Hajar Doubabi
email: hajardoubabi@gmail.com

Issam Salhi
email: isalhi@yahoo.fr

Mohammed Chennani
email: medchennani@gmail.com

Najib Essounbouli
email: najib.essounbouli@univ-reims.fr

High Performance MPPT based on TS Fuzzyintegral backstepping control for PV system under rapid varying irradiance -Experimental validation

Keywords: Maximum power point tracking, Integral Backstepping, Takagi-Sugeno Fuzzy, Photovoltaic system, DC-DC boost converter

With the recent focus marked on energy efficiency and solar energy development, much research is being dedicated to the development of enhanced maximum power point tracking (MPPT) algorithms for photovoltaic applications. However, the main criteria with regard to tracking performances and circuit implementation are still considered as a major challenge under rapid varying weather conditions. In this paper, a T-S Fuzzy-integral backsteppingbased hybrid MPPT technique is proposed for rapid, accurate and efficient tracking. The proposed technique enables reliable and stable operation under fast dynamic environmental changes. Besides, it is simple as it does not require extra atmospheric sensors. The theoretical analysis addressed in this study is verified through simulations via Matlab/Simulink and experimental outdoor tests. A comparison with different other MPPT techniques is provided to highlight the performances of the developed MPPT method.

I. Introduction

The global environmental harm, due to fossil fuels use, has led to an increased need for alternative power sources. In recent years, the transition to renewable energy sources has received greater consideration in various sectors owing to their incredible reduction of greenhouse gas emissions. Solar energy is a free, clean and inexhaustible source of power, which makes it a reliable means of supplying electricity to the world. Solar photovoltaic (PV) systems provide electric power by directly converting solar irradiance into electricity. PV systems are used in various applications and can produce power at levels of few watts to megawatts. The electrical characteristic of the PV system is non-linear and varies with the atmospheric conditions. Hence, ensuring the efficient generation of maximum power, especially for situations with rapidly changing irradiation conditions, is considered the main challenge.

Maximum power point tracking is a fundamental control strategy used to harvest the highest photovoltaic power under all environmental conditions. In general, MPPT algorithms are incorporated into switching power converters to provide the maximum available power from panels. Specifically, the converter is utilized as an adapting stage between the PV module and the load, so by controlling its duty ratio, the PV system could operate at the maximum power point (MPP) in spite of climate changes.

Several MPPT techniques have been developed in the literature [START_REF] Lyden | Maximum Power Point Tracking techniques for photovoltaic systems: A comprehensive review and comparative analysis[END_REF]. Perturb and observe (P&O) and incremental conductance (IC) are reviewed as conventional MPPT methods [START_REF] Thakran | Implementation of P&O Algorithm for MPPT in SPV System[END_REF][START_REF] Loukriza | Simulation and experimental design of a new advanced variable step size Incremental Conductance MPPT algorithm for PV systems[END_REF].

The P&O method is widely investigated due to its simplicity of implementation, but it introduces considerable oscillations near to the MPP that lead to power losses. On the other hand, the IC method is more flexible and accurate than the P&O. Nevertheless, it has as a main drawback the control circuit complexity that results in high response time to reach the MPP. However, the above-mentioned MPPT algorithms generally fail in tracking effectively the MPP under varying solar irradiation. These have led the researchers to explore and discover new soft computing techniques for enhanced MPPT controller performances.

Genetic Algorithm (GA) [START_REF] Megantoro | Simulation and Characterization of Genetic Algorithm Implemented on MPPT for PV System under Partial Shading Condition[END_REF], Particle Swarm Optimization (PSO) [START_REF] Zeddini | PSO-based MPPT control of winddriven Self-Excited Induction Generator for pumping system[END_REF], Random Search methods [START_REF] Sundareswaran | Application of random search method for maximum power point tracking in partially shaded photovoltaic systems[END_REF], Ant Colony Optimization [START_REF] Kumar Sahoo | Maximum power point tracking for PV panels using ant colony optimization[END_REF] and Shuffled Frog Leaping Algorithm [START_REF] Mao | Grid-connected modular PV-Converter system with shuffled frog leaping algorithm based DMPPT controller[END_REF] are bioinspired and population-based global search algorithms that have been proposed for MPPT control. They can well cope with different atmospheric conditions and track the MPP efficiently. However, these techniques present weak dynamic performances and long processes that increase the computational complexity. In addition, they exhibit a trade-off between convergence accuracy and convergence speed, making the choice of the population size, chromosome and the number of iterations very critical and need adjustment according to irradiation conditions.

