A Fuzzy Global Efficiency Optimization of a Photo Voltaic Water Pumping System

8/8/2019 A Fuzzy Global Efficiency Optimization of a Photo Voltaic Water Pumping System

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A fuzzy global efficiency optimization of a photovoltaic

water pumping system

K. Benlarbi a, L. Mokrani b,*, M.S. Nait-Said a

a LSPIE Laboratory, Electrical Engineering Department, Engineering Science Faculty, Batna University,

Chahid M.E.H. Boukhlouf Street, Batna 5000, Algeriab Materials Laboratory, Electrical Engineering Department, Engineering Science Faculty, Laghouat University, B.P. 37G,

Ghardaia Street, Laghouat 03000, Algeria

Received 23 July 2003; received in revised form 9 March 2004; accepted 26 March 2004

Available online 19 May 2004

Communicated by: Associate Editor Arturo Morales-Acevedo

Abstract

This paper presents an on-line fuzzy optimization of the global efficiency of a photovoltaic water pumping system

driven by a separately excited DC motor (DCM), a permanent magnet synchronous motor (PMSM), or an induction

motor (IM), coupled to a centrifugal pump.

The fuzzy optimization procedure stated above, which aims to the maximization of the global efficiency, will lead

consequently to maximize the drive speed and the water discharge rate of the coupled centrifugal pump. The proposed

solution is based on a judicious fuzzy adjustment of a chopper ratio which adapts on-line the load impedance to the

photovoltaic generator (PVG). Simulation results show the effectiveness of the drive system for both transient andsteady state operations. Hence it is suitable to use this fuzzy logic procedure as a standard optimization algorithm for

such photovoltaic water pumping drives.

2004 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic water pumping; Global efficiency optimization; Fuzzy logic controller; DC and AC actuators

1. Introduction

The increasing of the world energy demand, due to

the modern industrial society and population growth, ismotivating a lot of investments in alternative energy

solutions, in order to improve energy efficiency and

power quality issues. The use of photovoltaic energy is

considered to be a primary resource, because there are

several countries located in tropical and temperate

regions, where the direct solar density may reach up to

1000 W/m2.

One of the most popular applications of the photo-

voltaic energy utilization is the water pumping systemdriven by electrical motors. The two main restrictions

for using solar energy are the high initial installation

cost and the very low photovoltaic cell conversion effi-

ciency. The cell conversion ranges vary from 12% of

efficiency up to a maximum of 29% for very expensive

units (Sim~oes and Franceschetti, 2000). In spite of those

facts, there has been a trend in price decreasing for

modern power electronics systems and photovoltaic

cells, indicating good promises for new installations.

Moreover, the maximum power of a photovoltaic

system changes with solar intensity, and temperature;

and dynamic loads influence the performance by

* Corresponding author. Tel.: +213-2993-2117; fax: +213-

2993-2698.

E-mail address: [email protected] (L. Mok-

rani).

0038-092X/$ - see front matter 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2004.03.025

Solar Energy 77 (2004) 203216

www.elsevier.com/locate/solener
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changing continuously the operating point. In order to

amortize the initial investments, it is very important to

optimize the photovoltaic water pumping system, by the

use of power electronics converters to adapt dynamically

the electrical impedance to the PVG for different oper-

ating conditions (Matsui et al., 1999; Akbaba and

Akbaba, 1999).

Various studies have been done on the choice of the

drive system, which suits PVG, type of pumps to use and

ways to control and optimize the water pumping system.

This was firmly related to existing technologies.

At the early stage, only the DC motors were used to

drive pumps. Direct coupling of series, shunt, and sep-

arately excited DC motors to PVG in water pumping

systems were studied (Appelbum, 1986; Saied, 1988,

Fam and Balachander, 1988, Appelbaum and Sharma,

1989). Steady state and transient performances werepresented. The separately excited and the permanent

magnet DC motors were found more suitable for PV

water pumping systems (Roger, 1984; Singer, 1993;

Akbaba et al., 1998; Mummadi, 2000). The power

electronics converter used to adapt the dynamic electri-

cal impedance of DC motors to the PVG is a buck, a

boost, or a buck-boost chopper in general (Altas and

Sharaf, 1996; Martins, 1998; Hua and Shen, 1998).

The permanent magnets synchronous motors called

also brushless DC motors coupled to a centrifugal pump

were found suitable for PV water pumping systems

(Benlarbi, 2003; Swamy, 1995).

Moreover, the AC induction motors driving PV

water pumping systems were introduced mainly for their

robustness and relatively low cost. Steady state and

transient characteristics of such systems were presented

in (Olorunfemi, 1991; Eskander and Zaki, 1997). The

motor characteristics are severely affected by the PVG

which was considered as a current generator with

dependent voltage source.

For such applications, where the PV water pumping

system is driven by an AC motor (PMSM or IM), a

chopper and/or an inverter should be included in order

to perform the DCAC conversion stage (Benlarbi,

2003).

