# Feasibility of the Use of Variable Speed Drives in Center Pivot Systems Installed in Plots with Variable Topography

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## Abstract

**:**

^{−3}of distributed water obtained for the variable speed and fixed speed of the pumping station, respectively. The results also show that for an irrigation season, to meet the water requirements of the maize crop in the region of the study (627 mm), an average annual savings of 14,107.35 kWh was obtained, which resulted in an economic savings of 2821.47€.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Proposed Procedure

#### 2.2. Topography of the Irrigated Area

^{®}Desktop 3.2.1 software (QGIS Development Team, Open Source Geospatial Foundation). In this software, the geographical coordinates (X, Y) of the point referring to the center of the pivot (X

_{0}, Y

_{0}) were defined.

^{®}2018b software. Automatically, with the values of the geographic coordinates and the distance between towers, the elevation values were determined for 36 angular positions of the lateral line, equally spaced by 10°, with the North position of the lateral line as the position of angle 0°, as in Figure 2.

_{j}is the distance from the center tower to the index tower j, m.

#### 2.3. Hydraulic Model Description

#### 2.3.1. Flow Rate of the Emitters

^{3}h

^{−1}) was calculated according to the area corresponding to each water outlet, and the gross depth to be applied to the rotation time was specified by the manufacturer, as proposed by Valiantzas et al. [24]. The flow rate for the first outlet of each span (Equation (3)) and the remainder of each outlet (Equation (4)) was calculated. The lengths used are shown in Figure 3a:

_{x}is the flow rate of the outlet with order number x (1 ≤ x ≤ n), m

^{3}h

^{−1}, L

_{IE}is spacing between the tower and the first emitter (x = 1), m, L

_{E}is the spacing between the emitters with order number x (2 ≤ x ≤ n), m, R

_{inst}is the radius of the installation of the emitter, relative to the center tower, m, Lb is the gross irrigation depth (9 mm), and Tg is the rotation time (21 h).

_{x}), the discharge coefficient (k

_{e}, Equation (5)) of each emitter was determined. The value of the pressure in the emitter was the same as the value of the PRV nominal pressure (H

_{prv}), assuming an ideal valve:

_{e}is emitter discharge coefficient, m

^{2.5}h

^{−1}, H

_{prv}is the PRV nominal pressure, m, and β is the pressure exponent, in this case with a value of 0.5.

#### 2.3.2. Determination of Elevations and Lengths

_{S}is the length of span (m), L

_{FE}is the distance between the last emitter and next tower of the span (m), N

_{O}is the number of water outlets in the span, L

_{N}is the distance of the node referring to the water outlet in relation to the previous tower (m), N is the water outlet in the span, and R

_{T}is the radius of rotation of the tower relative to the centre tower (m).

_{n=x}is the node elevation x, m. Z

_{Tn-1}is the tower elevation previous to node n (m). Z

_{Tn}is the tower elevation posterior to node n (m). S

_{T}is the slope between towers n e n-1. Δh is the length of the drop pipe between the lateral line and the tower are variable for each lateral line water outlet (m). h

_{arc}is the maximum height of the lateral line arc (m). L

_{DP}is the total length of the drop pipe, which is variable for each lateral line water outlet (m). h

_{T}is the height of the moving towers (m). h

_{E}is the height of the emitter relative to the ground (m).

_{T}) of the last span of the lateral line was assumed in the calculation of the dimensions (Z

_{n=x}).

#### 2.4. Calculation of the Pumping Operation Point and Energy Consumption

#### Hydraulic Model

_{HW}) values of 100 (for the lateral line and water supply pipe) and 140 (for drop pipes).

_{t}is the total efficiency of the pumping station, η

_{p}is the pump efficiency, η

_{m}is the motor efficiency, η

_{v}is the VSD efficiency, and η

_{c}is the cable efficiency.

_{Nom}is the nominal power in kW and P

_{Abs(i)}is the absorbed power in kW.

_{v}/n

_{f})

#### 2.5. Determination of Specific Energy Consumption (CEE)

_{i}) was estimated:

_{p}is the pressure head at the fixed pumping speed (m), H

_{min(i)}is the minimum pressure head along the lateral line at each angular position i, m (obtained in EPANET), and ${\mathrm{H}}_{\mathrm{prv}}^{*}$ is the PRV pressure head, including the pressure regulator loss (69 kPa + 34 kPa).

