Download maximum power point tracking controller based on sliding mode

MAXIMUM POWER POINT TRACKING CONTROLLER BASED ON
SLIDING MODE APPROACH
Maissa Farhat*, Oscar Barambones**, Jose A. Ramos**, Jose M. Gonzalez de Durana**
*Research Unit of Photovoltaic, Wind and Geothermal Systems, National Engineering School of Gabes,
University of Gabes, Rue Omar Ibn-Elkhattab, Zrig, Gabès, 6029, Tunisia. [email protected]
**Advanced Control Group. Universidad del País Vasco, EUI, Nieves Cano 12, 01006 Vitoria, España.
[email protected]
Abstract
Recently, the solar energy has become an alternative
source of energy of great importance. Diverse
researches and efforts have been concentrated on the
photovoltaic (PV) systems efficiency improvement
and the accessibility to this technology. This paper
presents an intelligent approach for the improvement
and optimization of the PV system efficiency. A PV
system topology incorporating a maximum power
point tracking controller (MPPT) is studied. In order
to perform this goal a special interest was focused on
the sliding mode control and the P&O algorithm.
This paper presents a detailed study and design of a
MPPT controller to ensure a high PV system
performance which can be selected for practical
implementation issue. A simulation examples shows
that the MPPT is achieved using a DC/DC Boost
converter between the PV system and the resistive
load. Significant extracted results are given to prove
the validity of the proposed overall PV system.
Keywords: PV, Boost Converter, MPPT, SMC.
1 INTRODUCTION
This work analyses the control of a stand-alone PV
system. However the success of a PV application
depends on whether conditions where the power
electronics devices helped to extract a high power
from the PV generator (PVG). The extraction of the
maximum of power from the PVG is then
indispensable. Therefore, maximum power point
tracking (MPPT) controller accuracy becomes a key
control in the device operation for successful PV
applications. In general, the MPPT control is a
challenging, because the sunshine condition that
determines the amount of sun energy into the PVG
may change at any time. Therefore, the PV system
can be considered as a non-linear complex system.
Numerous MPPT methods have been developed and
implemented in previous studies, for instance,
perturb and observe (P&O), fractional open-circuit
voltage and fuzzy logic controller (FLC) approaches
[7] etc. These techniques have high tracking accuracy
under stable internal and external condition, but still
reveal some trade-offs between tracking speed and
tracking reliability when load values or weather
conditions rapidly changes [6].
Sliding mode controller has recently attracted
considerable attention of researchers, The main
benefit of the sliding sector technique is that it can
avoid chattering [1],[8], Its advantage among, is the
simplicity of implementation, robustness, and great
performance in different fields such as robotic, motor
control, etc. In this paper the interest was focus in the
use of SMC in the photovoltaic fields by maximizing
the power generated from the PV panels. Moreover,
the system stability is demonstrated [2].
The main role of this controller is to generate a
command using a voltage reference (Vref) in order to
force the system to work at the MPP. The Vref is
generated online via a voltage reference generator
that doesn’t require the irradiation measurement.
In this paper, the SMC algorithm generates directly
PWM signal. 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 converter IGBT gate. Contrariwise, other
algorithm such as P&O [7] generates a duty cycle
signal that will be used with a reference saw signal to
generate a PWM IGBT drive signal.
In general, a PV system is typically built around the
following main components as shown in figure 1:
1) A PVG that converts solar energy to electric one,
2) A DC-DC converter that manipulates produced
DC voltage by the PV arrays to a load voltage
demand,
3) A digital controller that drives the converter
operation with MPPT capability.
4) Resistive Load
Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)
q Vc  RS I c  

I d  I rs  exp
 1
 kT


I sh 
(3)
1
Vc  RS I c 
Rp
(4)
The reverse saturation current at reference
temperature can be approximately obtained as:
I rs 
I rs _ ref
(5)
 qVoc 
exp 
 1
 ns .n. .Tc 
Finally the cell current Ic can be given by
Figure 1: Synoptic diagram of PV system
Ic  I
2
PHOTOVOLTAIC
CONVERSION
ph



