Assessment and control of a photovoltaic energy storage system based on the robust sliding mode MPPT controller

Solar Energy 139 (2016) 557–568

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Solar Energy journal homepage: www.elsevier.com/locate/solener

Assessment and control of a photovoltaic energy storage system based on the robust sliding mode MPPT controller Hanane Yatimi ⇑, Elhassan Aroudam Modeling and Simulation of Mechanical Systems Team, Physics Department, Faculty of Sciences, Abdelmalek Essaadi University, Sebta Ave., Mhannech II BP 2121, Tetouan 93002, Morocco

a r t i c l e

i n f o

Article history: Received 17 August 2016 Received in revised form 8 October 2016 Accepted 21 October 2016

Keywords: PV system MPPT DC DC boost converter Storage battery Sliding Mode Control (SMC)

a b s t r a c t The energy produced by the photovoltaic systems is very intermittent and depends enormously on the weather conditions. As the output characteristic of a photovoltaic (PV) module is nonlinear and changes with solar irradiance and the cell’s temperature, its maximum power point (MPP) is not constant. Therefore, a maximum power point tracking (MPPT) technique is needed to draw peak power from the PV module to maximize the produced energy under varying conditions. This paper presents an assessment and control of a stand-alone photovoltaic system with battery storage using the robust sliding mode MPPT control for DC/DC boost converter operating in continuous conduction mode; under varying meteorological conditions. Simulation results are presented to verify the simplicity, the stability and the robustness of this control technique against changes in weather conditions. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction With the increasing demand for energy due to the indiscriminate use of electrical power by the people and industries, fossil energy reserves are becoming depleted; however, the consumption of this kind of energy causes severe pollution and also endangering human health and natural life. Energy shortages and the need for sustainable energy systems have enforced the search for energy supplies based mainly on renewable energy resources. Many renewable energy technologies today are well developed, reliable and cost competitive compared with conventional fuel supplied generators, in particular photovoltaic solar energy. Photovoltaic systems have been widely utilized in various applications (Ghosh et al., 2015; Lajouad et al., 2014), such as battery charging, water pumping (Hamrouni et al., 2009), and home power supply to convert the solar energy, as one of the main renewable energy sources due to its advantage direct electric power form, to electrical power through the semiconductor devices called photovoltaic cells based on photovoltaic effect (Boukenoui et al., 2016). Due to such advantages as easy maintenance, availability of sunlight and environmental friendly (Fattori et al., 2014; Mavromatidis et al., 2015; Rasool Mojallizadeh et al., 2016), the demand of PV power generation systems have been increased in recent years. On the other hand, high installation cost of PV systems and low efficiency during ⇑ Corresponding author. E-mail address: [email protected] (H. Yatimi). http://dx.doi.org/10.1016/j.solener.2016.10.038 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.

rapid changing in environmental conditions may restrict the extensive utilization. To increase the efficiency of such systems, various investigations have been carried out in three main areas as (i) designing sun tracking systems (Mousazadeh et al., 2009), (ii) implementing effective power converter topologies, and (iii) developing MPPT algorithms (Kamarzaman and Tan, 2014). The first two strategies are commonly adopted in designing and implementing the new PV systems, whereas developing MPPT schemes can be easily incorporated into the both new and installed systems. In fact, the MPPT problem is to adjust the PV operating point such that the PV power, delivered by the PV system, is maximized. In the presence of modeling errors, electrical noise, external disturbances, and model parameter variations, the characteristic curve of a photovoltaic solar cell, which is the fundamental element of the PV system, exhibits a nonlinear current-voltage characteristic and then designing an effective MPPT scheme is inevitable to ensure robust accurate tracking. Many MPPT techniques have been proposed in the literature; in both stand-alone and grid-connected PV systems. Each MPPT technique has its advantages and disadvantages. Examples are the Perturb and Observe (P&O) methods Femia and et al., 2005, the Incremental Conductance (IC) methods Lin and et al., 2011; Safari and Mekhilef, 2011, ripple correlation (Esram and et al., 2006), short circuit current (Noguchi et al., 2002) and open-circuit voltage (Dorofte et al., 2005), the quadratic maximization method (Ko and Chao, 2012; Moradi and Reisi, 2011), the Artificial Neural Network method (Rai and et al., 2011), the Fuzzy Logic method (Kyoungsoo