Artificial intelligence algorithms such as artificial neural network (ANN) [START_REF] Farajdadian | A new MATLAB/Simulink model of triple-junction solar cell and MPPT based on artificial neural networks for photovoltaic energy systems[END_REF] and Fuzzy logic control (FLC) [START_REF] Verma | Asymmetrical interval type-2 fuzzy logic control based MPPT tuning for PV system under partial shading condition[END_REF] have been also used for the MPPT control. They can successfully mitigate the shortcomings of the conventional algorithm namely the oscillations around MPP and the tracking speed. Moreover, the robust design of these techniques plays a key role in solving the nonlinearity and uncertainties problems of the PV system. However, the ANN method requires large data and suffers from high training time that results in a complex network and decreases the accuracy in MPPT. A comparative study has been conducted experimentally in [START_REF] Salah | Comparison of fuzzy logic and neural network in maximum power point tracker for PV systems[END_REF] revealing that the MPPT controller based on FLC extracts more PV power than the one using ANN. Even though, the FLC may fail to converge under rapid dynamic irradiance changes. Therefore, it is recommended to be combined with other techniques to achieve more attractive performances and reliable MPPT control [START_REF] Eltamaly | Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Systems[END_REF].

Most power converters that incorporate the MPPT algorithm in the PV system applications are nonlinear in nature, which has led researchers to think of advanced nonlinear controllers guaranteeing high convergence speed and robustness for MPPT under varying atmospheric conditions. Several researchers have tried to perform a high efficient MPPT algorithm using sliding mode (SM) control [START_REF] Farhat | A new maximum power point method based on a sliding mode approach for solar energy harvesting[END_REF][START_REF] Menaga | A novel nonlinear sliding mode controller for a single stage grid-connected photovoltaic system[END_REF]. This latter ensures the stability and robustness of the system; however, the chattering phenomena, the variable switching frequency and the significant steady-state error are the major shortcomings of the method. Therefore, other studies have included an integral action term in order to mitigate these associated SM control problems [START_REF] Pradhan | Double Integral Sliding Mode MPPT Control of a Photovoltaic System[END_REF][START_REF] Chatrenour | Improved double integral sliding mode MPPT controller based parameter estimation for a stand-alone photovoltaic system[END_REF]; however, undesirable disturbances and high overshoots are observed.

These limitations have led researchers in [START_REF] Kihal | An improved MPPT scheme employing adaptive integral derivative sliding mode control for photovoltaic systems under fast irradiation changes[END_REF] to propose a novel adaptive integral derivative SM -based strategy to enhance the dynamic response of MPPT and increase the PV power harvest under fast irradiation changes. However, the simulation and experimental validation of this method have been conducted only over a limited range of irradiance [500W/m²-1000W/m²]; while the performance evaluation is more substantive under high irradiance variations. Moreover, the SM control generally requires a priori knowledge about the uncertainty bounds, considered also as a main drawback. Reference [START_REF] Salimi | Practical implementation of the Lyapunov based nonlinear controller in DC-DC boost converter for MPPT of the PV systems[END_REF] proposes a Lyapunov based single-loop controller for MPPT of a standalone PV system. The asymptotic stability of the overall system is demonstrated. Nevertheless, the effects of climate variations have not been taken into consideration in the practical validation of the developed MPPT technique.

An intelligent non-linear discrete-PID controller is synthetized in [START_REF] Pathak | An Application of Intelligent Non-linear Discrete-PID Controller for MPPT of PV System[END_REF] for MPPT of the photovoltaic module. This method maintains the properties of the classic PID controller where the derivative and integral terms are discretized based on the Forward Euler Formula. PSO and GA are used to select adequate gains of the controller. However, this technique is not validated experimentally. In [START_REF]A New High Gain DC-DC Converter with Model-Predictive-Control Based MPPT Technique for Photovoltaic Systems[END_REF], an MPPT technique based on model predictive control was developed to extract the maximum available PV power at divers weather conditions. Nevertheless, this method faces considerable oscillations under abrupt irradiance changes.