For PV water pumping systems, two types of pumps

are widely used: the volumetric pump and the centrifugal

pump. It is found that the PVG energy utilized by the

centrifugal pump is much higher than by the volumetricpump. In fact, in the case of the centrifugal pumps, the

operation takes place for longer periods even for low

insulation levels, and the load characteristic is in closer

proximity to the PVG maximum power locus (Pote-

baum, 1984; Anis and Metwally, 1985; Appelbum, 1986;

Olorunfemi, 1991; Veerachary and Yadaiah, 2000).

In PV water pumping systems, the maximum power

point tracking (MPPT) is usually used as online control

strategy to track the maximum output power operating

point of the PVG for different operating conditions of

insolation and temperature of the PVG. Although, the

use of the MPPT control do not mean a systematic

Nomenclature

A PV generator surface

AP pump torque constant

Bm viscose friction coefficient

E insolationea armature voltage

H total pump head

I PV generator current

ia armature current

I0 PV generator reverse saturation current

Iph photocurrent

isd d-axis stator current

isq q-axis stator current

Jm moment of inertia

K chopper ratio

KE motor speed constant

KT motor torque constantLa armature inductance

Ld d-axis self inductance of the stator

Lq q-axis self inductance of the stator

Lr rotor self inductance

Ls stator self inductance

M mutual inductance

P number of pole pairs

Pn motor output rated power

Q water discharge rateR equivalent series resistance of the PVG

Ra armature resistance

Rr rotor resistance per phase

Rs stator resistance per phase

Te electromagnetic developed torque

TL load torque

TP pump torque

vsd d-axis stator voltage

vsq q-axis stator voltage

V PV generator voltage

Vth thermal voltage of the PV generator

wf permanent magnets total fluxwrd d-axis rotor flux

wrq q-axis rotor flux

xm drive angular speed

xs synchronous angular speed

g global efficiency

204 K. Benlarbi et al. / Solar Energy 77 (2004) 203216


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optimization of the motor or the whole system efficiency

(Yao and Ramshaw, 1995; Eskander and Zaki, 1997;

Matsui et al., 1999).

Thus, several control strategies of optimization

allowing the improvement of the photovoltaic water

pumping system operation were applied to the efficiency

maximization of the PVG, the motor, or the wholesystem. For example, two control strategies were pre-

sented in (Eskander and Zaki, 1997). Firstly, a water

pumping system driven by an induction motor coupled

to a centrifugal pump is controlled to operate on the

maximum power characteristic of the PVG. Secondly,

the induction motor is controlled to operate at its

maximum efficiency. A comparison is made, and it is

concluded that the MPPT is not necessarily the better

way to control a PVG in a water pumping system.

Elsewhere, many techniques such as gradient meth-

ods, and artificial intelligence techniques were applied

successfully to implement on-line the optimizationstrategy used for the photovoltaic water pumping sys-

tems optimization.

Fuzzy logic control has been successfully applied to

track the maximum power point in PV energy conver-

sion systems (Hilloowala and Sharaf, 1992; Won et al.,

1994), and to transfer the maximum electric power

available from a PVG to a three-phase induction motor

supplied via a PWM inverter (Altas and Sharaf, 1994).

The neural networks were used also to track on-line

the maximum power of the PVG as it was reported by

(Hiyama et al., 1995), and to identify the PVG optimal

point supplying via a chopper a separately excited DC

motor, coupled to a centrifugal pump or a volumetric

pump (Veerachary and Yadaiah, 2000).

In addition, the neuro-fuzzy networks were used in

the same context. Let us state for example the study

presented by (Della et al., 2000) which leads to an on-

line optimal operation point tracking of a PVG which

supplies an induction motor via a PWM voltage in-

verter.

One of the authors has shown the effectiveness of the

artificial intelligence techniques comparatively to the

gradient classical methods, in optimizing a water

pumping system driven by DC and AC motors (Ben-

larbi, 2003).This diversity of the control strategies used to opti-

mize water pumping systems driven by different electri-

cal motors coupled to a centrifugal pump, has

stimulated us to propose a general fuzzy global efficiency

optimization algorithm of such systems, able to become

a standard control strategy of all PV water pumping

systems, because of the fuzzy logic robustness and

effectiveness in the case of process with dynamic model

or nonlinear in nature.

Hence, the aim of this paper is to present a fuzzy self-

tuning of the chopper ratio intercalated between the

PVG and a PWM inverter and/or an electrical motor,

driving a centrifugal pump in order to optimize the

global efficiency of the whole photovoltaic water

pumping system driven by a separately excited DC

motor, a permanent magnet synchronous motor, or an

induction motor.

For this purpose, a fuzzy logic controller composed

by an inference rules base, is proposed for the on-lineadjustment of the chopper ratio according to the global

efficiency evolution of the water pumping system for

different illumination intensity levels.

