dynamic modeling, control, and analysis of a solar water

Research ArticleDynamic Modeling, Control, and Analysis of a Solar WaterPumping System for Libya

Muamer M. Shebani and Tariq Iqbal

Department of Electrical and Computer Engineering, Faculty of Engineering and Applied Science,Memorial University of Newfoundland, St. John’s, NL, Canada

Correspondence should be addressed to Muamer M. Shebani; [email protected]

Received 9 November 2016; Revised 7 March 2017; Accepted 14 March 2017; Published 24 April 2017

Academic Editor: Pallav Purohit

Copyright © 2017 Muamer M. Shebani and Tariq Iqbal. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

In recent years, one of the suitable solar photovoltaic (PV) applications is a water pumping system.The simplest solar PV pumpingsystem consists of PV array, DC-DC converter, DC motor, and water pump. In this paper, water pumping system sizing for Libyais evaluated based on a daily demand using HOMER software, and dynamic modeling of a solar PV water pumping system usinga Permanent Magnet DC (PMDC) motor is presented in Matlab/Simulink environment. The system performance with maximumpower point tracking (MPPT) based on Fractional Open Circuit Voltage (FOCV) is evaluated with and without a battery storagesystem. In some applications, a rated voltage is needed to connect a PMDC motor to a PV array through a DC-DC converter andin other applications the input voltage can vary. The evaluation of the system is based on the performance during a change insolar irradiation. Using Matlab/Simulink, simulation results are assessed to see the efficiency of the system when it is operating ata specific speed or at the MPPT. The results show that an improvement in the system efficiency can be achieved when the PMDCmotor is running at a specific speed rather than at the peak PV power point.

1. Introduction

In rural areas, standalone photovoltaic water pumping sys-tems have become very competitive solution for water supplybecause the access to an electric grid is not available orcostly effective. In Libya, standalone solar systems are gainingmore interest than other renewable energy sources becausemany sunny days are available. Moreover, because of theenvironment issues such as global warming, researchers areled to develop the renewable energy sources such as solarsystems.

One of the most important issues with PV standalonesystems is its efficiency and performance over various oper-ating conditions. In [1] a brushless DC motor solar waterpumping system is described and simulated. The systemmodel is developed from an individual component to assessthe overall performance of the system. The results show thatthe efficiency of solar PV water pumping system over variousoperating conditions is improved compared to the existingsystems. The performance of standalone solar systems is

also associated with the parallel and series combination ofPV module. In [2] a simulated model of directly connectedsolar PV system to a PMDC motor water pumping systemand its experimental results are carried out and analyzed.For different solar irradiation and ambient temperature, acombination of series and parallel PV modules is analyzedin terms of their performance. The results show that a goodmatching cannot be achieved at low solar irradiation. Agood matching can be achieved for a typical parallel andseries combination of the PVmodule. Furthermore, the solarwater pumping system performance is evaluated under fixedposition and manual tracking of PV panel. The evaluationshows that themanual tracking for the water pumping systemis 22.6% more efficient than the fixed PV panels.

Type of motor in standalone water pumping systemsaffects the overall system performance. In [3] a PV system, apermanent magnetic DCmotor, and a single phase inductionmotor models are implemented in Matlab/Simulink envi-ronment. The use of PV system is to feed a water pumpingsystem. A simulation and experimental results are carried out

HindawiJournal of Renewable EnergyVolume 2017, Article ID 8504283, 13 pageshttps://doi.org/10.1155/2017/8504283

https://doi.org/10.1155/2017/8504283

2 Journal of Renewable Energy

to evaluate the performance of the PMDC motor comparedto the single phase induction motor. The result shows thatthe single phase induction motor has lower performancecompared to the PMDC motor. The use of the PMDC motorto drive a water pump is simpler compared to using thesingle induction motor because the PMDC motor does notrequire an inverter and excitation system for its field. Theperformance of DCmotor varies also according to its type. In[4] a comparative study based onMatlab simulation betweena PMDC motor water pumping system and DC motor waterpumping system is presented. The two systems are fed by aPV source whose power output varies according to the solarirradiation and ambient temperature. The result shows thatthe performance of a PMDCmotor water pumping system isbetter.

Regulating water discharge of standalone solar waterpumping systems during the variation of solar irradiationis one of the keys to assess their performance. In [5] astandalone solar PV water pumping system driven by a per-manent magnetic synchronousmotor (PMSM) is modeled inMatlab/Simulink environment. The PV system is connectedto a boost converter to regulate and maintain the DC busvoltage at constant level. The three-phase voltage sourceinverter supplies the PMSM and it is controlled to regulatethe water discharge during a variation of solar irradiation.The result shows that the performance of solar photovoltaicPMSM water pumping system provides a satisfied motorspeed under a variation of solar irradiation.