 I rs  exp
q Vc  Rs I c 
kT



 1 
1
Rp
Vc  Rs Ic  (6)
ENERGY
The modeling of a PVG depending on series and
parallel number respectively Ns and Np as:
2.1 PVG MODEL
 I p  N p I c

V p  N s n s V c
One can substitute a PV cell to an equivalent electric
circuit which includes a power supply and a diode.
(7)
Figure 2: Simplified PV Cell Equivalent Circuit
The power source produces the Iph current, which
depends on impinging irradiation. Through diode
flows the current Id. The current Ic feeding the load
is the difference between Iph and Id which is reduced
by the resistance RS. This last represents resistances
of cell and connection among cells [5].
By exploiting the node law
Finally the PVG current (Ip) can be given by
I c  I ph  I d  I sh
(1)
The current Iph can be evaluated as:
I ph
G

G ref
I
rs _ ref
 K SCT Tc  Tc _ ref
Figure 3: A PVG Group of modules; Ns numbers
in series and Np in parallel.


Rs I P
q  Vp
 N p I rs  exp

I p  N pI

ph

kT  ns N s
Np

N p  Vp
(2)
Rs I P 




R p  ns N s
N p 
Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)
 
  1 
 
  (8)
The highly I-V nonlinear characteristics are shown in
figure 4 for different irradiation values.
70
60
G=1200W/m²
G=1000W/m²
G=500W/m²
G=300W/m²
Ip(A)
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
Vp(v)
Figure 5 shows the circuit diagram of a boost
converter, and a load.
5
4
Ip(A)
3
2
1
0
Figure 5: Circuit diagram of the Boost converter
0
2
4
6
8
10
12
14
16
18
20
Vp(v)
Figure 4: (a) P-V and (b) I-V characteristics at
fixed temperature value of 25.3°C
2.2 BOOST CONVERTER
DC-DC converters are electronic devices used
whenever is needed to change DC electrical power
efficiently from one voltage level to another. They’re
necessary because unlike AC, DC can’t simply be
stepped up or down using a transformer. In many
ways, a DC-DC converter feeding the load is going
through a regulated converter to hold its maximum.
Hence, the efficiency of the photovoltaic system is
performed.
In order to step up the voltage, the operation
consists of switching an IGBT shown in figure 5 at a
high commutation frequency, with output voltage
control by varying the switching duty cycle (D).
When the IGBT is switched on, current flows from
the input source through the inductor (L) and the
IGBT, then the energy is stored in the inductor. After
that there is no current through the Diode (D1), and
the load current is supplied by the capacitance hold
charge in(C). The IGBT is turned off; L opposes any
drop in current by immediately reversing its emf. So,
the inductor voltage adds to (i.e., .boosts.) the source
voltage and current due to this boosted voltage now
flows from the source through L, D1 and the load,
recharging C as well. The output voltage is therefore
higher than the input voltage, and it turns out that the
voltage step-up ratio is equal to [4]
The boost converter is assumed to operate in a
continuous conduction mode with two states based
on the status of the switch.
1
VO 
Vin
1 D
(9)
Based on the assumption where Pin=Pout it can be
deduce that
Rpv  (1  D)2 Rout
(10)
Where Rpv is the equivalent resistance connected to
the PV panel and 1-D is actually the proportion of the