The paper is organized as follows: in Section 2

mathematical model of the photovoltaic water pumping

system (PVG, chopper, electrical motors and centrifugal

pump) is given. In Section 3, the structure configuration

of the fuzzy logic controller applied to the global effi-

ciency optimization of the PV water pumping system is

presented. Simulation results of the whole PV water

pumping system driven by one horsepower three differ-

ent motors are presented, discussed, and compared inSection 4 of this paper. The effectiveness of the proposed

fuzzy controller is illustrated both in transient and

steady state operating conditions. Finally some con-

cluding remarks end the paper.

2. Mathematical model of the photovoltaic water pumping

system

A photovoltaic water pumping system is composed

mainly of a PV generator, power electronics con-

verter(s), and an electrical motor usually coupled to acentrifugal pump load (as shown in Fig. 1).

Mathematical models of the photovoltaic water

pumping system components are given in the following

sections.

2.1. Photovoltaic generator model

The direct conversion of the solar energy into elec-

trical power is obtained by solar cells. A PVG is com-

posed by many strings of solar cells in series, connected

in parallel, in order to provide the desired values of

output voltage and current. Fig. 2 shows the equivalent

circuit of a PVG, from which non linear IV charac-

teristic can be deduced.

PVG

Chopper

=

=Electrical

motorCentrifugal

pump

=

~

Inverter

Fig. 1. Photovoltaic water pumping system scheme.

K. Benlarbi et al. / Solar Energy 77 (2004) 203216 205


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As mentioned previously, one can express the general

formula of the PVG IV characteristic as follows:

I Iph ID Ip

Iph I0 expVJq

k0T

1

V RsI

RP1

Then the PV generator nonlinear IV characteristic can

be rewritten as:

V Vth lnIph 1

RsRP

I V

RP

I0

0@ 1

1A RsI 2

with:

Vth k0T

q3

where k0 is the Boltzman constant, T is the absolute

temperature, and q is the electron charge.

Usually, the shunt resistance effect is neglected,

consequently the expression of the PVG terminal volt-age, can be expressed by (Harakawa and Tujimoto,

2001; Veerachary and Yadaiah, 2000; Alghuwainem,

1992; Altas and Sharaf, 1994):

V Vth lnIph I

I0

1

RI 4

where Iph is the photocurrent, it is proportional to the

illumination intensity (Iph 4:82 A for an insolation of1000 W/m2 in our numerical case).

2.2. Power electronics converters modeling

The DCDC converter is a buck, a boost, or a buck-

boost chopper in general. It is inserted between the PVG

and its load in order to adjust the dynamic equivalent

impedance of the PWM inverter and/or the electric

motor. One can define the chopper gain K as the ratio

between the output and the input mean voltages or the

input and output mean currents when the conduction

regime is continuous. So, if the chopping frequency is

sufficiently higher, which is the case at low power levels,

one can replace the converter with an equivalent pure

gain model. By considering the mean values of the

electric quantities over a chopping period, on can write:

U VK and i I

K5

The inverter, inserted between the chopper and the AC

motor, is controlled by applying the field-oriented con-

trol strategy to the PMSM and IM, in order to ovoid

the coupling and the magnetic saturation problems inthe machines. This strategy uses the measured speed, the

nominal magnetic flux and the torque reference value, to

determine the frequency and the current references

necessary to control the PWM inverter.

2.3. Electrical motors modeling

2.3.1. DC motor model

The mathematical relation that describes the dynamic

model of a DC motor with constant magnetic flux, can

be expressed as follows (Grellet and Clerc, 1997):

ea iaRa La diadt

e 6

Te KTia 7

e KEdhm

dt KExm 8

The parameters of the DC motor are, KT the torque

constant, KE the back emf constant, La the armature

inductance, Ra the armature resistance, hm the rotor

position in mechanical degrees, xm the rotor angular

speed, and P the number of pole pairs.

2.3.2. Permanent magnet synchronous motor model

The mathematical dynamic model of a PMSM drive

can be described by the following equations in a syn-

chronously rotating dq reference frame (Grellet and

Clerc, 1997):

vdvq

Rs pLd PxmLqPxmLd Rs pLq

idiq

0

Pxmwf

9

where vd and vq, Ld and Lq, id and iq are stator voltages,

inductances, and currents components in the (d; q) axisrespectively; Rs is the stator resistance per phase, wf is

the rotor flux linkage due to the rotor permanent magnetframe, and p is the differential operator.

Moreover, the PMSM developed electromagnetic

torque is given by the following equation:

Te 3P

2wfiq Ld Lqidiq 10

2.3.3. Induction motor model

The mathematical dynamic model of a three-phase,

Y-connected induction motor is described by the equa-

tions set (11) expressed in the dq synchronously rotat-

ing reference frame as (Grellet and Clerc, 1997):

I

IphID

D Rp

Rs

IP

VVJ

Fig. 2. Equivalent circuit of a PVG.



5/14

where: Tr LrRr

, Ts LsRs

, and r 1 M2

LrLs.

In this case, the IM develop an electromagnetic tor-

que Te expressed as follows:

Te 3P

2

M

Lrisqwrd isdwrq 12

where, vsd and vsq, isd and isq, wsd and wsq are the stator

voltage, current and rotor flux dq axis components

respectively; Rs and Rr are the stator and rotor resis-

tances per phase, respectively; Ls and Lr are the statorand rotor self inductances respectively; M is the rotor

stator mutual inductance; xs is the angular speed of the

rotating magnetic field.