The nonlinear integral backstepping method is well known for both its excellent dynamic response and it ensures global asymptotic stability. Therefore, it has been proposed for MPPT in [START_REF] Arsalan | MPPT for photovoltaic system using nonlinear backstepping controller with integral action[END_REF], for a system consists of a PV array, buck-boost converter and load resistor. It is revealed that this method could be a suitable candidate for MPPT control under challenging environmental conditions as high dynamic performances are achieved. However, the experimental validation of this technique is not addressed. Furthermore, the MPP location is estimated using basic linear approximations, that are not able to precisely determine the MPP locus under changing weather conditions, which results in significant power loss [START_REF] Lyden | Maximum Power Point Tracking techniques for photovoltaic systems: A comprehensive review and comparative analysis[END_REF] [START_REF] Elzein | Assessing Under Varying Circumstances the Behavior of Photovoltaic Systems of Maximum Power Point Methods[END_REF].

In light of the above discussion, the present work proposes a high-performance MPPT method using Takagi-Sugeno (TS) fuzzy combined with nonlinear integral backstepping control.

Specifically, the contributions of this paper are as follow:

1) Designing a novel MPP approximator based on TS fuzzy technique for estimating, with higher precision, the exact MPP locus.

2) Developing an integral backstepping controller that enforces the PV system to generate the desired power by acting on the boost converter duty cycle.

3) The proposed MPPT method is supported by detailed mathematical investigation and validated through both simulations in MATLAB/Simulink and experimental tests using the dSPACE (DS1104) interface.

4) The performance of the proposed MPPT algorithm is examined under low/high irradiation levels, gradual/abrupt/step-up/step-down irradiation variations and dynamic test standard EN50530. 5) Comparison of the developed MPPT method to the existing ones (P&O, modified incremental conductance (MIC), PSO and a hybrid controller combines P&O with fractional-order proportional-integral (P&O-FOPI)) under varying irradiance profile.

The findings show that the proposed technique successfully monitors different dynamic variations of irradiation and achieves high accuracy in locating MPP, fast convergence velocity, zero steady-state error, stable operation and high MPPT efficiency. Moreover, the structure of the proposed MPPT controller is simple to implement and doesn't require environmental sensors, which makes it applicable for most PV system configurations. This research paper is structured as follows: Section II presents the overall structure of the proposed solar battery charging system and describes the MPPT technique in detail.

Simulations and experimental results are discussed in Section III. Concluding remarks are drawn in the last section.

II. Overview of the proposed PV system

II. 1. PV modeling

A PV module is generally made by the connection of PV cells in parallel and series to achieve the required output current and voltage. In the literature, different equivalent models have been introduced to represent the PV cell operation. The most popular one is the "single-diode model" depicted in Fig. 2. It typically composed of a current source, a diode and series/parallel resistances [START_REF] Rhouma | A simple method for extracting the parameters of the PV cell single-diode model[END_REF]. The electrical circuit can be mathematically described by the following equations = --exp 1

o o ph d ph rsc th V I I I I I V     = -         (1)
where rsc I is the reverse saturation current and th V is the thermal voltage of the diode. The generated photocurrent ph I is expressed linearly with the solar irradiation ( G ) as follows ( )

_ _ = ph sc STC sc cell cell STC STC G I I K T T G   + -   (2)
where _

sc STC I is the cell short circuit current measured at Standard Test Condition (STC), _ cell STC T is 25°C, STC
G is 1000W/m², and sc K is the short circuit current coefficient. The diode current is given by ( ) The electrical parameters of the PV module adopted in this work, provided at STC (i.e.1000W/m², 25°C) are tabulated in Table I.

3 1 1 _ _ _ = exp exp 1 cell G o d rsc STC cell STC cell cell STC B B cell T q E q V I I T T T k A k A T - -         × ×   - -         × × ×           (3)

II. 2. Boost-type DC-DC converter

The boost converter (or step-up converter) is utilized to convert the lower dc input voltage provided by the PV module ( pv V ) to higher dc output voltage for the battery charging ( b V ), which is the load. As shown in Fig. 3, the circuit topology of the converter consists mainly of an inductor L, input and output capacitors (Ci & Co), a power switch MOSFET M and a diode D. Table II gives the parameters values of the designed boost converter. The equations characterizing these parameters are expressed as follows ( ) The converter is considered operating under continuous conduction mode. The mathematical equations modeling the converter in the ON and OFF states of the switches are formulated in ( 5) and ( 6), respectively

1 1 b pv pv b pv ripple s b b o s ripple V V d V V V L I f V I d C f V    =    -     × -  =  ∆ × ×   ×  = × ∆   (4)
- (M-ON, D-OFF) pv pv L i i pv L dV I I dt C C V dI dt L  =     =   (5)
- (M-OFF,D-ON) - pv pv L i i pv b L dV I I dt C C V V dI dt L L  =     =   (6)
where pv I is the generated PV current and L I is the inductor current.

