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This paper is about the optimized design and analysis of two solar water pumping systems in which one of the systems is designed with a battery bank and other with a cylindrical water tank for a selected site in Pakistan. The design, sizing, cost analysis and steady state analysis of the proposed systems were done in HOMER and dynamic analysis of the designed system with battery bank was performed in MATLAB/Simulink. The simulations performed in HOMER involved proper mapping of the loads which helped to evaluate the PV panel requirement, inverter rating, batteries (in case of battery based solution), modeling of water tank as a deferrable load (in case of solution based of water tank) and detailed cost analysis for a life time of 25 years. To verify the design of the solar water pumping system with battery bank, a simulation in MATLAB/Simulink for study of dynamic behavior of the overall system was performed which involved mathematical modeling of a PV panel, buckboost converter, inverter, battery bank and motor/pump, a perturb and observe maximum power point tracking algorithm based control system. Analysis was conducted based on the economic results that indicate designed solar water pumping system with water tank would be a cheaper solution as compared to solar water pumping system with a battery bank. This work can be taken as a case study for the understanding and optimized designs of solar water pumping system with battery bank and with cylindrical tank in Pakistani conditions.

Pakistan is primarily an agricultural economy which contributes for about 22.2% for overall GDP [^{3} per capita in 1950s. It has shrunk to around 1000 m^{3} per capita currently [

To combat this shortage of water supply for irrigation, water pumps and tube-wells are installed and since the scenario of electricity in country is not great as a short fall of 5000 MW is faced by the country [

In Pakistan, there is a huge potential for renewable which is around 167.7 GW [^{2}/day [

Keeping in view all the scenarios discussed above, it suggests a direction for implementation of running water pumping systems on renewable sources instead of fossil fuels in Pakistan. The primary reasons are as Pakistan is not a country rich in fossil fuel resources along with its environmental hazards and Pakistan is rich in solar resources which can be tapped to overcome energy requirements for running water pumps.

Choudhary et al. has discussed evolution [

There have been many methods used to design and optimise a solar water pumping system. These methods can be classified into two broader categories Manual Formulation Methods and Computer based Methods.

Over the time many manual computation methods have evolved. They are simple and cheap to implement. One such method [

Computers based method is based on computer simulations but these software are computation intensive. There are two types of analysis which are done using computer based software of a solar water pumping system. One is steady state analysis and other is dynamic analysis of the designed system. In steady state analysis software perform calculations related to sizing of a PV system keeping in view a specific interval of time; they also help to determine the power generated from the source, load mapping and different parameters related to battery and power converter requirements [

A lot of work is available in literature for conducting steady state analysis of the Solar systems. As we have chosen HOMER for steady state analysis, the work regarding this in the literature is discussed further. Chaichan et al. [

For dynamic modeling a lot of work is available in literature but the scope of this paper is limited to dynamic modeling in MATLAB/Simulink. In [^{2} and an overall efficiency of 71% was obtained at solar insolation of 400 W/m^{2}. A solar water pumping system is modeled in MATLAB/Simulink [

Keeping in view the above literature review, while designing and sizing of a solar water pumping system for this work we chose HOMER for steady state analysis as it gave the most consistent and reliable sizing results and was found to be most widely used software. For dynamic analysis of the designed system MATLAB was chosen because as per literature many results of dynamic analysis from MATLAB were compared with manufacture’s data and they found simulation results to be in line with manufacturer’s data which not only verified the results but also suggest MATLAB to be a good option for dynamic analysis of the designed solar water pumping system.

Since the MATLAB blocks do not allow large set of data for irradiance and temperature to be processed at a rapid speed as they are more complex and reduce computation speed for analysis of large set of input data. To overcome this issue and make our system simpler to increase computation speed, mathematical modeling of different components of the overall solar water pumping system used in our designed system was done in MATLAB namely PV Panel, MPPT, Buck-Boost Converter, Battery Bank, Inverter and water pump using 3 phase induction motor.

A suitable site was selected where a solar water pumping system can be implemented for that purpose an agricultural area known as “Mustafa Research Farms” which is located at Wasti Jiuan Shah, Tehsil Sadiqabad, Rahim Yar Khan, Pakistan. The coordinates of location are 28˚14'24.0"N 69˚37'16.0"E [

The Mustafa Research Farms can be seen in

The solar insolation details along with clearness index can be seen in ^{2}/day and its clearness index varies in the range of 0.601 to 0.69.

