PV-Grid Tie System Energizing Water Pump

doi:10.4236/sgre.2013.45047

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Smart Grid and Renewable Energy, 2013, 4, 409-418

http://dx.doi.org/10.4236/sgre.2013.45047 Published Online August 2013 (http://www.scirp.org/journal/sgre)

409

PV-Grid Tie System Energizing Water Pump

Sameer Khader, Abdel-Karim Daud

Electrical Engineering Department, Palestine Polytechnic University (PPU), Hebron, Palestine.

Email: [email protected]

Received June 27th, 2013; revised July 27th, 2013; accepted August 4th, 2013

tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop-

erly cited.

ABSTRACT

This paper presents the behaviours of three-phase induction motor driving centrifugal pump under various solar irradia-

tion levels, where the motor speed and torque depend on the source voltage and frequency, while the water-flow rate

depends on the motor speed, density, and static head according to affinity flow. Matlab/Simulink model is proposed for

studying the behaviours of these machines with respect to water flow capacity, motor current, electro-magnetic torque,

and motor efficiency. The proposed photovoltaic with maximum power point tracking model based on observation and

perturbation (O&P) maximum power tracking model is applied. The output voltage is regulated throughout Buck-Boost

converter with purpose maintaining the output voltage at predetermined values. Since Induction motors are widely used

in pump systems, the electromagnetic torque, water-flow rate are studied for various source frequencies. Comparison

analysis is conducted for both motors with respect to water flow-rate, heads elevation, and motor current. In addition to

that, the proposed system presents Photovoltaic-Grid (PV-Grid) Integrated model, where the power shortage required

for normally operation of the pump is drawn from the electrical grid.

Keywords: Photovoltaic; Induction Motor; Centrifugal Pumps; Electrical Grids; Matlab/Simulink

1. Introduction

Photovoltaic energy resources presents alternative and

friendly to the environment sources. It presents unique

solution for providing remote area with clean and sus-

tainable energy during the daytime in heating, lighting,

refrigeration and water pumps systems [1-3] without the

need of battery system, while during the night time the

accumulated energy can be fully or partially used to

cover the energy domain. The output circuit connected to

the photovoltaic system is usually dc-dc converters main-

ly boost choppers in order to boost the voltage to the

predetermined levels.

The DC/DC converters are widely used in regulated

switch mode power supplies, where the input voltage to

these converters varies in wide range especially in the

case of Photovoltaic (PV) supply source due to unpre-

dictable and sudden change in the solar irradiation level

as well as the cell operating temperature. Several con-

nection topologies concerning the switching systems

have been proposed [4-8] aiming at realizing the required

voltage level during different periods of day for certain

applications such as pumps, motors in general and power

supplies.

On the other hand water flow consumption determines

the rate of motor speed according to affinity law [6,7]

which in turn determines the elevation (static head) and

consumed power. Variable Frequency Drive (VFD) can

be applied to achieve up mentioned facts.

The proposed model consists of several modules as

shown in Figure 1 with the following functions:

 PV Photovoltaic Array (PV) that converts the solar

irradiation into voltage Vpv and current Ipv.

 Buck-Boost DC Chopper Module that boosts up the

PV voltage to the predetermined levels. Conversely in

case of high Vpv the output voltage is reduced.

 MPPT, maximum power point tracking unit that

tracks the optimized operation point for power extrac-

tion by controlling the chopper duty cycle.

 Variable Frequency Drive that controls the speed

and torque of three-phase induction motor driving

centrifugal pump by controlling the voltage and fre-

quency.

 Speed-Flow Control Unit that determines the requir-

ed voltage and frequency aiming at regulating the

motor speed and torque according to actual water

flow consumption.

PV-Grid Tie System Energizing Water Pump

410

PV Array Buck-Boost

Chopper

Power

Estimator

AC-DC

Converter

PV-Grid

Integrator

Va ri abl e

Frequency

Drive

3-phase

Speed-Flow

Control Unit

Pump

MPPT

AC Grid

act

ref

mech

Figure 1. Functional block diagram of proposed model.

 Power Estimator that detects the available Ppv power,

the consumed motor power PL and the amount of

power shortage PG that should be supplied from AC-

grid.