Parameters Value

Inductor ( L ) 300μH As the PV current parameter ( pv I ) enables the detection of the irradiance intensity, it has been identified as an input of the fuzzy inference system that process it employing pre-specified fuzzy rules to produce the corresponding outputs r and r V . For typical values of pv I , the fuzzy inference rules have the form in Eq.8, : IF is THEN and

Capacitors ( i C , o C ) 440 μF, 100 μF Switching frequency ( s f ) 30 kHz Ripple current ( ripple I ∆ ) 1.6 A Ripple current ( ripple V ∆ ) 0.1 V

II. 3. Proposed MPPT controller

i i i pv i i r R I r V σ (8)
where i=1, 2…n; n is the number of inference rules (corresponding to MPP lines), i σ is the fuzzy set. The premise variable pv I is a measurable variable of the system. Crisp input data is converted into fuzzy values using membership functions. In this study, the number and value of each membership function were selected depending on the collected data from the PV system. The shape of membership functions has been decided using the trial-and-error method.

Using a standard fuzzy inference method that uses singleton fuzzifier, product inferred, and weighted average defuzzifier, the fuzzy system inferred outputs are 1

i i i i i pv pv p r n i i p i n i i n i i r n v i v i r r I V I I I V µ µ µ µ = = = =    =       =     ∑ ∑ ∑ ∑ (9) 1 1 1 ( ) ( ) ( ) ( )
where µ is the normalized membership function and

II. 3.2. Integral backstepping controller

The nonlinear integral backstepping control method aims to let the PV panel output voltage (

pv i i b I x x C C V x x d L L  =     =   & & (10)
where d ϵ [0, 1] and is the control signal.

The general objective of the integral backstepping method is to stabilize the system states at the origin considered as the equilibrium point. Its algorithm is based on reclusively defining some states as "virtual controls" to get the ultimate control laws using the control Lyapunov function. The main merit of this method is the asymptotic stability and nonlinearities elimination. For this system, two steps are required to obtain the control law "d".

Step1:The error z1 between the state variable x1 and the reference

ref pv V is set as follow 1 1 ref pv z x V = - (11)
The second errorz2 between x2that is considered as a virtual control input of the system in [START_REF] Verma | Asymmetrical interval type-2 fuzzy logic control based MPPT tuning for PV system under partial shading condition[END_REF] (or a reference of the inner loop) and the stabilizing function α1 is given by -

z x α = (12)
Calculating the derivative of z1 in [START_REF] Salah | Comparison of fuzzy logic and neural network in maximum power point tracker for PV systems[END_REF] with respect to time, and by using [START_REF] Eltamaly | Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Systems[END_REF] and the model in [START_REF] Verma | Asymmetrical interval type-2 fuzzy logic control based MPPT tuning for PV system under partial shading condition[END_REF], we obtain

1 2 1 1 1 1 - - -ref pv pv i i i z z I V C C C α = + & & ( 13
)
Integral action is introduced into the error term as

1 1 = e z ψ + (14)
where ( )

1 1 0 0 t t ref pv x V dt z dt ψ = - = ∫ ∫ (15)
According to the definition of the Lyapunov function provided in [START_REF] Zhou | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation[END_REF], the first Lyapunov function is chosen to be globally positive definite as follow

2 2 1 1 1 2 2 a V z ψ = + ( 16
)
where a is a positive definite real number.

