A Robust MPP Tracker Based on Sliding Mode Control for a ... · pumping system. The performance...

International Journal of Automation and Computing

DOI: 10.1007/s11633-016-0982-6

A Robust MPP Tracker Based on Sliding Mode Control

for a Photovoltaic Based Pumping System

Farhat Maissa1, 2 Oscar Barambones2 Sbita Lassad3 Aymen Fleh3

1Department of Electrical, Electronics and Communications Engineering, American University of Ras Al Khaimah,

Ras Al Khaimah 10021, UAE2Advanced Control Group, Faculty of Engineering of Vitoria-Gasteiz, University of the Basque Country, Bilbao, Spain

3Electrical and Automatic Engineering Department, Engineering School of Gabes, University of Gabes, Zrig, Gabes 6029, Tunisia

Abstract: In this paper, a mathematical model of the photovoltaic (PV) pumping system′s main components is firstly established.

Then, the design of maximum power point tracking (MPPT) stage that ensures battery charging is described. This work is motivated

by the need of photovoltaic generator (PVG) that efficiently extracts maximum power. The PVG is a special source of energy which has

nonlinear current-voltage characteristics depending on variations in temperature and solar irradiance. In order to achieve the MPPT

operating goals, a special interest is focused on the variable structure sliding mode (SM) control strategy and the classic perturb and

observe (P&O) algorithm. The permanent magnet synchronous motor (PMSM) is selected as a pump driver. The field oriented control

is performed as the motor drive strategy. Simulation results show a high level of efficiency, obtained with the proposed PV based

pumping system. The performance comparison between SM controller and P&O controller has been carried out to demonstrate the

effectiveness of the former in drawing more energy and a fast response against irradiation disturbances.

Keywords: Photovoltaic (PV), pump, storage battery, boost, sliding mode control (SMC), maximum power point tracking (MPPT).

1 Introduction

Nowadays, renewable energy techniques for power pro-

duction are mature and reliable. The photovoltaic (PV)

energy is the most promising source of energy since it is

pollution free and abundantly available everywhere in the

world. PV energy is especially beneficial in remote sites like

deserts or rural zones where the difficulties to transport fuel

and the lack of energy lines make the use of conventional

resources impractical. Pumping water in these sites is a vi-

tal task that requires a feasible source of energy to supply

power to the electrical elements of the pumping system.

This work analyses the control of a stand-alone PV

pumping system. The success of a PV application depends

on the effectiveness of the power electronic devices to effi-

ciently operate the photovoltaic energy (PVG) even under

variable climatic condition.

There is a greater need to extract the maximum of power

from the PVG at any input levels. Therefore, the reliability

of the maximum power point tracking (MPPT) controller is

of paramount importance in successful PV based pumping

applications.

The MPPT control is a challenge, because the input flux

from sunshine energy of the PVG may change at any time.

In fact, the PV system is considered as a nonlinear complex

one. For these reasons, the designs of an appropriate set up

controller is difficult to build[1].

Research ArticleManuscript received June 23, 2014; accepted January 26, 2015Recommended by Editor-in-Chief Guo-Ping Liuc© Institute of Automation, Chinese Academy of Sciences and

Springer-Verlag Berlin Heidelberg 2016

In the literature, numerous MPPT methods have been

developed[2, 3], e.g., hill climbing, incremental conductance

and the perturb and observe P&O[4]. These algorithms

consist of introducing a crisp values positive or negative

(decrease or increase) all around the actual PVG operating

point. From the previous power point position, the trajec-

tory of the new one helps the algorithm to decide on the

command output value. These algorithms may fail to act

as an accurate MPPT because of the used crisp value (step

size) that is mainly fixed by trial in running tests.