Operating motor at maximum efficiency can enhance theoverall efficiency of a solar water pumping system. In [6] asystem that consists of a directly connected solar PV arrayto a Switched Reluctance Motor (SRM) driving a centrifugalwater pump is presented. The system considers the SRMbecause its efficiency, reliability, and cost are comparative tothe DC and AC conventional electric machine for this typeof application. The system is mathematically modeled andsimulated in Matlab environment. By controlling the motorinput current, the solar PV array is operated at the pointof extracting maximum power. For a set of different solarirradiation and ambient temperature, simulation results arecarried out. The simplicity of the control system helps toachieve themaximumpower point tracking of the PV system.This control demonstrates its achievement result throughthe dynamic simulation. However, in the case of inductionmotor water pumping system, the operation of the inductionmotor at its maximum efficiency is better than operatingthe solar PV array at its maximum power point to extractthe peak power. In [7] a dynamic analysis and steady stateoperation of a water pumping system is presented. The waterpumping system consists of an induction motor, a three-phase voltage source inverter, and solar PV array. The three-phase voltage inverter is controlled to achieve the maximumefficiency operation of the induction motor.The results showthat the maximum efficiency of the induction motor andoverall standalone solar system is achieved under a variationof the solar irradiation.

Improving efficiency of standalone solar water pumpingsystems can be achieved when a PV array operates at MPPT.In [8] photovoltaic DC motor water pumping system is

Table 1: Daily water requirement for some application.

Application Approximation usageEach person, for all purposes 50 gallons per dayEach milking cow 20–30 gallons per dayEach horse and every cattle 10–15 gallons per dayEach sheep and each goat 2 gallons per dayEvery 100 chickens 6–12 gallons per day

modeled and simulated in Matlab. A DC motor is used anddriven by a solar PV source through a DC-DC converter.The model evaluates the performance of the system usingactual irradiation data. The performance is examined usingP&O basedMPPT algorithm and without MPPT algorithms.The performance parameters consider the produced powerand the volume of the pumped water per day. The sim-ulation results indicate that the system with P&O basedMPPT algorithm has better efficiency and performance incomparison to the system without implementing the MPPTalgorithm. However, the best performance for standalonewater pumping systems without MPPT can be achievedwith matching electromechanical characteristics of a motorand a solar PV array. In [9] theoretical and experimentalresults for a directly coupled solar PV water pumping systemare presented. A centrifugal pump is driven by a PMDCmotor which is directly connected to solar PV array. Theexperimental and simulation results are carried out based ona good match between the electromechanical characteristicsof the PMDC motor and the solar PV array at various solarirradiation values. For low solar irradiation, the torque-speedcurve should be steeper than the torque-speed curve forhigh solar irradiation. The performance of the simulatedand experimented system is used for selecting a suitablePV array that has a good match with an electromechanicalsystem.

This paper aims to achieve the highest efficiency of a stan-dalone water pumping system by implementing MPPT andrunning a PMDCat the highest efficiency. By adding a storagebattery system, the MPPT tracking can be implemented andthe extra power can be stored.Thewater pumping system canrun at specific speed tomeet the daily demand for the specificlocation in Libya. At the same time the PMDC runs at thehighest efficiency. The paper focuses on the performance ofa directly coupled water pumping system with MPPT basedon FOCV and compared it with the performance of solarwater pumping system with a battery storage system. Thecomparison is based on the PMDC motor efficiency for adifferent scenario of rotor speed.

2. System Sizing and Components

The amount of water needed is the first step toward sizinga solar water pumping system. However, if the water needsare varying, the sizing should use the highest amount ofwater needs. Table 1 shows the approximated water usage perday.

Journal of Renewable Energy 3

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SCB 20-45

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SCS 21-150-120VSCS 21-150-105VSCS 21-150-90 VSCB 20-45-105VSCB 20-45-90VSCB 20-45-75VSCB 20-45-60V

Figure 1: Centrifugal booster pump selection guide.

The solar water pumping system is designed in this paperto water the needs of a small farm. The needs of the farmare associated with a family of six people water needs, twomilking cows, two horse, twenty sheep, ten goats, and fivethousand chickens in Libya. From Table 1 and the daily waterneeds for the farm, the total daily water needs per day are 750gallons/day.

The peak sun hours in Libya are 3000–3500 hours peryear. As a result, the number of peak sun hours per day isnine hours per day. To sustain the daily watering needs, theproposed solar water pumping system has to be capable ofpumping (750/(9 ∗ 60)) gallons per minute. This is about1.4 gallons per minute. Because of the variation in the peaksun hours between the winter and the summer, the amountof 1.4 gallons per minute should be considered as minimumrate flow of water. To meet the requirement in winter, theamount of 2 gallons perminutes is suitable.The total depth ofthe well is 90 ft. Figure 1 shows the relationship between thetotal depth and the rate flow of the water for different type ofcentrifugal water pump.