The time derivative of V1 is

1 1 1 1 2 1 1 1 1 - - -ref pv pv i i i V z z a z z I V a C C C ψψ α ψ = +   = + +     (17) 1
V & must be negative definite to guarantee a global asymptotic stability. This can be imposed by taking the stabilizing function as

1 1 1 - ref i pv i pv i C k z I CV C a α ψ = + + & (18)
From ( 13) and [START_REF] Salimi | Practical implementation of the Lyapunov based nonlinear controller in DC-DC boost converter for MPPT of the PV systems[END_REF], we obtain

2 1 1 1 1 2 1 - - i V k z z z C = & (19) 1 1 1 2 1 - - i z k z z a C ψ = - & (20)
Where k1is a constant and positive parameter, then the stability is verified. It is worth mentioning that the term

1 2 1 i z z C
will be eliminated automatically in the next step.

Step2: From ( 12), the time derivative of the second error z2 can be expressed as

2 2 1 - z x α (21)
Substituting ( 10) into (21) yields to

2 1 1 1 1 - - b b d z x V V L L L α = + & & (22)
The time derivative of the stabilizing function α1 is obtained as

1 1 1 2 1 1 1 1 2 1 1 - ( )( ) ( ) - ref i pv i pv i ref ref i pv pv i pv i C k z I C V C a C a k x V k x I C V C k a α ψ α α ψ = + + = - - - - + - (23)
The second Lyapunov function is chosen with similar proprieties as ( 16)

2 2 1 2 1 2 V V z = + (24)
The Lyapunov function [START_REF] Zhou | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation[END_REF] derivative with respect to time is

2 1 2 2 V V z z = + & & & (25)
Substituting ( 19) and ( 22) into (25) yields to

2 2 1 1 2 1 1 1 1 1 1 - - - - b b i d V k z z z x V V C L L L α   = + + +     & & (26)
To ensure stability, the 2 V & value must be negative definite and keep

2 2 2 1 1 2 2 - - V k z k z = &
. This can be achieved if

2 2 1 1 1 1 1 1 - - - - b b i d k z z x V V C L L L α = + + & (27)
Where k2is a constant and positive parameter, from ( 22) and ( 27), we obtain

2 2 1 2 1 - - i k z z z C = + & (28) Thus, 2 z & is given by 2 2 2 1 1 - i z k z z C = + & (29)
By solving equation ( 27) and using [START_REF] Rhouma | A simple method for extracting the parameters of the PV cell single-diode model[END_REF], the control input of the system is

2 1 1 1 1 2 2 1 2 2 1 1 1 2 1 2 1 2 1 1 - ( ) ( ) -( ) - ( ) - ( ) ( ) - ( ) - - ( i i i b b b b b ref i pv i pv b i b b b ref ref pv i pv pv i i i b b b b b LC L L L d x a k C k k k x k k C V V V V V LC L L L V a k C k k k I k k V C V V V L L L L L V C k k I V C C k a C V V V V V ψ     = + - + + + + +             - - + + +           + + + +     & & && 1 2 ) 1 k k a   + +     (30)
where 0 d 1 p p .

The flowchart structure of the proposed MPPT control is described in Fig. 5.

Using ( 20) and ( 29), the new system model expressed in the coordinates (z1, z2) can be given by ( 31)

[ ] 1 2 1 - - 1 0 - i i A k C a z z k C ψ     -     = +           & 14243 (31)
The matrix [A]can be decomposed as follow

[ ] [ ] [ ] [ ] 1 2 1 0 - 0 - 0 1 0 - i i d a C k A k C A M M         = +           = + (32) where[ ] d M is a diagonal matrix and[ ] a M is an anti-symmetric matrix. [ ] [ ] [ ] ( ) 1 - 2 T a M A A = ,[ ] [ ] - T a a M M = ,[ ] [ ] [ ] (
)

1 2 T d M A A = + and [ ] 0 T a z M z = z 0 ∀ ≠ . Since 2 1 2 T V z z = thus [ ] [ ] [ ] 2 (- ) - 0 T T T d a d V z z z M z M z z M z = = + = & & p
This implies that (z1, z2) = (0, 0) results to be an equilibrium point of the closed-loop system.

This ultimately results in 1 ref pv

x V = Based on the MPP lines and the resulted MPP trail marked in Fig. 6, the fuzzy system parameters are set; namely the number of inference rules n=7, the membership functions for the pv i variable portrayed in Fig. 7.

III. 1. Simulation validation

In order to confirm the effectiveness of the proposed MPPT controller, simulation tests have been performed in Matlab/Simulink on the solar charging battery system depicted in Fig. 1.