 PV-Grid Integrator that provides the load with nec-

essary power taken from either one of the sources PV

or AC grid, or from both.

 Amount of power shortage PG that should be supplied

from AC-grid.

 AC-DC Converter that converts the grid voltage into

smoothed DC voltage that should be easily tied to the

PV output terminal aiming at avoiding synchronizing

procedures.

The proposed model differs from other models, where

the system is consumed energy from the grid in case of

energy shortages and night time operation. It is fully

simulated using Matlab/Simulink, where the system pa-

rameters can be changed and investigated.

2. Modeling of Proposed Electrical Model

2.1. PV Performances

The application of Photovoltaic solar energy in energiz-

ing electrical load on-grid connected, where the pump

power is controlled based on the extracted from the PV

module power.

2.1.1. Phot ov o l tai c Mo del In terpretation

Basically, PV cell is a P-N semiconductor junction that

directly converts light energy into electricity. It has the

equivalent circuit shown in Figure 2 [9,10].

The following are the simplified equations describing

Figure 2. Equivalent circuit for PV cell.

the cell output voltage and current:

ln ph do

oso

III

AKT

VRI















(1)

qV N

AKT

op phd

INI I









 





(2)

311

KT T

dor















 (3)









; t

hpscncr nr

NI ITTGG



  (4)

The idealistic diode idealistic factors A & B are with

values vary between 1 and 2 depending on I-V perform-

ance shaping and approximations.

2.1.2. Photovoltaic I-V Performance

In order to study the I-V performance of the PV circuit

and to look for appropriate dc chopper for boosting up

the output voltage to predetermined value it is necessary

to illustrate the obtained PV voltage and current for boost

chopper according to specifications given in Table 1 at

PV-Grid Tie System Energizing Water Pump

411

reference irradiation (Gr = 1000 W/m2). The PV Array

voltage can be obtained by multiplying the module volt-

age and current by Nsm and Npm. Figure 3 illustrates the

proposed PV array built in Matlab/Simulink [11] with

R-L load, where the obtained results for different varia-

tion levels are presented. From these performances it is

shown that the total output PV voltage and current varies

according to irradiation level with approximated 65 W

maximum power at G = 1000 W/m2.

Table 1. Data specification for PV Array.

q K Iph I

d R

S R

1.602e - 19 C1.38e - 23J/˚K4 A 0.2 mA 1 m10 k

NS N

P V

O V

OC I

SC V

MPP

38 4 0.6 V 21.5 V 4 A 17.5 V

IMPP N

Sm N

Pm V

pv R

load T

3.7 A 6 1 130 V 44 25˚C

powergui

ontinuous

T_ var

11.2903

Rf- Cf

R-L

PV Array

GND

+V pv

Output

Nsm

Npm

G_var2

G_T

(a)

05 10 15 20 25

0.5

1.5

2.5

3.5

4.5

Ipv,A

I-V performance

Vpv, V

1200W/m2

1000W/m2

800W/m2

600W/m2

400W/m2

(b)

Figure 3. PV model with I-V performances. (a) Proposed model for PV array in Simulink environment; (b) I-V performance

of PV module.

PV-Grid Tie System Energizing Water Pump

412

2.2. The Integration of PV with Water Pumping

System

A centrifugal pumps are used as electrical load [6],

where the pump power, speed and torque are directly

affected by either load-side parameters in form of water

flow-rate, static head, water pressure, and line side in

form of solar irradiation, weather conditions, and ex-

tracted power. Figure 4 illustrates PV solar system ener-

gized water pump installation, where the water pumping

system can be directly energized from the PV or indi-

rectly throughout battery bank [10]. Both configurations

have their advantages and disadvantages.

Direct-coupled pumping systems illustrated in Figure

4(a) are sized to store extra water on sunny days so it is

available on cloudy days and at night. Water can be stor-

ed in a larger-than-needed watering tank or in a separate

storage tank and then gravity-fed to smaller watering

tanks. Water-storage capacity is important in this pump-

ing system.