TheSCB20-45 at 105V is chosen based on thewater needssince the 2 gallons perminute is the goal of thewater pumpingsystem and the total depth is 90 ft.The power needs for waterpump are 0.5 hp driven by a PMDC motor.

Table 2 indicatesmonthly averaged insolation incident ona horizontal surface (kWh/m2/day) in Libya [10].

Since the electrical load is 0.37285 kw (0.5 hp) which isapproximately 0.4 kW and the number of peak sun hours

Table 2: Monthly averaged insolation incident (kWh/m2/day) inLibya.

Month kWh/m2/dayJanuary 4.426February 5.361March 6.199April 6.846May 7.376June 7.877July 7.878August 7.450September 6.695October 5.784November 4.621December 4.142

CP12240D

PV

Primary load 13.2 kWh/d749W peak

DC

Figure 2: System implementation in Homer.

per day in Libya is nine hours per day, the Homer software(http://homerenergy.com) can be used to size the proposedwater pumping system. Based on the Homer optimizationresult, the pump load needs fifteen 0.075 kWPVmodules andsixteen batteries to sustain the daily watering needs. Theseresults are based on themonthly averaged insolation incidenton a horizontal surface (kWh/m2/day) in Libya. Figure 2shows the system implementation in Homer software.

The categorized result of the optimization analysis indi-cates that the rated PV array is 1.2 kW and the number ofbatteries needed is sixteen.

The PVmodule uses a single diodemodel which is shownin Figure 3. Depending on solar irradiation and ambienttemperature, the output power from the PV module varies.

The mathematical modeling of a PV cell is described by(1)–(6). The output current (𝐼) from the PV module is givenas

𝐼 = 𝐼PV − 𝐼𝐷 − 𝐼SH, (1)

where 𝐼PV is the photon generated current from the PVmodule. 𝐼PV is given as

𝐼PV = 𝐺𝐺𝑛 ∗ (𝐼pv𝑛 + 𝑘𝑖 ∗ (𝑇 − 𝑇𝑛)) , (2)

where 𝐺 is the actual solar irradiation, 𝐺𝑛 is the nominalirradiation at standard condition STC 1000W/m2 and 25∘C,

http://homerenergy.com


G

I

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Figure 3: Single diode model of a solar cell.

Table 3: Parameters of the ISOFOTON I-75 module at 25∘C and1000W/m2.Parameters ValueShort circuit current (𝐼sc) 4.67AOpen-circuit voltage (𝑉oc) 21.6 VMPP current (𝐼mpp) 4.34AMPP voltage (𝑉mpp) 17.4 VTemperature coefficient of 𝐼sc (𝑘𝑖) 0.0032A/KTemperature coefficient of 𝑉oc (𝑘V) −0.01214V/KNumber of cells in series (𝑁𝑠) 36Diode ideality factor (𝑎) 1.3Series resistance (𝑅𝑠) 0.15ΩParallel resistance (𝑅𝑝) 163.59883Ω

𝐼pv𝑛 is the short circuit of the PV array at STC, 𝑘𝑖 istemperature coefficient of 𝐼pv𝑛, 𝑇 is the actual temperature,and 𝑇𝑛 is 25∘C.The diode current 𝐼𝐷 is given by

𝐼𝐷 = 𝐼𝑟 ∗ (exp ((𝑉 + 𝐼 ∗ 𝑅𝑠) ∗ 𝑉𝑡𝑎) − 1) , (3)

where 𝐼𝑟 is the diode saturation current and it is given by (4)and 𝑉𝑡𝑎 is given by (5):

𝐼𝑟 = 𝐼rs ∗ ( 𝑇𝑇𝑛)3

exp(𝑞 ∗ 𝐸𝑔𝐾 ∗ 𝑎) ∗ ( 1𝑇𝑛 −1𝑇) , (4)

where 𝐼rs is the diode reverse saturation current, 𝑞 isthe charge of electron (1.61 ∗ 10−19 C), 𝐾 is Boltzmann’sconstant (1.38 ∗ 10−23 J/K), and 𝑎 is the diode idealityfactor.

𝑉𝑡𝑎 = 𝑞(𝑎 ∗ 𝑁𝑠 ∗ 𝐾 ∗ 𝑇) , (5)

where𝑁𝑠 is the number of series cells in the PV module. Thediode reverse saturation current is given by

𝐼rs = 𝑘𝑖 ∗ (𝑇 − 𝑇𝑛) ∗ 𝐼scexp (𝑉oc ∗ 𝑘V ∗ (𝑇 − 𝑇𝑛) 𝑉𝑡𝑎) . (6)

The characteristic of the PV module can be obtained bymodeling (1)–(6) in Matlab/Simulink. The standard test con-dition (1000W/m2 and 25∘C) parameters for a ISOFOTONI-75 photovoltaic system is shown in Table 3.

Table 4: Operating values for the boost converter.