The data collected from the selected agricultural site for motor/pump load calculation is as follows and the yearly operation of the motor is summarised in

Months | Operation of Motor/Pump | |
---|---|---|

Days of full operation (24 × 7) | Days of idle operation | |

January | First 7 days of the month | Next 24 days of the month |

February | First 10 days of the month | Next 18 days of the month |

March | First 11 days of the month | Next 20 days of the month |

April | First 14 days of the month | Next 16 days of the month |

May | First 17 days of the month | Next 14 days of the month |

June | First 20 days of the month | Next 10 days of the month |

July | First 22 days of the month | Next 9 days of the month |

August | First 24 days of the month | Next 7 days of the month |

September | First 18 days of the month | Next 12 days of the month |

October | First 14 days of the month | Next 17 days of the month |

November | First 10 days of the month | Next 20 days of the month |

December | First 0 days of the month | Next 31 days of the month |

Water level = 25 ft = 7.62 m

Dynamic head = 35 ft = 10.668 m

Water flow requirement = 2 cusec (cubic feet/sec) = 204 m^{3}/hr = 898.2 gpm

The brand selected for the water pump/motor is Wilo, it has an online tool [

Now, the next step was to map the load details in HOMER as per the motor operation table summarized in

After the simulation was performed in HOMER, the sizing results which came are summarised in

number came out to be 450, DC bus voltage 360 V, the inverter requirement came out to be 16.7 kW and for that purpose an SMA Sunny Tripower 20000TL-30 [

The overall proposed system can be seen in

The economic analysis of the overall proposed system over its life cycle of 25 cycles was also done using HOMER. The cost summary of the overall proposed system is summarised in

the overall system is $273,570, the levelized cost of energy of the system comes out to be $0.48 along with operating cost which is $5692.37 per year.

As per cash flow over the life cycle of 25 years for the proposed system which can be seen in

The dynamic modeling of the proposed system was done in MATLAB/Simulink. Mathematical modeling for different design components was done so that speedy simulation with a much overall simplified system can be done. The model of the proposed system can be seen in

The data was simulated for the first seven days of the April, when the motor is in operation to evaluate the dynamic behavior of the proposed solar water pumping system. The solar data which include solar irradiance and temperature for the first seven days of April which makes it a total simulation for 10,080 minutes can be seen in ^{2} and temperature varied from 25˚C to 49.5˚C during a week of simulation.

Simulation results are split into two figures (A and B) for the proposed system which can be seen in

with the varying irradiance and temperature. The voltage output varied from 0 to a maximum of 658 V and current varied from 130 A to 0 A. This output in next step is fed to the buck-boost converter which is controlled by the duty cycle which in turn is controlled by Perturb and Observe MPPT technique block. The voltage output from buck-boost converter varies from 0 to 987 V and current output varied from 0 to 87 A.

The initial SOC (State of charge) of the battery was 80% which declined to 79% after 1st discharge varied between 84% and 100% afterwards throughout the simulation as can be seen in

V during 1st discharge but other than that it varied from 385.6 V to 379.5 V. The momentarily pointed peak in battery voltage at the top as it reaches an SOC of 100% is because during the charging it takes into consideration the battery’s internal resistance but once it stop charging since battery has reached 100% of

SOC it no longer takes into consideration the battery’s internal resistance hence, there is a slight decrease in overall battery’s output voltage.

The voltage output of inverter varied from +326.6 V to −326.6 V peak as can be seen in

The detailed simulation results for the seven day simulation from April month of the motor/pump can be seen in

Before proceeding with the design the first step was to determine an optimum size of a tank which could be large enough to keep a storage of water for 1 day. So for this flow rate for 1 day was calculated as can be seen below.

204 m^{3}/hr × 24 = 4896 m^{3}

So flow rate for one day is 4896 m^{3}. Hence, if the motor runs for 5 hours each day during active days of the month (when continuous water flow is required). The flow rate required of the motor is 4896/5 = 979.2 m^{3}/hr.