2.4. Centrifugal pump model

The mechanical part modeling of an electric motor is

given by

Te Jmpxm Bmxm TL 13

where Bm is the viscous-friction coefficient, Jm is the total

inertia of motor shaft, and TL is the load torque.In this case TL is the hydrodynamic load torque of the

centrifugal pump, which is given by the following

equation (Anis and Metwally, 1994):

TL TP APx2m 14

where:

AP Pn

x3n

15

The centrifugal pump is also described by an HQ

characteristic given by (Caro and Bonal, 1997):

H C1x2m C2xmQ C3Q

2 16

where C1, C2 and C3 are constant parameters.

The pump performance is predicted by specifying a

load curve (Caro and Bonal, 1997):

H Hg DH 17

where, Hg is the geometrical height which is the differ-

ence between the free level of the water to pump and the

highest point of the canalization, and DH is the pressure

losses in the whole canalization, they are given by:

DH kl

d

n

8Q2

p2d4g18

with, k is a coefficient of the regular pressure losses in the

canalization, l length, and d diameter; n is a coefficient

of the local or singular pressure losses in elbows, valves,

and connections,. . .of the canalization.

3. Fuzzy logic controller structure and design

The fuzzy logic permits to define control laws of any

process starting from a linguistic description of the

control strategy to be adopted. Fuzzy logic uses instead

of numerical variables linguistic ones, which are vari-

ables whose values (fuzzy subsets) are labels or sentences

in a natural or artificial language. Hereafter a descrip-

tion of a fuzzy logic controller proposed to the global

efficiency optimization of a PV water pumping system.

3.1. Fuzzy logic controller structure

In a typical basic configuration of a fuzzy logic

controller (FLC) one can find (Buhler, 1994):

1. Fuzzification or linguistic coding of input variables,

which transforms a given set of numerical inputs

(measured or calculated) into a fuzzy linguistic vari-

ables set composed of fuzzy subsets called also mem-

bership functions.

2. Inference fuzzy rules which contains a set of fuzzy

rules in linguistic form as well as the database which

is a collection of expert control knowledge allowing

to achieve the fuzzy control objectives. This control

rules base can be set up using IF-THENrules, basedon expert experience and/or engineering knowledge,

and learning fuzzy rule-based system which has learn-

ing capabilities. The fuzzy reasoning used to built a

decision-making unit, is usually expressed as rules

with sentence conjunctives AND, and OR.

3. Defuzzification of the inference engine, which evalu-

ates the rules based on a set of control actions for a

given fuzzy inputs set. This operation converts the in-

ferred fuzzy control action into a numerical value at

the output by forming the union of the outputs

resulting from each rule. At this stage the controller

has to resolve the conflict between the different rules

vsqvsd0

0

2664

3775

Rs M2

LrTr prLs

rLsxs

MLrTr

MLrPxm

rLsxs Rs M2

LrTr prLs

MLrPxm

MLrTr

MTr

0 p 1Tr

xs Pxm

0MTr xs Pxm p

1Tr

26666664

37777775

isqisdwrqwrd

2664

3775

11



6/14

that may fire at the same time. The defuzification

produces a non-fuzzy output control action that best

represents the recommended control actions of the

different rules.

3.2. FLC design for global efficiency optimization

The PV water pumping system global efficiency is the

ratio of the hydrodynamic centrifugal pump power to

the input incidental power captured by the photovoltaic

generator, it is defined as follows:

g APx

3m

EA19

The optimization of this global efficiency is done by

maximizing the power of the centrifugal pump for a

given illumination intensity E, which vary slowly with

the time. This will lead consequently to maximize the

electrical motor speed or the water discharge rate.A DCDC converter with an adjusted ratio K per-

mits the maximization of this efficiency, by an online

adaptation of the load impedance to the photovoltaic

generator. A self-tuning of the chopper ratio K using a

fuzzy logic controller is proposed for this purpose. Fig. 3

shows the block diagram of this fuzzy controller.

The two input control variables of the fuzzy con-

troller are the global efficiency variation dgk, and thechopper ratio variation dKk at the kth sampling peri-od. They are updated using the following equations:

dgnk Gdggk gk 1 20

dKnk GdK1Kk Kk 1 21

dgk and dKk are normalized using the two inputscaling factors Gdg and GdK1. The output of the con-

troller is a new ratio Kk 1 to be applied to controlthe chopper, calculated according to a decision table

rules, it is given by:

Kk 1 Kk GdK2 dKnk 1 22

where GdK2 is the output scaling factor of the fuzzy logic

controller. The three FLC scaling factors play an

important role in fixing the optimization performance,

and they can be chosen using trial and error method.

