## Materials and methods

Experiments were carried out in Bani Salamah, Al-Qanater, Giza Governorate, Egypt, located at latitude 30.325364° N, longitude 30.805797° E, and 19 m above sea level, from September 2020 to June 2021, and measurements were taken every 15 min through the day between sunrise and sunset.

### PV water pumping system sizing

The design of the solar water pumping system goes through several stages, and some information such as daily water consumption, static water level, and the pumping pipes length and diameter must be known. In the present case, average water consumption = 175 m3/day, static level = 47 m, draw down = 5 m, the pumping pipes length = 70 m, the pressure of irrigation network = 1 bar, and the pumping pipes diameter = 3 Inches = 76.2 mm.

### Pump selection

Total dynamic head TDH (m) and flow rate Q (m3/hr.) should be specified accurately to select the suitable pump.

### Total dynamic head TDH (m)

The friction head Hf (m) represents the loss of pressure in pipe due to fraction. The friction head could be calculated from Hazen William as Eq. (1)26.

$${\mathrm{H}}_{\mathrm{f}}=K\times L\times {(\frac{Q}{C})}^{1.852}\times {d}^{-4.87}$$
(1)

where Hf = friction losses (m) , K = constant coefficient = 1.22*1010, L = Length of pumping pipes (m) , Q = discharge (lit/s) , d = internal diameter of pumping pipes (mm).

$${h}_{f}={1.22*10}^{10}\times 70\times ({\frac{6.94}{150})}^{1.852}\times {76.2}^{-4.87}=3m$$

The total dynamic head TDH could be expressed as Eq. (2)27:

$${\mathrm{TDH }} = {\mathrm{ H}}_{{{\mathbf{st}}}} + {\mathrm{ H}}_{{\mathrm{d}}} + {\mathrm{H}}_{{\mathrm{f}}} + {\mathrm{H}}_{{\mathrm{p}}}$$
(2)

$${\mathrm{TDH}} = {47} + {5} + {3} + {1}0.{2} = {65}.{2}\;{\mathrm{m}}$$

The appropriate pump must be chosen from the Pump efficiency schemes using discharge (25 m3/h) and TDH (70 m). Schemes recommended a pump with 10 hp and 8 stages.

The required hydraulic power HP (W) could be expressed as Eq. (3)22.

$$HP=\frac{Q\times \rho \times g\times TH}{3600}$$
(3)

where HP = hydraulic power (W), Q = discharge (m3/h), ρ = water density (1000 kg/m3), g = Gravity acceleration (9.81 m/s2).

Inverter: The appropriate inverter for the pump can be chosen as follows28: Inverter power ≥ motor power.

$${\mathrm{Inverter}}\;{\mathrm{power}} \ge {\mathrm{motor}}\,{\mathrm{power}}.$$

Lorentz solar inverter 15 kw will be used. From inverter data sheet (MPPT voltage 500 to 600 V).

### Sizing of PV panels

The panels output drops during the morning, cloudy, and sunset periods. The total power needed to operate the pump Multiply by 1.25 determines the size of the PV panels29. Solar panel’s power = 1.25 × 10 hp = 12.5 hp = 12.5 hp × 745.7 W = 9321 W. Panels number = 9321/26036 panels.

\begin{aligned} {\mathrm{Solar}}\;{\mathrm{panel}}{\hbox{'}}{\mathrm{s}}\;{\mathrm{power}} = & 1.25\; \times \;{\mathrm{pump}}\;{\mathrm{motor}}\;{\mathrm{power}} \\ = & 1.25 \times 10\;{\mathrm{hp}} = 12.5\;{\mathrm{hp}} = 12.5\;{\mathrm{hp}} \times 745.7\;{\mathrm{W}} = 9321\;{\mathrm{Watts}} \\ \end{aligned}
$${\mathrm{Panels}}\;{\mathrm{number}} = {\mathrm{The}}\;{\mathrm{overall}}\;{\mathrm{Panels}}\;{\mathrm{power}}/{\mathrm{The}}\;{\mathrm{power}}\;{\mathrm{of}}\;{\mathrm{one}}\;{\mathrm{panel}} = {{9321}}\;{\mathrm{w}}/260\;{\mathrm{W}} = 35.{{85}}\;{\mathrm{panels}} \approx {{36}}\;{\mathrm{panels}}$$