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and Rahman, 1998), the genetic algorithm (Messai et al., 2011; Chaouachi et al., 2010; Zagrouba et al., 2010) and evolutionary algorithms which due to its ability to handle non-linear objective functions (Ishaque and Salam, 2011; Ishaque et al., 2011; Ishaque and et al., 2012; Salam et al., 2013), envisaged with the MPPT difficulties effectively. These techniques vary between them in many aspects, including simplicity, convergence speed, hardware implementation, sensors required, cost, range of effectiveness and need for parameterization. The P&O and IC techniques, as well as variants thereof, are the most widely used. The P&O is the most widely used algorithm due to the simplicity of implementation practically. Its main advantages are simple structure and ease of implementation, with both stand-alone and grid-connected systems. But it has limitations that reduce efficiency of MPPT. In the lower solar irradiance cases, it is difficult to determine the exact location of MPP, and the output power is oscillating around the MPP reducing the generated power. In literature, IC method was determined to operate with more efficiency under randomly generated conditions (Roman et al., 2006). However, the cost of IC method is high due to requirements of high sampling compliance and speed control as a result of complex structure (Libo et al., 2007). Classically, P&O and IC methods that are the most widely used techniques have two major disadvantages. In these methods, decisionmaking speed increases in proportion to the step size of error. However, higher error step size reduces the efficiency of MPPT. The second major problem is the direction errors under rapid atmospheric changes especially in P&O algorithm (Kazmi et al., 2009). In this paper, the sliding mode control is applied to track maximum power of photovoltaic system. The advantages of this control are various and important such as, high precision, good stability, simplicity, invariance, and robustness (Slotine and Li, 1991; Chiu et al., 2012). It has powerful ability for the control of uncertain systems; therefore, the controlled system with sliding mode exhibits robustness properties with respect to both internal parameter uncertainties and external disturbances (Rasool Mojallizadeh et al., 2016). Removing some drawbacks of the previous works, the main contributions of this investigation are, (i) reducing the required sensors by estimating the output voltage by an adaptation mechanism, (ii) the bound of system uncertainties and environmental disturbances are not required to be known in the design procedure, and (iii) robust tracking performance is ensured, as shown analytically by using the Lyapunov stability theorem. The rest of this paper is organized as follows. The PV system description is presented in Section 2. Section 3 describes the robust MPPT method. In Section 4, the analysis based on the simulation results is conducted. The concluding remarks and some ideas for the future investigations are given in Section 5. 2. System description The complete studied system is schematically shown in Fig. 1. In our analysis, we consider a photovoltaic module supplying a

DC load, e.g. a battery through an adaptation stage considered by boost converter, driven by a MPPT assuming the maximum efficiency for the energy transfer. T and G are the input signals of the system, and are respectively the solar cell temperature (in K) and the solar irradiance (in W/m2) on the surface of PV module. 2.1. Mathematical modeling of PV module The direct conversation of the solar energy into electrical power is obtained by solar cells. And as the PV module is composed of group of cells, its model is based on that of a PV cell, associated in series and/or parallel. The equivalent circuit of the photovoltaic cell is shown in Fig. 2 (Yu et al., 2004; Cuce and Cuce, 2014; Picault et al., 2010). Rs: mainly due to losses by Joule effect through grids collection and to the specific resistance of the semiconductor, as well as bad contacts (semi conductor, electrodes). Rsh: Parallel resistance comes from the recombination losses mainly due to the thickness, the surface effects and the non-ideality of the junction. The nonlinear current-voltage characteristic of a PV cell with 5 parameters is governed by the following equation, (Reisi et al., 2013; Zhao et al., 2015; Yıldıran and Tacer, 2016):

Ip ¼ Iph  Id  Ish h

q   i V þ I R  p p S ðV p þ Ip RS Þ  1  ¼ Iph  I0 exp aKT Rsh where

 Iph ¼ ½ISCR þ K i ðT  T r Þ

I0 ¼ Irs

 G 1000

 3    qEg0 T 1 1 exp  Tr Tr T aK

G

PV Module

V

ð2Þ

ð3Þ

where Iph: generated photocurrent (A); it depends mainly on the radiation and cell’s temperature. I0: reverse saturation current of diode (A), it is influenced by the temperature. Vp: output voltage of the PV cell (V). Ip: output current of the PV cell (A). Iscr: short-circuit current at reference condition (A). Ki: short-circuit temperature coefficient. Tr: reference temperature (K). G: solar irradiance (W/m2). Irs: saturation current at reference temperature (A). q: electron charge (1.60217 ⁄ 1019 C). K: Boltzmann constant (1.38 ⁄ 1023 J/K). a: diode ideality factor. T: temperature (K). Rs: series resistance of cell (X). Rsh: parallel resistance of cell (X).