While Figure 4(b) illustrates battery-coupled water

pumping systems which consist of photovoltaic (PV)

panels, charge control regulator, batteries, pump control-

ler, pressure switch, tank, and AC water pump. The elec-

tric current produced by PV panels during daylight hours

charges the batteries, and the batteries in turn supply

power to the pump anytime water is needed. The use of

batteries spreads the pumping over a longer period of

time by providing a variable voltage and frequency de-

pending on the water-consumption rate, which in turn

reduces the pump losses and increases the battery dis-

charging time which is an important factor during the

night and low light periods, the system can still deliver a

needed rate of water for livestock.

2.2.1. Centrifugal Pump Performances

According to [8] the power demand of the water pump is

expressed using the following expression:







 (5)

The pump operational performance which presents the

relationships between total head including static head and

friction head, water flow-rate, and pump efficiency are

illustrated in Figure 5 for certain commercial pump.

By applying the principle of motor-pump power bal-

ance, Equation (5) can be integrated with motor speed-

torque performance as:

gQH T





   (6)

Now referring to Figure 5 where the pump (H-Q)

curve is illustrated, which normally used to locate the

pump’s operation point. For exact determining the men-

tioned operation point there is a need to determine the

total head of the installation HA, which is the sum of the

(a)

(b)

Figure 4. PV system energizing water-pumping systems. (a)

Direct-coupled water-pumping systems; (b) Battery-cou-

pled water-pumping systems.

Figure 5. Water pump operational characteristic.

static head HS known as elevation difference, and the

network hydraulic losses HL, thus :

AsL

HH hQ





 (7)

The friction coefficient



depends on the system in-

stallation, pipes section, and liquid viscosity. The opera-

tion point results by the application of the following

equation:



(8)

This condition can be obtained by intersecting of the

corresponding curves of Figure 5.

2.2.2. Electrical Motor Performances

Centrifugal pumps can be driven by either direct current

motors [9] or alternating current motors, mainly induc-

PV-Grid Tie System Energizing Water Pump

413

tion motors [12]. Due to massive exploitation of induc-

tion motors in water pump system, the electromagnetic

performances of induction motor are going to be de-

scribed in the following sections.

2.2.2.1. M at h ematical Model

Utilizing the induction motor as prime mover source for

providing the pump machine with needed energy. Three-

phase induction motor is going to be describes as follows

[13].

The stator winding is supplied with balanced three-

phase ac voltages, which produces induced voltages in

the rotor windings due to transformer action. The distri-

bution of stator windings is arranged, so that there is an

effect of multiple poles, producing several cycles of

magneto motive force (or field) around the air gap. This

field establishes a spatial distribution sinusoidal flux den-

sity in the air gap. The synchronous speed of the rotating

filed is defined by [14]:

4π and 120

sn nsnn

pn fp



 (9)

A very useful quantity in studying induction machines

is the slip s:









(10)

Per-phase equivalent circuit of a three-phase induction

motor is shown in Figure 6(a) [15]. An expression for

the torque of an induction machine as a function of its

slip may be obtained by application of Thevenin’s theo-

rem to the circuit model to the circuit model (Figure

6(b)). The rotor circuit, as referred to the stator, may be

considered as being attached to an equivalent Thevenin

generator, as shown in Figure 6(b).

As well known for electrical machines theory in order

to maintain constant maximum torque and to avoid motor

saturation and to minimize the losses the (volt/hertz) ra-

tion must be kept constant for speeds less than the syn-

chronous speed, while for speeds over the synchronous

the voltage is maintained at its rated value and the fre-

quency is increased over the rated limits.

(a) (b)

Figure 6. Equivalent circuit of 3-phase inducti on motor. (a)

Equivalent circuit for one phase; (b) Application of Theve-

nin’s theorem.

According to [13] if the frequency is increased above

rated value, the flux and torque would decrease. If the

synchronous speed corresponding to the rated frequency

fn is called base speed



sn, or nsn, the synchronous speed

at any other frequency becomes:

osnsosn

nKn





 (11)

where on



Substituting Equation (11) in Equation (17) the elec-

tromagnetic torque can be expressed as:

em p

Rsf

sR RXX

sff f

 















 



 







(12)

where 22

pmsn

Xw.