The type of connection between panels (parallel or series) depends on the voltage and current that the inverter needs to work efficiently. As a result, according to the Lorentz inverter datasheet, the MPPT voltage range is 500 to 600 V. Therefore, every 18 panels were connected in series to form two arrays. Voltage of each array = 18 × 30.5 = 549 V.

$$\mathrm{Voltage\, of\, each\, array}=18 \times 30.5= 549\mathrm{ V}.$$

The two sets of arrays were connected in parallel in order to give a current = 2 × 8.53 = 17.06 amps. Figure 1 shows the electric diagram for a PV water pumping system, the electrical components, and connection methods.

### System installation and components

PV cells are the fundamental building blocks of almost all PV modules. To increase the voltage, panels are connected in series. Several of these strings of cells can be connected in parallel to increase current. Implemented photovoltaic system (PV) consisting of two array groupings, each of which is made up of 18 modules connected to a metal structure in series whose tilt angle can be changed manually as shown in Fig. 2. To give the inverter a current of 17 A and 549 V, two groups were linked in parallel. The type of module used in these experiments is Renesola (JC260M-24/Bb) 260 W. The datasheet for the module is illustrated in Table 2.

### Inverter

The inverter converts the DC power produced by the PV modules to the AC power used to drive the pump motor. It also adjusts the output frequency in real time based on the prevailing irradiation levels, and it works with MPPT (Maximum Power Point Tracking) technology to maximize power output at all irradiation levels. Table 3 illustrates the Lorentz inverter data sheet.

The pumping unit is made up of three key components: a three-phase alternating current motor, a multistage submersible pump, and a deep well. Table 4 shows the technical data about the Vansan VSM 6/10 submersible 3-phase electric motor. The Vansan VSP-SS 06030/08 centrifugal submersible pump technical data is presented in Table 5, and the performance curves are shown in Fig. 3.

A pyranometer was used to measure solar radiation, as shown in Fig. 4. It is made up of a glass dome, a thermopile sensor, and instrument housing. Across a wide wavelength range, incoming radiation is virtually totally absorbed by a blackened horizontal surface. According to the temperature difference between the black absorbing surface and the instrument enclosure, the detector produces a very small voltage. This is on the order of 10 microvolts per square meter (W). The calibration process determines the specific sensitivity of each pyranometer, which is used to translate the output signal in microvolts into the total irradiance in W/m2. The sensitivity of the used KIPP&ZONEN pyranometers is (12.11*10–6) V/Wm-2 and (14.11*10–6) V/Wm−2. To convert the output signal of pyranometer in mV into global irradiance in W/m2 the Eq. (4) was used.

$${\mathrm{I}}_{{\mathrm{R}}} = \frac{mV}{{1000 \times {\mathrm{ pyranometer\,sensitivity}}}}$$
(4)

where IR: insolation, W/m2, Pyranometer sensitivity: (12.11*10–6) V/Wm-2, and (14.11*10–6) V/Wm-2, mV= Pyranometer output.

### PV Panels temperature

The solar panels’ temperature was measured every hour from sunrise to sunset with a digital infrared thermometer, and Table 6 illustrates the infrared thermometer datasheet. Also, a thermocouple thermometer was used to measure temperature, and Table 7 illustrates the infrared thermometer datasheet.