Different dynamic variations of irradiance were examined, the MPPT controller performance was evaluated through the EN50530 dynamic test standard and a comparison to other existing MPPT controllers was provided.

III. 1.1.Simulation results under solar irradiance fluctuations

The proposed MPPT controller performances were firstly verified through an irradiance profile comprising different changes as depicted in Fig. 9.a. The simulation results are plotted in Fig. 9. In the beginning, the PV module received a constant irradiance of 100W/m 2 for 126ms. A fast start-up transient of only 0.4ms without overshoots is achieved V curve quite perfectly. Thus, the operating point is restricted from being diverted. This is achieved thanks to the proposed MPPT mechanism described earlier. The TS fuzzy approximator continuously located the exact peak power voltage ( ref pv

V ) according to the irradiance intensity, which is efficiently tracked using the integral backstepping controller.

In general, the PV system continuously experiences changes in irradiance. Hence, when the PV system is installed under real outdoor conditions, the long-term production investment benefits would be affected by the dynamic MPPT performance. In this regard, the EN50530 dynamic test standard defines a procedure to investigate and quantify the proposed MPP tracker dynamic performance [START_REF] Alonso | Testing microinverters according to EN50530. 29th EU PVSEC[END_REF]. The procedure is based on testing the controller under several irradiation ramp sequences with different irradiance levels and slopes ( 2

G W t m s   ∆   ∆  
). Specifically, irradiation changing ramps from 10% to 50%, 30% to 100%, and 1% to 10%

of STC irradiation level have to be applied with slopes ranging from 0.5 W/m²/s to 50W/m²/s, 10W/m²/s to 100W/m²/s and 0.1W/m²/s respectively. As part of the test sequence results,

III. 1.2.Comparison of the proposed and existing MPPT techniques

The performance of the proposed MPPT technique is evaluated with respect to different existing techniques, namely P&O [START_REF] Loukriza | Simulation and experimental design of a new advanced variable step size Incremental Conductance MPPT algorithm for PV systems[END_REF], modified incremental conductance (MIC) [START_REF] Tey | Modified incremental conductance MPPT algorithm to mitigate inaccurate responses under fast-changing solar irradiation level[END_REF], particle swarm optimization (PSO) [START_REF] Sundareswaran | Application of random search method for maximum power point tracking in partially shaded photovoltaic systems[END_REF], and a hybrid scheme combines P&O with fractionalorder proportional-integral (P&O-FOPI) [START_REF] Yang | Energy reshaping based passive fractional-order PID control design and implementation of a grid-connected PV inverter for MPPT using grouped grey wolf optimizer[END_REF]. These techniques are selected on purpose to compare the effectiveness of the proposed one: P&O represents the conventional type; MIC is the conventional type with an adaptive feature; PSO represents the metaheuristic algorithm;

while P&O-FOPI is the hybrid MPPT control types. The simulation parameters including sampling time and switching frequency are selected the same for all techniques in order to have a fair comparison. The proposed MPPT method is first compared to the PSO in simulation under constant conditions (1000W/m² and 25°C) as shown in Fig. 11 (a). The results reveal that the PSO method provides proper steady-state operation with negligible PV power disturbance. However, compared to the proposed method, the PSO algorithm faces considerable overshoots and has a very slow convergence speed (2.8s) to be used under rapid varying sun irradiance. The other MPPT techniques have been tested in simulation under varying solar irradiance and ambient temperature (25°C). The solar irradiance profile applied to the PV system is presented in Fig. 11 The maximum power is successfully transmitted to the load throughout the boost converter.

Figure 15 shows the measured waveform of the converter output terminals and reveals that the batteries kept charged as the maximum rated voltage constantly maintained. which reveals the optimal working of the PV system control. It can be also observed from the PV power profile that despite the large abrupt perturbation of irradiance, the proposed MPPT controller has ensured fast convergence, high sensitivity to irradiance change, and negligible oscillations, which alleviate energy losses and guarantee higher dynamic tracking efficiency.

The behavior of the proposed MPPT controller has been also tested under the low sun irradiation profile presented in Fig. 17 (a). Repeated step-up and step-down of irradiance level from 180W/m² to 500W/m² and vice-versa were applied during a period of 20s. Fig. 17 (b) represents the excellent power tracking ability of the photovoltaic system using the proposed MPPT algorithm under dynamic changes of low irradiation levels. Stable operation with almost negligible power ripples at steady-state can be also observed. The results of this test demonstrated the precision in locating the right MPP position even for low irradiation levels, which is achieved owing to the TS fuzzy approach used in the proposed MPPT controller.

