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Enhancement of Power Production of an Autonomous PV System Based on Robust MPPT Technique
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The 12th International Conference Interdisciplinarity in Engineering The 12th International Conference Interdisciplinarity in Engineering
Enhancement of Power Production of an Autonomous PV System Enhancement ofBased PoweronProduction of anTechnique Autonomous PV System Robust MPPT Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30 June Based 2017, on a,Robust MPPT Technique a a Vigo (Pontevedra), Spain Hanane Yatimi *, Youness Ouberri , Elhassan Aroudam a, a a a Hanane Yatimi *, Youness Ouberri , Elhassan Aroudam Modeling and Simulation of Mechanical Systems Team, Physics Department, Faculty of Sciences, 0F
Costing models for capacity optimization in Industry 4.0: Trade-off Abdelmalek Essaadi University, Sebta Ave., Mhannech II BP 2121, Tetouan, 93002, Morocco Modeling and Simulation of Mechanical Systems Team, Physics Department, Faculty of Sciences, between usedUniversity, capacity operational efficiency Abdelmalek Essaadi Sebta Ave.,and Mhannech II BP 2121, Tetouan, 93002, Morocco 0F
a
Abstract
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Abstract a University of Minho, 4800-058techniques, Guimarães,the Portugal This paper presents two MPPT (Maximum Power Point Tracking) incremental conductance (IC) and the sliding b Unochapecó, 89809-000system, Chapecó, SC, Brazil mode control (SMC), applied to an autonomous photovoltaic under varying solar irradiance. The whole system is This paper presents two MPPT (Maximum Power Point Tracking) techniques, the incremental conductance (IC) and the sliding simulated in Matlab/Simulink environment. Simulation results show that the IC technique provides good efficiency under rapidly mode control (SMC), applied to an autonomous photovoltaic system, under varying solar irradiance. The whole system is changing climatic conditions, but the accuracy for finding the MPP is quite low. Whereas, the SMC technique provides good simulated in Matlab/Simulink environment. Simulation results show that the IC technique provides good efficiency under rapidly performance under the climatic changes in term of stability and robustness to solar irradiance variation. Through simulations, changing climatic conditions, but the accuracy for finding the MPP is quite low. Whereas, the SMC technique provides good Abstract SMC can accurately track the MPP of the PV module and then improve the PV system efficiency, better than IC technique can. performance under the climatic changes in term of stability and robustness to solar irradiance variation. Through simulations, SMC can accurately MPP of 4.0", the PVproduction module and then improvewill the PV better than IC interconnected, technique can. Under the concepttrack of the "Industry processes be system pushedefficiency, to be increasingly
information based on a real time basis Ltd. and, © Published by © 2018The 2019 TheAuthors. Authors. Published byElsevier Elsevier Ltd. necessarily, much more efficient. In this context, capacity optimization goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability and value. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018The Authors. Published and by Elsevier Ltd. improvement approaches suggest capacity optimization instead of Indeed, management continuous Selection lean and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) maximization. The study of capacity optimization and costing models is an important research topic that deserves Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Keywords: Photovoltaic system; converter; Incremental ConductanceThis (IC); paper Sliding presents Mode Control contributions from both theBoost practical andMPPT; theoretical perspectives. and(SMC). discusses a mathematical model forPhotovoltaic capacity management based on different costing models (IC); (ABC andMode TDABC). A generic model has been Keywords: system; Boost converter; MPPT; Incremental Conductance Sliding Control (SMC). developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity optimization might hide operational inefficiency. 1. Introduction Research on renewable energy andB.V. especially on photovoltaic energy has received increased attention since the © 2017 The Authors. Published by Elsevier last years due to many advantages; it is clean, inexhaustible and free to Engineering harvest [1].Society However, there are two main Peer-review under of the scientific committee the Manufacturing International Conference Research onresponsibility renewable energy and especially on of photovoltaic energy has received increased attention since the drawbacks of PV system, namely the high installation cost and the low conversion efficiency of PV modules [2]. In 2017. last years due to many advantages; it is clean, inexhaustible and free to harvest [1]. However, there are two main fact, a PV module is a nonlinear power source, and its output power depends on weather conditions. To increase the drawbacks of PV system, namely the high installation cost and the low conversion efficiency of PV modules [2]. In Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
fact, a PV module is a nonlinear power source, and its output power depends on weather conditions. To increase the 1. Introduction * Corresponding author. Tel.: +21262008-4090.