The fuzzy controller membership functions for both

inputs and output variables are triangle-shaped func-

tions as it is shown in Fig. 4. Hence, the space of dgkand dKk is partitioned with a fuzzy subset functionsnamed fNB; NS; EZ; PS; PBg. Each of these acro-nyms is described by a given mathematical membership

function, and means namely, NB negative big,NS negative small, EZ zero, PS positive small,and PB positive big.

The generated rules should be done properly andarranged in a fuzzy matrix table. Twenty five rules have

been deduced from a qualitative analysis of the influence

of the chopper ratio variation dKon the global efficiency

variation dg (see Table 1), on the basis of Fig. 5.

The following scenario justifies the reasoning behind

the chosen rules which determine the FLC action (see

also Fig. 5 and Table 1):

1. If the global efficiency variation is sufficiently close to

0 which means that its maximum is reached, then we

would not make any variation in the chopper ratio.

2. If a positive variation of the global efficiency is going

with a negative variation of the chopper ratio, then

Z-1

d k( )

Calculation FLC

k( )

dK(k)

d n(k)

dKn(k)G

GdK1

dKn(k+1) K(k+1)

GdK2

d

Fig. 3. Synoptic scheme of the proposed fuzzy controller.

(d n), (dKn)

d n, dKn

PSEZNSNB PB

1-1 -0.5 0 0.5

Fig. 4. Membership functions of dgn, and dKn.

Table 1

Inference rules matrix used to update the chopper ratio

dKk 1

dKk dgk

NB NS EZ PS PB

NB PB PS EZ NS NB

NS PS PS EZ NS NS

EZ NS NS EZ PS PS

PS NS NS EZ PS PS

PB NB NS EZ PS PB

d

> 0 d< 0

dK> 0dK> 0

K

Fig. 5. Fuzzy rules deduction from g versus K function.



7/14

we would decrease the future chopper ratio, and vice

versa.

3. If a negative variation of the global efficiency is

accompanied with a negative variation of the chopper

ratio, then we would increase the new chopper ratio,

and vice versa.

One can note from Table 1 that for a zero variation

of the ratio K, a small variation is proposed for its future

variation, in order to start the tuning at the initial

sampling periods.

The product-sum inference mechanism is used to

calculate the fuzzy output of the controller. This is

achieved by forming the union of the fuzzy output

resulting from each rule, which is the corresponding

output membership function weighted by the rule

strength (Buhler, 1994).

Many strategies can be used for performing the de-

fuzzification process which converts the fuzzy output ofthe fuzzy controller into a numerical value. The gravity

center defuzification method is used in this paper. The

main idea of this method is that the larger the firing

strength of a rule, the more this rule contributes to the

global output of the fuzzy controller. In this case, the

change of the controller output at the kth sampling

interval is updated as it is mentioned in (22), with:

dKnk 1

P25i1 lixiSiP25i1 liSi

23

where li is the ith rule degree of fulfillment at the kth

sampling period, xi is the gravity center abscissa of theoutput fuzzy membership function corresponding to the

ith rule, and Si is its surface.

4. Simulation results and discussion

In this section the simulation results of the fuzzy

global efficiency optimization of a photovoltaic pumping

system driven by three types of electrical motors coupled

to a centrifugal pump are presented. All the parameters

of the photovoltaic water pumping system components

are depicted in the Appendix A.

4.1. Optimization procedure

For a given insolation level E, the chopper ratio K is

initialized to 1 (for the non-optimized system K is fixed

to this value) and its variation to 0, the PVG voltage is

set to the open circuit value. Then the motor dynamic

model (6, 9 or 11) associated to the mechanical differ-

ential Eq. (13) are solved using the fourth order Runge

Kutta numerical method considering the motor starting

point as initial solution. This will define the motor state

(current(s), (fluxes), and speed) for each iteration. The

obtained new and previous speed values are used to

calculate the efficiency variation from Eq. (19), and

determine the new chopper ratio and its variation from

(22) and (23) respectively. Moreover, the calculated

motor current(s) impose the PVG current which is used

to determine the operating point voltage using the IV

characteristic of Eq. (4). The dynamic model of themotor coupled to the centrifugal pump is solved again

with the new chopper ratio issued from the fuzzy con-

troller, and the PVG output voltage, starting from the

last iteration motor state as initial solution until the

steady state characterized by a constant speed is

reached. Then the water discharge rate is calculated

using Eqs. (16) and (17).

In order to speed up the algorithm we have used the

solution obtained for a given insolation level as initial

point to start the calculation for this insolation level

increased or decreased by a moderate step of (25 W/m2).

4.2. Steady state simulation results

Firstly, Fig. 6 proves the utility of the optimization of

the photovoltaic pumping system driven by a DC motor,

in fact a considerable increase of the speed, and a clear

improvement of the system global efficiency for low

insolation levels can be noted (see Figs. 7 and 8

respectively). At a nominal level of illumination intensity

(E 1000 W/m2) the direct coupling of the separatelyexcited DC motor with the PV generator is naturally

optimized. We note also that the optimum operation

points of the photovoltaic water pumping system char-acterized by maximal drive speeds are almost confused

with those offering a maximum electric power of the PV

generator (see Fig. 6).