### PV system current and voltage

A UNI-T UT39C multimeter was used to measure the PV system’s output voltage and current. A multimeter, commonly referred to as a Volt/Ohm meter, is an electronic measurement device that incorporates multiple features into a single device. Voltage, current, and resistance measurements are among the capabilities of a typical multimeter. The digital multimeter’s datasheet is displayed in Table 8. Ohm's law was used to determine the power (Eq. 5).

$${\mathrm{P}}_{{{\mathrm{DC}}}} = {\mathrm{I}}_{{{\mathrm{DC}}}} \times {\mathrm{V}}_{{{\mathrm{DC}}}}$$
(5)

where PDC: PV system output power, W; IDC: current, ampere; VDC: voltage, volt.

### Flow meter

The 4-inch, 10-bar flow meter (ISO 4064 class B) is a device used to continuously measure, record, and display the volume of water passing through the measurement transducer under metering conditions. The flowmeter datasheet is illustrated in Table 9.

## Results and discussion

### The intensity of solar radiation

The average daily sunshine hours across Egypt are about 9–11 h, so Egypt receives abundant solar energy with an annual direct solar radiation of about 2,000–3,200 kWh/m2/year30. Measurements of the intensity of the solar radiation were made using a pyranometer and digital solar radiation meter. Figure 5 shows hourly-average solar radiation (W/m2) for the months of December 2020, March 2021, and June 2021. Results showed that the highest values for solar radiation reached 976.5, 1067.3, and 981.0 W/m2, respectively, at 12:00 p.m.

Daily average solar radiation is shown in Fig. 6, which illustrates the increase in daily average solar radiation in June (805.7 W/m2) compared to March (792.7 W/m2), and December (755.7 W/m2). It is noticeable that the intensity of solar radiation increases on sunny days and decreases on cloudy days, where clouds disperse the sun's rays. Also, the intensity of solar radiation varies with the earth`s circulation around its orbit and around the sun, where the radiation decreases in the early morning and winter (Dec.) because the altitude angle of the sun is small and the radiation penetrates a long distance of the atmosphere, while in the noon and summer (June) the intensity of the solar radiation increases because the altitude angle becomes large. and the radiation is penetrating the atmosphere over a short distance31.

### PV panels output current (Dc)

The current produced by the panels is directly and uniformly affected by solar radiation32. Where the produced current increases when radiation increases and decreases when solar radiation decreases. Figure 7 illustrates the correlation between direct current (DC) generated by solar panels and the intensity of solar radiation in March and June, respectively. The direct current (DC) produced by solar panels is positively affected by intensity of solar radiation as shown in Fig. 8.

### PV panels output voltage (VDC)

The hourly average voltages that were delivered by the PV generator are shown in Fig. 9 for the months of December, March, and June. It is clear that December has the highest voltage values of all months, followed by March, and the lowest values in June. It is observed that the highest months in solar radiation and temperature were the ones with the lowest output voltage from PV systems, which may be affected by high temperatures in the summer and a clear atmosphere. It is also apparent that the voltage is not significantly affected by solar radiation33 as illustrated in Fig. 10.

### PV panels power (PDC)

The DC power produced by solar panels is affected by the intensity of solar radiation. Figure 11 illustrates the correlation between DC power and irradiance in March and June, respectively. Figure 12 depicts the positive relationship between solar radiation and the electrical power generated by the panels, which is based on the positive relationship between radiation and electrical current. Figure 13 displays the daily-average electric DC power generated by PV panels for the months of December, March, and June. It is observed that March has the highest power values all day, followed by June, and the lowest values are in December. It’s clear that June has the highest month of solar radiation, but in this month the power was less than March because the module temperature in June was higher than March, so the efficiency in March was greater than June33.

### Hydraulic power that is delivered by the pump (H.P.)

It turns out there is a direct correlation between hydraulic power and the intensity of solar radiation, as shown in Fig. 14 for March and June. Experiments have revealed an increase in hydraulic power as the intensity of solar radiation increases. Figure 15 illustrates the positive relationship between solar radiation and electric power. The daily average values of hydraulic power in December, March, and June reached 3795.2, 4312.3, and 4207.4 W, respectively.