Unconventional techniques have been, in recent years,

widely used in literature[5−7], such as fuzzy logic controller

(FLC) and artificial neural network (ANN)[8]. Although

ANN has good performance, it presents some drawbacks

especially in rapid variation of weather condition. There-

fore, its robustness requires a huge data base[9]. On the

other hand, the FLC is known to be robust and has an

excellent immunity to disturbances[10]. However, for the

fuzzy algorithm, it is too difficult to formulate the fuzzy

rules regulators, which are usually obtained from an ex-

pert knowledge base[11]. Sliding-mode based MPPT have

recently attracted the interest of engineers due to several

facts, the most primary advantage of the sliding mode (SM)

is the simple implementation and robustness. On the other

hand, it causes chattering because of the high frequency

switching control[12].

Most of the frequently used MPPTs controllers present

some limitations, for instance, divergence or oscillation

around the maximum power point (MPP) using the P&O

algorithm. Complexity of fuzzy logic control and memory

capacity limitation in providing a huge data base for ANN-

2 International Journal of Automation and Computing

MPPT control are the major challenges to face. In order to

overcome these problems, a new design of robust variable

structure SM is proposed in this work.

In fact, SM control has been used for different applica-

tions as self-optimization for a PV system connected to a

battery[13], this control offers fast convergence[14] and sim-

plicity of combination with classical extremum seeking[15].

However, this research work has focused on the study of

purely resistive loads. In this work, the proposed SM goal

is to control a PV water pumping system.

In this work, the control strategy is described and tested

in the context of a highly dynamic input. In this paper, a

stand-alone PV pumping system topology is proposed. The

main components are: a MPPT controlled boost converter,

a storage battery feeding the direct current (DC) bus and

the pump-motor. The main function of the battery is to

provide a suitable power source for the inverter. In this

way, the system abandons the use of the energy that comes

from the electric grid. Thus, the proposed pumping system

will be completely autonomous. which is crucial in remote

zones.

A permanent magnet synchronous motor (PMSM) is the

most frequently selected in many applications such as the

pumping system. PMSM has some advantages compared to

other motors such as induction, DC and reluctance motors,

namely: high efficiency, low inertia, high torque to current

ratio, high power factor and almost no need for mainte-

nance. These characteristics as well as its smaller size make

this motor the most appealing option for high performance

applications.

The main contribution of this paper is to enable the sys-

tem to operate with the PVG with maximum power. A

variable speed reference for the pump-motor depending on

the power generated in the PV panel is applied. In this way,

the pump-motor will be able to consume all the power pro-

vided by the photovoltaic generator in the MPP and hence

allows a maximal pump flow.

2 Photovoltaic energy conversion

2.1 PV generator model

One can substitute a PV cell to an equivalent electric cir-

cuit which includes a current source, resistors and a diode.

Fig. 1 Simplified PV cell equivalent circuit

The power source produces the Iph current which de-

pends on irradiation intensity. Through diode flows the

current Id. The current IC feeding the load is the differ-

ence between Iph and Id. which is reduced by the resistance

series resistance (RS). This last variable stands for cells re-

sistances and connections among cells[11, 16].

Use the node law

Ic = Iph − Id − Ish. (1)

The current Iph can be evaluated as

Iph =G

Gref(Irsref + KSCT (Tc − Tcref )) (2)

Id = Irseq(Vc+RsIc)

α×K×T−1 (3)

Ish =1

Rp(Vc + RsIc). (4)

The reverse saturation current at reference temperature

can be approximately obtained as

Irs =Irsref

eqVoc

ns×n×β×Tc − 1. (5)

Finally, the cell current Ic can be given by

Ic = Iph − Irs

(e

q(Vc+RsIc)αKT − 1

)− 1

Rp(Vc + RsIc). (6)

The model of a PVG depending on the number of series

Ns, and the number of parallel cells, Np is as shown in

Fig. 2[17].

Ip = NpIc

Vp = NsnsVc.