E-mail address:[email protected] * The Corresponding author. Tel.: +21262008-4090. cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address:[email protected] in modern production systems. In general, it Ltd. is defined as unused capacity or production potential and can be measured 2351-9789© 2018The Authors. Published by Elsevier Thisseveral is an open accesstons articleofunder the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) in ways: production, available hours of manufacturing, etc. The management of the idle capacity 2351-9789© Authors. Published by Elsevier Ltd.International Conference Interdisciplinarity in Engineering. Selection and2018The peer-review under responsibility of the 253 12th * Paulo Afonso. Tel.: +351 253 510 761; fax: +351 604 741 This is an open access article under the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail address: [email protected] Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2019.02.232
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing 00 (2018) 000–000
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efficiency of the PV system, the PV module must operate on its MPP, thus the need of using MPPT techniques. Maximum power point trackers (MPPTs) play an important role in PV power systems because they maximize the output power from a PV module for a given set of conditions. Many MPPT techniques have been addressed in the literature, in both stand-alone and grid-connected PV systems. Most control schemes use the perturbation and observation (P&O) technique [3], which is based on iterative algorithms, because it is easy to implement, the IC technique [4] which requires complex control circuit, and the fuzzy logic control search method (FLC) [5] which is used very successfully in the implementation for MPP searching. In this paper, two MPPT techniques are applied to a photovoltaic system, the Incremental Conductance (IC) and the Sliding Mode Control (SMC). The paper is organized as follows: in section 2, modeling of the overall PV system is developed, in section 3 the design of the two MPPT techniques IC and SMC is carried out, and in section 4 obtained simulation results and discussions are presented to show the performances of SMC comparing to IC method. Finally, some conclusions are drawn. 2. Modeling of PV system The studied system is composed of a PV Module, a DC-DC boost converter, which is used to interface the PV output to the load and to track the MPP of the PV module, an MPPT power stage and a load which is a battery. 2.1. Modeling and characteristics of PV module As the PV module is composed of group of cells, its model is based on that of a PV cell. The equivalent circuit of a PV cell [4, 6] is composed of a current source associated with a diode and a shunt resistor Rp in parallel, in series with a resistor Rs. The output current–voltage characteristic of a PV cell is given Eq. 1 [7]:
q V pv + I pv Rs G I pv = I SCR + K i (T − Tr ) - I 0 exp (V pv + I pv Rs ) -1 - Rp 1000 aKT
(1)
q G I N p I SCR + K i (T − Tr ) = - N p I 0 exp 1000 akT
(2)
Where, I0 is the reverse saturation current of diode (A),Vpv, Ipv, ISCR, Ki, q, K, a, Tr, T, G, Rs and Rp refer to PV cell output voltage and current, short-circuit current at reference condition, short-circuit temperature coefficient, electron charge (1.60217.10-19 C), Boltzmann constant (1.38.10-23 J/K), diode ideality factor, reference temperature (K), PV cell Temperature (K), solar irradiance (W/m2), series resistance of PV cell (Ω), parallel resistance of PV cell (Ω), respectively. The PV module mathematical model is represented by the equation [8]:
IR N p V + S -1 N s N p Rsh
V IR + S Ns N p
Fig. 1, [9] shows the behavior of a PV module simulation in accordance to solar irradiance variation (and constant temperature). It is clear that the short-circuit current and the power are highly affected by the solar irradiance, while the effect on the open circuit voltage is quite low. 2
903.65 W/m ²
4 p.m (575.54 W/m²)
1
Power (W)
Current (A)
1.5
9 a.m (551.13 W/m²)
0.5 46.27 W/m ²
0
0
10
20 30 Voltage (V)
40
50
903.65 W/m ²
4 p.m (575.54 W/m²)
60
9 a.m (551.13 W/m²)
40 20 0
46.27 W/m ²
0
10
20 30 Voltage (V)
Fig. 1. I-V and P-V characteristics at varying solar irradiance and constant temperature (25°C).
40
50
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So the more solar irradiance is high, the more the module generates power. To conclude, the use of the MPPT techniques to extract the maximum available power at any changes is primordial. 2.2. DC-DC boost converter and load modeling The DC/DC boost converter (chopper) which connects the PV module to the DC load (battery) is considered. If the chopping frequency is sufficiently higher than the system characteristic frequencies, the converter can be replaced with an equivalent continuous model as shown in fig. 2 [8]. It is operates in continuous conduction mode with an input filter (Ci, L) and an output filter Co. It’s controlled periodically with a modulation period T. Over this period, ton is called the closing time and toff is the opening time, T = ton+toff. The duty cycle of the converter is defined as, α = ton/T. The switches are alternatively opened and closed. I
IL
L Lo G
V
Io
MOSFET
Vo
Co
Rb
Ci
Vb Vg
Ton
T
Time(s) Fig. 2. Boost converter and battery model.
Considering the periods of open and closed circuit operation, the state equations of the boost converter average model [10] operating in continuous conduction mode are:
(3)
Where: (4) I and V are the output current and voltage of the PV module, IL is the inductor current, Io and Vb are the average states of respectively the battery current and the battery voltage, Vo is the DC/DC converter output voltage, α is the duty cycle, which represents the control input, L is the DC/DC converter inductance and Ci and Co are respectively the input capacitor and the output capacitor of the converter. 2.3. System model By combining the different equations describing the system, the global mathematical model of the PV system can be expressed by Eqs. 5. Where:
, x is the state vector, u
is the control law and y is chosen as the system output. Based on the power-voltage characteristic curves of the PV module shown in fig 1, the condition of maximum power point is given by Eq. 6.
Hanane et al.Manufacturing / Procedia Manufacturing 32 (2019) 397–404 Author nameYatimi / Procedia 00 (2018) 000–000
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1 I − x2 x1 = Ci Ci u 1 x2 x1 − x 3 = L L Vb u 1 + x3 + x2 x3 = Co Rb Co Rb Co
(5)
∂P ∂ (V .I ) ∂I y == I +V 0 = = ∂V ∂V ∂V
(6)
So, y is the system output to be force to zero. The relative degree of the system corresponds to the number of times the output y has to be differentiated with respect to time before the control law u appears explicitly in the resulting equations. In our case, after the second derivation of the output of the system we obtain the following expression:
= y
f1 ( x, t ) + f 2 ( x, t )u
Where,
∂2 I ∂3 I f1 ( x, t ) = 3 2 + V ∂V 3 ∂V
(7)
∂V 2 1 ∂I ∂2 I + C 2 ∂V + V ∂V 2 i ∂t
∂I ∂V V − ∂V ∂t L
(8)
= f 2 ( x, t )
1 ∂I ∂ 2 I Vo +V 2 Ci ∂V ∂V 2 L
(9)
3. MPPT techniques 3.1. Incremental conductance (IC) This technique requires the values of the PV module output current and voltage to calculate the conductance and the incremental conductance [4]. The operating point tracks MPP by comparing the immediate conductance (I/V) to the Incremental Conductance (dI/dV). Once, the MPP is reached, the operation of the PV module is maintained at this point unless a change in dI is noticed, indicating a change in meteorological conditions. So, the task of this technique is to track the voltage operating point which conductance is equal to incremental conductance. The equations (10) are used to determine the direction in which a perturbation must occur to shift the operating point toward the MPP and the perturbation is repeated until dP/dV=0.