Secondly, the simulation results obtained for the

optimized and the non-optimized global efficiencies of

0 50 100 150 200 2500

1

2

3

4

5

Voltage (V)

Curren

t(A)

o Non-optimized system* Optimized system

1000W/m

900W/m

800W/m

700W/m

600W/m

500W/m

400W/m

200W/m

300W/m

Fig. 6. Operation points of the photovoltaic pumping system

driven by a DCM.



8/14

the photovoltaic water pumping system driven by a

PMSM, are represented by Figs. 911. One can note that

the proposed fuzzy self-tuning of the chopper ratio

could shift the system operation points to be close to

those of maximum PVG power. In fact the curve of the

optimized operation points overlaps practically thatoffering a maximum electric power of the PV generator

(curve IV in continuous line). We note also a speedincrease of the optimized system with the illumination

intensity increasing (see Fig. 10), and an improvement of

its global efficiency (see Fig. 11). Moreover, for an

insolation of 725 W/m2 the optimized and non-opti-

mized global efficiencies coincide, this means that the

group PMSMcentrifugal pump is well adapted to the

PVG at this insolation level.

Thirdly, the simulation results of the photovoltaic

water pumping system driven by an induction motor in

the optimized and the non-optimized global efficiencies

200 400 600 800 10003

4

5

6

7

8

9

10

Insolation (W/m)

Globalef

ficiency

(%)

Optimized global efficiency

Non-optimized global efficiency

Fig. 8. Global efficiency of the Photovoltaic pumping system

driven by a DCM.

0 50 100 150 200 2500

1

2

3

4

5

Voltage (V)

Curren

t(

A)

o Non-optimized system* Optimized system

1000W/m

900W/m

800W/m

700W/m

600W/m500W/m

400W/m

200W/m

300W/m


driven by a PMSM.

200 400 600 800 100060

80

100

120

140

160

180

200

Insolation (W/m)

Speed(rad/s)

Non-optimized speeds

Optimized speeds

Fig. 10. Speeds of the photovoltaic pumping system driven by a

PMSM.

200 400 600 800 10002

3

4

5

6

7

8

9

10

Insolation (W/m)

Globalefficiency(%)




driven by a PMSM.

200 400 600 800 100080

100

120

140

160

180

200

Insolation (W/m)

Speed(rad/s)


Optimized speeds

Fig. 7. Speeds of the photovoltaic pumping system driven by a

DCM.



9/14

cases, are illustrated by Figs. 1214. It can be noted that

the system global efficiency is improved by the proposed

fuzzy logic controller (see Fig. 14). Also, Fig. 12 illus-

trates the load characteristic in the PV plan IV. It isnoted that the photovoltaic water pumping system

operation points curve corresponding to the optimized

system is shifted towards the maximum electric powerpoints of the PV generator (curve IV in continuousline). For an insolation different from that to which the

motor-pump is well adapted to the PVG (700 W/m 2), the

curve IV of the non-optimized system deviates con-siderably from that of the PVG offering a maximum

electric power. We notice also in this case a clear in-

crease of the speed for low illumination intensities in

particular (see Fig. 13). But, it is to note also that the

IV optimized curve and the PVG maximum powerpoints characteristic are clearly distinct.

For comparison, the Figs. 15 and 16 represent the

optimized global efficiencies as well as the water dis-

charge rates versus the solar illumination intensity, of

the photovoltaic pumping systems driven by a one

horsepower three different motors. It can be noted that

the same centrifugal pump starts pumping water at

illumination intensities of 275.37, 294.39, and 361.50 W/

m2, for the optimized systems driven by a separately

excited DC motor, a permanent magnet synchronous

motor, and an induction motor respectively. Whereas,

this is reached with illumination intensities of 404.14,

382.78, and 486.21 W/m2, respectively for the non-

optimized systems. Let us present the daily pumped

water quantity, which is of 115.557, 120.720, and 98.620

m3 for the optimized pumping systems driven by a sep-

arately excited DCM, a PMSM, and an IM respectively.

200 400 600 800 10000

2

4

6

8

10

Insolation(W/m)

Globaleffeciency(%

)

IM

DCM

PMSM

Fig. 15. Optimized global efficiencies of the photovoltaic

pumping systems driven by a DCM, a PMSM and an IM.

0 50 100 150 200 2500

1

2

3

4

5

Voltage (V)

Curren

t(A)

o Non-optimized system

* Optimized system

1000W/m

900W/m

800W/m

700W/m

600W/m

500W/m

400W/m

200W/m

300W/m


driven by an IM.

200 400 600 800 100040

60

80

100

120

140

160

180

200

Insolation (W/m)

Speed(rad/s)


Optimized speeds

Fig. 13. Speeds of the Photovoltaic pumping system driven by

an IM.

200 400 600 800 10000

1

2

3

4

5

6

7

8

Insolation (W/m)

Globalefficiency(%)




driven by an IM.



10/14

However, it is only of 104.424, 110.204, and 84.932 m3

respectively, for the non-optimized system.

