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The main purpose of this paper is to design and model a water-pumping sys tem using a submersible multi-stage centrifugal pump driven by a three-phase induction motor. The system is intended for pumping water to the surface from a deep well using three power supply systems: a general network, a photo-voltaic (PV) system, and a PV system with a battery bank. These systems are used to compare two three-phase induction motors —namely, a motor with a drive and another one without a drive. The systems dynamic models are simulated in MATLAB/Simulink and the results compared with the manufacturer’s data for validation purposes. The simulation results generally show system dynamics and expected performance over a range of operation.

Of the several different types of water pumps commercially available, the two most common ones are centrifugal pumps and positive displacement pumps. Centrifugal pumps use a rotating impeller to generate a centrifugal force that sucks the water while the impeller directs the water to the pump outlet with high velocity and pressure [

Both centrifugal and positive placement pumps are used for the same purpose, which is to reduce downtime from main events and to continuously move water from point A to point B [

Especially in rural areas and places that are underserved by national or regional grids, photovoltaic water pumping systems (PVPSs) have been shown to have great promise for providing solar energy [

Water pumping systems operated by direct coupled DC and AC solar-run water pumps are being used in many places around the world. The key parameters to determine the viability of these systems are as follows: adequate amounts of solar radiation based on geographical location; daily water needs during maximum usage periods; static level measurements; and piping requirements, as determined by pressure drops, height of tanks, and maximum drawdown [

PV modules can be linked in parallel and in series to operate pump-motor sub-systems. These systems need power in order to generate the required water flow and pressure [

Rising energy needs have occurred at the same time as increasing pollution and subsequent concerns over the environment. The cost of energy generation is also a factor in discussions around power generation options and alternatives, including legacy (oil, gas, diesel, etc.) and renewable (solar, wind, water, etc.) options. The issue of GHG emissions is also a factor. The trend to adopt renewable energy options as alternatives to legacy energy resources is growing exponentially, particularly with regard to solar energy options. Although the early solar photovoltaic (PV) energy converters lacked efficiency (5% - 6%) and were quite expensive to build and operate, newer PV arrays have achieved 15% - 16% and incur much lower costs [

Making a choice from the wide variety of Photovoltaic Pumping System (PVPS) options can be contingent on water flow rate requirements, reduced downtime, low costs, height of discharge, quality of pumped water, and high performance and durability [

There is a growing interest in PV water pumping from deep wells. In such cases, battery storage could be added or, alternatively, multi-stage centrifugal submersible pumps with three-phase motors could offer more advantages [

Centrifugal Pump | Positive Displacement Pump |
---|---|

High pumping water volume | Low pumping water volume |

Low maintenance required | Frequent maintenance required |

High efficiency that is degraded when the pump deviates from Rated speed | The pump is able to operate efficiently over a wide speed range away from the Rated speed |

The pump can pump water with low solar radiation by using PVPS | Requires high starting torque to operate by PVPS |

The pumping flow rate varies according to the pumping head | The pumping flow rate is approximately equal, regardless of the pumping head |

As the water viscosity increases, the flow rate decreases | As water viscosity increases, flow rate also increases |

Widely used in PVPS | Rarely used in PVPS |

Submersible pumps are not only more efficient than jet pumps, but their basic operational principle has remained the same even through years of continuous constructional and operational evolution. The submersible pumps used in electric submersible pump installations featuring multi-stage centrifugal pumps operate in a vertical position [

Another feature of submersible pumps is that they are completely submerged in the surface of the water and pump water with the help of their sealed body. The main advantage of this approach is avoiding pump cavitation. Other pumps have problems associated with high elevation differences between the pump and fluid surface. The issue with the impeller is that it increases the surface pressure, which forces water to move [

There are two main kinds of electric motors available for solar water pumping systems: AC (Alternating Current) induction motors and DC (Direct Current) motors. When choosing the most appropriate motor, factors such as size, efficiency requirements, price, reliability of the system, and availability are taken into consideration.