dI I dP = − , at MPP 0⇒ dV = dV V dI I dP >0⇒ > − , left of MPP dV V dV dI I dP dV < 0 ⇒ dV < − V , right of MPP
(10)
3.2. Sliding mode control based MPPT Sliding mode control (SMC) is a nonlinear robust controller which consists in moving the state trajectory of the
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing00 (2018) 000–000
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system toward a predetermined surface called sliding or switching surface [11] and in maintaining it around this latter with an appropriate switching logic. So, the main idea is to find a sliding mode controller for the system defined in state space by (5) to ensure that the system remains in the sliding surface. By an appropriate choice of this surface, the output of the system (5) is steered to zero in finite time, which assure the maximum power tracking and then improve the dynamic performance under rapidly varying conditions. The design of SMC involves two tasks: The first one is the definition of the sliding surface which is chosen according to the output to be forced to zero in finite time and the relative degree of the system. The relative degree of the system r 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:
∂y ( r ) (t ) ∂y (i ) (t ) ≠ 0 and ==− 0 for i 0,....., r 1 ∂u ∂u
(11)
The switching function can be given by:
σ (= t ) y ( r −1) (t ) + br − 2 y ( r − 2) (t ) + ...... + b0 y (t )
(12)
Where the coefficients b0 ……. br − 2 are chosen so that the characteristic polynomial associated to σ (t ) have its roots strictly in the left half complex plane. Then, the output y (t ) tends asymptotically to zero in a finite time when σ tends to zero in a finite time. In sliding surface, σ (t ) = 0 . In our case r=2 and the switching function is given as:
σ =by + y ⇒ σ =by + y
(13)
Where b is a positive constant. Replacing y by its expression (7), the following expression is obtained:
σ = ( f1 + by ) + f 2 u
(14)
The second one is the determination of the control law. The control law u(t) forcing approximately the output y to zero in finite time is composed of two terms ueq and ur. Where ueq is the equivalent linear control term which makes the undisturbed nominal system state slide on the sliding surface, and ur is the term forcing the system to remain on the sliding surface in presence of disturbances and parameters variations. To determine these two terms, two state of the sliding surface will be considered. In sliding surface where, σ(t)=0, u = ueq is the control law obtained from the equivalent control method which is determined from the solution of equation σ (t ) = 0 in Eq. (14), the first term of the control law is obtained:
u= ueq = − ( f1 + by ) / f 2
(15)
For the disturbed switching function σ(t)≠0, in order to demonstrate stability, the candidate Lyapunov function is adopted:
V =
1 2 V σσ σ ( t ) ⇒= 2
(16)
σ = −m sign (σ )
(17)
V = − mσ sign (σ ) = −m σ < 0
(18)
By choosing: We obtain:
Where m is a positive parameter. From Eq. (14) and Eq. (17), the control law u is found:
( f1 + by ) − m sign
u= ueq + ur = −
f2
f2
(σ )
(19)
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing 00 (2018) 000–000
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4. Simulation results and analysis To demonstrate the effectiveness of the proposed technique, simulation results are presented for the coupling between the PV module and the battery load through the boost converter. The whole system is implemented in Matlab/Simulink as illustrated in Fig. 3 (the simulated structure of the global system: blocks in Simulink with eventually function Matlab calls for each block).
p Goto6
vp [v]
v2
Signal 2
Temperature
[v]
[T] Goto8
Température
v1
From4
[E] Goto7
P
Terminator Eclairement
Signal 2
Eclairement
Product1
v
From
i
[i]
[ip]
[alpha]
Module PV i
[i]
ip1
From1 [v]
[v]
il
Goto4 [il]
vs
Goto3 [vs]
is
Goto14 [is]
i
From3
Goto1
v
From7
alpha
Convertisseur Boost et Batterie
[alpha] vp1
Goto2
alpha
Goto5
is
From2 Commande MPPT
Fig. 3. Block diagram model of the studied PV system on Matlab/Simulink.
The Mono-crystalline SW 255 Mono PV module manufactured by Solar World, has been chosen to validate the model. The used PV system to validate the proposed MPPT technique has the parameters summarizes in the tab. 1. A simulation study was made to illustrate the response of the system to solar irradiance variation G and constant temperature (T = 298.15 K (25°C)). To investigate the performance of the proposed MPPT technique under fast solar irradiance change, the real data of June have been considered. So, the initial irradiance level for the simulation is 712.6195 W/m². At t = 1 s, the irradiance level increases to 903.6524 W/m², decreases to 575.5439 W/m² at t = 2 s. as shown in fig. 4. Fig. 5 shows the PV module voltage variations under the effect of solar irradiance. A can be seen, the PV module voltage is well controlled to track the optimum voltage with solar irradiance variation, with oscillations for IC technique and without oscillations for SMC technique, around the MPP. Fig. 6 shows the PV module power variations under the effect of solar irradiance. It can be noticed that the MPP is well tracked whatever is the solar irradiance variation with oscillations for IC technique and without oscillations for the SMC technique. In addition, the system steady state is reached within the order of milliseconds for SMC compared to the IC technique. Fig. 7 shows the duty cycle behavior of the boost converter, which is chosen as the controller law, under the effect of solar irradiance. It can be clearly noticed that for both the increasing and the decreasing of the solar irradiance levels, the duty cycle variation is well adjusted and stabilized by the SMC technique to track the MPP without oscillations compared to the conventional IC technique. It is concluded from the simulations that, when the solar irradiance varies, the duty cycle of the boost converter α is judiciously adjusted to its desired value (fig. 7), which forces the PV module voltage to follow its optimal value (figs. 5). Consequently, the PV module power reached its maximal value (figs. 6). Fig. 8 shows 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, after a smooth transient response. This way, the robustness of the system control with changes of solar irradiance is evaluated. To conclude, the SMC gives good results, and the behavior of the complete closed loop system is more stable, more accurate and robust to the variation of solar irradiance, with good static and dynamic performance, compared to the results given by the IC MPPT technique.