(7)

Fig. 2 PVG modules association: Ns stands for the numbers in

series and Np stands for the number in parallel

Finally, the PVG current can be given by

Ip = NpIph −NpIrs

(e

qαKT

(Vp

nsNs+

RsIp

Np

)− 1

)−

Np

Rp

(Vp

nsNs+

RsIp

Np

). (8)

The terms containing Rs and Rp parameters are not con-

sidered (using simplification and assumption Rp >> Rs).

M. Farhat et al. / A Robust MPP Tracker Based on Sliding Mode Control for a Photovoltaic Based Pumping System 3

Here, the model is with Rs = 0 and Rp = ∞.

Ip = NpIph −NpIrs

(e

qnβTc

(Vp

nsNs

)− 1

). (9)

The highly nonlinear characteristics are shown in Figs. 3

and 4, which show three specific operating zones of the

GPV:

1) The V zone is characterized by a small current value

and a big voltage value. This voltage could reach the open

circuit voltage VOC .

2) The I zone is characterized by a small voltage value

and a big current value. This current could reach to the

short circuit one ISC .

3) The Pmax zone is characterized by the maximum of the

power, where the optimal voltage value is relatively close to

0.7VOC . It is efficient to operate in the third zone.

Fig. 3 PVG characteristic curves at a various irradiation levels

from 100W/m2 to 1 200 W/m2 and at a fixed temperature of

25(C)

Fig. 4 I−V and P−V characteristic curves at a fixed irradiation

(1 000W/m2) and a temperature values (25(C))

2.2 Matching stage

The role of the matching stage is to ensure operation

of the PVG at its maximum power point, in the face of

changing atmospheric conditions and load variations.

Fig. 5 shows a PVG connected to a matching stage which

consists of a boost converter, MPPT controller and a stor-

age battery[18].

In the case of a boost converter type and in a continuous

conduction mode (CCM)[19], the output voltage is related

to the input one as

Vout =

(1

1−D

)× Vin (10)

where Vin corresponds to the input voltage power (Vin),

Vout is the converter output voltage and D is the converter

duty cycle as a switching command signal.

Sw represents the switch state command.

Sw = 0 indicates that the switch is off.

Sw= 1 indicates that the switch is on.

Fig. 5 Matching stage incorporating a MPPT Boost converter

between a PVG and a storage battery

The dynamic model of the Boost converter circuit is

dVp

dt=

1

C1(ip − iL)

diLdt

=1

LVp +

1

L(Sw − 1)Vout

dVout

dt=

1

C2(iL − iout)− 1

C2SwiL.

(11)

Then,

x = f(x) + g(x)Sw (12)

where

x =

Vp

iL

Vout

, f(x) =

1

C1(ip − iL)

1

L(Vp − Vout)

1

C2(iL − iout)

g(x) =

01

LVout

− 1

C2iL

.

The MPPT controls the PV system and applies the opti-

mal duty cycle to the Boost converter. This paper is focused

on the sliding mode MPPT method as a robust and high

performance dynamic controller[13, 15].

The battery model is based on the electrical diagram

given in Fig. 6, the batteries are described by just two el-

ements (whose characteristics depend on a set of parame-

ters): a voltage source and an internal resistance. For the


nb battery cells in series, the output voltage Vbat can be

expressed as

Vbat = nb × Eb + nb ×Ri × Ibat (13)

where Vbat and Ibat are the battery voltage and current

(according to receptor convention), Eb is the electromotive

force, and Ri is the internal resistance.

For any time instant (t), the state of charge SOC(t) ac-

tual value is deduced from the previous one following the

model given by (14). SOC(0) which is the initial state

charge value corresponds to the open circuit battery termi-

nal voltage

SOC(t) =

∫ t

t−1

K(Vbat × Ibat)

60× Socm− SOC(t− 1)×D

60dt.

(14)

with Socm (Wh) as the maximum state of charge. K is the

charge/discharge battery efficiency and D(h−1) stands for

the battery self-discharges which are empirical constants

depending on the battery characteristics. Depending on

Vout compared to the Vbat one, the battery is operating in

states as charging or discharging respectively. When PV is

higher than Vbat, the battery charge operation occurs. On

the other hand, when Vbat is lower than Vout, the battery

goes in a discharging mode[20−21].