DC motors are a more specialized and expensive product, since they are used on a much smaller scale than AC induction motors. DC motors are also not suitable for high-powered applications (i.e., higher than 7 kW). On the other hand, AC induction motors are widely available and relatively low-cost. The most widely available motor for industrial use is the squirrel cage induction motor, which has low manufacturing costs, robust construction, adaptability to submersible and flameproof applications, and the ability to accept a wide range of voltage/power ratings, all of which makes the AC induction motor an obvious choice [

A comparison [

A three-phase induction motor is an electromechanical device or motor that converts electrical energy into mechanical energy. The main benefit of using this

DC Motor | AC Motor |
---|---|

Requires commutator and brushes, making the motor bulky and heavy | Does not require commutator or brushes |

High cost | Low cost |

Requires frequent maintenance | Requires less maintenance |

Requires battery or inverter | Battery not required |

type of motor is that it does not require any starting device to operate, since it is a self-operated or self-induction motor [

Three-phase induction motors have two major parts—a stator and a motor. The stator features a three-phase winding circuit comprising a number of slots and is connected to a three-phase AC source. The rotor has a laminated core which holds conductors like copper and platinum. The slots are present for holding the entire assembly, but they are placed at a slight angle from the main axis, so there is no effect on the RPMs and magnetic field of the motor [

Three-phase induction motors have been shown to be a viable alternative in commercial water pumping systems. There are two stages in SPV array-fed water pumping systems that employ induction motors. The first stage restrains the DC-DC boost converter duty ratio in order to extract the solar PV array’s maximum power. The second stage uses a controller to handle Voltage Source Inverter (VSI) switching pulses [

The VSI voltage source inverter is more popular than the CSI. The VSI is usually applied in systems that use pulse-width modulation (PWM) speed control in three-phase AC motors. The system uses purpose-designed LSI circuits for creating PMW, utilizing sine-wave modulation. Variable-speed induction motor drives have been employed in a number of industry usages, with PWM inverters generally being the first choice on account of their optimal control level in frequency, harmonics and control voltage [

Specifications for the pump and motors to be used in the projects:

• Submersible pump power: 7.5 hp

• Well depth: 50 m

• Total pipe length: 66 m

• Pipe diameter (for transporting water): 2 inches

• Motor voltage: 380 V

• Motor power: 5.5 kW

• Motor frequency: 50 Hz

The system in this paper was designed as shown in

Total dynamic head (TDH) is a major factor that determines the optimal performance of submersible pumps. If the TDH of the system increases, the volume of the discharge will be reduced proportionally until it stops [

T D H = P l + V r + F l (1)

where

P l = Pumping level = 50 m = 164.04 ft

V r = Vertical rise = 3 m = 9.84 ft

F l = Friction loss, which can be defined as:

F l = [ L t + ∑ ( n f ⋅ f e ) ] × F h 100 (2)

where

L t = Total length of pipe in the system = 66 m =216.54 ft

f e = Fittings, in feet, of pipe, which has a standard value in feet, depending on the pipe’s diameter and type = 5

n f = Number of same fittings in the system = 2 elbows

F h = Friction loss of head per 100 feet of pipe, depending on the pipe’s diameter and flow rate. In this system, which has a 2-inch diameter and an 18 m^{3}/h or 80 gpm flow rate, friction loss is equal to 10.9 [

By substituting the values in Equations (1) and (2), the TDH is:

T D H = 164.04 + 9.84 + [ 216.54 + 2 × 5 ] × 10.9 / 100 = 198.58 f t = 60.53 m

As we require a submersible pump that will deliver 18 m^{3}/h to a water tank with TDH 60.5 m and 7.5 HP, the Grundfos SP 17-8—12AB6908 pump, which uses the performance curves of Grundfos (as shown in

^{3}/h are shown for the motor power P_{1} =5.3 kW and the shaft power P_{2} = 4.26 kW, respectively. From the above values, the efficiency of the pump was calculated as 69.6%, while the total efficiency of the system was 56%.

The moment of inertia was calculated by choosing the pump size (6") and inserting the number of stages (8) using Equation (3) [

J p = ( 4.0 + n × 4.1 ) × 10 − 4 = 0.0037 [ kg ⋅ m 2 ] (3)

where

n = number of stages = 8.

According to the above data from

τ shaft = P shaft ω = 4265 304.1 = 14.03 [ N-m ] (4)

where P shaft is the power of the pump shaft (P_{2}) in [W] and ω = 2 π n [ rpm ] / 60 is the angular velocity of the shaft in [rad/s].

Earlier studies helped to determine the dimensions of our PV system [^{2} and drops to 600 w/m^{2} in 1.5 seconds. In addition, the temperature was kept constant at 25˚C.

We can use MPPT in order to achieve the following:

- Ensure the system functions at or near MPPT conditions if the environmental conditions are in some way altered or in broad variations of conditions.

- Ensure efficiency in conversion.

