a robust mpp tracker based on sliding mode control for a ... · pumping system. the performance...
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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
4 International Journal of Automation and Computing
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
M. Farhat et al. / A Robust MPP Tracker Based on Sliding Mode Control for a Photovoltaic Based Pumping System 5
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
6 International Journal of Automation and Computing
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)
M. Farhat et al. / A Robust MPP Tracker Based on Sliding Mode Control for a Photovoltaic Based Pumping System 7
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
8 International Journal of Automation and Computing
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
M. Farhat et al. / A Robust MPP Tracker Based on Sliding Mode Control for a Photovoltaic Based Pumping System 9
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
10 International Journal of Automation and Computing
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
12 International Journal of Automation and Computing
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.
E-mail: [email protected] iD: 0000-0002-6589-3976
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.
E-mail: [email protected] iD: 0000-0002-3463-6096