^{−3}, Equation (16)) for 0° ≤ i ≤ 350° was calculated by the values of the pumping pressure head (H

_{i}, m), the water specific weight (γ, N m

^{−3}), and the efficiencies (η) of the pump, motor, VSD, and cable:

^{f}, em kWh m

^{−3}), was determined through Equation (17):

_{av}is the average of the specific energy consumption in the different angular positions of the lateral line, and T

_{o}is the operating time of the irrigation system.

#### 2.6. Case Study

^{3}h

^{−1}and has a supply pipe with a length of 920 m made of PVC with a nominal pipe diameter of 300 mm, which leads to the pivot point’s water from a fixed level reservoir with a capacity of approximately 7000 m

^{3}. The pumping station is composed of a pump (from the brand KSB, model WKL 150/1), with rotor 360 mm in size, which is driven by a three phase electric motor whose nominal voltage, power, and rotation values are 400V, 90 kW, and 1750 rpm, respectively. The electrical installation, with a power factor of 0.85, has electric copper cables with a length of 50 m and a cross-section of 16 mm².

_{o}) of 1440 h.

^{−1}was adopted as the reference price of the electric energy in the study region.

## 3. Results and Discussion

#### 3.1. Hydraulic Model

#### 3.2. Operating Point

_{p}, Q-η

_{p}, and Q-P

_{Abs}), adjusted through data taken from the manufacturer, are shown in Figure 5. The operating point of the index characteristic curve “f”, relative to the configuration of the pumping unit with a fixed speed is shown. In addition, the operating point of the index characteristic curve “v” refers to the configuration with a variable speed. In both cases, the angular position of the lateral line of 40° was represented with the fixed speed (n

_{f}= 1750 rpm and α = 1.00) and variable speed pump (n

_{v}= 1523 rpm and α = 0.85). This position was chosen because it has a minor pressure head value.

_{p})

_{v}and (Q-P

_{Abs})

_{v}to (Q-H

_{p})

_{f}and (Q-P

_{Abs})

_{f}did not result in significant differences in pump efficiency (Q-η

_{p})

_{f,v}. This result demonstrates that the use of the VSD in the irrigation system does not significantly interfere with the pump efficiency, whose high and low values were close to 80.26% (α = 0.85) and 78.54% (α = 1.00). This displacement also demonstrates the reduction of energy consumption (12.2%) through the influence of the VSD on the pumping station of the irrigation system under study. This same behavior of curve displacement was reported by Brar et al. [20] in a study on energy efficiency in center pivots. They determined that by reducing the speed of the pumping station’s rotation through the VSD, it was possible to reduce its head pressure, thereby maintaining the efficiency of the pump. Also, as described by Córcoles et al. [27], the ratio (in kWh m

^{−3}) can be higher at lower frequencies than the nominal value, thus presenting another source of energy saving.

#### 3.3. Pressure Distribution Along the Lateral Line

#### 3.4. Energy Analysis

^{−3}). On the other hand, position I = 250° presents the highest values−61.37 m and 0.234 kWh m

^{−3}, respectively. It should be noted that for these positions, the determination of the CEE with the variable speed of the pump is different from the CEE with a fixed speed, because, in this configuration, the value of VSD efficiency is not considered.

^{−3}) values for the fixed speed (without VSD) and variable speed (with VSD) pumping stations were determined. The specific energy consumption using the VSD was computed as the average values considering all the angular positions of the lateral line. In general, due to the small variations in the topography of the irrigated area, the average value of the CEE with variable speed of the pumping station was close to the value of the CEE with a fixed speed (0.214 and 0.244 kWh m

^{−3}, respectively), resulting in an energy reduction value of 12.2%. This percentage is lower than the values found by [18] (32% energy savings using variable speed well pumps in a center pivot system), [19] (27% to 35% of energy savings can be achieved using VSD in two Italian irrigation districts operating with three parallel horizontal axis pumps), and higher than those found by Brar et al. [20] (9.6% energy reduction is possible for 13.6 m difference in the irrigated area for a study containing 100 center pivots in Nebraska (USA), with each pivot containing a pumping station). However, these studies did not take into account the efficiency of VSD. The energy reduction value of this study is close to that found by King et al. [13] (7.5% to 15.8%), who considered the variable speed drive efficiency of a center pivot pumping unit. This result demonstrates that using VSD can reduce energy consumption in pumping units for water distribution.

#### 3.5. Economic Analysis

^{−1}) in the region where the study was conducted, which resulted in a low average annual saving (564.30 €). The average annual energy savings (kWh) presented by [13] were similar to those determined in the present study. However, due to the unit cost of energy consumption, the financial savings were lower. This fact shows that the cost of energy, besides the topography of the irrigated area, must be taken into account for this type of analysis.