A comparison between the global efficiencies and the

water discharge rates of the photovoltaic water pumping

systems driven by the three electrical motors can be

deduced from the two Figs. 15 and 16 respectively and

Tables 24. In fact, one can note that the permanentmagnet synchronous motor and the separately excited

DC motor represent the two best choices for the

pumping system drive comparatively with the induction

motor in terms of water quantity pumped per day. It is

to be noted also that the global efficiency of the pho-

tovoltaic pumping system driven by the permanent

magnet synchronous motor is the best along an illumi-

nation intensity range varying from 400 W/m2 approx-

imately to 1000 W/m2. As a result the water pumped

quantity per day, is largely higher than that pumped by

the systems driven by the separately excited DC motor,

and the induction motor in particular.

200 400 600 800 10000

2

4

6

8

10

12

14

16

Insolation (W/m)

Waterdischargeratem/h)

IM

DCM

PMSM

(m3/h)

Fig. 16. Water discharge rates of the photovoltaic pumping

systems driven by a DCM, a PMSM, and an IM.

Table 2

Simulation results of the photovoltaic water pumping system driven by a DCM, with and without fuzzy optimization

E (W/m2) Non-optimized results Optimized results

x (rad/s) g (%) Q (m3/h) K x (rad/s) g (%) Q (m3/h)

1000 188.237 8.662 14.729 0.982 188.336 8.675 14.743

900 182.228 8.731 13.903 0.966 182.634 8.790 13.960

800 173.956 8.545 12.728 0.927 175.725 8.808 12.983

700 164.101 8.198 11.252 0.886 168.152 8.820 11.870

600 152.706 7.707 09.394 0.841 159.748 8.823 10.565

500 136.746 6.641 06.256 0.792 150.269 8.813 08.966400 121.999 5.895 00.000 0.736 139.333 8.782 06.836

300 106.254 5.193 00.000 0.671 126.271 8.715 03.132

200 085.644 4.079 00.000 0.591 109.724 8.577 00.000

Quantity of

water per

day (m3)

104.424 115.557

Table 3

Simulation results of the photovoltaic water pumping system driven by a PMSM, with and without fuzzy optimization


x (rad/s) g (%) Q (m3

/h) K x (rad/s) g (%) Q (m3

/h)

1000 186.998 8.492 14.561 1.166 194.527 9.559 15.573

900 183.697 8.944 14.107 1.127 187.646 9.533 14.648

800 179.318 9.360 13.495 1.047 180.279 9.511 13.631

700 171.974 9.436 12.438 0.979 172.110 9.458 12.458

600 159.877 8.845 10.586 0.900 162.880 9.353 11.062

500 143.819 7.726 07.761 0.826 149.926 9.162 09.311

400 125.948 6.486 02.990 0.730 139.524 8.818 06.877

300 105.032 5.015 00.000 0.624 123.648 8.183 01.676

200 078.769 3.173 00.000 0.495 101.697 6.829 00.000

Quantity of

water per

day (m3)

110.204 120.720



11/14

In addition, Tables 24 recapitulate the simulationresults of the non-optimized and the optimized photo-

voltaic water pumping system driven by the three elec-

trical motors types, for some illumination intensity

levels. This shows explicitly the significance of the pro-

posed fuzzy optimization algorithm in terms of the

global efficiency improvement and the water discharge

rates increasing.

4.3. Effectiveness of the drive in the case of some transient

operations

Let us discuss now, the effectiveness of the PV water

pumping system driven by a PMSM for example, for

starting transient and an abruptly solar insolation vari-

ation, which will appear or disappear on a cloudy day.

The Figs. 17 and 18 present, respectively, the chopper

ratio evolution tuned by the fuzzy controller and the

speed transient behavior, at the starting of a photovol-

taic water pumping system driven by a PMSM, for an

insolation level of 1000 W/m2. One can note that the

chopper ratio is fine-tuned by the fuzzy logic controller,

in fact it reaches its optimal value of 1.166 in the steady

state operation (see Table 3). Consequently an optimal

speed of 194.527 rad/s is obtained in this case.Fig. 20 represents the speed variation of the photo-

voltaic water pumping system driven by a PMSM for an

abrupt insolation variation from 1000 to 500 W/m2 and

vice versa, studied as extreme case to prove the effec-

tiveness of the drive system. It is noted that when the

insolation varies from 1000 to 500 W/m2 between 2 and

4 s, the chopper ratio is judiciously tuned by the fuzzy

logic controller to its new optimal value. In fact, it

changes from 1.166 to 0.826 and vice versa (see Fig. 19

and Table 3). Consequently the PMSM optimum speed

changes rapidly from 194.527 to 149.926 rad/s in about

0.6 s. Hence, one can conclude that the chopper ratio

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (s)

Chopperra

tio

K

Fig. 17. Chopper ratio behavior during the starting transient of

a PV water pumping system driven by a PMSM for an inso-

lation level of 1000 W/m2.