Fig. 6 Equivalent electrical diagram of nb battery elements in

series

2.3 Modeling of the three phase voltageinverter

A three-phase voltage inverter as shown in Fig. 7 is used

to interface the PVG with the moto pump by converting

the power. It allows the conversion of a DC power to an

alternating current (AC) one.

The function of an inverter is to transform a DC input

voltage to a three phase symmetric AC output voltage of

a desired magnitude and frequency. The DC input voltage

could be fixed or variable. As in a previous paper, the use

of a directly coupled pump to PVG gives a poor result per-

formance when the DC input voltage varies[20]. The present

work focuses on the use of a constant DC bus input volt-

age by the use of battery fed by an MPPT Boost converter.

The inverter provides a three-phase voltage system which

is generated according to the three pulse width modula-

tion (PWM) commands reference voltages. The a, b and c

output voltages feed the PMSM coupled to the centrifugal

pump. These output voltages can be expressed as indicated

in (16)[22].

Va

Vb

Vc

=

VDC

3

2 −1 −1

−1 2 −1

−1 −1 2

g1

g2

g3

(15)

with VDC as the Boost output voltage. g1, g2 and g3 are

the PWM gates control signals.

Fig. 7 Voltage source inverter topology

2.4 Modeling of the DC bus

A DC bus is used to ensure an energy balance between

the power generated by the PVG and the power feeding the

PMSM pump, this is done by simply charging or discharging

the capacitor. The inverter input voltage VDC is given by

ic =dVDC

dt(16)

and the node law gives

Iout = Ibat + ie + ic. (17)

The relationship that connects the input current and the

output current of the inverter is given by the following ex-

pression:

ie = iag1 + ibg2 + icg3. (18)

3 Moto-pump modelling

3.1 PMSM modeling

In this section, the PMSM mathematical modeling is pro-

posed using the electrical equations presented in (19). The

electromagnetic torque is described in (20), and the me-

chanical expression is described in (19)[22−23]. R and L are

the stator resistance and inductance. λm is the permanent

magnet flux produced by the magnet inserted in the rotor,

P is the number of poles, J is the rotor inertia and Tl is the


load torque.

vd = Rid + Ldiddt

− ω × L× iq

vq = Riq + Ldiqdt

+ ω × L× id + ωλm

(19)

Te =

(3

2

) (P

2

)(λdiq − λqid)

λd = Lid + λm

λq = Liq

(20)

(Te − Tl) =

(P

2

) (J

dω

dt+ fω

). (21)

3.2 Centrifugal pump

The centrifugal pump is designed for a given total head

(TH). The flow rate of the pump varies in accordance with

the rotational PMSM shaft speed. So the torque increases

very rapidly with the speed as shown in (22). The rotational

speed of the motor must be too fast to ensure a good flow.

The power consumption is proportional to flow rate Q. A

typical centrifugal pump is used for high flow rates and low

or medium depths. The aerodynamic load is characterized

by[24, 25]

Tl = k × ω2 (22)

where k is the pump constant. The centrifugal pump head

to flow rate characteristics are given by

H = a1ω2 + a2 × ω ×Q + a3 ×Q2 (23)

where a1 , a2 and a3 are the coefficients generally given by

the manufacturers. Fig. 8 shows the characteristics of the

head versus capacity (h = f(Q)). Those characteristics are

shown for different speed values.

Fig. 8 Pump characteristics

The hydraulic power load torque and the mechanical

power are given as

PH = ρ× g ×Q×H. (24)

Assuming that the efficiency of the coupling between the

drive machine and the pump is equal to 1, then the me-

chanical power of the PMSM is equal to the pump power

demand. The mechanical power of the PMSM is

Pm = k × ω3. (25)

The pump efficiency is defined as the ratio of the

power transmitted by hydraulic pump and input mechani-

cal power.