According to [15] vLn

Vf for n

f; and





max 11

, , , , , ,.

vthth

KfTRXfXR for n



The electromagnetic power Pem and the losses can be

defined as follow:





ememo snemmechconst

PTK sTPP



  (13)

Varying the frequency of the motor causes significant

change in the drawn by the motor current, and in turn the

consumed power. According to Figure 6, the power and

current can be given as follows:



; 3 cos; tan

ph inp

LinpLLL

in inp

in inpinpo

IPVI

ZR jXRjKX

jKXRsjKo X











 



 

(14)

2.2.2.2. Simulation Resul ts

Considering the rated parameter values of the selected

induction motor [15]:

n = 2835 rpm; Pn = 1100 W; Vn = 127 Vac; R1 = R’2 =

1.27 ; X1 = X’2 = 3.860 ; Xm = 60 .

Substituting the outlined motor parameters in the de-

veloped mathematical model, we obtain through simula-

tion the motor torque as a function of speed (and slip) for

different supply frequencies as shown in Figure 7. For a

constant (V/F) ratio, the motor develops a constant ma-

ximum torque, except at low speeds (or frequencies).

From this curve the motor develops two operation modes:

constant torque modes for frequencies less than the rated

where the torque is maintained constant; and constant

power mode for frequencies greater than the rated where

the speed exceeds the synchronous and the torque falls

down keeping the power at constant value.

PV-Grid Tie System Energizing Water Pump

414

0 1 2 345 6 78

500

1000

1500

2000

2500

3000

3500

4000 s peed n(T)

T, N.m

n,rpm

f=30Hz

f=40Hz

f=50Hz

f=60Hz

Figure 7. Simulation results of the mechanical performance

of three-phase induction motor.

Having the mechanical performance of the motor at

various frequencies, where two operation mode can be

applied constant torque (V/F = const) & constant power

(V = const, f > fn) throughout VFD inverter we can build

the pump performance. Way out from the natural curve

of the pump at rated motor speed, where f, H & Q are

nominal values, and known from the pump data sheet.

Taking into consideration the affinity law and derived

equation stated in [16,17] for various motor speeds the

water flow-rate changes at various elevations (static head)

as follows:

223

; & mech

n nmechn

nf f

nfP f

  

 

  

 

 (15)

Applying Equation (15) in presented model requires to

select the whether the pump operates at maximum effi-

ciency where the water-flow rate has optimized value



max), thus:

max

max max

max

; for

1;for

fQQ

HQQ fQQ



































(16)

where



max max

;

@ 50 Hz &

and

QQ f

QQfn

or ffff















 

(17)

The simulated results are displayed in Figure 8, where

the pump flow-rate and static heads changed at different

frequencies. According to pump data sheet the value of



max = 9.5 m3/hr) is taken as a reference value obtained

at maximum efficiency and 50 Hz frequency. Also it’s

shown that regulating the source frequency directly af-

fects the static head and water-flow rate.

On other hand regulating the frequency causes signifi-

cant change in motor current as shown in Figure 9,

where at low frequency the drawn by the motor current is

the highest comparing with others at both operation

modes, starting and rated operation.

At different frequencies there is a stable operation

points where the motor operates at its rated slip (sn)

where the amount of pumped water depends on the me-

chanical torque developed at these frequencies and given

head. Referring to Equation (6) and substituting the value

of rated slip in Equations (12) and (14), the water flow-

rate can be written as:





4π1n

em n

QTss

gHP







  (18)

0 24 6810 12 1416

H=f(Q)

Q m3/hr

H,m

f=50Hz

f=40Hz

f=30Hz

Q m

Figure 8. Simulation results of the pump performance H =

f(Q).

05001000 1500 2000 2500 3000 3500 4000

35 Curren t I(n )

30Hz

40Hz

50Hz60Hz

Figure 9. Simulation results of the motor current at various

frequencies Iph = f(n).

PV-Grid Tie System Energizing Water Pump

415

The obtained simulation results at rated motor opera-

tion for various frequencies and elevation are givenin

Figure 10 for water flow-rates at three heads (10 m, 25

m and 40 m) where it can be seen that for frequencies

below the rated (f < 50 Hz) Q has quadratic relation with

speed.

3. SIMULINK Model of Described Pump

System

3.1. Simulation Model

A Matlab/Simulink for proposed mathematical model is

presented for induction motor pump, taking into account

that varying the motor voltage and frequency in accor-

dance with water flow-rate level saves energy and oper-

ates the motor at maximum pump efficiency.