I T

ð1Þ

DC/DC Converter

Ib

Battery Load

MPPT Method Fig. 1. Block diagram of the stand-alone PV system with storage battery.

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remarkable effect on both the short circuit current and the power of the module. The Table 2 gives the MPP of the PV module for the typical clear day of June for the maximum and the minimum values of the temperature and at a given solar irradiance. The more temperature is low the more cell generates power. These figures are using the real meteorological data locally measured at regular intervals (1 h) Aroudam, 1992 throughout the typical clear day of June in Northern Morocco (Tetouan). To conclude, the use of the MPPT techniques to extract the maximum available power at any changes is primordial.

Fig. 2. Equivalent electrical circuit of a PV cell.

The PV module mathematical model is represented by the equation: !      V þ I NNps RS q Ns I ¼ N p Iph  N p I0 exp ð4Þ 1  V þ I RS Ns Np N s akT R N p sh where Ns: series PV cell per module. Np: parallel PV cell per module. 2.2. Reference model for validation The polycrystalline ‘‘SW 255 Poly” has been chosen to validate the model. The key specifications of the PV module are shown in Table 1. The module is made of 60 solar cells connected in series to give a maximum power output of 255 W. The performance of solar cell is normally evaluated under the standard test condition (STC), where an average solar spectrum at AM 1.5 is used, the solar radiation is normalized to 1000 W/m2, and the cell temperature is defined as 25 °C. 2.3. Effect of solar irradiance and temperature on PV characteristics The response of a PV cell at different levels of solar irradiance at constant temperature 25 °C shows that solar irradiance has a significant effect on the short-circuit current (Fig. 3), while the effect on the voltage in open circuit is quite low. Regarding the power, we can clearly notice the existence of the maximum on the power curves, (Fig. 3) corresponding to the Maximum Power Point PMPP. This figure represents the curves of the generated current and power by one PV module for the typical clear day of June. The PV power increases during the first hours of the day and gradually decreases, as seen in the figures above: the more solar radiation is high, the more the cell generates power. The temperature is an important parameter in the behavior of solar cells. It has an influence on the characteristics of a PV module. In Fig. 4, the curves show the variation of the characteristics of a PV module at different levels of temperature and at a given solar irradiance (fixed at the maximum of the typical clear day of June). These curves represent the generated current and power by one PV module of the typical clear day of June. From these curves, we can clearly detect that the temperature has a very important effect on the open circuit voltage and a no Table 1 Electrical characteristics data of the polycrystalline PV module SW 255 at STC. Parameter

Name

Value

Pmax Vmp Imp Voc Isc Ki Ns Tr E

Maximum power Voltage at maximum power Current at maximum power Open circuit voltage Short circuit current Temperature coefficient of Isc Number of cells per module Reference temperature Reference solar irradiance

255 W 30.9 V 8.32 A 38 V 8.88 A 0.051%/K 60 298.15 K 1000 W/m2

2.4. Boost converter average model and battery storage A DC/DC boost converter is a power converter steps up voltage (while stepping down current) from its input (PV module) to its output (load-battery), in order to force the PV module to operate at the MPP. It is composed of two semiconductor switches (a diode and a switch or transistor), an inductor, an input and output capacitors and one energy storage element. It is controlled periodically with a modulation period T. Over this period, ton called the closing time and toff for the opening time, we have: T = ton + toff. The duty cycle of the converter is defined as: a = ton/T. The specific connections are shown in Fig. 5. The input capacitor Ci and the inductor L are selected to limit ripple of the PV Module input voltage and the output capacitor Cb to limit ripple of the output voltage. The switches are alternatively opened and closed. As long as transistor is ON, the diode is OFF, being reversed biased. The input voltage, applied directly to inductance L which stores energy, determines a linear rising current. When the transistor on OFF, the voltage across the inductor will change the polarity and the diode will switch in ON state. The output that results is a regulated voltage of higher magnitude than input voltage. Considering the periods of open and closed circuit operation, the state equations of the boost converter average model (Chen et al., 2001) operating in continuous conduction mode (the current through the output inductor never reaches zero), by applying Kirchhoff’s theorem are:

8 > C dv ¼ i  iL > < i dt L didtL ¼ v  ð1  aÞðEb þ Rb ib Þ > > : C dv b ¼ i þ ð1  aÞi

ð5Þ

v b ¼ Eb þ Rb ib

ð6Þ

b dt

L

b

where i and v: are the output current and voltage of the PV module, iL: the inductor current, vb: the DC/DC converter output voltage, a: the duty cycle, which represents the control input, L: the DC/DC converter inductance, Ci and Cb: the input capacitor and the output capacitor of the converter. 2.5. Model of the overall system By combining the different equations describing the system, the global mathematical model of the PV storage system can be written as follows:

h


 i
 8 N S > i ¼ Np Iph  Np I0 exp Ns qakT v þ i NNps RS  1  R p Nvs þ iR > N > p sh > > > < dv ¼ 1 i  1 i dt

Ci L

Ci

diL > > ¼ 1L v  1L ð1  aÞv b > dt > > > : dv b ¼  1 i þ 1 ð1  aÞi L C b C dt b

b

ð7Þ

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2

903.65 W/m²

4 p.m (575.54 W/m²)

June

9 a.m (551.13 W/m²)

1 0.5

Power (W)

Current (A)

1.5

903.65 W/m²

4 p.m (575.54 W/m²)

60

9 a.m (551.13 W/m²)

40 June 20

46.27 W/m²

46.27 W/m²

0

0

10

20

40

30

0

50

0

10

20

Voltage (V)

30

40

50

Voltage (V)

Fig. 3. I-V and P-V characteristics at constant temperature and variable solar irradiance for the typical clear day of June-Tetouan (Yatimi and Aroudam, 2016).

24°C

1.5 June 1

27.24°C

0.5 0

10

0

June

60 40

27.24°C

20 0

60

50

40

30

20

24°C

80

Power (W)

Current (A)

2

0

10

20

Voltage (V)

30

40

50

60

Voltage (V)

Fig. 4. I-V and P-V characteristics at constant solar irradiance and variable temperature for the typical clear day of June-Tetouan (Yatimi and Aroudam, 2016).

Table 2 MPP under the influence of temperature for typical clear day of June (Yatimi and Aroudam, 2016). Month

Temperature (°C)

June

24 27.24

i PV

v

PMPP (W)

VMPP (V)

IMPP (A)

84.5 79.27

62.25 59.14

1.861 1.861

L

iL

Cb

y¼

@P @ðv  iÞ @i ¼ ¼iþv ¼0 @v @v @v

ð9Þ

The relative degree r = 2 of PV system (8) corresponds to the number of times the output y has to be differentiated with respect to time before the input u appears explicitly in the resulting equations. We have the first and second time derivative of the controlled output y. after the second derivation of the output of the system we obtain the following expression:

Rb

ib

G

Ci

Module

Constant solar irradiance (W/m2)

The proposed MPPT method is based on the fact that the slope of the PV module power versus voltage curves oP/ov equal to zero at the maximum power point (MPP), as shown in Figs. 3 and 4. So, the output system to be forced to zero in finite time is:

vb

Eb

€ ¼ f ðx; tÞ þ gðx; tÞu y

ð10Þ

with

vG

ton

f ðx; tÞ ¼

T

Time

@3P @v 3

!  !    2 @v 1 @2P @i @v v þ  Ci @v 2 @v @t @t L

1 @2P gðx; tÞ ¼ Ci @v 2

Fig. 5. Boost converter coupling the PV module to the battery.