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing00 (2018) 000–000
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Table 1. Electrical characteristics of the Mono crystalline PV module at STC Parameters Name Monocrystalline SW 255 Mono PV module SW 255 Mono Pmax Vmp Imp Voc Isc Ki Ns Rs Rsh a ISCR Irs DC-DC converter L Ci , Co Battery Vb Rb
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 Series resistance Parallel resistance Ideality factor Short circuit current at STC Saturation current at Tr
255 W 30.6 V 8.43 A 38.7 V 9.05 A 0.044 %/K 60 0.3090 Ω Rsh = 6500 Ω 1.3257 9.0504 A 5.4389.10-8 A
Inductance Input and output capacitors
L = 2.2 mH Ci = 47 mF, Co = 4.7 mF
Battery voltage Battery resistance
48 V 2Ω
Solar radiation (W/m 2)
1000
903.6524 W/m 2
900 800
712.6195 W/m 2
700
575.5439 W/m 2
600 500
3
2.5
2
1.5 Time (s)
1
0.5
0
Fig. 4. Change of solar irradiance.
35 30
32
25
30
20 15
40
IC PV voltage (V)
PV voltage (V)
40
0
1.55
1.5
1.45 0.5
1
2
1.5 Time (s)
30 32 31 30
25 20 15
3
2.5
SMC
35
1.45 0
1.55
1.5 1
0.5
1.5 Time (s)
2
3
2.5
Fig. 5. PV voltage variation using IC and SMC techniques. IC
200 150
200 180 160 0.320.340.360.38 0.4 0.42
100 50
0
0.5
1
1.5 Time (s)
2
2.5
SMC
250 PV power (W)
PV power (W)
250
3
200 150
200 190 180
100 50
0.3 0
0.5
1
Fig. 6. PV power variation using IC and SMC techniques.
0.35
0.4
1.5 Time (s)
2
2.5
3
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing 00 (2018) 000–000
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SMC
0.4 0.45
0.2
0.4 0
Duty cycle
Duty cycle
IC
0
0.5
1
0.340.360.38 0.4 0.42 2
1.5 Time (s)
0.4 0.45 0.2
3
2.5
0.4 0
0.5
1
0.3
0.2
0.4
1.5 Time (s)
2
2.5
3
1.5 Time (s)
2
2.5
3
10
400
5
Sliding surface
Controllet output y(W/V)
Fig. 7. Duty cycle variation using IC and SMC techniques.
0 -5 -10
0
0.5
1
1.5 Time (s)
2
2.5
3
200 0 -200 -400
0
0.5
1
Fig. 8. Controlled output (y=dP/dV) and sliding surface of SMC technique.
5. Conclusion In this paper, modeling and simulation of an autonomous PV system with battery storage were presented; numerical simulations (using Simulink/Matlab) were carried out for PV system containing the two MPPT techniques, under varying solar irradiance. The simulation analysis shows that IC technique has precise control and faster response, but presents oscillations around the MPP. Whereas, SMC has shown, through these numerical simulations better performance compared to the IC technique. The SMC ensures better tracking performance and high robustness, regardless of the ranges of variation of solar irradiance; the responses are more stable, more accurate and robust. References [1] Fattori, F., Anglani, N., Muliere, G., Combining photovoltaic energy with electric vehicles, smart charging and vehicle-to-grid, Solar Energy, 110 (2014) 438–451. [2] Hanane Yatimi, Elhassan Aroudam, A robust sliding mode MPPT controller applied to a stand-alone photovoltaic system, In Proceeding of the 33rd European Photovoltaic Solar Energy Conference and Exhibition, Amsterdam. Netherland, (2017) 2201-2206. [3] Hanane Yatimi, Elhassan Aroudam, Modeling, Analysis and Simulation of MPPT Technique for Off-Grid Photovoltaic System, Journal of Energy and Power Source, 3(1) (2016) 5–10. [4] Hanane Yatimi, Elhassan Aroudam, Standalone Photovoltaic System with Maximum Power Point Tracking: Modeling and Simulation, International Journal of System Dynamics Applications, 7(3) (2018) 94–111. [5] Liu, F., A variable step size INC MPPT method for PV systems, IEEE Trans. on Ind. Electr., 55(7) (2008) 2622–2628. [6] Hanane Yatimi and Elhassan Aroudam, Mathematical Modeling and Simulation of Photovoltaic Power Source using Matlab/Simulink, International Journal of Innovation and Applied Studies, 16(2) (2016) 322-330. [7] H. Yatimi and El.H. Aroudam, A Detailed Study and Modeling of Photovoltaic Module under Real Climatic Conditions, International Journal of Electronics and Electrical Engineering, 3(3) (2015) 171-176. [8] Hanane Yatimi and Elhassan Aroudam, MPPT algorithms based modeling and control for photovoltaic system under variable climatic conditions, Procedia Manufacturing, 22 (2018) 757-764. [9] H. Yatimi and E. Aroudam, Evaluation of the Characteristics of the PV Module Considering Effects of Real Climatic Conditions, In:Ali Sayigh Editor. Renewable Energy in the Service of Mankind Vol II. United Kingdom; Springer International Publishing Switzerland, (2016) 457-467. [10] J. Chen, R. Erickson, and D. Maksimovid, Averaged Switch Modeling of Boundary Conduction Mode Dc-to-Dc Converters, IECON'O1: The 27th Annual Conf. of the IEEE Ind. Electr. Society, Denver, Colorado, USA, (2001) 844-849. [11] Slotine, J.J.. Adaptive Sliding controller synthesis for nonlinear systems, Int. J. of Control, 43(6) (1986) 1631-1651.