Figure 11 presents the whole Simulink model includ-

ing solar PVmodel, Variable voltage-variable frequency

inverter system, Pump system, and water flow-rate sys-

tem, that predicts the water flow-rate and regulates both

voltage and frequency by using the variable voltage-

variable frequency (VFD) technology in order to keep

the motor operating at constant torque.

3.2. Simulation Results

The obtained simulation results from above mentioned

model are displayed in Figure 12 for various water flow-

rate and corresponding reference and actual speed, where

it’s shown that the motor adjusts its speed in accordance

with the needed flow-rate, which in turn significantly

reduces the power consumption.

While Figure 13 illustrates the generated by PV gen-

erator effective power at various radiations and con-

sumed by the pump effective power at water elevation of

05001000 1500 2000 2500 3000 3500

50 Q= f(N)

n, rpm

Q, m3/hr

H=10m

H=25m

H=40m

Q, m

/hr

Figure 10. Simulation results for pump performance at dif-

ferent heads (elevations).

(N. m)

1500

rpm

Discrete,

Ts = 2e-05 s.

-K -

n/wm1

-K -

n/wm

Head

Vph

Eff_pump

Qref

Pinp

Qnet

Tmech

Nrpm

Water

Water Pump

Vpv

-speedpulses

Vector control

Vab

TDH, m

298

T,[K]

Sg2

Sg1

Scope3

Ra te2

Ra te1

Radiation

Running

RMS

Q, m3/hr

Ipv

+Vout

-Vout

PV-MPPT

Outpu t

Max flow

1.5 HP / 380

IGBT In verter

380

Grid, V

Iabc

Speed

Q, m3/hr

Flow diagram

0.65

Eta_pump

0.5

Iabc (A)

Vab (V)

Figure 11. Matlab/Simulink model of induction-motor pump.

PV-Grid Tie System Energizing Water Pump

416

00.5 11.5 22.5 3

x 10

0.4

0.6

0.8

1.2

1.4

1.6

1.8

time,s

Q, m3/hr

Water flow-rate di agram

Q, m

/hr

(a)

00.5 11.5 22.5 3

x 10

-200

200

400

600

800

1000

1200

1400

time

Speed, rpm

VF D of IM-Pum p

Nref

Nact

(b)

Figure 12. Simulation results of water flow-rate and ob-

tained speed. (a) Water flow-rate diagram; (b) Pump actual

& reference speed at 20 m elevation.

20 m. It can be seen that at various water consumption

the PV system is capable to energize the pump system

and the excess of power at light consumption rate can be

used for energizing another loads. Furthermore applying

(VFD) saves energy and gives the pump system the abil-

ity for normally operation even at light irradiations or

cloudy weather.

3.3. Grid-Integrated Simulation Model

The proposed pump system is mainly energized from the

PV source, while the AC utility serves to recover the ener-

gy shortages [17]. Figure 14 illustrates the complete si-

mulation model including power estimator module, grid

compensation module, grid-tie module, etc.

Avoiding synchronizing procedure when two AC sources

are parallel connected, the AC utility is converted into

DC and connected to the load based on switching com-

mands sent by power estimator module to switch Q4 by

mean of the logic depicted in Equation (19).

The total power in form of voltage and current are

0246810 12 1416

x 10

100

200

300

400

500

time,s

Prms

RMS PV & Pump Power

Ppump

PpvG=1000W/m2

(a)

0 2 4 6810 12 14 16

x 10

100

150

200

250

300

350

time, s

Prms,W

RMS PV & Pump Power

Ppv

G= 400..800W/m 2

Ppump

(b)

Figure 13. Generated and consumed power at various irra-

diations. (a) Power diagram at constant irradiation; (b)

Power diagram at various irradiations.

converted into AC through out inverter circuit.

if Pure Source

/ if Combined

for Night time.

pv L

OFF PPPV

QONOFFPP















 (19)

Figure 15 illustrates the results obtained from the

mentioned simulation model, and proposed logic in Equa-

tion (19) where it’s shown that the grid will be switched

on only when there are a power shortages (Ppv < PLoad)

and the load needs to be fully energized. Meanwhile,

on-off grid connection can be realized in cases of load

level fluctuation or cloudy weather. During the night

time the load is energized from the AC utility. The pro-

posed circuit can be applied for either AC load or pump

system, single or three phase pumps.