switching cycle that the IGBT is off, rather than on.
3
MPPT CONTROLLERS
3.1 P&O ALGORITHM
Due to its simplicity, P&O algorithm presented in
figure 6 is the most popular [10], The principle of
this controller is to provoke perturbation by acting
(decrease or increase) on the PWM duty cycle
command and observe 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 [3].
The ∆D crisp value is chosen by trial and tests in
simulation. The P&O diagram is:
If the crisp value ∆D is very big or very small then
we may lose information. Despite the P&O algorithm
is easy to implement it has mainly the following
problems
 The PV system will always operates in an
oscillating mode.
 The PV system may fail to track the
maximum power point and as result operate in
current or voltage zones.
Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)
involves the maximum of extractable power, a
number of such couples for different irradiation
values have been collected and then interpolated to
get the suitable function (VMPP= F(PMPP)).
Ip (k ),V p ( k )
This function is created using Matlab Fitting Curve
Toolbox. In this work several test has been done
using diferent type of function such as, Fourier,
gaussian, rational, and the polynomial function like
the work of Abderrahim, [10]. Finely we deduce that
the power function fits more the Atersa model.
The constructed function is denoted as :
P (k )  Ip (k )  V p ( k )
P  0
V p  0
D(k)  D(k 1) D
V p  0
D(k)  D(k 1) D
D(k)  D(k 1) D
F(x) = a xb +c
D(k)  D(k 1) D
(11)
Where the a, b, c coefficient as numerical values
specific for the used PV panel. With: a=-8.638; b=0.1697; c=19.74;
Figure 6: P&O Algorithm global structure
Step 2
3.2 SLIDING MODE CONTROL
The method of control is divided into two steps the
first is determine the voltage value at which the
system operates with its maximum of power, and
then the second is to operate the system with this
voltage value that gives the maximum power.
After determined the Vref the implemented (SMC)
algorithm calculate the difference between the
acquired PV voltage and the Vref and then, via the
boost converter force the PVG to operate at the
reference voltage value (Vref) and therefore at the
maximum power zone.
S = e = V p  V ref
(12)
Step 1
In this part of the work, the main objective is to
construct a MPP voltage-reference generator that
meets the MPP. Specifically, this generator is
expected to compute on-line the optimal voltage
value VMPP so that, if the voltage Vp is made equal to
VMPP then, maximal power is captured. In fact this
method does not require irradiation measurement
u 
1
1  S ig n ( S ) 
2
1
u
0
S 0
S 0
(13)
(14)
Stability demonstration:
The stability can be analyzed using the Lyapunov
stability method. A positive definite function V is
defined as:
18
17
reference Voltage (v)
16
V 
15
14
1 2
S 0
2
(15)
Whose time derivative is:
dS
V  S
= SS
dt
13
12
11
10
0
10
20
30
40
50
60
70
80
Power(W)
Considering
Figure 7: Optimal power-voltage characteristic
The figure 7 present the curve of optimal powervoltage characteristic obtained from the polynomial
interpolation. It is easy to see from figure 4 that for
any radiation G, there is a unique couple (Vp, P) that
 S  e  V p  VMPP *