### Pump flow rate (discharge m3/hr)

The intensity of solar radiation (IR) has a significant impact on pump discharge (Q)34. The correlation between flow rate and intensity of solar radiation is illustrated in Fig. 16 for March and June. Figure 17 shows the hourly average pump discharge through three months. The hourly average flow rate in December, March, and June reached values of 18.2, 22.2, and 22.8 m3/h. The number of operating hours of the pump were 7, 7, and 8 h, and the amount of water that was pumped during the day was 129, 164.1, and 181.8 m3/day, respectively.

### Temperature of PV panels at different seasons

Environmental factors surrounding solar panels directly affect solar panel production, with temperature having the greatest impact on panel efficiency35. Where the panel heats up and the performance of the panel degrades as a result of the increased air temperature. Figure 18 shows the average temperature of the panels with values 35.7 °C, 39.9 °C, and 44 °C in December, March, and June, respectively.

### Effect of PV panels temperature on its efficiency

The efficiency of solar panels is negatively affected by temperature increasing as shown in Fig. 19. So, the performance in a high-temperature month such as June is lower than the performance in a moderate-temperature month such as March. The efficiency of panels has the lowest value at 12:00 pm because at noon the temperature has the highest value through the daytime. It’s noticeable from Fig. 20 that when temperature increases, the panels efficiency decreases, and when the temperature reaches the highest value during the day 47.4 °C at noon, the panels efficiency decreased to the lowest value 12.8%. also, it’s clear that when the temperature increases by 1 °C the panels efficiency ηpanels decreases by 0.48%. Previous studies found a decrease in efficiency of 0.5%/1 °C36.

### Variable frequency drive (Inverter)

The inverter can be considered the heart of the system because of its importance. It is an electronic device that converts the direct current (DC) produced by solar panels to a suitable alternative current (AC) to operate the pump. It is also controlling the pump, regulating its work, and protecting it from changes in the current produced by solar panels. The inverter's performance was studied by studying several factors, such as its frequency, output power, and efficiency.

### Inverter frequency (Hz)

The inverter frequency was directly affected by the direct current produced by solar panels37, as shown in Fig. 21. While the highest current was in March, the average frequency reached 46.6 Hz, and the lowest current was in December, the average frequency reached 44.6 Hz. where, the average frequency value was 46.4 Hz in June as shown in Fig. 22. The highest frequency values were at 12:00 noon, that reached 47.4, 50, and 48.5 Hz in December, March, and June, respectively, as seen in Fig. 23.

### Inverter output power (AC power)

The values of electric AC power delivered by the inverter are positively dependent on the values of input electric DC power and inverter efficiency38. The correlation between AC and DC power is illustrated in Fig. 24 for March and June. The highest DC power value was in March, and the lowest value was in December. Therefore, it is noticeable from Fig. 25 that the highest AC power values were in March, and the lowest values were in December. Where The average AC power values reached 6416.2, 7119.7, and 6748.6 W in December, March, and June, respectively.

### Inverter efficiency

As illustrated in Fig. 26, direct current delivered by solar panels has a direct impact on inverter efficiency. Where the inverter should be supplied with the appropriate voltage and the appropriate direct current to operate it efficiently38. While the average direct current values in December and March reached 12, and 13.64, amperes, respectively. Therefore, the average inverter efficiency reached 89.64%, and 90.43%, respectively, as shown in Fig. 27.

### Pumping unit efficiency (ηpump)

The average pumping unit efficiency (ηpump) for different months is shown in Fig. 28 where the efficiency (ηpump) values in December, March, and June reached 63.5%, 67.6%, and 68.7%, respectively. It’s clear that the pumping unit efficiency (ηpump) is affected by the intensity of solar radiation IR, panels temperature, and AC power (PAC). Figure 29 illustrate the correlation between pumping unit efficiency and solar radiation, and Fig. 30 illustrate the correlation between pumping unit efficiency AC power.