It is expressed by

η =PH

Pm. (26)

So,

η =ρ× g ×Q×H

kω3. (27)

4 MPPT algorithm

4.1 P&O algorithm

The principle of this optimization algorithm is to pro-

voke perturbation by acting (decreasing or increasing) on

the PWM duty cycle boost converter command and ob-

serve the output PV power reaction. If the actual power

P (k) is greater than the previous computed one P (k − 1),

then the perturbation direction is maintained, otherwise it

is reversed.

Referring to Figs. 9 and 10, this can be detailed as

follows[1]:

Fig. 9 P&O algorithm chart


Fig. 10 P&O algorithm signifies variations of power to voltage

ratio

When dPdV

> 0, the voltage is increased, this yields to

D(K) = D(K) + ∆D(∆D: crisp value).

When dPdV

< 0, the voltage is decreased through D(k) =

D(k − 1)−∆D.

The ∆D crisp value is chosen by trial and tests in simu-

lation.

If ∆D is very big or very small, then we may lose infor-

mation.

Despiting the P&O algorithm is easy to implement, it

has mainly the following problems[25]:

1) The PV system always operates in an oscillating mode.

2) The operation of PV system may fail to track the

maximum power point.

The ∆D crisp value is chosen by trial and tests in simu-

lation.

4.2 Variable structure sliding mode con-trol

Like all other MPPT controllers, the modeling of the vari-

able structure sliding mode MPPT controller is based on the

output power of the photovoltaic cell which is P = Vp× Ip.

The optimization of the output PVG power is achieved as

shown in Fig 10 by solving the following function[26]:

∂P

∂Vp= 0. (28)

So,

∂P

∂Vp= Ip +

∂Ip

∂VpVp. (29)

This control system is characterized by a suite of feed-

back control laws and a decision rules. These decision rules,

that called the switching function, select a particular feed-

back control in harmony with the systems behavior. The

switching variable is defined as

S =∂P

∂Vp= Ip +

∂Ip

∂VpVp. (30)

And therefore, when S = 0, the PV system reaches the

maximum power point. The switching surface is S = 0

and then the system dynamics can be divided in two states

S < 0 and S > 0.

Based on the two states of PVG in Fig. 10, if the control

function for the boost power gate drive signal is designed

as[26, 27]

SW =

1, if S < 0

0, if S ≥ 0

(31)

then the PV system reaches the surface S = 0, so the PV

system reaches the maximum power point.

Equalizing expression (29) to zero seems to meet the in-

cremental conductance method[1]. However, the proposed

maximum power point tracker is based on a variable struc-

ture law that forces the system to reach the state given by

S = 0, that is the state of the maximum power point.

So unlike the incremental conductance method that acts

by decreasing or increasing the duty cycle that will be used

with a reference saw signal to generate a PWM signal, this

controller generates directly the PWM insulated gate bipo-

lar transistor (IGBT) signal using the sliding surface (S)

whose zero value is the maximum power point.

Proof. Based on Lyapunov function the variable struc-

ture mode control requires that

V =1

2S2 > 0, V = S

dS

dt< 0, SS < 0. (32)

If the control law (32) is adopted for the system, it could

make the system stabilizing from any initial state.

S =∂P

∂Vp= Ip +

∂Ip

∂VpVp. (33)

With the above, (9) can be written as

Ip = NpIph −NpIrseAVp−1 = NpIrsAeAVpVp.

And with A = qn×β×Tc

1ns×Ns

,

S = Np[(Iph − Irs)− Irs(1 + AVp)eAVp (34)

when S < 0.

The switch command is at high level, this implies that

the duty cycle will increase.

Based on the assumption where Pin = Pout, it can be

deduced that Rpv = (1−D)2 Rout where Rpv is the equiv-

alent resistance connected to the PV panel and Rout is the

load seen by the converter.