Hence, using online source of Wilo pump [

After the size of the motor was evaluated, the load was mapped in keeping the operational hours of the motor to be 5 hours. The load of the motor since is associated with a water tank storage so a deferrable load is used in HOMER and as the motor is running for 5 hours, so 55 × 5 = 275 kWh is the storage capacity required. The detailed load mapping in the deferrable load in HOMER can be seen in

The overall proposed system with water tank in HOMER appears as can be seen in the

After the simulation of the overall proposed solar water pumping system was conducted; the requirement of the PV Panel network came out to be 72.3 kW, the inverter requirement came out to be 59.9 kW, which is fulfilled by 60 kW SMA American STP60-US-10. The overall result is seen in

The overall proposed system with water tank can be seen in

The overall cost summary for the proposed system was performed in HOMER

and the result can be seen in

The cash flow for the proposed system over the 25 years of life time can be seen in

As the total water discharge in one day is 4896 m^{3}, so a tank of 5000 m^{3} is planned. For this the mathematical details are as follows.

Considering a cylindrical tank of 5000 m^{3} with a height of 2 m. The radius of the tank can be calculated using Equation (1).

V = π r 2 h (1)

Here V is for volume in m^{3}; r is radius of the cylinder in meters; h is the height of the tank in meter

5000 = 3.142 × r 2 × 2

r = 28.21 m

Hence, the radius of the tank is 28.21 m.

Local rate for construction including material, labour, digging and supervision lumped together costs Rs 300/ft^{2}.

As the tank is open from top, so the total surface area can be calculated using Equation (2).

Surface Area = π r 2 + 2 π r h (2)

Surface area = 3.142 × 28.212 + 2 × 3.142 × 28.21 × 2

Surface area = 2854.6 m^{2} = 30726.6587ft^{2}

Overall price for tank is 30,727 × 300 = Rs 92,181.00 = $54,540.88

A detailed sizing and economic analysis of solar system with battery bank was performed using HOMER software to evaluate the steady state analysis of system. It was found out that 73.8 kW of PV panel network, 450 batteries of Trojan SAGM 12 105 and 16.7 kW of inverter are required to realise a system for a motor load of 11 kW. To further study the system, dynamic analysis of the proposed system was done in MATLAB/Simulink. Mathematical modeling of PV panel, battery bank, inverter, buck-boost converter and selected model and pump along with a control system was done to represent the overall system in shape of maximum power point tracking by Perturb and observe algorithm that was used to control the duty cycle. This helped to further validate the designed solar water pumping system in HOMER.

A detailed sizing of another option was also proposed for the selected agricultural site which was supported by a cylindrical water tank instead of a battery bank. For this system, the PV panel network requirement came out to be 72.3 kW, the inverter requirement came out to be 59.9 kW and this all was required for the motor of load 55 kW and the water tank volume requirement came out to be 4896 m^{3}.

To compare the solar water pumping systems design their economic analysis is considered, which was also performed using HOMER software. It can be seen in the results that overall net present cost of the system with battery bank was $273,570 and the net present cost for the system with water tank came out to be 103,858.3 + 54,540.88 = $158,399. Levelized cost for the system with battery was $0.48 and levelized cost for the system with water tank was $0.1783. Hence, keeping in view the net present costs and levelized costs of the systems, the PV system with water tank can safely be regarded as a better option. Operating costs per year are $5692.37 and $4649.93 for systems with battery and without battery respectively which again goes in favour of system without battery. Last parameter is initial investments which are $199,981.86 and 43,746.27 + 54,580.88 = $98,327.15 for systems with battery and without battery respectively which again goes in favour of system without battery. This factor is less as compared to battery based system, because construction of tank is relatively cheaper in Pakistan due to availability of cheap labour.

Hence, it can be concluded that solar water pumping system based on water tank is cheaper as compared to solar water pumping system based on battery.

We specially like to thank Mr. Aslam Yusuf (Advisor Technical Services) of Farm Dynamics Pakistan (Pvt) Ltd. and Mr. Tahir Mushtaq serving as manager Mustafa Research Farm for providing us with necessary site details which were very helpful while writing this paper. At the end, thanks to NSERC for funding this research.

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

Ashraf, U. and Iqbal, M.T. (2020) Optimised Design and Analysis of Solar Water Pumping Systems for Pakistani Conditions. Energy and Power Engineering, 12, 521-542. https://doi.org/10.4236/epe.2020.1210032