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The 12th International Conference Interdisciplinarity in Engineering The 12th International Conference Interdisciplinarity in Engineering
Enhancement of Power Production of an Autonomous PV System Enhancement ofBased PoweronProduction of anTechnique Autonomous PV System Robust MPPT Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30 June Based 2017, on a,Robust MPPT Technique a a Vigo (Pontevedra), Spain Hanane Yatimi *, Youness Ouberri , Elhassan Aroudam a, a a a Hanane Yatimi *, Youness Ouberri , Elhassan Aroudam Modeling and Simulation of Mechanical Systems Team, Physics Department, Faculty of Sciences, 0F
Costing models for capacity optimization in Industry 4.0: Trade-off Abdelmalek Essaadi University, Sebta Ave., Mhannech II BP 2121, Tetouan, 93002, Morocco Modeling and Simulation of Mechanical Systems Team, Physics Department, Faculty of Sciences, between usedUniversity, capacity operational efficiency Abdelmalek Essaadi Sebta Ave.,and Mhannech II BP 2121, Tetouan, 93002, Morocco 0F
a
Abstract
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Abstract a University of Minho, 4800-058techniques, Guimarães,the Portugal This paper presents two MPPT (Maximum Power Point Tracking) incremental conductance (IC) and the sliding b Unochapecó, 89809-000system, Chapecó, SC, Brazil mode control (SMC), applied to an autonomous photovoltaic under varying solar irradiance. The whole system is This paper presents two MPPT (Maximum Power Point Tracking) techniques, the incremental conductance (IC) and the sliding simulated in Matlab/Simulink environment. Simulation results show that the IC technique provides good efficiency under rapidly mode control (SMC), applied to an autonomous photovoltaic system, under varying solar irradiance. The whole system is changing climatic conditions, but the accuracy for finding the MPP is quite low. Whereas, the SMC technique provides good simulated in Matlab/Simulink environment. Simulation results show that the IC technique provides good efficiency under rapidly performance under the climatic changes in term of stability and robustness to solar irradiance variation. Through simulations, changing climatic conditions, but the accuracy for finding the MPP is quite low. Whereas, the SMC technique provides good Abstract SMC can accurately track the MPP of the PV module and then improve the PV system efficiency, better than IC technique can. performance under the climatic changes in term of stability and robustness to solar irradiance variation. Through simulations, SMC can accurately MPP of 4.0", the PVproduction module and then improvewill the PV better than IC interconnected, technique can. Under the concepttrack of the "Industry processes be system pushedefficiency, to be increasingly
information based on a real time basis Ltd. and, © Published by © 2018The 2019 TheAuthors. Authors. Published byElsevier Elsevier Ltd. necessarily, much more efficient. In this context, capacity optimization goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability and value. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018The Authors. Published and by Elsevier Ltd. improvement approaches suggest capacity optimization instead of Indeed, management continuous Selection lean and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) maximization. The study of capacity optimization and costing models is an important research topic that deserves Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Keywords: Photovoltaic system; converter; Incremental ConductanceThis (IC); paper Sliding presents Mode Control contributions from both theBoost practical andMPPT; theoretical perspectives. and(SMC). discusses a mathematical model forPhotovoltaic capacity management based on different costing models (IC); (ABC andMode TDABC). A generic model has been Keywords: system; Boost converter; MPPT; Incremental Conductance Sliding Control (SMC). developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity optimization might hide operational inefficiency. 1. Introduction Research on renewable energy andB.V. especially on photovoltaic energy has received increased attention since the © 2017 The Authors. Published by Elsevier last years due to many advantages; it is clean, inexhaustible and free to Engineering harvest [1].Society However, there are two main Peer-review under of the scientific committee the Manufacturing International Conference Research onresponsibility renewable energy and especially on of photovoltaic energy has received increased attention since the drawbacks of PV system, namely the high installation cost and the low conversion efficiency of PV modules [2]. In 2017. last years due to many advantages; it is clean, inexhaustible and free to harvest [1]. However, there are two main fact, a PV module is a nonlinear power source, and its output power depends on weather conditions. To increase the drawbacks of PV system, namely the high installation cost and the low conversion efficiency of PV modules [2]. In Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
fact, a PV module is a nonlinear power source, and its output power depends on weather conditions. To increase the 1. Introduction * Corresponding author. Tel.: +21262008-4090.