If the duty cycle D increases, then Rpv decreases. So

based on the PV dynamics given by the I-V characteris-

tic shown in Fig. 11, the Ip will increase and Vp will de-

crease. It can be deduced that, when the voltage Vp in-

creases/decreses, the current Ip decreases/increases. So, if

the resistance connected to the PV panel decreases, then

Ip increases and Vp decreases. So as a consequence in this

case, this implies that

dVp

dt< 0. (35)


Fig. 11 I-V characteristics

From (12) and (33), it is obtained

S =∂S

∂xTx =

∂S

∂xTf(x) +

∂S

∂xTg(x)Sweq . (36)

So,

S =∂S

∂VpVp (37)

S =d

dtNp[(Iph − Irs)− Irs(1 + AVp)eAVp ] (38)

S = −NpIrsA[eAVp + (1 + AVp)eAVp ]Vp. (39)

Using (35) in (39) gives S > 0.

Finally,

SS < 0 (40)

when S > 0.

We use the same method as before. The switch command

is at low level, this implies that the duty cycle will decrease.

If the duty cycle D decreases, then Rpv = (1 − D)2. Rout

increases. So, based on the PV dynamics given by the I-

V characteristic shown in Fig. 10, Ip will decrease and Vp

increase, it can be deduced that, when the voltage Vp de-

creases/increases, the current Ip increases/decreases. So, if

the resistance connected to the PV panel increases, then Vp

increases and Ip decreases, this implies that

dVp

dt> 0. (41)

So,

S < 0, SS < 0. (42)

According to (31), when S < 0, the circuit operates in

the right side of PVG characteristics (Fig. 10), the switch is

then open. Otherwise the switch is closed.

Taking into account that the Lyapunov function (32)

tends to infinity when the absolute value of the variable |S|tends to infinity, it can be concluded that the equilibrium

point S = 0 is globally stable[28].

According to (30), and for S = 0, the system may achieve

global stability and operate at its MPP. As shown in Fig. 16,

the surface is locked at a zero value. ¤

5 Simulation results

In this section, globally stable controlled pumping system

as given in Figs. 12 and 13 is proposed. The PMSM is used

as the pump rotational engine. The parameters used in this

application are given in the Table 1.

Table 1 Specifications

Parameters Rated characteristics

R 5.2Ω ω 2 500 rpm/min

Ld = Lq = L 21.5mH Torque 1.5Nm

λm 0.24Wb Current I=2.5A

J 85× 10−6 Kgm2 PMSM 5A

f 0.000 36Nmsrad−1 Np 2

ρ 1 000Kgm2 Ns 2

g 9.81m/s2 ns 36

The proposed control scheme illustrated in Figs. 12 and

13 shows the PMSM with the field oriented control strategy

(FOC). The desired speed (ω∗) will be created according to

power generated from PV panels by using (25) in order to

consume all power generated from the panel. Effectively,

after comparing the shaft and the desired (ω∗) speeds, the

PI controller is added in the outer loop to generate the

transversal stator current as a reference one. This latter

current signal is also compared with the measured one as

an inner loop. The obtained error is injected in the PI con-

troller which generates the quadrature voltage as a reference

one. In the conventional FOC strategy, the direct reference

stator current is clamped to zero. Therefore, for the direct

currents, just an inner control loop is built around a PI

controller.

The load torque applied to the motor is that of the cen-

trifugal pump.

To increase the PVG available power, the PV current

and voltage must be increased as well, this is allowed by

increasing the number of parallel and series mounted mod-

ules. The used PVG in such a study case is consisting

of Np= 2 and Ns= 2. The I − V and P − V character-

istics are shown in Fig. 14 (for the irradiation 500Wm−2

and 1 000 Wm−2). In Fig. 14, for an irradiation value of

1 000Wm−2, the MPP couple power and voltage is men-

tioned (P = 666.8, Vp = 45.6).