- Ensure that the output interface has compatibility features that match the battery-charging needs [

Several different MPPT algorithms can be employed for obtaining maximum power in PV systems. Among these is the perturbation and observation (P&O) approach. We use the P&O method in the present study due to its simplicity and ease of implementation. For P&O algorithms, the PV system operating voltages increment at lesser values while also observing PV system power extraction. So, when the system’s extracting power is lower compared to the earlier observed PV power, the system’s operating voltages are raised by raising the converter’s duty cycle. Conversely, when the system’s extracting power is higher compared to earlier observed PV power, the system’s operating voltages are reduced by reducing the converter’s duty cycle [

The DC/DC boost converter is another type of solar PV water pumping system for power conversion. As the name describes, boost converters boost PV voltage levels, such that V DC indicates DC voltage that has been boosted or increased. Boost converters get maximum power out of solar PV arrays through controlling their duty ratios in Insulated Gate Bipolar Transistor (IGBT) inverters.

A boost converter’s duty cycle (D) can be formulated as follows:

D = 1 − V i n ( min ) × η V o = 1 − 350 × 0.9 390 = 0.19 (5)

In this calculation, V i n ( min ) denotes minimum input voltage and V_{o} expresses output voltage, while η indicates converter efficiency [

Based on this formulation, we can calculate a boost converter inductor as shown in Equation (6):

L ≥ V i n ( min ) × D Δ I l × f s = 350 × 0.19 0.3 × 15000 = 0.48 mH (6)

In this calculation, f s denotes switching frequency, while Δ I l expresses permissible current ripple, estimated to represent 20% - 40% of output current.

We can estimate the DC-link capacitor through the following calculation [

C 1 ≥ I o ( max ) × D f s × Δ V C (7)

Here, I o ( max ) vindicates maximum output current and Δ V c denotes capacitor voltage ripple, estimated to be [

Δ V c = 1 % to 5 % of V C = 0.01 * V o = 0.01 * 390 = 3.9 V (8)

∴ C 1 > 8.99138 × 10 − 5 F

In this simulation, the capacity was chosen to be: C 1 > 8.99138 × 10 − 5 × 3 = 2.697 × 10 − 4 F . The value of the capacity was multiplied by 3 because the lower values of the capacity show instability in the system, especially Model 4.

An IGBT is used for built-in two-phase DC to three-phase AC conversion, with a PI controlling the pulse.

The battery bank comprises a lead-acid battery featuring 360 V as nominal voltage and rated capacity at 40 Ah.

We use a three-phase transformer for boosting voltage output (240 V up to 380 V) from our IGBT inverter to our LC filter.

Different pump models (centrifugal, impulse, etc.) can be used based on the unit’s head and water discharge. In centrifugal pumps, water flow rate is generally proportional to motor speed, resulting in consistent and smooth head operation. The decision on the right motor for a given job is dependent in large part on the pump’s efficiency level and relevant hydrological data [

The simulation used two different induction motors: a standard motor without a drive, and an induction motor featuring a PWM VSI drive (380 3-phase AC Volts—50 Hz). In both of these induction motors, the torque was identical, with the mechanical load passing from 14 N.m. to −14 N.m. This led the electromagnetic torque into stabilization almost immediately after −14 N.m [

The simulations in this study were performed using MATLAB/Simulink, as this software can work with extremely complicated simulations [

First, the system is simulated using a 380 V ideal AC voltage source.

From the simulation of the dynamic system model, the following results were found and plotted.

torque of the pump [N-m] versus time, in sec. The results show the shaft power and adjusts its value accordingly. The total torque of the pump is calculated to be 14 [N-m].

^{−3} [m^{3}/sec] and 318 [lpm], respectively. This is almost the actual calculated value. From the figure, it can be seen that the pump starts to deliver the water after almost 1.5 sec due to the pressure of the check valve and the speed of the shaft.

In this model, an induction motor with no drive to power the pump has been used. To use the motor in MATLAB/Simulink, the high value of resistance has to be connected in parallel with the motor or the transformer to make the simulation run, as shown in

From the simulation of the dynamic system in Model 2, the following results were found and plotted.

the figure. The total power of the shaft is 5.16 kW.

^{−3} [m^{3}/sec] and 320 [lpm], respectively, which then increases to 5.85 × 10^{−3} [m^{3}/sec] and 350 [lpm], which is slightly higher than the actual calculated value.

From the simulation of the dynamic system Model 3, the following results were found and plotted. The MPPT algorithm was used to obtain better power output from the PV system, as shown in ^{2} but drops to 6.5 kW if irradiance decreases to 600 W/m^{2}.

and adjusts its value accordingly. The total torque of the pump is 15 [N-m], which then decreases to 14.5 [N-m].

^{−3} [m^{3}/sec] and 325 [lpm], respectively, which is slightly higher than the actual calculated value.

In this model, the induction motor has been used without a drive to initiate the pump. The high value of resistance has to be connected in parallel with the transformer to make the simulation run, as shown in

The following results were calculated and plotted based on the simulation of the dynamic system for Model 4.