0 0.5 1 1.5 20

50

100

150

200

Time (s)

Spee

d(rad

/s)

Fig. 18. Speed behavior during the starting transient of a PV

water pumping system driven by a PMSM for an insolation

level of 1000 W/m2

.

Table 4

Simulation results of the photovoltaic water pumping system driven by an IM, with and without fuzzy optimization


x (rad/s) g (%) Q (m3/h) K x (rad/s) g (%) Q (m3/h)

1000 168.139 6.173 11.868 1.258 180.686 7.660 13.688

900 166.105 6.613 11.560 1.200 173.763 7.570 12.700800 163.330 7.073 11.132 1.098 166.327 7.469 11.594

700 158.055 7.325 10.291 1.018 158.114 7.333 10.301

600 146.313 6.779 08.242 0.916 149.080 7.171 08.753

500 125.666 5.154 02.861 0.812 139.045 6.982 06.773

400 105.401 3.801 00.000 0.708 127.552 6.737 03.644

300 82.128 2.398 00.000 0.591 113.964 6.407 00.000

200 055.832 1.130 00.000 0.459 096.935 5.914 00.000

Quantity of

water per

day (m3)

84.932 98.620



12/14

fuzzy update is carried out quickly, and allows an on-

line optimization of the global efficiency of the PV water

pumping system, even in extreme case of solar insolation

changes.

5. Conclusion

In this paper, an on-line novel view point optimiza-

tion of the global efficiency of a photovoltaic water

pumping system driven by a DCM, a PMSM, and an IM

coupled to a centrifugal pump using a fuzzy logic con-

troller, is proposed. The main concluding remarks are

summarized as follows:

1. The obtained simulation results have shown the good

performance of the proposed controller in terms of

global efficiency optimization of the PV water pump-

ing system, and water quantity pumped per day in the

steady state operation. The effectiveness of the drive

system for both, starting transient and severe solar

insolation variations, were also shown.

2. It is shown that the PMSM is a better choice for the

photovoltaic water pumping system drive, because a

DCM requires an excitation source and/or periodicalrepair and maintenance. On the other hand the IM is

note technically a competitive choice.

3. Furthermore, the expected insensitivity of the pro-

posed fuzzy controller against parametric and non-

parametric variations (such as temperature, motors

parameters, . . . etc.) will be proved.

4. It is shown also via this paper, that the MPPT control

strategy is not always the better way to optimize the

photovoltaic water pumping system, especially in the

case of the IM drive. Hence it is preferable to opti-

mize the output power or the global efficiency instead

of the PVG power for example.5. The proposed fuzzy controller provides a highly on-

line accurate tracking of the optimal global efficiency

operating point, of the photovoltaic pumping systems

driven by the conventional electrical actuators, and

can become a standard regulator for optimizing such

systems. In fact with the same inference table, it can

be generalized to optimize a given objective function

of a PVG supplying a given load via a DCDC con-

verter.

Appendix A

PV generator parameters

Vth 12:227 V; I0 4:877e6 A; R 2:25 X

DCM parameters

Pn 746 W; xn 183:259 rad=s; ea 180 V;

ia 5:5 A; Ra 8:03 X; La 0:045 H;

KE 0:741 V=rad=s; KT 0:741 N m=A;

Jm 0:024 kg=m2; Bm 0 Nm=rad=s

PMSM parameters

Pn 746 W; xn 188:495 rad=s; vsn 208 V;

Isn 3 A; Rs 1:93 X; Ld 0:0424 H

Lq 0:0795 H; wf 0:3140 Wb; P 2; f 60 Hz;

Jm 0:003 kg=m2; Bm 0:0008 Nm=rad=s

IM parameters

Pn 746 W; xs 188:495 rad=s; vsn 208 V;

Isn 3:4 A; Rs 4X; Rr 1:143X

Ls 0:3676 H; Lr 0:3676 H; M 0:3489 H; P 2;

f 60 Hz; Jm 0:03kg=m2

; Bm 0:00098 Nm=rad=s

1 2 3 4 5 6120

130

140

150

160

170

180

190

200

210

Time (s)

Spee

d(rad

/s)

1000W/m 1000W/m

500W/m

Fig. 20. Speed transient of a PV water pumping system driven

by a PMSM for an abrupt variation of insolation.

1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (s)

Chopperra

tioK

1000W/m 1000W/m

500W/m

Fig. 19. Chopper ratio evolution in the case of a PV water

pumping system driven by a PMSM for an abrupt variation of

insolation.



13/14

Centrifugal pump parameters

Pn 559:5 W; xn 183:2595 rad=s; C1 4:9234e4 m=rad=s

2;

C2 1:5825e5 m=rad=sm3=h; C3 0:0410 m=m

3=h2

Canalization (pump load) parameters

Hg 7:4 m; k 0:0396 m; l 7:4 m;

d 0:06 m; n 6:3 m

Fuzzy controller scaling factors (Table 5).

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System driven

by PMSM

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A Fuzzy Global Efficiency Optimization of a Photo Voltaic Water Pumping System

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