E-mail address:[email protected] * The Corresponding author. Tel.: +21262008-4090. cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address:[email protected] in modern production systems. In general, it Ltd. is defined as unused capacity or production potential and can be measured 2351-9789© 2018The Authors. Published by Elsevier Thisseveral is an open accesstons articleofunder the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) in ways: production, available hours of manufacturing, etc. The management of the idle capacity 2351-9789© Authors. Published by Elsevier Ltd.International Conference Interdisciplinarity in Engineering. Selection and2018The peer-review under responsibility of the 253 12th * Paulo Afonso. Tel.: +351 253 510 761; fax: +351 604 741 This is an open access article under the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail address: [email protected] Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2019.02.232
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing 00 (2018) 000–000
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efficiency of the PV system, the PV module must operate on its MPP, thus the need of using MPPT techniques. Maximum power point trackers (MPPTs) play an important role in PV power systems because they maximize the output power from a PV module for a given set of conditions. Many MPPT techniques have been addressed in the literature, in both stand-alone and grid-connected PV systems. Most control schemes use the perturbation and observation (P&O) technique [3], which is based on iterative algorithms, because it is easy to implement, the IC technique [4] which requires complex control circuit, and the fuzzy logic control search method (FLC) [5] which is used very successfully in the implementation for MPP searching. In this paper, two MPPT techniques are applied to a photovoltaic system, the Incremental Conductance (IC) and the Sliding Mode Control (SMC). The paper is organized as follows: in section 2, modeling of the overall PV system is developed, in section 3 the design of the two MPPT techniques IC and SMC is carried out, and in section 4 obtained simulation results and discussions are presented to show the performances of SMC comparing to IC method. Finally, some conclusions are drawn. 2. Modeling of PV system The studied system is composed of a PV Module, a DC-DC boost converter, which is used to interface the PV output to the load and to track the MPP of the PV module, an MPPT power stage and a load which is a battery. 2.1. Modeling and characteristics of PV module As the PV module is composed of group of cells, its model is based on that of a PV cell. The equivalent circuit of a PV cell [4, 6] is composed of a current source associated with a diode and a shunt resistor Rp in parallel, in series with a resistor Rs. The output current–voltage characteristic of a PV cell is given Eq. 1 [7]:
q V pv + I pv Rs G I pv = I SCR + K i (T − Tr ) - I 0 exp (V pv + I pv Rs ) -1 - Rp 1000 aKT
(1)
q G I N p I SCR + K i (T − Tr ) = - N p I 0 exp 1000 akT
(2)
Where, I0 is the reverse saturation current of diode (A),Vpv, Ipv, ISCR, Ki, q, K, a, Tr, T, G, Rs and Rp refer to PV cell output voltage and current, short-circuit current at reference condition, short-circuit temperature coefficient, electron charge (1.60217.10-19 C), Boltzmann constant (1.38.10-23 J/K), diode ideality factor, reference temperature (K), PV cell Temperature (K), solar irradiance (W/m2), series resistance of PV cell (Ω), parallel resistance of PV cell (Ω), respectively. The PV module mathematical model is represented by the equation [8]:
IR N p V + S -1 N s N p Rsh
V IR + S Ns N p
Fig. 1, [9] shows the behavior of a PV module simulation in accordance to solar irradiance variation (and constant temperature). It is clear that the short-circuit current and the power are highly affected by the solar irradiance, while the effect on the open circuit voltage is quite low. 2
903.65 W/m ²
4 p.m (575.54 W/m²)
1
Power (W)
Current (A)
1.5
9 a.m (551.13 W/m²)
0.5 46.27 W/m ²
0
0
10
20 30 Voltage (V)
40
50
903.65 W/m ²
4 p.m (575.54 W/m²)
60
9 a.m (551.13 W/m²)
40 20 0
46.27 W/m ²
0
10
20 30 Voltage (V)
Fig. 1. I-V and P-V characteristics at varying solar irradiance and constant temperature (25°C).
40
50
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So the more solar irradiance is high, the more the module generates power. To conclude, the use of the MPPT techniques to extract the maximum available power at any changes is primordial. 2.2. DC-DC boost converter and load modeling The DC/DC boost converter (chopper) which connects the PV module to the DC load (battery) is considered. If the chopping frequency is sufficiently higher than the system characteristic frequencies, the converter can be replaced with an equivalent continuous model as shown in fig. 2 [8]. It is operates in continuous conduction mode with an input filter (Ci, L) and an output filter Co. It’s controlled periodically with a modulation period T. Over this period, ton is called the closing time and toff is the opening time, T = ton+toff. The duty cycle of the converter is defined as, α = ton/T. The switches are alternatively opened and closed. I
IL
L Lo G
V
Io
MOSFET
Vo
Co
Rb
Ci
Vb Vg
Ton
T
Time(s) Fig. 2. Boost converter and battery model.
Considering the periods of open and closed circuit operation, the state equations of the boost converter average model [10] operating in continuous conduction mode are:
(3)
Where: (4) I and V are the output current and voltage of the PV module, IL is the inductor current, Io and Vb are the average states of respectively the battery current and the battery voltage, Vo is the DC/DC converter output voltage, α is the duty cycle, which represents the control input, L is the DC/DC converter inductance and Ci and Co are respectively the input capacitor and the output capacitor of the converter. 2.3. System model By combining the different equations describing the system, the global mathematical model of the PV system can be expressed by Eqs. 5. Where:
, x is the state vector, u
is the control law and y is chosen as the system output. Based on the power-voltage characteristic curves of the PV module shown in fig 1, the condition of maximum power point is given by Eq. 6.
Hanane et al.Manufacturing / Procedia Manufacturing 32 (2019) 397–404 Author nameYatimi / Procedia 00 (2018) 000–000
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1 I − x2 x1 = Ci Ci u 1 x2 x1 − x 3 = L L Vb u 1 + x3 + x2 x3 = Co Rb Co Rb Co
(5)
∂P ∂ (V .I ) ∂I y == I +V 0 = = ∂V ∂V ∂V
(6)
So, y is the system output to be force to zero. The relative degree of the system corresponds to the number of times the output y has to be differentiated with respect to time before the control law u appears explicitly in the resulting equations. In our case, after the second derivation of the output of the system we obtain the following expression:
= y
f1 ( x, t ) + f 2 ( x, t )u
Where,
∂2 I ∂3 I f1 ( x, t ) = 3 2 + V ∂V 3 ∂V
(7)
∂V 2 1 ∂I ∂2 I + C 2 ∂V + V ∂V 2 i ∂t
∂I ∂V V − ∂V ∂t L
(8)
= f 2 ( x, t )
1 ∂I ∂ 2 I Vo +V 2 Ci ∂V ∂V 2 L
(9)
3. MPPT techniques 3.1. Incremental conductance (IC) This technique requires the values of the PV module output current and voltage to calculate the conductance and the incremental conductance [4]. The operating point tracks MPP by comparing the immediate conductance (I/V) to the Incremental Conductance (dI/dV). Once, the MPP is reached, the operation of the PV module is maintained at this point unless a change in dI is noticed, indicating a change in meteorological conditions. So, the task of this technique is to track the voltage operating point which conductance is equal to incremental conductance. The equations (10) are used to determine the direction in which a perturbation must occur to shift the operating point toward the MPP and the perturbation is repeated until dP/dV=0.