Parameters ValueSwitching frequency 𝑓 25 kHzInductance 𝐿 30mHCapacitance 𝐶 200 𝜇FLoad resistance 𝑅 25Ω

Figure 4 shows the model of a ISOFOTON I-75 array inMatlab/Simulink.The ISOFOTON I-75 module is connectedto a variable load resistance to examine the characteristic ofthe PV.

The 𝑃-𝑉 curves for the PV array are shown in Figure 5.The model is simulated for various solar irradiation valueswhich are 200W/m2, 400W/m2, 600W/m2, 800W/m2, and1000W/m2.

Figure 5 shows an increase in the PV array output powerdue to the increase in the solar irradiance. Figure 6 shows𝑉-𝐼 curves for the PV array. The results are carried out forvarious solar irradiance values. When the solar irradiancebecomes higher, the PV array output is increased. As a result,the voltage across the PV output and the drawn current fromthe PV array becomes larger.

Figure 7 shows 𝑃-𝑉 curves for the PV array at a differentambient temperature. As it is shown in Figure 7, the increasein ambient temperature decreases the output power of the PVarray.

Figure 8 shows 𝐼-𝑉 for the PV array at different ambienttemperature.

Figure 8 indicates that the output voltage and current arelowered due to an increase in the ambient temperature.

3. DC-DC Boost Converter

The equivalent circuit of a boost converter is shown inFigure 9.The boost converter is connected to the photovoltaicarray.

The parameters of the boost converter are shown inTable 4. These parameters are determined according to theripple limit (𝛿 = 1%) and by using the following expression:

𝐷 = 1 − 𝑉in𝑉out, (7)


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ISOFOTON I-75 PV model 54 cell in series

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Figure 4: The model of a ISOFOTON I-75 array in Matlab/Simulink.

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Figure 5: 𝑃-𝑉 curves for PV array.

where 𝐷 is the duty ratio, 𝑉in is the input voltage, and 𝑉out isthe output voltage. The inductance is calculated as

𝐿 = (𝑉in ∗ 𝐷)(𝛿 ∗ 𝐼in ∗ 𝑓) , (8)

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Figure 6: 𝐼-𝑉 curves for PV array.

where 𝑓 is the switching frequency and 𝐼in is the inputcurrent. The capacitance is calculated as

𝐶 = (𝐼out ∗ 𝐷)(𝛿 ∗ 𝑉out ∗ 𝑓) , (9)

where 𝐼out is the output current.The DC-DC boost converter operates in continuous

mode. There are two states of operation which are ON stateand OFF state. During each state, a state of differentialquestion is driven to describe the dynamic operation of the


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Figure 7: 𝑃-𝑉 curves for PV array with different ambient tempera-ture.

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Figure 8: 𝐼-𝑉 curves for PV array with different ambient tempera-ture.

boost converter. Equations (10) are the state space model forthe boost converter during ON and OFF state of operation.

[ ̇𝑖𝐿̇V𝑐] = 𝐴1 [𝑖𝐿V𝑐] + 𝐵1𝑉in,

𝑉out = 𝐶1 [𝑖𝐿V𝑐] ,

[ ̇𝑖𝐿̇V𝑐] = 𝐴2 [𝑖𝐿V𝑐] + 𝐵2𝑉in,

𝑉out = 𝐶2 [𝑖𝐿V𝑐] .

(10)

The matrices 𝐴 𝑖, 𝐵𝑖, and, 𝐶𝑖 are given by

𝐴1 = [[0 00 −1𝑅𝐶

]],

𝐴2 = [[[[0 −1𝐿1𝐶 −1𝑅𝐶

]]]],

𝐵1 = 𝐵2 = [[1𝐿0]]

,𝐶1 = 𝐶2 = [0 1] .

(11)

The state space averaging technique is used.Therefore, thestate vector 𝑥(𝑡) which is [𝑖𝐿(𝑡) V𝑐(𝑡)] is given as

�̇� (𝑡) = 𝐴𝑥 + 𝐵𝑢,𝑦 = 𝐶𝑥. (12)

The computation of 𝐴 matrix, 𝐵 matrix, and 𝐶 matrix isbased on the state space averaging which is given as

𝐴 = 𝐷𝐴1 + (1 − 𝐷)𝐴2,𝐵 = 𝐷𝐵1 + (1 − 𝐷) 𝐵2,𝐶 = 𝐷𝐶1 + (1 − 𝐷)𝐶2.

(13)

From the transfer function of the boost converter, the PIcontroller is determined using SISO tool inMatlab/Simulink.The transfer function of the converter is given as

𝐻(𝑠) = 0.543 ∗ 𝑆2 + 108.6 ∗ 𝑆 + 9.507 ∗ 104𝑆2 + 200 ∗ 𝑆 + 3.481 ∗ 104 . (14)

Also, the parameters of the PI controller are given as

PI = 𝐾𝑃 + 𝐾𝐼𝑆 . (15)

Therefore, the parameters of the PI controller are 𝐾𝑃 =0.810525 and𝐾𝐼 = 32.421.The step response for the system is shown in Figure 10.

