6 | 32.25 | 9.75 | 205.96 | 13.5 | 230.40 | 17.25 | 65.55 |

6.25 | 42.90 | 10 | 214.98 | 13.75 | 223.15 | 17.5 | 54.02 |

6.5 | 54.02 | 10.25 | 223.15 | 14 | 214.98 | 17.75 | 42.90 |

6.75 | 65.55 | 10.5 | 230.40 | 14.25 | 205.96 | 18 | 32.25 |

7 | 77.42 | 10.75 | 236.66 | 14.5 | 196.18 | 18.25 | 22.11 |

7.25 | 89.55 | 11 | 241.86 | 14.75 | 185.73 | 18.5 | 12.52 |

7.5 | 101.88 | 11.25 | 245.96 | 15 | 174.70 | 18.75 | 5.17 |

7.75 | 114.31 | 11.5 | 248.92 | 15.25 | 163.18 | 19 | 2.57 |

8 | 126.75 | 11.75 | 250.70 | 15.5 | 151.29 | 19.25 | 0.02 |

8.25 | 139.11 | 12 | 251.30 | 15.75 | 139.11 |

^{2}, the power supplied at every time of the day is a result of multiplying the previous values by this area. As there are some other efficiency factors (pump efficiency = 0.85; asynchronous motor efficiency = 0.80, and converter efficiency = 0.95) involved in calculating the net energy transferred to water by one single modulus is presented in Table A1. Figure 4 also shows the restriction of number of irrigation hours to 9 h (from 7.5 to 16.5 h).

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**Figure 2.**Workflow for the process to calculate the most energy-efficient combination of temporal consumption.

**Figure 5.**Hourly comparison between energy available and required in the Albamix irrigation network.

β = 15° | H_{avg} = 8 kWh m^{−2} | n = 198 (-) | ${\eta}_{am}$ = 0.8 (-) |

${I}_{sc}$ = 1367 W m^{−2} | ${T}_{STC}$ = 25 °C | ρ = 0.2 (-) | ${\eta}_{fc}$ = 0.95 (-) |

${I}_{STC}$ = 1000 Wm^{−2} | T_{avg} = 24.9 °C | PP = 250 W | |

d = 0.004 °C^{−1} | φ = 39.47° | ${\eta}_{p}$ = 0.75 (-) |

Month | January | February | March | April | May | June |

Irr. time (h) | 0.52 | 0.69 | 1.12 | 1.29 | 1.93 | 2.92 |

Month | July | August | September | October | November | December |

Irr. time (h) | 3.25 | 2.70 | 1.62 | 0.75 | 0.43 | 0.30 |

**Table 3.**Shaft work required and minimum pressure at every node for every water requirement combination.

Combination | 1 | 2 | 3 | 4 | 5 | 1-2 | 1-3 | 1-4 |

Injected flow (L/s) | 85.1 | 84.4 | 85.4 | 85.3 | 84 | 169.5 | 170.5 | 170.4 |

Shaft work (Kwh) | 5.24 | 5.20 | 5.26 | 5.25 | 5.18 | 8.41 | 8.42 | 8.42 |

Min Pressure (m.w.c.) | 42.75 | 40.77 | 39.02 | 38.61 | 38.48 | 30.33 | 29.29 | 28.91 |

Combination | 1-5 | 2-3 | 2-4 | 2-5 | 3-4 | 3-5 | 4-5 | |

Injected flow (L/s) | 169.1 | 169.8 | 169.7 | 168.4 | 170.7 | 169.4 | 169.3 | |

Shaft work (Kwh) | 8.40 | 8.41 | 8.41 | 8.39 | 8.43 | 8.41 | 8.40 | |

Min Pressure (m.w.c.) | 28.75 | 29.02 | 28.65 | 28.46 | 28.44 | 28.24 | 28.27 |

Time | 1 | 2 | 3 | 4 | 5 | Time | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 0 | 0 | 0 | 0 | 4.50 | 1 | 0 | 0 | 1 | 0 |