4. Conclusions

A complete mathematical model has been developed for

studying the pump behaviours at various elevations, wa-

ter consumption rate and source voltage frequencies.

The proposed PV model consists of variable tracking

module and voltage drop compensating module that can

be used for either dc or ac loads with precise voltage

tracking procedure.

The proposed Simulink model for induction motor

PV-Grid Tie System Energizing Water Pump

417

Ipv

Vact_rms

V grid_rms

Grid

Continuous

powergui

RMS

(

discrete)

Vrms+dv

220

Vref_var

Vref1

RMS

iscrete

Vpv_rms

RMS

iscrete

Vout_ rms

Vout3

Vout2

Vout-ac

Vout

110

Vac_grid_rms

Vact

Vref Gate

VVT

GVg_Q1

VGT

110.1

T_var

Scope1

R-L

Ppv_rms

current

Voltage

Max current

PV-Power

P_status

Pulse_G

Ptot

Power Status Estimater

Ipv

GND

+Vpv

PV Array

Output chopper

DCi DCO

OCP

Npm

Lb7

Lb4

Lb3

Lb2

Lb1

Irms_load

RMS

(discrete)

Iout_rms1

RMS

(discrete)

Iout_rms

Io2

Io1

AC2

AC1

Inverter

Igrid-max1

Grid_co nnector

[Vg_p]

Goto

821.1984

G_var1

G_var

[Vg_p]

From

AC Grid Voltage

1:1

Vpv

Iload_r ms/Ipv

Vac_grid_rms

Vout_boost

VG_ch

Vgrid+DV

PV-Grid Compensation

Output inverter

NOT

Figure 14. Matlab/Simulink for grid-integrated configuration.

00.5 11.5 22.5 3

1000

2000

G, W/ m2

00.5 11.5 22.5 3

100

200

300

Ppv, Pload, W

00.5 11.5 22.5 3

-200

200

dp, W

00.5 11.5 22.5 3

0. 5

Pulse-Q4

Tim e, S

PV-Grid Contribution .. . .

Grid-off

Grid-on

Ppv

Pload

Figure 15. Power diagram at various irradiations & loading

status.

pumps shows the effect of applying VFD control on the

speed and water-flow rate. The added power-status esti-

mator module creates new aspect to this model, where

the power shortages can be measured and delivered from

alternative sources or main ac-grid.

The saved energy due to applying VFD control may

reaches 30% of consumed power, therefore being more

suitable to be energized from PV generator.

REFERENCES

[1] Q. Meng and W. Hu, “Roof Cooling Effect with Humid

Porous Medium,” Energy and Buildings, Vol. 37, No. 1,

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[2] P. C. Agrawal, “A Review of Passive Systems for Natural

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doi:10.1016/0741-983X(89)90091-X

[3] M. Chikh, A. Mahrane and A. Chikouche, “A Proposal

for Simulation and Performance Evaluation of Stand-

Alone PV Systems,” Proceedings of the 23rd EPVSEC,

Valence, Spain, 2008, pp. 3579-3584.

[4] E. Worrell, S. Ramesohl and G. Boyd, “Advances in En-

Ergy Forecasting Models Based on Engineering Eco-

nomics,” Annual Review of Environmental Resources,

Vol. 29, 2004, pp. 345-381.

doi:10.1146/annurev.energy.29.062403.102042

[5] S. B. Kjaer, J. K. Pedersen and F. Blaabjerg, “A Review

of Single-Phase Grid-Connected Inverters for Photovol-

taic Modules,” IEEE Transactions on Industry Applica-

tions, Vol. 41, No. 5, 2005, pp. 1292-1306.

doi:10.1109/TIA.2005.853371

[6] I. Odeh, Y. G. Yohanis and B. Norton, “Economic Viabil-

Ity of Photovoltaic Water Pumping Systems,” Journal of

Solar Energy, Vol. 80, No. 7, 2006, pp. 850-860.

doi:10.1016/j.solener.2005.05.008

[7] I. I. Lonel, “Pumps and Pumping,” Elsevier Publications,

PV-Grid Tie System Energizing Water Pump

418

Amsterdam, 1986.