Fig. 12 Power line of the PV pumping system


Fig. 13 Command line

Obviously, in the reality, the radiation changes are

smooth, but in order to prove the good performance of the

proposed MPPT algorithm, an abrupt and instantaneous

irradiation variation signal in step form is applied to the

PVG as shown in Fig. 15.

The results shown in Fig. 16 demonstrate the obtained

performance of P&O and sliding mode (SM) MPPT track-

ers. The SM has very small response time and overshoots.

Moreover SM presents a reduced oscillation signal in the

MPP compared with the P&O one.

P&O produces a delay time to converge (in that case,

a delay of 1.5 s). This delay is due to the choice of the

crisp value, the crisp value (∆D) applied to the system is

the main factor determining the amplitude of oscillations

as well as the convergence rate to the MPP. If the crisp

value will be larger, the algorithm will find the MPP faster.

Nevertheless, a larger crisp value will lead to a higher value

of oscillation amplitude. On the other hand, if the applied

crisp value is too small, the oscillations around the MPP

will be reduced, but the rate of convergence will decrease

as well. In other words, in this algorithm, there is a trade-off

between the rate of response and the amount of oscillations

under steady state conditions[28]. In this work, the selected

crisp value avoids a bigger oscillation around the MPP and

generates an acceptable delay.

Fig. 17 presents the duty cycle signal delivered by the

P&O algorithm. In fact, the duty cycle is within the range

of [0, 1]. Actually, there is an additional saturation block

between the range [0, 1] after this signal. This latter will be

used with a reference saw signal to generate a PWM IGBT

drive signal. Fig. 18 shows the PWM signal generated by

the SM algorithm. This last has the benefit to avoid the

use of a PWM commutation signal (saw signal). It permits

to build directly a PWM output signal toward the IGBT

gate. In Fig. 18, zoomed version (the variation at second

number 2), it is clear that the PWM frequency is affected

by the irradiation changes.

Figs. 19 to 21 show respectively the dynamic evolution of

the PVG current, voltage and power signals for the same

irradiation (Fig. 15). One can easily see that the PVG under

the P&O or the SM tracker meets the maximum power

operating points. It is clearly pointed that the SM controller

is much more suitable for rapid and good dynamic PVG

signal responses.

Fig. 22 presents the battery voltage used as a DC link.

This latter remains at a constant level as long as the MPPT

trackers fit the maximum power operating region.

Figs. 23 to 25 show respectively the speed, load and elec-

tromagnetic torques. Finally, Fig. 26 shows the pump flow

rate.

Fig. 14 I-V and P-V PVG curves

Fig. 15 Irradiation variation

Fig. 16 Controllers performance


Fig. 17 P&O output

Fig. 18 Variable structure PWM output

Fig. 19 PVG current

Fig. 20 PVG voltage

Fig. 21 PVG power

Fig. 22 Battery voltage

Fig. 23 Speed

Fig. 24 Load torques


Fig. 25 Electromagnetic torques

Fig. 26 Pump flow

All the obtained results show that the use of variable

structure sliding mode is much more effective compared to

the P&O one. The VSC ensures a very fast convergence to

the MPP, there are no oscillations around the MPP, hence,

losses are minimized. Moreover the tracking is kept in spite

of sharp irradiance changes.

6 Conclusions

In this paper, a whole PV pumping system with two op-

timal control strategies has been presented. The first one

uses the perturb and observe algorithm P&O and the sec-

ond is the variable structure MPP control strategy. The

proposed algorithms are formulated and applied to the PV

pumping system. The effectiveness of the proposed MPPT

using sliding mode control algorithm is proven by simula-

tion results.

The designed SM showed good results as it successfully

and precisely tracked the MPP with a significantly higher

efficiency that was clearly shown by convergence speed, pre-

cision and robustness than the well-known P&O method

of control. This new algorithm is applicable in industries.

Eventually, the economic benefits would be enormous be-

cause it is an economic controller that does not require a

lot of sensors. This control law could be implemented by

means of standard operational amplifiers, analog multipli-

ers and digital devices in an experimental platform, or using

an acquisition and control DSP board.