dI I dP = − , at MPP 0⇒ dV = dV V dI I dP >0⇒ > − , left of MPP dV V dV dI I dP dV < 0 ⇒ dV < − V , right of MPP
(10)
3.2. Sliding mode control based MPPT Sliding mode control (SMC) is a nonlinear robust controller which consists in moving the state trajectory of the
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system toward a predetermined surface called sliding or switching surface [11] and in maintaining it around this latter with an appropriate switching logic. So, the main idea is to find a sliding mode controller for the system defined in state space by (5) to ensure that the system remains in the sliding surface. By an appropriate choice of this surface, the output of the system (5) is steered to zero in finite time, which assure the maximum power tracking and then improve the dynamic performance under rapidly varying conditions. The design of SMC involves two tasks: The first one is the definition of the sliding surface which is chosen according to the output to be forced to zero in finite time and the relative degree of the system. The relative degree of the system r 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:
∂y ( r ) (t ) ∂y (i ) (t ) ≠ 0 and ==− 0 for i 0,....., r 1 ∂u ∂u
(11)
The switching function can be given by:
σ (= t ) y ( r −1) (t ) + br − 2 y ( r − 2) (t ) + ...... + b0 y (t )
(12)
Where the coefficients b0 ……. br − 2 are chosen so that the characteristic polynomial associated to σ (t ) have its roots strictly in the left half complex plane. Then, the output y (t ) tends asymptotically to zero in a finite time when σ tends to zero in a finite time. In sliding surface, σ (t ) = 0 . In our case r=2 and the switching function is given as:
σ =by + y ⇒ σ =by + y
(13)
Where b is a positive constant. Replacing y by its expression (7), the following expression is obtained:
σ = ( f1 + by ) + f 2 u
(14)
The second one is the determination of the control law. The control law u(t) forcing approximately the output y to zero in finite time is composed of two terms ueq and ur. Where ueq is the equivalent linear control term which makes the undisturbed nominal system state slide on the sliding surface, and ur is the term forcing the system to remain on the sliding surface in presence of disturbances and parameters variations. To determine these two terms, two state of the sliding surface will be considered. In sliding surface where, σ(t)=0, u = ueq is the control law obtained from the equivalent control method which is determined from the solution of equation σ (t ) = 0 in Eq. (14), the first term of the control law is obtained:
u= ueq = − ( f1 + by ) / f 2
(15)
For the disturbed switching function σ(t)≠0, in order to demonstrate stability, the candidate Lyapunov function is adopted:
V =
1 2 V σσ σ ( t ) ⇒= 2
(16)
σ = −m sign (σ )
(17)
V = − mσ sign (σ ) = −m σ < 0
(18)
By choosing: We obtain:
Where m is a positive parameter. From Eq. (14) and Eq. (17), the control law u is found:
( f1 + by ) − m sign
u= ueq + ur = −
f2
f2
(σ )
(19)
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing 00 (2018) 000–000
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4. Simulation results and analysis To demonstrate the effectiveness of the proposed technique, simulation results are presented for the coupling between the PV module and the battery load through the boost converter. The whole system is implemented in Matlab/Simulink as illustrated in Fig. 3 (the simulated structure of the global system: blocks in Simulink with eventually function Matlab calls for each block).
p Goto6
vp [v]
v2
Signal 2
Temperature
[v]
[T] Goto8
Température
v1
From4
[E] Goto7
P
Terminator Eclairement
Signal 2
Eclairement
Product1
v
From
i
[i]
[ip]
[alpha]
Module PV i
[i]
ip1
From1 [v]
[v]
il
Goto4 [il]
vs
Goto3 [vs]
is
Goto14 [is]
i
From3
Goto1
v
From7
alpha
Convertisseur Boost et Batterie
[alpha] vp1
Goto2
alpha
Goto5
is
From2 Commande MPPT
Fig. 3. Block diagram model of the studied PV system on Matlab/Simulink.
The Mono-crystalline SW 255 Mono PV module manufactured by Solar World, has been chosen to validate the model. The used PV system to validate the proposed MPPT technique has the parameters summarizes in the tab. 1. A simulation study was made to illustrate the response of the system to solar irradiance variation G and constant temperature (T = 298.15 K (25°C)). To investigate the performance of the proposed MPPT technique under fast solar irradiance change, the real data of June have been considered. So, the initial irradiance level for the simulation is 712.6195 W/m². At t = 1 s, the irradiance level increases to 903.6524 W/m², decreases to 575.5439 W/m² at t = 2 s. as shown in fig. 4. Fig. 5 shows the PV module voltage variations under the effect of solar irradiance. A can be seen, the PV module voltage is well controlled to track the optimum voltage with solar irradiance variation, with oscillations for IC technique and without oscillations for SMC technique, around the MPP. Fig. 6 shows the PV module power variations under the effect of solar irradiance. It can be noticed that the MPP is well tracked whatever is the solar irradiance variation with oscillations for IC technique and without oscillations for the SMC technique. In addition, the system steady state is reached within the order of milliseconds for SMC compared to the IC technique. Fig. 7 shows the duty cycle behavior of the boost converter, which is chosen as the controller law, under the effect of solar irradiance. It can be clearly noticed that for both the increasing and the decreasing of the solar irradiance levels, the duty cycle variation is well adjusted and stabilized by the SMC technique to track the MPP without oscillations compared to the conventional IC technique. It is concluded from the simulations that, when the solar irradiance varies, the duty cycle of the boost converter α is judiciously adjusted to its desired value (fig. 7), which forces the PV module voltage to follow its optimal value (figs. 5). Consequently, the PV module power reached its maximal value (figs. 6). Fig. 8 shows 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, after a smooth transient response. This way, the robustness of the system control with changes of solar irradiance is evaluated. To conclude, the SMC gives good results, and the behavior of the complete closed loop system is more stable, more accurate and robust to the variation of solar irradiance, with good static and dynamic performance, compared to the results given by the IC MPPT technique.