^{−1}, resulting in average annual savings of 407.40€. The difference of the values in this study can be explained by the smaller difference in elevation, their low energy cost, and their lower gross irrigation requirements.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A_{c} | cross-sectional area of cable (mm^{2}) |

C_{c} | electrical conductivity of copper (m Ω^{−1} mm^{−2}) |

CEE^{f} | specific energy consumption, considering the pumping station with fixed speed (kWh m^{−3}) |

${\mathrm{CEE}}_{\mathrm{i}}^{\mathrm{v}}$ | specific energy consumption using the VSD, for each angular position i (kWh m^{−3}) |

(${\mathrm{CEE}}_{\mathrm{i}}^{\mathrm{v}}$)_{av} | average of the specific energy consumption in the different angular positions (kWh m^{−3}) |

C_{HW} | roughness coefficient of the pipe material of the Hazen-Williams equation |

cosϕ | power factor |

D | pipe diameter of the lateral line |

DEM | Digital Elevation Model |

EC | Energy Consumption (kWh) |

ER | Energy Reduction (%) |

GIWR | gross irrigation water requirement (mm) |

h_{arc} | maximum height of the lateral line arc (m) |

h_{E} | height of the emitter relative to the ground (m) |

hf | head loss (m) |

H_{i} | pressure head that the pump must provide for each angular position i (m) |

H_{min(i)} | minimum pressure along the lateral line for each angular position i (m) |

H_{p} | pressure head at the fixed pumping speed (m) |

H_{prv} | nominal pressure of the PRV (m) |

${\mathrm{H}}_{\mathrm{prv}}^{*}$ | PRV pressure, including the minimum regulator requirement (m) |

h_{T} | height of moving towers (m) |

i | angular position of the lateral line (0°, 10°, …, 350°) |

j | number of moving towers |

k_{e} | emitter discharge coefficient (m^{2.5} s^{−1}) |

L | equivalent length of lateral line (m) |

Lb | gross irrigation depth (mm day^{−1}) |

L_{c} | cable length (m) |

L_{DP} | total length of the drop pipe (m) |

L_{E} | spacing between emitters (m) |

L_{FE} | distance between the last emitter and next tower of the span (m) |

L_{IE} | spacing between the tower and the first emitter (m) |

L_{j} | distance from the centre tower to the index tower j (m) |

L_{N} | distance of the node referring to the water outlet in relation to the previous tower (m) |

L_{S} | length of span (m) |

N | water outlet in the span |

N_{O} | number of water outlets in the span |

P_{H} | hydraulic power (kW) |

PNOA | Spanish National Program of aerial photogrammetry |

P_{Abs(i)} | absorbed power (kW) |

P_{Nom} | nominal power (kW) |

PRV | Pressure Regulator Valve |

Q | total flow rate of the irrigation system |

q_{x} | flow of the outlet with order number x (m^{3} h^{−1}) |

R_{inst} | radius of installation of the emitter, relative to the centre tower (m) |

R_{T} | radius of rotation of the tower relative to the centre tower (m) |

S_{T} | slope between towers n e n −1 |

Tg | rotation time (h) |

T_{o} | operating time of irrigation system (h) |

U | nominal voltage (V) |

VSD | Variable Speed Drive |

VSPM | Variable Speed Pivot Model |

${\mathrm{X}}_{\mathrm{i}}^{\mathrm{j}}$, ${\mathrm{Y}}_{\mathrm{i}}^{\mathrm{j}}$ | geographical coordinates of the moving towers j (m) |

Z_{n=x} | elevation of the node x (m) |

Z_{Tn} | tower elevation posterior to node n (m) |

Z_{Tn-1} | tower elevation previous to node n (m) |

α | ratio between the speed of the variable speed drive and the maximum speed as a fixed speed drive |

β | exponent of the pressure |

γ | water specific weight (N m^{−3}) |

Δh | length of the drop pipe between the lateral line and the tower (m) |

η_{c} | cable efficiency |

η_{m} | motor efficiency |

η_{p} | pump efficiency |

η_{t} | total efficiency of the pumping station |

η_{v} | VSD efficiency |

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**Figure 3.**(

**a**) Center pivot lateral line span dimensions, (

**b**) EPANET network map of the first span of the center pivot lateral line.

**Figure 4.**Network maps of the center pivot system from EPANET inp files generated by the VSPM (Variable Speed Pivot Model) tool considering two different lateral line angular positions (

**a**) 250° uphill and (

**b**) 40° downhill.

**Figure 5.**Pumping station characteristic curves for the 40° angular position lateral line with a fixed speed (f) and variable speed (v), (

**a**) (Q-H) and (Q-η) curves, (

**b**) (Q-P

_{Abs}) curve.