Appendix

vd, vq: Direct and quadrature stator voltage

λd, λq: Direct and quadrature stator field

id, iq: Direct and quadrature stator current

G, Gref : Global, reference insulation (Wm−2)

Ip, Vp: Cell output current and voltage

Rp, Rs: Cell parallel and series resistance (Ω)

n, Eg: Solar ideal factor and band gap energy (ev)

Irs: Reverse diode saturation current (A)

KSCT : Short circuit current temperature (A/(K))

Tc, Tcref : Cell junction and Reference temperature

((C))

β, D: Boltzmann constant 1.38×10−23) and duty cy-

cle

Ns, Np: Number of series and parallel modules

ns: Number of series cells

H: Pumping height

g: Gravity acceleration

ρ: Water density

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Farhat Maissa received the M. Sc. de-gree in automatic and intelligent techniquesfrom National School of Engineering ofGabes, Tunisia in 2011, and the Ph.D. de-gree in electrical and computer engineeringfrom the University of the Basque Coun-try, Spain in 2015. In 2011, she joinedthe Department of Electrical Engineering atthe National Engineering School of Gabes

(ENIG) as an assistant. In 2011, she joined the Department ofElectrical, Electronics and Communications Engineering in theAmerican University of Ras Al Khaimah, UAE as an assistant


professor. Now her research project is dealing with optimiza-tion and control systems. She is a member of a research unitof photovoltaic, wind and geothermal systems which its code isUR11ES82 at the University of Gabes, Tunisia.

Her research interests include power electronics, electrical ma-chines control and drives, renewable energies.

E-mail: [email protected] (Corresponding author)ORCID iD: 0000-0003-4706-686X

Oscar Barambones received the M. Sc.degree in applied physics, the Ph.D. degreein control systems and automation, andthe M. Sc. degree in electronic engineering,from the University of the Basque Country,Spain in 1996, 2000 and 2001, respectively.Since 1999, he has held several teaching po-sitions at the Systems Engineering and Au-tomation Department in the University of

the Basque Country, Spain, where he is currently a professor ofsystems and control engineering. He is also the vice dean of re-search and master in the University College of Engineering ofVitoria. He has more than 100 papers published in the maininternational conferences of the automatic control area, bookchapters, and journal citation report (Institute for Scientific In-formation), indexed journals. He has served as a reviewer inseveral international indexed journals and conferences, and hassupervised several Ph.D. theses.

His research interests include the applied control of dynamicsystems, particularly induction machines and its application towind turbine systems.

E-mail: [email protected] iD: 0000-0002-4430-8088

Sbita Lassaad received the M. Sc. andthe Ph.D. degrees in electro technique fromthe University of Tunis, Tunisia in 1987 and1997, respectively. In 2008, he obtained thehabilitation of conducting research (HDR)degree in electrical engineering from theNational Engineering School of Sfax, Uni-versity of Sfax, Tunisia. In 1988, he joinedthe Department of Electrical Engineering,

University of Sfax, as an assistant lecturer, and became an as-sistant professor and an associate professor at the National En-gineering School of Gabes (ENIG), University of Gabes, Tunisiain 1998 and 2009, respectively. Since January 2014, he is afull lecturer professor. He is the director of a research unit ofphotovoltaic, wind and geothermal Systems which its code isUR11ES82 at the University of Gabes, Tunisia.

His research interests include power electronics, electrical ma-chines control and drives, renewable energies.


Aymen Flah received the M. Sc. de-gree in automatic and intelligent techniquesfrom National School of Engineering ofGabes, Tunisia in 2009, and the Ph.D. de-gree in electrical engineering from Nationalschool of engineering of Gabes, Tunisia in2012. He has extensive experience in motorcontrol applications. In addition, he haselaborated a number of applications using

intelligent techniques such as fuzzy logic, neural network, opti-mization techniques as PSO and BFO.


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