[8] E. V. Meidanis, G. A. Vokas and J. K. Kaldellis, “Theo-

retical Simulation and Experimental Analysis of a PV-

Based Water Pumping System,” Lab of Soft Energy Ap-

plications & Environmental Protection, TEI of Piraeus.

powerelectronics.teipir.gr/Papers/MEDPOWER08_170.pdf

[9] J. Appelbaum and J. Bany, “Performance Analysis of DC

Motor Photovoltaic Converter System,” Solar Energy,

Vol. 22, No. 5, 1979, pp. 439-445.

doi:10.1016/0038-092X(79)90173-7

[10] M. Abu-Aligh, “Design of Photovoltaic Water Pumping

System and Compare It with Diesel Powered Pump,”

JJMIE, Vol. 5, No. 3, 2011, pp. 273-280.

[11] The Mathworks, Inc., “Matlab and Simulink,” Version

R2010a. http://www.mathworks.com

[12] S. B. Kjaer, J. K. Pedersen and F. Blaabjerg, “A Review

of Single-Phase Grid-Connected Inverters for Photovol-

taic Modules,” IEEE Transactions on Industry Applica-

tions, Vol. 41, No. 5, 2005, pp. 1292-1306.

doi:10.1109/TIA.2005.853371

[13] S. J. Chapman, “Electric Machinery Fundamentals,” Mc-

Graw-Hill, New York, 2003.

[14] G. McPherson and R. D. Laramore, “An Introduction to

Electric Machines and Transformers,” Wiley, New York,

1990.

[15] A. K. Daud and M. M. Marwan, “Solar Powered Induc-

tion-Motor Water Pump Operating on a Desert Well,

Simulation & Field Tests,” Renewable Energy Journal,

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doi:10.1016/j.renene.2004.02.016

[16] M. Benghanem and A. H. Arab, “Photovoltaic Water

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No. 1-3, 2007, pp. 50-57.

[17] S. Khader and A. K. Daud, “Photovoltaic-Grid Integrated

System,” 2012 First International Conference on Renew-

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26-28 March 2012, pp. 60-65.

doi:10.1109/REVET.2012.6195249

Nomenclature

A,B diode idealistic factors

Eg band gap energy of the semiconductor

fn rated supply voltage frequency

g gravity acceleration (9.8 m/s2)

G solar irradiation

Gr reference solar irradiation

h reservoir elevation (m)

H total head (m)

HA total installation head (m)

HS static head (m)

HL network hydraulic losses (m)



water density (1000 kg/m3)

ηp pump efficiency (%)

Id diode saturation current

IMPP PV module current at maximum power

Io cell current

Iph cell photo current

Ipv Photovoltaic current

Isc short circuit current

Ior,It constants given at standard conditions

IL1 motor line current

K Boltzman constant

n rotor speed in rpm

ns motor synchronous speed in rpm

Np number of parallel connected cells

Npm number of parallel connected PV modules

Ns number of series connected cells

Nsm number of series connected PV modules

p number of motor poles

PG grid power

Pconst constant losses power

PL load consumed power

Pem electromagnetic power

Pmech net mechanical power

RLoad load resistance

Rp PV intersinc shunt resistance

Rs PV intersinc series resistance

R1 stator resistance of induction motor

R’2 rotor resistance motor referred to stator

R’th Thevinen resistance referred to stator

Rinp total input stator resistance

Q electric charge (Coulomb)

Q water flow-rate (m3/hr)

Ppv Photovoltaic generated power

PV Photovoltaic

Pinp motor input power

Tc cell temperature in Kelvin

Tem electromagnetic torque (N·m)

Tm motor net mechanical torque (Nm)

Tr reference temperature in Kelvin

VFD Variable Frequency Drive

VMPP PV module voltage at maximum power

VO cell output voltage

VOC PV module open circuit voltage

Vph terminal phase voltage

Vpv array photovoltaic voltage

Vth Thevinen voltage

Xm magnetic reactance

X1 stator reactance of induction mptor

X’2 rotor reactance of induction motor referred to stator

X’th Thevinen reactance referred to stator

Xinp total input stator reactance

Zth Thevinen impedance

Zinp total input stator impedance

n normalized insulation



motor phase shift angle



rotor speed in rad/s



friction coefficient