4. Fractional Open Circuit AlgorithmBased MPPT

The variation in voltage and maximum power point is asso-ciated with the unpredictable solar irradiation and ambienttemperature. The approximated voltage at maximum powerpoint is a fraction of the open circuit voltage. The fractionopen circuit voltage method is based on the followingformula:

𝑉MPP = 𝐾 ∗ 𝑉oc. (16)

Figure 11 shows the block diagram implementation of PIcontroller in Matlab/Simulink.


DC DC boost output

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Figure 9: DC-DC boost converter Matlab/Simulink.

Step response

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Figure 10: Step response of the system.

Proportional0.76

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1Duty cycle

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2 −+ ++

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KI

s

Figure 11: PI controller implementation in Matlab/Simulink.

Factor 𝐾 in (16) is less than a unity, and it variesaccording to the solar irradiation and ambient temperature.The variation of factor 𝐾 is between 0.71 and 0.8, but thecommonly used value for this factor is 0.76.

−

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Figure 12: Equivalent circuit of a permanent magnetic DC motor.

5. Permanent Magnetic PMDC Motor Model

In PMDC motors, the field winding is permanent magnetic,so the PMDC motors do not need an external excitation.Figure 12 shows the equivalent circuit of a PMDC motor.

From Figure 12, the terminal voltage (𝑉𝑡) can be writtenas

𝑉𝑡 = 𝐼𝑎 ∗ 𝑅𝑎 + 𝐿𝑎𝑎 ∗ 𝑑𝐼𝑎𝑑𝑡 + 𝑘𝑚 ∗ 𝜔𝑚, (17)

where 𝑉𝑡 is the DC source voltage (V), 𝐼𝑎 is the armaturecurrent (A), 𝑅𝑎 is the armature resistance (Ω), 𝐿𝑎𝑎 is thearmature inductance (H), 𝑘𝑚 is the torque constant (V⋅s/rad),and 𝜔𝑚 is motor speed (rpm). The electrical torque 𝑇𝑒 (Nm)is given by

𝑇𝑒 = 𝑘𝑚 ∗ 𝐼𝑎. (18)


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Figure 13: Detailed model of a permanent magnetic DC motor.

The motor speed as function in the electrical torque andthe load torque 𝑇𝐿 (Nm) is given by

𝐽 ∗ 𝑑𝜔𝑚𝑑𝑡 = 𝑇𝑒 − 𝑇𝐿 − 𝐵𝑚 ∗ 𝜔𝑚, (19)

where 𝐽 is inertia constant (kg ∗m2) and 𝐵𝑚 is constant (N ∗m∗ s). By rearranging (17), (18), and (19), the dynamic modelfor a PMDC motor can be described as

𝑑𝐼𝑎𝑑𝑡 = 1𝐿𝑎𝑎 ∗ (𝑉𝑡 − 𝐼𝑎 ∗ 𝑅𝑎 − 𝑘𝑚 ∗ 𝜔𝑚) ,𝑑𝜔𝑚𝑑𝑡 = 1𝐽 (𝑇𝑒 − 𝑇𝐿 − 𝐵𝑚 ∗ 𝜔𝑚) .

(20)

Equation (20) can be implemented in Matlab/Simulinkenvironment. Figure 13 shows the detailed model of a PMDCmotor in Matlab.

A typical performance of a PMDC motor is shown inFigure 14. The highest efficiency can be achieved at a certainspeed. Therefore, by controlling the PMDCmotor speed, thePMDC can run efficiently.

The parameters for the PMDCmotor are given in Table 5.

6. Directly Coupled PV Water PumpingSystem with MPPT Based FOCV

Figure 15 shows theMatlabmodel for the PV array connecteddirectly to a permanentmagnetic DCmotor through aMPPTbased FOCV method.

TheMatlab model in Figure 15 is simulated and its poweroutput for solar irradiance values 400W/m2, 600W/m2, and200W/m2 including initial transient is shown in Figure 16.

Figure 16 indicates that the fractional open circuit FOCbased MPPT tracks the peak power from the PV array.


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Io

Ts/2 Ts

Figure 14: Typical torque versus speed, current, and power curvesfor a PMDC motor.

Table 5: PMDC motor parameters.