!

vo L

ð11Þ

ð12Þ

where The state equation given in (7) is a nonlinear system and can be expressed as:

8 x_ ¼ i  1 x > > < 1 Ci Ci 2 x_ 2 ¼ 1L x1  uL x3 > > : x_ ¼ Eb  1 x þ u x 3 3 2 C R C C R b b

b b

ð8Þ

x2 ¼ iL ;

x3 ¼ v b ;

u ¼ 1  a;

y¼

@P : @v

ð13Þ

and,

@3P @2i @3i ¼ 3 þ v @v 3 @v 2 @v 3

b

where

x1 ¼ v ;

@2P @i @2i ¼2 þv 2 2 @v @v @v

ð14Þ

We consider u as the applied control law and a can be deduced from the relation u = 1  a. with the main objective of u is to steer the output to zero in finite time.

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3. Robust MPPT control Sliding mode control is well known for its robustness to disturbances and parameter variations. Its basic principle consists in moving the state trajectory of the system toward a predetermined surface called sliding or switching surface (Afonso et al., 2013; Soltani and Payam, 2006; Islam et al., 2010; Slotine, 1986) and in maintaining it around this latter with an appropriate switching logic. A typical sliding mode control has two mode of operation. One is called the approaching mode, where the system state converges to a pre-defined manifold named sliding surface where the switching function r = 0 in finite time. The other mode is called the sliding mode, where the system state is confined on the sliding surface. The main idea is to find a sliding mode controller for the system defined in state space by (8) to ensure that the system remains in the sliding surface. By an appropriate choice of this surface, the output of the system (9) is steered to zero in finite time, which assure the maximum power tracking and then improve the dynamic performance under rapidly varying conditions. In this study, we introduce the concept, by selecting the sliding surface as oP/ov = 0, which guaranteed that the system state will hit the surface and produce maximum power output persistently.

Proof. To determine these two elements, two state of the sliding surface will be considered.

3.1. Choice of sliding surface

r_ ¼ ksignðrÞ

ð23Þ

The sliding surface is chosen according to the output to be forced to zero in finite time and the relative degree of the system. The relative degree r of the system is defined to be the least positive integer i for which the derivative y(i)(t) is an explicit function of the control law u(t) such that:

V_ ¼ krsignðrÞ ¼ kjrj < 0

ð24Þ

@yðrÞ ðtÞ – 0 and @u

@yðiÞ ðtÞ ¼ 0 for i ¼ 0; . . . ; r  1: @u

rðtÞ ¼ yðr1Þ ðtÞ þ kr2 yðr2Þ ðtÞ þ . . . þ k0 yðtÞ where the coefficients k0 . . . kr2 are chosen so that the characteristic polynomial associated to r(t) have the negative roots. Then, the output y(t) tends asymptotically to zero in a finite time when r tends to zero in a finite time. In sliding surface we have r(t) = 0. In our case r = 2 and the switching function is:

ð15Þ

where k is a positive constant.

r_ ¼ ky_ þ y€

ð16Þ

€ by its expression (10), we obtain: Replacing y

r_ ¼ F þ gu

ð17Þ

_ where F ¼ f þ ky. 3.2. Determination of the control law The control law u(t) forcing approximately the output y to zero in finite time for the system described by (10) is given by:

    F k þ  signðrÞ u ¼ ueq þ ur ¼  g g

ð18Þ

where ueq is the equivalent linear control element which makes the undisturbed nominal system state slide on the sliding surface, and ur is the element of robustness that forces the system to remain on the sliding surface in presence of disturbances and parameters variations. The duty cycle control is:

a ¼ 1  u ¼ 1  ueq  ur

u ¼ ueq ¼ 

F g

ð20Þ

 For the disturbed switching function r(t) – 0, in order to demonstrate stability, we adopt the candidate Lyapunov function:

V¼

1 rðtÞ2 2

ð21Þ

Then we have:

V_ ¼ rr_

ð22Þ

By choosing:

where k is a positive parameter. From (17) and (23), we have:

k  signðrÞ ¼ F þ g  u

ð25Þ

Then:

F k u ¼ ueq þ ur ¼   signðrÞ g g

The switching function can be selected as follows:

r ¼ ky þ y_

 In sliding surface where r(t) = 0, u = ueq is the control law obtained from the equivalent control method which is determined from the solution of equation r_ ðtÞ ¼ 0 in (20), we obtain:

ð19Þ

_ F ðf þ kyÞ ueq ¼  ¼  g g

k and ur ¼  signðrÞ g

ð26Þ 

4. Simulation results and discussions The PV module model, the average boost converter model and the proposed MPPT method are implemented in Matlab/Simulink as illustrated in Fig. 6 (the simulated structure of the global system). In this study, SW 255 Poly PV module manufactured by Solar Word has been selected as PV power source. The key specifications of the PV module are shown in Table 1. For simulation we consider the parameters of the system, tabulated in Table 3. The proposed MPPT method is evaluated from two aspects: robustness to solar irradiance and temperature. In each figure, two different values of irradiance or temperature are presented for comparison in order to show the robustness. In the case of robustness to solar irradiance, during the first time interval t = [0, 2] (s), the irradiance level is 700 W/m2 and the optimal PV current and voltage are 5.8 A and 30.7 V, respectively. Accordingly, maximum PV power is about 178.9 W. During the second time interval t = [2, 4] (s), the irradiance level is 1000 W/m2. In this condition, optimal PV current and voltage are about 8.32 A and 30.91 V, respectively. Therefore, the maximum PV power is 257.2 W. Compared to the previous time interval, the maximum PV power is increased about 78.3 W. It can be seen that the proposed system successfully tracks maximum PV power. In the case of robustness to temperature, during the first time interval t = [0, 2] (s), the temperature level is 298.15 K (25 °C) and the optimal PV current and voltage are 8.32 A and 30.91 V, respectively. Accordingly, maximum PV power is about 257.2 W.

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[vp] vp [vp]

[vp]

vp vp1

From

vp

[vp]

vp1

From2

Terminato

[vp] From4

Goto2

[ip]

[E] Goto7

[ip]

[ip]

ip température

ip

[il]

il

From1

Goto1

ip

[ib]

Goto3 [il]

PV Module

il

[alpha]

alpha

ib p

[y]

y

From5

Goto8

Goto13

[ib]

ib

[ib]

Goto4

From7

ip [il] il

From3

Step1 [T]

[alpha]

alpha

Goto5

eclairement

Step

[ip]

vp

ib

From6 DC/DC converter et battery

sigma

[T]

T

[sigma] Goto14

From8

p

var.mat

[alpha]

To File

control [E] p1 [T] p2

MPPT Sliding mode controller

[y] p3 [sigma] Figures

p4 TM

Fig. 6. Block diagram model of the proposed PV energy storage system on Matlab/Simulink .

Table 3 Simulation parameters. Parameter

Name

Value

PV module SW 255 Poly Rs Series resistance Rsh Parallel resistance a Ideality factor ISCR Short circuit current at STC Irs Saturation current at Tr Ki Temperature coefficient Tr Reference temperature

0.2035 O 7 kO 1.2654 8.8803 A 3.0981  108 A 5.1  104 A/K 298.15 K

DC-DC converter L Ci Cb

Inductance Input capacitor Output capacitor

2.2 mH 47 mF 4.7 mF

Battery Vb Rb

Battery voltage Battery resistance

48 V 2O

During the second time interval t = [2, 4] (s), the temperature level is 313.15 K (40 °C). In this condition, optimal PV current and voltage are about 8.26 A and 29.1 V, respectively. Therefore, the maximum PV power is 240.5 W.

4.1. Robustness to solar irradiance

Solar irradiance (W/m²)

Figs. 8–11 illustrate the tracking results with step irradiance input from 700 W/m2 to 1000 W/m2 at 2 s as shown in Fig. 7, under

the same temperature T = 298.15 K (25 °C). The system reaches steady state of both irradiance levels within the order of milliseconds, which is faster compare to the other MPPT tracking methods. Figs. 12 and 13 show current-voltage and power-voltage characteristics and maximum power point (MPP) for different solar irradiance levels and constant temperature for PV module: MPP1 (G = 700 W/m2 and T = 298.15 K–25 °C), (IMPP = 5.8266 A, VMPP = 30.7081 V, PMPP = 178.9236 W). MPP2 (G = 1000 W/m2 and T = 298.15 K–25 °C), (IMPP = 8.3201 A, VMPP = 30.9165 V, PMPP = 257.2268 W). It can be noted that the MPP is always achieved after a smooth transient response without oscillations. This way, the validation of the robustness of the proposed sliding mode controller in presence of solar irradiance variation is guaranteed. Figs. 14 and 15 show the evolution of the controlled output y and the sliding surface. When the maximum power is reached, the controlled output y = dP/dv and the sliding surface converge to zero. 4.2. Robustness to temperature Figs. 17–20 depict the system response under rapid temperature changes, from 298.15 K (25 °C) to 313.15 K (40 °C) at 2 s as shown in Fig. 16, under the same solar irradiance E = 1000 W/m2. The system reaches steady state of both temperature levels within the order of milliseconds, which is faster compare to the other MPPT tracking methods.