S  e  Vp

When S>0
The switch will be open, this imply that the duty
cycle will increase. From the boost converter model
Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)
equation (10) we have, R pv  (1  D)2 Rout and using
this equation, we can observe that if the duty cycle D
increases, then Rpv= (1  D) 2 Rout decreases so
based on the PV dynamic given by the I-V
characteristic shown in figure 8, the Ip will increase
and Vp will decrease equivalently from eq (8), it can
be deduced that, when the voltage (Vp)
increase/decrees the current (Ip) decrease/increase,
so, if the resistance connected to the PV panel
decrease then (Ip) increases and (Vp) decreases
1
R pv
5
4.5
1
RMPP
4
I MPP3.5
Ip(A)
3
2.5
2
1.5
1
1
R pv
0.5
0
0
5
10
15
Vp(v)
VMPP
20
25
Figure 8: I-V characteristics
So as a consequence in this case, this imply that
  0 and S  0
Vp
4 SIMULATION RESULTS
In this section, the PV system global control shown
in figures 1 is implemented
The sliding-mode MPPT, with optimal voltage
reference, is compared to P&O algorithm. The
robustness of both controllers is tested over internal
and external variation. The system is tested over a
sudden step load variation and irradiation change.
Figure 9 present the I-V and P-V characteristic at
fixed temperature and different irradiation values
(500 and 1000W/m²)
Figures 10, 11 show respectively the irradiation and
load variation.
Figure 12 (a) shows the controllers output. The SMC
build directly a PWM output Signal toward the
converter IGBT gate, however the P&O algorithm
generate a duty cycle signal that will be used with a
reference saw signal (MLI) to generate a PWM IGBT
drive signal. Figure 12(b) in a zoom of figure 12 (a)
and shows the impact of the irradiation variation on
the SMC frequency.
Figures 13, 14, 15 show the PVG current, voltage
and power respectively. These figures show that in
spite of the load change: the operation point of the
PV remains constant in the MPP due to the
robustness of controllers. When the irradiation
changes, the MPP also changes its position, so the
controller act in order to track the new MPP.
Figure 16 and 17 show the load voltage and current.
SS  0
and finally
60
G=1000W/m²
G=500W/m²
5
When S<0 , using the same method
The switch will be close, this imply that the duty
cycle will decrease. If the duty cycle D decreases,
then Rpv= ( (1  D) 2 Rout ) increases so based on the
PV dynamic given by the I-V characteristic shown in
figure 8, the Ip will decrease and Vp increase
equivalently from eq (8), it can be deduced that,
when the voltage (Vp) decrease/increase the current
(Ip) increase/decrease, so if the resistance connected
to the PV panel increase then (Vp) increases and (Ip)
decreases, and this imply that:
Ip(A)
4
40
3
2
20
1
0
0
5
10
15
20
0
25
Vp(v)
Figure 9: I-V and P-V characteristic under constant
temperature (25°C)
1200
and then
S  0
SS  0
G(W/m²)
1000
  0 and
Vp
800
600
400
200
0
0
0.5
1
Time(s)
Finally, using the Lyapunov stability theory it can
be concluded that S reaches the state S = 0 means
that the system reaches the desired voltage value Vref
and hence the convergence to the point of maximum
power.
Figure 10: irradiation
Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)
1.5
60
1.5
50
1
IR(A)
R()
40
30
20
0.5
10
0
0
0.5
1
1.5
0
0
0.5
Time(s)
1
1.5
Time(s)
Figure 11: Load Value
Figure 17: current Load
(a)
1
The obtained simulation results show that both
systems using different controller present a good
maximum power tracking, however the SMC
controller present less oscillations and fast tracking in
the response.
SMC
P&O
D
0.5
0
-0.5
0
0.5
1
1.5
Time(s)
Figure 12 a: Controller output
5 CONCLUSION
1
0.8
0.6
0.4
0.2
0
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
Figure 12 b: Controller output
4
3
Ip(A)
3.55
3.5
2
In this work, a complete study of PV systems
integrating an MPPT controller was studied. The
proposed PV system is composed of a PV generator,
a boost converter and a resistive load. In order to
bring up the system efficiency a designed SMC
MPPT controller was presented. This controller
guarantees high dynamic system performances.
Simulation results are given to highlight the obtained
performances. This study is the foundation of a
practical implementation follow-up this research
work.
3.45
3.4
3.35
0.4
1
0.45
0.5
0.55
0.6
Agradecimientos
0
0
0.5
1
1.5
Time(s)
Figure 13: PVG current
25
Este trabajo ha sido realizado parcialmente gracias
al apoyo de la Universidad del País Vasco (GIU13/41
y UFI11/07)
Vp(v)
20
15
17
10
16
5
0
APPENDIX A
16.5
15.5
0.45
0.5
0
0.55
0.5
1
1.5
Time(s)
Figure 14: PVG Voltage
60
50
40
P(W)
30
30
29
28
20
27
1
10
0
G,Gref
I p, Vp
Rp, Rs
n
Eg
Irs
KSCT
0
1.05
1.1
1.15
0.5
1.2
1
1.5
Time(s)
Figure 15: PVG Power
60
50
Tc,
Tc_ref
β
D
Ns, Np
ns
Global, Reference insulation (W /m2).
Cell output current and voltage.
Cell parallel and series resistance (Ω).
Solar ideal factor
Band gap energy (ev)
Reverse diode saturation current (A)
Short circuit current temperature
(A/°K).
Cell
junction
and
Reference
temperature (°C).
Boltzmann constant (1. 38e-23)
duty cycle
Number of series and parallel modules.
Number of series cells
VR(v)
40
30
20
10
0
0
0.5
1
1.5
Time(s)
Figure 16: The load voltage
Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)
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Actas de las XXXV Jornadas de Automática, 3-5 de septiembre de 2014, Valencia
ISBN-13: 978-84-697-0589-6 © 2014 Comité Español de Automática de la IFAC (CEA-IFAC)