Parameters ValueArmature voltage 𝑉𝑡 105VArmature Current 𝐼𝑎 5.2 AArmature resistance 𝑅𝑎 20ΩArmature Inductance 𝐿𝑎 1.06mHMoment of inertia 𝐽 1.06 ∗ 10−6 kg⋅m2Viscous friction coefficient 𝐵𝑚 3.79 ∗ 10−3 N⋅m⋅s/radConstant 𝑘𝑚 0.52

The input power to the PMDC motor is increased whenthe solar irradiance increases from 400W/m2 to 600W/m2.The input solar irradiation is increased at 0.32 seconds from400W/m2 to 600W/m2. Since the PV array is directlycoupled to the PMDC motor through a FOC based MPPT,the power causes an increase in themechanical output torque.Since the torque is proportional to the armature current, thecurrent at 0.32 seconds is increased as shown in Figure 16.In addition, the rotor speed of the PMDCmotor is increasedproportionally to the increase in the solar irradiation asshown in Figure 17. The flow rate of the centrifugal pumpis increased as well due to the increase in the PMDC rotorspeed. Figure 17 shows the increase of the flow rate when thesolar irradiance is increased at 0.32 seconds.

However, the input power to the PMDC motor isdecreased when the solar irradiance decreases from600W/m2 to 200W/m2. The input solar irradiation isdecreased at 0.48 seconds from 600W/m2 to 200W/m2.Since the PV array is directly coupled to the PMDC motorthrough a FOC based MPPT, the power causes a decreasein the mechanical output torque as shown in Figure 16.Because the armature current is proportional to the torque,the armature current is decreased as well. The rotor speed isdecreased since the input power is decreased. This results indecreasing the flow rate are shown in Figure 17.

Table 6: Operating values for boost converter.

Parameters ValueSwitching frequency 𝑓 25KHzInductance 𝐿 30mHCapacitance 𝐶 80 𝜇FLoad resistance 𝑅 25Ω

7. Controlling the PMDC Motor Input Voltagewith Boost Converter

To maintain the input voltage of the 0.5 hp PMDC motor, anadditional boost converter is connected between the storagesystem and the PMDC motor to maintain the input voltageconstant.The parameters of the boost converter for this stageare shown in Table 6.

By using the state space averaging technique in (13), the PIcontroller is designed using SISO tools in Matlab/Simulink.The open loop transfer function of the converter and theparameters of the PI controller are given as

𝐻(𝑠) = 0.543 ∗ 𝑆2 + 271.5 ∗ 𝑆 + 2.377 ∗ 105𝑆2 + 500 ∗ 𝑆 + 8.702 ∗ 105 . (21)

Also, the parameters of the PI controller are given as

PI = 𝐾𝑃 + 𝐾𝐼𝑆 . (22)

Therefore, the parameters of the PI controller are 𝐾𝑃 =0.23 and𝐾𝐼 = 115.The step response for the system is shown in Figure 18.

8. Battery Stoarge System

The charging control implementation in Matlab/Simulink isshown in Figure 19. Depending on the state of charge (SOC),the charging control works. The SOC contains a relay whichopens when the battery reaches 95% of its charge. The SOCcontrol does not allow the battery to be charged 100%. Inaddition, when the discharge of the battery reaches 50%, thebattery is isolated from the load by opening its switch.

9. Water Pump Model

Acentrifugal pump load ismodeled by the following equationwhich indicates the load torque [11].

𝑇 = 4.8 ∗ 10−6 ∗ 𝜔2 + 0.00019 ∗ 𝜔 + 0.092. (23)

The flow rate according to [12] can be given as

𝑄 = (𝜂 ∗ 𝑃)(𝜌 ∗ 𝑔 ∗ 𝐻) , (24)

where (𝑃) is the input power required (W), (𝜌) is thefluid density (kg/m3), (𝐻) is the energy head added tothe flow (m), (𝑔) is the standard acceleration of gravity(9.80665m/s2), (𝑄) is the flow rate (m3/s), and (𝜂) is theefficiency of the pump plant.


25

Temperature_op

Irradiance

Temperature

m

+


Duty cycle

+

+out

−out

DC-DC boost converter

m D

MPPT

rpm+

Permanent magnetic DC motor

Discrete,

Powergui

v+

Voltage measurement

i+

Current measurement

Product

PV MPPT output

rpm Torque

Centrifugal pump

PumpSignal 1

Group 1

Irradiance

−

−

−

−

−

×

Ts = 5e − 05 s.

(W/m2 ) TL

Te

Te

Ia

Q (m3/s)P (W)

Figure 15: Directly coupled solar water pumping system model.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Out

put p

ower

bas

ed

0

200

400

600

Irra

dain

ce (W

/m2)

0200400600800

on M

PPT

(W)

00.20.40.60.8

Torq

ue (N

∗m

)

Figure 16: PV power and PMDC torque at various solar irradiationvalues.

10. Solar Water Pumping System with MPPTBased FOCV and Battery Storage System

The PV array model with charging battery controller hastwo effective components as shown in Figure 19. The batterystorage with charging controller and boost converter toregulate the input voltage for the PMDC motor is added tothe model as shown in Figure 20.