1100 1000 900 800 700 600 0

0.5

1

1.5

2

2.5

Time (Sec) Fig. 7. Change of solar irradiance.

3

3.5

4

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H. Yatimi, E. Aroudam / Solar Energy 139 (2016) 557–568

PV Voltage (V)

35 30 25 20 15 10

0

0.5

1

1.5

2

2.5

3

3.5

4

Time (Sec) Fig. 8. PV voltage-constant temperature and variable solar irradiance.

8 PV Current (A)

PV Current (A)

9

7

6

8 6 1.8

1.9

2

2.1

2.2

Time (Sec)

5 0

0.5

1

1.5

2

2.5

3

3.5

4

Time (Sec) Fig. 9. PV current-constant temperature and variable solar irradiance.

250 PV Power (W)

PV Power (W)

300

200 150 100

300 200 100 1.8

50 0

0.5

1

1.5

2

2.5

1.9

2 2.1 2.2 Time (Sec) 3

3.5

4

Time (Sec)

0.4

Duty Cycle

Duty Cycle

Fig. 10. PV power-constant temperature and variable solar irradiance.

0.2

0.4 0.2 1.8

0

0.5

1

1.5

2.5

2

2.2 2 Time (Sec) 3

3.5

4

Time (Sec) Fig. 11. Duty cycle-constant temperature and variable solar irradiance.

Figs. 21and 22 show current-voltage and power-voltage characteristics and maximum power point (MPP) for constant solar irradiance and different temperature levels for PV module: MPP1 (G = 1000 W/m2 and T = 298.15 K–25 °C), (IMPP = 8.3201 A, VMPP = 30.9165 V, PMPP = 257.2268 W).

MPP2 (G = 1000 W/m2 and T = 313.15 K–40 °C), (IMPP = 8.2657 A, VMPP = 29.1031 V, PMPP = 240.5579 W). It can be noted that the MPP is always achieved as well. This way, the validation of the robustness of the proposed sliding mode controller in presence of temperature variation is guaranteed.

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9

PV Current (A)

MPP2 8 7 6

MPP1 5 10

15

20

25

30

35

PV Voltage (V) Fig. 12. Characteristic curves current-voltage at different solar irradiance and constant temperature.

300

PV Power (W)

MPP2 200

MPP1 100

0 10

15

20

25

30

35

PV Voltage (V)

Controlled Output y=dP/dv (W/V)

Fig. 13. Characteristic curves power-voltage at different solar irradiance and constant temperature.

5

0

-5 0

0.5

1

1.5

2

2.5

3

3.5

4

Time (Sec) Fig. 14. Controlled output (y = dP/dv).

Sliding Surface

500

0

-500 0

0.5

1

1.5

2

2.5

3

3.5

4

Time (Sec) Fig. 15. Sliding surface-constant temperature and variable solar irradiance.

Figs. 23 and 24 show the evolution of the controlled output y and the sliding surface. When the maximum power is reached, the controlled output y = dP/dv and the sliding surface converge to zero.

For all the results above, the sliding mode approach is able to maintain the output at optimum point, stable, accurate and robust to the variation of the external conditions.

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Temperature (K)

315 310 305 300 295 0

0.5

1

1.5

2

2.5

3

3.5

4

3

3.5

4

3.5

4

3.5

4

Time (Sec) Fig. 16. Change of temperature.

PV Voltage (V)

35 30 25 20 15 10 0

0.5

1

1.5

2

2.5

Time (Sec) Fig. 17. PV voltage-constant solar irradiance and variable temperature.

PV Current (A)

10

9

8

7

6 0

0.5

1

1.5

2

2.5

3

Time (Sec) Fig. 18. PV current-constant solar irradiance and variable temperature.

