# AS-Solar, a Tool for Predictive Maintenance of Solar Groundwater Pumping Systems

^{*}

## Abstract

**:**

## 1. Introduction

^{−3}), are out of a range. Several publications [20] for pump maintenance engineers and technicians describe classical approaches for the performance analysis of pumping systems, based on the predictive maintenance of pumps using condition monitoring [18], which relies on classical measures of the performance of these systems.

## 2. Materials and Methods

#### 2.1. Hydraulic and Energy Modelling

_{p}is the pump efficiency.

^{3}·h

^{−1}), the pipe diameter (D, in m), the pipe length (L, in m) and the Hazen–Williams coefficient (C), using Equation (7) for the determination of the head loss (Δh, in m).

^{−1.85}·L·Q

^{1.85}·D

^{−4.87}

_{electric}) in the equation of the absorbed power (Equation (8)) was considered.

_{T}is the absorbed power (kW)’ γ is the specific weight of water (KN·m

^{−3}); Q is the pump discharge (m

^{3}·s

^{−1}); H is the piezometric height of the pump (m); η

_{p}is the pump efficiency; η

_{m}is the motor efficiency, which is considered a constant value in this work and η

_{electric}is a variable that considers the efficiency of the rest of the system’s electric components.

_{POW}is the power losses in the cables (kW), I

_{max}is the circulating current (A), N is the number of cables, L

_{c}is the length of the cable (m) and R is the resistance according to the temperature reached (Ω).

#### 2.2. The Case Study

^{2}spacing were established. The irrigation system in the plot was subsurface drip irrigation energized using a photovoltaic (PV) system. The irrigation system consisted of 20 subunits with a highly irregular shape and topography with elevation differences of up to 60 m. Thus, the energy demand of the irrigation system was highly variable depending on the activated irrigation subunit. A full description of the irrigation system can be found in [24].

^{2}and a length of 470 m, and (2) a line from the borehole inlet up to the submersible motor, which involves a copper cable RVK 0.6/1kV with a section of 25 mm

^{2}and a length of 225 m.

#### 2.3. Monitoring System

^{−1}) with a Woltman flowmeter WST-SB (Arad Group, Dalia, Israel) and calibrated using a General Electric PT878 ultrasound flowmeter (General Electric Company, Boston, MA, USA), and pressure was measured (in kPa) with a pressure transducer WIKA model A-10 bar (Instruments WIKA, S.A.U, Barcelona, Spain). Data were acquired over 9 months (December 2017–August 2018). This monitoring period describes the performance of the system in periods of low-, medium- and high-water demand of the crop (almond trees in this case study) and also includes different values of the water table level. Thus, the data set considers all the conditions of the system performance, which make it ideal for system modelling under different conditions. After the replacement of the whole pumping system in 2016, intensive testing was performed utilizing the methodology of energy audits [10,12] and the proper performance of the system was verified. Figure 1 shows the illustration of the complete monitoring system.

#### 2.4. Model Calibration and Determination of Robust Monitoring Variables

_{electric}”, which determines electrical problems in a VFD, cables and motor. The objective function was to minimize the root mean squared error (RMSE) between measured and simulated power and discharge.

#### 2.5. Statistical Analysis of the Results

^{2}) using programed functions in MATLAB

^{®}R2018b. Moreover, the adjustment to the normal of the residuals and homoscedasticity were evaluated.

## 3. Results and Discussion

#### 3.1. Optimizing Variables

_{electric}= 0.8333.

_{electric}) results in a value far below the expected one in a system replaced a short time ago. This is due to the different assumptions considered in the development of the energy model such as (1) the motor efficiency is considered to be constant, (2) inaccuracies in the determination of energy losses in the cables and (3) considering the efficiency values for the VFD supplied by the manufacturer.