**Figure 6.**(

**a**) Value and (

**b**) location of the point of minimum pressure head in the different angular positions of the center pivot lateral line.

**Figure 7.**Absorbed power at the pumping station for the different angular positions of the lateral line.

**Table 1.**Flow rate (Q), pumping pressure head (H

_{i}), hydraulic power (P

_{H}), speed of the pumping station (n), variable speed ratio (α), efficiencies (η), and specific energy consumption (CEE) in the different angular positions of the lateral line.

Angular Position | Q (m ^{3} h^{−1}) | Hi (m) | P_{H}(kW) | n | α | η_{p}(%) | η_{m}(%) | η_{v}(%) | η_{c}(%) | η_{t} ^{1}(%) | CEE (kWh m ^{−3}) |
---|---|---|---|---|---|---|---|---|---|---|---|

Fixed | 326.61 | 65.23 | 58.04 | 1750 | 1.00 | 78.54 | 94.13 | 98.60 | 72.90 | 0.244* | |

0° | 326.61 | 50.72 | 45.12 | 1574 | 0.90 | 80.08 | 93.86 | 96.75 | 98.65 | 71.74 | 0.193 |

10° | 326.61 | 48.64 | 43.27 | 1547 | 0.88 | 80.20 | 93.77 | 96.21 | 98.66 | 71.38 | 0.186 |

20° | 326.61 | 47.77 | 42.50 | 1535 | 0.88 | 80.23 | 93.73 | 95.95 | 98.66 | 71.19 | 0.183 |

30° | 326.61 | 47.07 | 41.88 | 1526 | 0.87 | 80.26 | 93.69 | 95.71 | 98.66 | 71.01 | 0.181 |

40° | 326.61 | 46.84 | 41.67 | 1523 | 0.87 | 80.26 | 93.68 | 95.63 | 98.67 | 70.94 | 0.180 |

50° | 326.61 | 47.49 | 42.25 | 1531 | 0.88 | 80.24 | 93.71 | 95.86 | 98.66 | 71.12 | 0.182 |

60° | 326.61 | 49.16 | 43.74 | 1553 | 0.89 | 80.17 | 93.79 | 96.36 | 98.66 | 71.48 | 0.187 |

70° | 326.61 | 52.69 | 46.88 | 1599 | 0.91 | 79.93 | 93.93 | 97.13 | 98.64 | 71.93 | 0.200 |

80° | 326.61 | 55.29 | 49.20 | 1631 | 0.93 | 79.70 | 94.00 | 97.43 | 98.63 | 72.00 | 0.209 |

90° | 326.61 | 56.24 | 50.04 | 1643 | 0.94 | 79.61 | 94.02 | 97.48 | 98.63 | 71.96 | 0.213 |

100° | 326.61 | 57.57 | 51.22 | 1659 | 0.95 | 79.47 | 94.04 | 97.51 | 98.63 | 71.88 | 0.218 |

110° | 326.61 | 58.33 | 51.90 | 1669 | 0.95 | 79.39 | 94.05 | 97.50 | 98.62 | 71.80 | 0.221 |

120° | 326.61 | 58.15 | 51.73 | 1666 | 0.95 | 79.41 | 94.05 | 97.50 | 98.62 | 71.82 | 0.221 |

130° | 326.61 | 58.45 | 52.01 | 1670 | 0.95 | 79.38 | 94.06 | 97.50 | 98.62 | 71.79 | 0.222 |

140° | 326.61 | 59.38 | 52.83 | 1681 | 0.96 | 79.27 | 94.07 | 97.45 | 98.62 | 71.67 | 0.226 |

150° | 326.61 | 60.00 | 53.38 | 1689 | 0.96 | 79.20 | 94.08 | 97.41 | 98.62 | 71.58 | 0.228 |

160° | 326.61 | 60.49 | 53.82 | 1695 | 0.97 | 79.14 | 94.09 | 97.37 | 98.62 | 71.49 | 0.230 |

170° | 326.61 | 58.63 | 52.16 | 1672 | 0.96 | 79.36 | 94.06 | 97.49 | 98.62 | 71.77 | 0.223 |

180° | 326.61 | 60.33 | 53.67 | 1693 | 0.97 | 79.16 | 94.08 | 97.38 | 98.62 | 71.52 | 0.230 |

190° | 326.61 | 59.99 | 53.37 | 1688 | 0.96 | 79.20 | 94.08 | 97.41 | 98.62 | 71.58 | 0.228 |