Figure 21 indicates the PV output peak power which isextracted by the FOCVBasedMPPTmethod.The input solarirradiation is increased at 0.32 seconds from 400W/m2 to600W/m2. Since the PV array is not directly coupled to thePMDC motor, the mechanical output torque remains con-stant because of the regulating boost converter as shown inFigure 18. Although the input solar irradiation is decreased at0.48 seconds from 600W/m2 to 200W/m2, the mechanicaltorque remains constant due to the regulating boost converteras shown in Figure 21.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

×10−3

0

1

2

3

Flow

rate

(m3/s

)

0

1000

2000

3000

4000

Spee

d (r

pm)

0

1

2

3

4

I a(A

)

Figure 17: Flow rate, PMDC motor rotor speed, and armaturecurrent at various solar irradiation values.

Step Response

0

0.2

0.4

0.6

0.8

1

1.2

1.4

edutilpmA

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450Time (seconds)

Figure 18: Step response of the system.


+

m

BatteryIn1

+

SOC control

[SOC]

[SOC]

1+

2

3

+V

4

−V

In1

+

SOC control 1

−

−

−

−

⟨SOC (%)⟩

Figure 19: Battery charging controller.

25

Temperature_op

Irradiance

Temperature

m

+


Duty cycle

+

+out

−out

DC-DC boost converter

m D

MPPT

Discrete,

Powergui

Signal 1Group 1

Irradiance

v+

Voltage measurement

+ i

Current measurement

Product

+ +V

−V

Battery storage system with charging controller

PV MPPT output

Duty cycle

+

+out

−out

DC-DC boost converter 1

v+

Voltage measurement 1

+ i

Current measurement 1

m D

Speed controller

Product 1

rpm+

Permanent magnetic DC motor

rpm Torque

Centrifugal pump

Pump

−

−

−

−

−

−

−

−

−

×

×

Ts = 5e − 05 s.

(W/m2 ) TL

Te

Te

Ia

P (W) Q (m3/s)

Figure 20: Solar water pumping system with battery storage system.

Out

put p

ower

bas

ed

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0

500

1000

Irra

dain

ce (W

/m2)

0

500

1000

on M

PPT

(W)

0.050.1

0.150.2

0.25

Torq

ue (N

∗m

)

Figure 21: PV power and PMDC torque at various solar irradiationvalues.

The input power to the PMDC motor remains con-stant when the solar irradiance increases from 400W/m2to 600W/m2. Because of the boost converter connectedbetween the battery and PMDC motor, the input voltage iscontrolled by the boost converter. This makes the PMDCmotor run at constant speed with different solar irradiationvalues. As a result of regulating boost converter, the rotorspeed, the flow rate, and the armature current remain con-stant when the input solar irradiation is varying. This allowsthe PMDCmotor to run at a constant speedwith various solarirradiation values as shown in Figure 22. Initial simulationtransient is also shown.

The added stage (Battery Storage and Regulation BoostConverter) controls the input power to the PMDC motor.Figure 18 shows that the solar irradiation is varying at 0.32seconds and at 0.48 seconds. At 0.32 seconds, the solarirradiation is changed from 400W/m2 to 600W/m2 and itis changed at 0.48 seconds from 600W/m2 to 400W/m2.However, the input power to the PMDC motor remains


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

×10−4

−5

0

5

10

Flow

rate

(m3/s

)

−1000

0

1000

2000

Spee

d (r

pm)

00.5

11.5

2

I a(A

)

Figure 22: Flow rate, PMDC motor rotor speed, and armaturecurrent at various solar irradiation values.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0

500

1000

Irra

dain

ce (W

/m2)

0

500

1000

PV o

utpu

t pow

er (W

)

0

50

100

150

200

PMD

C m

otor

pow

er (W

)

Figure 23: Peak extracted power from PV and PMDC input powerat various solar irradiation values.

constant as shown in Figure 23 due to the regulating boostconverter.

A part of the generated power by the PV array drivesthe PMDC motor which drives the centrifugal pump load,and the rest of the generated power by the PV array chargesthe battery. The charging controller is closed when the statecharge percentage of the battery is less than 95%. The solarirradiance is changed from 400W/m2 to 600W/m2 at 0.32seconds. At 0.32 seconds the PV array output power becomeshigher. This increases the rate of charging for the battery asshown in Figure 24. State of charge at 0.32 becomes faster

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

59.999960

60.000160.000260.0003

Stat

e of c

harg

e (%

)

−10

−5

0

5

Char

ging

curr

ent (

A)

51.8151.8251.8351.8451.85

Char

ging

vol

tage

(V)

Figure 24: Battery state of charge at various solar irradiation values.

since the charging current and voltage become larger. How-ever, when the solar irradiance is decreased from 600W/m2to 200W/m2 at 0.48 seconds, the battery is slightly chargedbecause the highest percentage of the PV output power goesdirectly to the PMDC motor. As shown in Figure 23, at 0.48the charging current is small.