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing00 (2018) 000–000
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Table 1. Electrical characteristics of the Mono crystalline PV module at STC Parameters Name Monocrystalline SW 255 Mono PV module SW 255 Mono Pmax Vmp Imp Voc Isc Ki Ns Rs Rsh a ISCR Irs DC-DC converter L Ci , Co Battery Vb Rb
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 Series resistance Parallel resistance Ideality factor Short circuit current at STC Saturation current at Tr
255 W 30.6 V 8.43 A 38.7 V 9.05 A 0.044 %/K 60 0.3090 Ω Rsh = 6500 Ω 1.3257 9.0504 A 5.4389.10-8 A
Inductance Input and output capacitors
L = 2.2 mH Ci = 47 mF, Co = 4.7 mF
Battery voltage Battery resistance
48 V 2Ω
Solar radiation (W/m 2)
1000
903.6524 W/m 2
900 800
712.6195 W/m 2
700
575.5439 W/m 2
600 500
3
2.5
2
1.5 Time (s)
1
0.5
0
Fig. 4. Change of solar irradiance.
35 30
32
25
30
20 15
40
IC PV voltage (V)
PV voltage (V)
40
0
1.55
1.5
1.45 0.5
1
2
1.5 Time (s)
30 32 31 30
25 20 15
3
2.5
SMC
35
1.45 0
1.55
1.5 1
0.5
1.5 Time (s)
2
3
2.5
Fig. 5. PV voltage variation using IC and SMC techniques. IC
200 150
200 180 160 0.320.340.360.38 0.4 0.42
100 50
0
0.5
1
1.5 Time (s)
2
2.5
SMC
250 PV power (W)
PV power (W)
250
3
200 150
200 190 180
100 50
0.3 0
0.5
1
Fig. 6. PV power variation using IC and SMC techniques.
0.35
0.4
1.5 Time (s)
2
2.5
3
Hanane Yatimi et al. / Procedia Manufacturing 32 (2019) 397–404 Author name / Procedia Manufacturing 00 (2018) 000–000
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SMC
0.4 0.45
0.2
0.4 0
Duty cycle
Duty cycle
IC
0
0.5
1
0.340.360.38 0.4 0.42 2
1.5 Time (s)
0.4 0.45 0.2
3
2.5
0.4 0
0.5
1
0.3
0.2
0.4
1.5 Time (s)
2
2.5
3
1.5 Time (s)
2
2.5
3
10
400
5
Sliding surface
Controllet output y(W/V)
Fig. 7. Duty cycle variation using IC and SMC techniques.
0 -5 -10
0
0.5
1
1.5 Time (s)
2
2.5
3
200 0 -200 -400
0
0.5
1
Fig. 8. Controlled output (y=dP/dV) and sliding surface of SMC technique.
5. Conclusion In this paper, modeling and simulation of an autonomous PV system with battery storage were presented; numerical simulations (using Simulink/Matlab) were carried out for PV system containing the two MPPT techniques, under varying solar irradiance. The simulation analysis shows that IC technique has precise control and faster response, but presents oscillations around the MPP. Whereas, SMC has shown, through these numerical simulations better performance compared to the IC technique. The SMC ensures better tracking performance and high robustness, regardless of the ranges of variation of solar irradiance; the responses are more stable, more accurate and robust. References [1] Fattori, F., Anglani, N., Muliere, G., Combining photovoltaic energy with electric vehicles, smart charging and vehicle-to-grid, Solar Energy, 110 (2014) 438–451. [2] Hanane Yatimi, Elhassan Aroudam, A robust sliding mode MPPT controller applied to a stand-alone photovoltaic system, In Proceeding of the 33rd European Photovoltaic Solar Energy Conference and Exhibition, Amsterdam. Netherland, (2017) 2201-2206. [3] Hanane Yatimi, Elhassan Aroudam, Modeling, Analysis and Simulation of MPPT Technique for Off-Grid Photovoltaic System, Journal of Energy and Power Source, 3(1) (2016) 5–10. [4] Hanane Yatimi, Elhassan Aroudam, Standalone Photovoltaic System with Maximum Power Point Tracking: Modeling and Simulation, International Journal of System Dynamics Applications, 7(3) (2018) 94–111. [5] Liu, F., A variable step size INC MPPT method for PV systems, IEEE Trans. on Ind. Electr., 55(7) (2008) 2622–2628. [6] Hanane Yatimi and Elhassan Aroudam, Mathematical Modeling and Simulation of Photovoltaic Power Source using Matlab/Simulink, International Journal of Innovation and Applied Studies, 16(2) (2016) 322-330. [7] H. Yatimi and El.H. Aroudam, A Detailed Study and Modeling of Photovoltaic Module under Real Climatic Conditions, International Journal of Electronics and Electrical Engineering, 3(3) (2015) 171-176. [8] Hanane Yatimi and Elhassan Aroudam, MPPT algorithms based modeling and control for photovoltaic system under variable climatic conditions, Procedia Manufacturing, 22 (2018) 757-764. [9] H. Yatimi and E. Aroudam, Evaluation of the Characteristics of the PV Module Considering Effects of Real Climatic Conditions, In:Ali Sayigh Editor. Renewable Energy in the Service of Mankind Vol II. United Kingdom; Springer International Publishing Switzerland, (2016) 457-467. [10] J. Chen, R. Erickson, and D. Maksimovid, Averaged Switch Modeling of Boundary Conduction Mode Dc-to-Dc Converters, IECON'O1: The 27th Annual Conf. of the IEEE Ind. Electr. Society, Denver, Colorado, USA, (2001) 844-849. [11] Slotine, J.J.. Adaptive Sliding controller synthesis for nonlinear systems, Int. J. of Control, 43(6) (1986) 1631-1651.