First, the output power of the PV array was not as stable as that in Model 3. At an irradiance of 1000 W/m^{2}, the PV output power was around 10.5 kW. However, at around 1 sec, it dropped sharply to 3.5 kW, and when the irradiance reduced to 600 W/m^{2}, the PV output power fluctuated around 6 kW. Moreover, at an irradiance of 1000 W/m^{2}, the PV voltage was unstable, fluctuating in a wide range between 250 to 425 V, whereas the PV voltage was in range of 350 to 400 V when the irradiation was 600 W/m^{2}.

Furthermore, ^{2}, which causes a shortage in the power to operate the system appropriately.

^{−3} [m^{3}/sec] and 364 [lpm], respectively, which exceeds the actual calculated value.

The following results were intended and plotted based on the simulation of the dynamic system Model 5. ^{2}, the PV output power was around 10.5 kW, and at an irradiance of 600 W/m^{2}, the power dropped sharply to 6.5 kW. Moreover, at both irradiance levels, the PV voltage was stable at around 325 V.

shaft power and adjusts its value. The total torque of the pump starts at 15 [N-m] and then decreases to 14.5 [N-m].

^{−3} [m^{3}/sec] and 325 [lpm], respectively, which is somewhat higher than the actual values.

^{2} the radiation stabilizes at 7.2 kW. However, when the radiation reduces to 600 W/m^{2}, the power increases and stabilizes at 8.9 kW.

boost converter, the battery bank and IGBT inverter are feeding the induction motor.

The following results were intended and plotted based on the simulation of the dynamic system model 6.

is stable at both radiations. Specifically, at an irradiance of 1000 W/m^{2}, it is around 10.6 kW, while at an irradiance of 600 W/m^{2}, the PV output power drops sharply to 6.55 kW. In addition, the PV voltage increases smoothly from around 320 V to 343 V. ^{2}. However, when the radiation is 600 W/m^{2}, the motor rotor speed increases to around 3060 [rpm].

^{−3} [m^{3}/sec] and 320 [lpm] and then increases to 5.84 × 10^{−3} [m^{3}/sec] and 350 [lpm]. The increase is due to the rise in the operating voltage, which in turn leads to an increase in the motor rotor speed.

^{2} radiation, it stabilizes at -5.63 kW. However, when the radiation reduces to 600 W/m_{2}, the power decreases and stabilizes at -10 kW.

Six systems of submersible water pumps driven by a PWM inverter and three-phase induction motor were modeled and simulated in MATLAB/Simulink. The six models were then tested and compared. The following points show the unique designs of the six models:

1) Induction model with a drive operated using a general network.

2) Induction model without a drive operated using a general network.

3) Induction model with a drive operated using a PV system.

4) Induction model without a drive operated using a PV system.

5) Induction model with a drive using a PV system with a battery bank.

6) Induction model without a drive using a PV system with a battery bank.

Based on the simulation’s outcomes, there were slight differences in the results between the calculated values stated in the manufacturer’s data and those from the simulations. These differences can be caused by factors such as the effects of fluid inertia and moment of inertia of the motor on the pump, friction loss, and the check valve effect. Moreover, significant conclusions are described below:

• Models 1 and 2 were considered as reference models for the other simulations. Through these models, the performance of the induction motor and submersible water pump were optimized based on the ideal operated source, which is the general electrical network with 380 V.

• Models 3 and 4, which operated using a PV system, the performance of the system indicated that the induction motor with a drive gave better results than the one without a drive. However, the system with a drive gave lower voltage, which affected the system over a period of time.

• Models 5 and 6 operated using a PV system with a battery bank. Although one model had a drive and the other did not, both results were acceptable when compared with the reference models. However, the model with the drive indicated that the battery was discharging, whereas the model without a drive showed the battery was charging.

Finally, the results indicated that the PV system with the battery should be used to operate similar models due to the stability in the voltage and the power of the system. Overall, for comparing results in simulations and cases, MATLAB/Simulink is a highly useful tool.

The authors thank the Libyan government for financial support of this research.

The authors declare no conflicts of interest regarding the publication of this paper.

Alkarrami, F., Iqbal, T., Pope, K. and Rideout, G. (2020) Dynamic Modelling of Submersible Pump Based Solar Water-Pumping System with Three-Phase Induction Motor Using MATLAB. Journal of Power and Energy Engineering, 8, 20-64. https://doi.org/10.4236/jpee.2020.82002

1) Friction loss in equivalent number of feet of straight pipe [

2) Frictional loss in feet of head per 100 feet (30.48 m) of pipe [