11. Discussion and Conclusion

The directly coupled solar water pumping system withMPPT and the solar water pumping system with batterystorage through MPPT are modeled and simulated in Mat-lab/Simulink environment. The results are obtained fromthe simulation. For directly coupled solar water pumpingsystem, the rotor speed, flow rate, and armature current areproportional to the solar irradiation. They vary accordingto the variation in the solar irradiation. This makes theperformance of a PMDC less efficient since the efficiencyof PMDC motor is a function of rotor speed. The highestefficiency of a PMDC motor can be achieved at one speedaccording to its characteristic curves. In addition, accordingto the demand of water, the input power cannot exceed therated power of the PMDCmotor. This leads to an increase inthe hp rating of the chosen PMDCmotor which is a functionof the capital cost. Furthermore, water storage system (tank)needs to be bigger since the extra powerwill be stored aswaterfor the next day.This leads to an increase in the capital cost ofhaving bigger water tank. On the other hand, the solar waterpumping system with battery storage and regulating boostconverter leads to an efficient system because the system canbe run at a specific speed. This allows the PMDC motorto be run at higher efficiency. The battery storage can beused to store the extra power for a few cloudy days whichmakes the system more reliable. The motor can be chosenwith lower hp rating power which means lower capital costand the storage water tank can be smaller in comparison tothe directly coupling solar water pumping system. Although


the battery storage and the extra converter can increase thecapital cost, the efficiency and reliability of the solar waterpumping system with battery storage and regulating boostconverter are comparative.

The solar water pumping system with battery storage andregulating boost converter is an efficient and reliable systemin comparison to directly coupling water pumping system.This is due the advantage of running the system at one speedwhich allows higher efficiency of PMDCmotor, lower PMDCmotor hp rating, and smaller water tank system.

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper.

Acknowledgments

The authors would like to thank the Libyan Government forfunding this research.

References

[1] W. Lawrance, B. Wichert, and D. Langridge, “Simulation andperformance of a photovoltaic pumping system,” in Proceedingsof the International Conference on Power Electronics and DriveSystems, vol. 1, pp. 513–518, February 1995.

[2] A. F. Minai, A. Tariq, and Q. Alam, “Theoretical and exper-imental analysis of photovoltaic water pumping system,” inProceedings of the India International Conference on PowerElectronics (IICPE ’10), pp. 1–8, January 2011.

[3] N. Chandrasekaran andK.Thyagarajah, “Simulation and exper-imental validation of AC motor and PMDC motor pumpingsystem fed by photovoltaic cell,” Indian Journal of Engineeringand Materials Sciences, vol. 21, no. 1, pp. 93–103, 2014.

[4] N. Chandrasekaran, B. Ganeshprabu, and K. Thyagarajah,“Matlab based comparative study of photovoltaic fed DCmotor and PMDC motor pumping system,” ARPN Journal ofEngineering and Applied Sciences, vol. 7, no. 5, pp. 543–547, 2012.

[5] M. Dubey, S. Sharma, and R. Saxena, “Solar PV stand-alonewater pumping system employing PMSM drive,” in Proceedingsof the IEEE Students’ Conference on Electrical, Electronics andComputer Science (SCEECS ’14), Bhopal, India, March 2014.

[6] S. Belliwali, A. Chakravarti, and A. B. Raju, “Mathematicalmodelling and simulation of directly coupled PV water pump-ing system employing Switched Reluctance Motor,” in Proceed-ings of the IEEE PES Innovative Smart Grid Technologies—India(ISGT India ’11), Kollam Kerala, India, 2011.

[7] A. B. Raju, S. RameshKarnik, andR. Jyoti, “Maximumefficiencyoperation of a single stage inverter fed induction motor PVwater pumping system,” in Proceedings of the 1st InternationalConference on Emerging Trends in Engineering and Technology(ICETET ’08), pp. 905–910, Nagpur, India, July 2008.

[8] A. Oi, M. Anwari, and M. Taufik, “Modeling and simulationof photovoltaic water pumping system,” in Proceedings of the3rd Asia International Conference onModelling Simulation, Bali,Indonesia, 2009.

[9] M. Kolhe, J. C. Joshi, and D. P. Kothari, “Performance analysisof a directly coupled photovoltaic water-pumping system,” IEEETransactions on Energy Conversion, vol. 19, no. 3, pp. 613–618,2004.

[10] M. Boxwell, Solar Electricity, Greenstream Publishing, Coven-try, UK, 2016, edition.

[11] M. Taoufik, H. Karima, S. Lassaad, and G. Abdessattar, “Pho-tovoltaic water pumping system with three-level NPC inverter,”International Journal of Engineering Sciences, vol. 3, no. 10, pp.99–108, 2014.

[12] S. K. Gupta, M. R. Khan, and K. Jahan, “Modeling, Analysisand Control of Solar Water Pumping System,” http://www.krishisanskriti.org/vol image/10Sep201511091751.pdf.

http://www.krishisanskriti.org/vol_image/10Sep201511091751.pdf

http://www.krishisanskriti.org/vol_image/10Sep201511091751.pdf

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