0.17 | 1 | 0 | 0 | 0 | 0 | 4.67 | 1 | 0 | 1 | 0 | 0 |

0.33 | 1 | 0 | 0 | 0 | 0 | 4.83 | 1 | 0 | 1 | 0 | 0 |

0.50 | 1 | 0 | 0 | 0 | 0 | 5.00 | 1 | 0 | 1 | 0 | 0 |

0.67 | 1 | 0 | 0 | 0 | 1 | 5.17 | 1 | 0 | 1 | 0 | 0 |

0.83 | 1 | 0 | 0 | 0 | 1 | 5.33 | 1 | 0 | 1 | 0 | 0 |

1.00 | 0 | 0 | 0 | 0 | 1 | 5.50 | 0 | 1 | 1 | 0 | 0 |

1.17 | 1 | 0 | 0 | 0 | 1 | 5.67 | 0 | 1 | 1 | 0 | 0 |

1.33 | 1 | 0 | 0 | 0 | 1 | 5.83 | 0 | 1 | 1 | 0 | 0 |

1.50 | 1 | 0 | 0 | 0 | 1 | 6.00 | 0 | 1 | 1 | 0 | 0 |

1.67 | 1 | 0 | 0 | 0 | 1 | 6.17 | 0 | 1 | 1 | 0 | 0 |

1.83 | 1 | 0 | 0 | 0 | 1 | 6.33 | 0 | 1 | 1 | 0 | 0 |

2.00 | 1 | 0 | 0 | 0 | 1 | 6.50 | 0 | 1 | 1 | 0 | 0 |

2.17 | 1 | 0 | 0 | 0 | 1 | 6.67 | 0 | 1 | 0 | 1 | 0 |

2.33 | 0 | 1 | 0 | 0 | 1 | 6.83 | 0 | 1 | 0 | 1 | 0 |

2.50 | 0 | 1 | 0 | 0 | 1 | 7.00 | 0 | 1 | 0 | 1 | 0 |

2.67 | 0 | 1 | 0 | 0 | 1 | 7.17 | 0 | 1 | 0 | 1 | 0 |

2.83 | 0 | 1 | 0 | 0 | 1 | 7.33 | 0 | 1 | 0 | 1 | 0 |

3.00 | 0 | 1 | 1 | 0 | 0 | 7.50 | 0 | 0 | 0 | 1 | 1 |

3.17 | 0 | 1 | 1 | 0 | 0 | 7.67 | 0 | 0 | 0 | 1 | 1 |

3.33 | 0 | 1 | 1 | 0 | 0 | 7.83 | 0 | 0 | 0 | 1 | 1 |

3.50 | 0 | 1 | 1 | 0 | 0 | 8.00 | 0 | 0 | 0 | 1 | 1 |

3.67 | 0 | 0 | 1 | 1 | 0 | 8.17 | 0 | 0 | 0 | 1 | 1 |

3.83 | 0 | 0 | 1 | 1 | 0 | 8.33 | 0 | 0 | 0 | 1 | 1 |

4.00 | 0 | 0 | 1 | 1 | 0 | 8.50 | 0 | 0 | 0 | 1 | 0 |

4.17 | 0 | 0 | 1 | 1 | 0 | 8.67 | 0 | 0 | 0 | 1 | 0 |

4.33 | 1 | 0 | 0 | 1 | 0 | 8.83 | 0 | 0 | 0 | 1 | 0 |

**Table 5.**Results of the energy audit for Case 0 (irrigation time 16.8 h) and Case 1 (irrigation time 9 h).

Case 0 | Case 1 | |
---|---|---|

${E}_{N}$ (kWh) | 3134.95 | 3134.98 |

${E}_{B}$ (kWh) | 522.66 | 428.74 |

${E}_{U}$ (kWh) | 3634.87 | 3492.72 |

${E}_{F}$ (kWh) | 22.70 | 70.94 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pardo Picazo, M.Á.; Juárez, J.M.; García-Márquez, D. Energy Consumption Optimization in Irrigation Networks Supplied by a Standalone Direct Pumping Photovoltaic System. *Sustainability* **2018**, *10*, 4203.
https://doi.org/10.3390/su10114203

**AMA Style**

Pardo Picazo MÁ, Juárez JM, García-Márquez D. Energy Consumption Optimization in Irrigation Networks Supplied by a Standalone Direct Pumping Photovoltaic System. *Sustainability*. 2018; 10(11):4203.
https://doi.org/10.3390/su10114203

**Chicago/Turabian Style**

Pardo Picazo, Miguel Ángel, Juan Manzano Juárez, and Diego García-Márquez. 2018. "Energy Consumption Optimization in Irrigation Networks Supplied by a Standalone Direct Pumping Photovoltaic System" *Sustainability* 10, no. 11: 4203.
https://doi.org/10.3390/su10114203