200° | 326.61 | 60.35 | 53.69 | 1693 | 0.97 | 79.16 | 94.08 | 97.38 | 98.62 | 71.52 | 0.230 |

210° | 326.61 | 59.75 | 53.16 | 1686 | 0.96 | 79.23 | 94.08 | 97.43 | 98.62 | 71.61 | 0.227 |

220° | 326.61 | 59.52 | 52.96 | 1683 | 0.96 | 79.25 | 94.07 | 97.44 | 98.62 | 71.65 | 0.226 |

230° | 326.61 | 60.86 | 54.15 | 1699 | 0.97 | 79.10 | 94.09 | 97.33 | 98.62 | 71.43 | 0.232 |

240° | 326.61 | 60.21 | 53.57 | 1691 | 0.97 | 79.17 | 94.08 | 97.39 | 98.62 | 71.54 | 0.229 |

250° | 326.61 | 61.37 | 54.60 | 1705 | 0.97 | 79.03 | 94.10 | 97.27 | 98.61 | 71.33 | 0.234 |

260° | 326.61 | 61.24 | 54.48 | 1703 | 0.97 | 79.05 | 94.09 | 97.28 | 98.61 | 71.36 | 0.234 |

270° | 326.61 | 58.61 | 52.15 | 1672 | 0.96 | 79.36 | 94.06 | 97.49 | 98.62 | 71.77 | 0.222 |

280° | 326.61 | 57.68 | 51.32 | 1661 | 0.95 | 79.46 | 94.04 | 97.51 | 98.63 | 71.87 | 0.219 |

290° | 326.61 | 59.07 | 52.56 | 1677 | 0.96 | 79.31 | 94.07 | 97.47 | 98.62 | 71.71 | 0.224 |

300° | 326.61 | 59.24 | 52.70 | 1679 | 0.96 | 79.29 | 94.07 | 97.46 | 98.62 | 71.69 | 0.225 |

310° | 326.61 | 57.53 | 51.19 | 1659 | 0.95 | 79.48 | 94.04 | 97.51 | 98.63 | 71.88 | 0.218 |

320° | 326.61 | 55.85 | 49.69 | 1638 | 0.94 | 79.65 | 94.01 | 97.47 | 98.63 | 71.98 | 0.211 |

330° | 326.61 | 55.22 | 49.13 | 1630 | 0.93 | 79.71 | 93.99 | 97.42 | 98.63 | 72.00 | 0.209 |

340° | 326.61 | 55.05 | 48.98 | 1628 | 0.93 | 79.73 | 93.99 | 97.41 | 98.63 | 72.00 | 0.208 |

350° | 326.61 | 52.50 | 46.71 | 1596 | 0.91 | 79.95 | 93.92 | 97.10 | 98.64 | 71.92 | 0.199 |

^{1}Total efficiency * variable speed drives (VSDs) efficiency not considered.

**Table 2.**The consumption and cost of energy for the pumping stations with fixed and variable speeds.

Crop | Maize | |
---|---|---|

GIWR (gross irrigation water requirement) | mm | 627.00 |

Flow rate | m^{3} h^{−1} | 326.61 |

Operation time | h | 1440.00 |

EC_{f} | kWh | 114739.03 |

EC_{v} | kWh | 100632.47 |

Average cost | € kW h^{−1} | 0.20 |

C_{f} | € | 22947.96 |

C_{v} | € | 20126.49 |

Energy Savings | € year^{−1} | 2821.47 |

© 2019 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**

Buono da Silva Baptista, V.; Córcoles, J.I.; Colombo, A.; Moreno, M.Á.
Feasibility of the Use of Variable Speed Drives in Center Pivot Systems Installed in Plots with Variable Topography. *Water* **2019**, *11*, 2192.
https://doi.org/10.3390/w11102192

**AMA Style**

Buono da Silva Baptista V, Córcoles JI, Colombo A, Moreno MÁ.
Feasibility of the Use of Variable Speed Drives in Center Pivot Systems Installed in Plots with Variable Topography. *Water*. 2019; 11(10):2192.
https://doi.org/10.3390/w11102192

**Chicago/Turabian Style**

Buono da Silva Baptista, Victor, Juan Ignacio Córcoles, Alberto Colombo, and Miguel Ángel Moreno.
2019. "Feasibility of the Use of Variable Speed Drives in Center Pivot Systems Installed in Plots with Variable Topography" *Water* 11, no. 10: 2192.
https://doi.org/10.3390/w11102192