#### 3.2. Calibration of the AS-Solar Model

## 4. Conclusions

_{electric}” solved this weakness.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

a | Coefficient of characteristic curve Q-H |

AC | Alternate current |

b | Coefficient of characteristic curve Q-H |

c | Coefficient of characteristic curve Q-H |

C | Hazen–Williams coefficient |

CPU | Central Processing Unit |

D | Pipe diameter (m) |

DC | Direct current |

Do | Diameter of the original impeller (m) |

Dr | Diameter of the impeller cut (m) |

DSS | Decision Support System |

e | Coefficient of curve Q-efficiency |

EEA | European Environmental Agency |

f | Coefficient of curve Q-efficiency |

H | Piezometric height of the pump (m) |

I_{max} | Circulating current in cable (A) |

Isc | Short circuit current (A) |

kWp | kilo Watts peak |

L | Pipe length (m) |

L_{c} | Cable length (m) |

lmpp | Maximum power current (A) |

LO_{POW} | Power losses in cables (kW) |

N | Number of cables |

NOCT | Nominal Operating Cell Temperature (°C) |

N_{T} | Absorbed power (kW) |

Q | Pump discharge (m^{3}·s^{−1}) |

R | Resistance according to the temperature (Ω) |

R^{2} | Coefficient of determination |

RE | Relative error |

RMSE | Root Mean Squared Error |

rpm | Revolutions per minute |

STC | Standard Testing Conditions |

VFD | Variable Frequency Drive |

Vmpp | Maximum power voltage (V) |

Voc | Open circuit voltage (V) |

λ | Coefficient to simulate the wear out of the pump impeller |

γ | Specific weight of water (KN·m^{−3}) |

α | Relationship between the supplied frequency to the motor and nominal frequency of the electrical grid |

Δh | Head losses (m) |

η_{m} | Motor efficiency |

η_{p} | Pump efficiency |

η_{electric} | Electrical efficiency |

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**Figure 3.**Comparison between the VFD efficiency supplied by the manufacturer and the output power measured.

Power, STC | 265 | Wp |
---|---|---|

Maximum power voltage (Vmpp), STC | 31.16 | V |

Maximum power current (lmpp), STC | 8.57 | A |

Open circuit voltage (Voc), STC | 38.12 | V |

Short circuit current (Isc), STC | 9.01 | A |

Efficiency | 16.2 | % |

Power temperature coefficient | −0.42 | %/K |

Current temperature coefficient | 0.059 | %/K |

Voltage temperature coefficient | −0.32 | %/K |

Nominal Operating Cell Temperature (NOCT) | 46 ± 2 | °C |

Q (L·min^{−1}) | H (m) | Efficiency (%) |
---|---|---|

0 | 331 | 1.27 |

150 | 319 | 41.12 |

200 | 308 | 51.24 |

250 | 296 | 59.65 |

300 | 284 | 66.35 |

350 | 272 | 71.33 |

400 | 259 | 74.61 |

450 | 241 | 76.18 |

500 | 221 | 76.03 |

550 | 193 | 74.17 |

600 | 162 | 70.60 |

650 | 127 | 65.33 |

RMSE (kW) | RE (%) | R^{2} |
---|---|---|

0.6 | 2.89 | 0.98 |

RMSE (L·min^{−1}) | RE (%) | R^{2} |
---|---|---|

26.9 | 7.93 | 0.78 |

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**MDPI and ACS Style**

Cervera-Gascó, J.; Montero, J.; Moreno, M.A.
AS-Solar, a Tool for Predictive Maintenance of Solar Groundwater Pumping Systems. *Agronomy* **2021**, *11*, 2356.
https://doi.org/10.3390/agronomy11112356

**AMA Style**

Cervera-Gascó J, Montero J, Moreno MA.
AS-Solar, a Tool for Predictive Maintenance of Solar Groundwater Pumping Systems. *Agronomy*. 2021; 11(11):2356.
https://doi.org/10.3390/agronomy11112356

**Chicago/Turabian Style**

Cervera-Gascó, Jorge, Jesús Montero, and Miguel A. Moreno.
2021. "AS-Solar, a Tool for Predictive Maintenance of Solar Groundwater Pumping Systems" *Agronomy* 11, no. 11: 2356.
https://doi.org/10.3390/agronomy11112356