PV Power (W)

300 250 200 150 100 50 0

0.5

1

1.5

2

2.5

3

Time (Sec) Fig. 19. PV power-constant solar irradiance and variable temperature.

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Duty Cycle

566

0.5 0.4 0.3 0.2 0

0.5

1

1.5

2.5

2

3

3.5

4

Time (Sec) Fig. 20. Duty cycle-constant solar irradiance and variable temperature.

PV Current (A)

9

8.5

MPP1

MPP2 8

7.5 10

15

20

25

30

35

PV Voltage (V) Fig. 21. Characteristic curves current-voltage at constant solar irradiance and different temperature.

300

PV Power (W)

MPP1 250

MPP2

200

150 100 10

20

15

25

30

35

PV Voltage (V)

Controlled Output y=dP/dv (W/V)

Fig. 22. Characteristic curves power-voltage at constant solar irradiance and different temperature.

30 20 10 0 -10 -20 -30 0

0.5

1

1.5

2

2.5

Time (Sec) Fig. 23. Controlled output (y = dP/dv).

3

3.5

4

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Sliding Surface

500

0

-500 0

0.5

1

1.5

2

2.5

3

3.5

4

Time (Sec) Fig. 24. Sliding surface-constant solar irradiance and variable temperature.

5. Conclusions and future work In this work, we presented a modeling, simulation and control of a stand-alone PV system. One-diode model of PV module was selected; DC/DC boost converter operating in continuous conduction mode is used to supply the needed power to the load. The Sliding Mode MPPT Control is presented and analyzed. The proposed system was simulated in Matlab/Simulink environment. In the sliding mode technique, regardless of the ranges of variation of meteorological parameters, the responses are more stable, more accurate and robust. In fact, the variations in solar irradiance, cell temperature and system perturbations, form an uncertain mathematical model for a PV system. Removing the necessity of output voltage measurement, a sliding mode control is presented to solve the underlying MPPT problem. Ensuring the robust stability property by the Lyapunov stability theorem, the numerical studies are demonstrated to verify the robust tracking performance (stability and accuracy) in both static and dynamic responses of the proposed method. The following of this work is based on optimizing the performance of the standalone photovoltaic systems using more efficient methods with other types of batteries, to minimize the influence of the meteorological parameters on the PV energy production. Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Afonso, L.P., Pinto, S.F., Silva, J.F., 2013. Maximum power point tracker for wind energy generation systems using matrix converters. In: IEEE, 4th Int. Conf. on Power Eng., Energy and Elect. Drives (POWERENG13), Istanbul, Turkey, pp. 978– 983. Aroudam, El H., 1992. Evaluation du Gisement solaire dans la région de Tétouan Doctoral Thesis. Faculty of Sciences, Abdelmalek Essaadi Univ, Morocco. Boukenoui, R., Salhi, H., Bradai, R., Mellit, A., 2016. A new intelligent MPPT method for stand-alone photovoltaic systems operating under fast transient variations of shading patterns. Sol. Energy 124, 124–142. Chaouachi, Aymen, Kamel, Rashad M., Nagasaka, Ken, 2010. A novel multi-model neuro-fuzzy-based MPPT for three-phase grid-connected photovoltaic system. Sol. Energy 84, 2219–2229. Chen, J., Erickson, R., Maksimovid, D., 2001. Averaged switch modeling of boundary conduction mode Dc-to-Dc converters. In: IECON’O1: The 27th Annual Conference of the IEEE Ind. Electronic. Society, Denver, Colorado, USA, pp. 844–849. http://dx.doi.org/10.1109/IECON.2001.975867. Chiu, Chian-Song, Ouyang, Ya-Lun, Ku, Chan-Yu, 2012. Terminal sliding mode control for maximum power point tracking of photovoltaic power generation systems. Sol. Energy 86, 2986–2995. Cuce, E., Cuce, P.M., 2014. Improving thermodynamic performance parameters of silicon photovoltaic cells via air cooling. Int. J. Ambient Energy 35 (4), 193–199. Dorofte, C., Borup, U., Blaabjerg, F., 2005. A combined two-method MPPT control scheme for grid-connected photovoltaic systems. In: Power Electron. Appl. Eur. Conf., 10, p. 10.

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