A comparative analysis is conducted to prove how MPPT control performances can be improved when using the integral backstepping method instead of the classical backstepping method [START_REF] Ch | Control of an Off-Grid PV System based on the Backstepping MPPT Controller[END_REF]- [START_REF] Cano | Centralized MPPT Controller System of PV Modules by a Wireless Sensor Network[END_REF]. The experimental test starts by adopting the classical backstepping in the MPPT algorithm, then, it is replaced by integral backstepping at the instant 28.95s. Figure 18 depicts the resulted PV voltage and PV power waveforms. PV voltage and reference voltage are plotted together as presented in Fig. 18

Figure 1

 1 Figure 1 illustrates the structure of the proposed MPPT-based solar battery charging system. It comprises mainly a PV array and a battery load that are interconnected via a boost type DC-DC converter controlled by the proposed MPPT algorithm.

Fig. 1 .

 1 Fig.1. Block diagram of the PV battery charging system with the proposed MPPT control loop

Fig. 2 .

 2 Fig. 2. PV cell equivalent model

Fig. 3 .r

 3 Fig. 3. Boost type DC-DC converter structure

Fig. 4 .

 4 Fig. 4. The MPP trail under different irradiance levels based on I-V characteristic of the PV array

pvV

  ) reach the maximum voltage ( ref pv V ) by adjusting the boost converter duty cycle. ref pv V is considered as a reference voltage and expressed by . (5) and (6), the pv V voltage and the inductor current L I are defined as state variables of the system x1 and x2respectively, the corresponding 2-D differential equation is set as shown in (10).

Fig. 5 .

 5 Fig. 5. Flowchart structure of the proposed MPPT control

  asymptotical stability of the system. Specifically, by using the control signal deduced in[START_REF] Tey | Modified incremental conductance MPPT algorithm to mitigate inaccurate responses under fast-changing solar irradiation level[END_REF], the proposed backstepping controller stabilizes the PV panel voltage pv V to the desired reference voltageref pv V as t → ∞ .III. Results and discussionsAn experimental test has been firstly carried out to plot the I-V characteristic of the PV panel under different sun irradiance. The measurements were carried out in clear weather) on November 10, 2019, in Marrakesh city, Morocco. The irradiance was recorded using a pyranometer oriented and tilted at the same angle as the PV module. The equipment typically used in such experiment is current and voltage sensors as well as an adjustable resistor with high value to meet the open-circuit condition. The current and voltage provided by the PV panel change by varying the resistor, which shifts the operating point on the PV panel characteristics. Figure6illustrates the resulted experimental data. The measurement uncertainties generally come from instrumentation and calibration. In this test, the uncertainty of the employed voltage and current sensors is estimated to be ±0.1%.

Fig. 6 .

 6 Fig.6. Experimental I-V characteristic of the PV panel for different irradiance levels

Fig. 8 .Fig. 7 .

 87 Fig. 8. Simulink block diagram of the proposed MPPT controller

Fig. 9 .

 9 Fig. 9. Performance of the proposed MPPT controller under changing irradiance (a) Solar irradiance profile (b)PV array voltage compared to the setpoint ref pv V (c) PV array current (d) generated power by the PV array

Fig. 10 .

 10 Fig. 10. Dynamic test sequences results according to EN50530 standard

  Fig.11 (c).To have better clarification about the algorithm's behavior at the steady-state and the transients, some parts of the curves are zoomed in Images 1, 2, 3 and 4 of Fig.11. From the comparison plot, it can be observed that the developed MPPT control strategy demonstrated performance superiority. It has the shortest MPP tracking period, the least transient fluctuations, zero oscillation around MPP and high tracking accuracy so low power losses. While the conventional P&O method suffers from steady-state power oscillation and the reached average value of power is less than the true MPP. The MIC shows better tracking performances and lower oscillation in steady-state than P&O. The hybrid technique P&O-FOPI provides faster convergence and better accuracy in locating the MPP compared to P&O and MIC and can mitigate the P&O steady-state oscillations. Nevertheless, it appears from this comparison that the developed MPPT techniques exhibit the most attractive features to be used under rapid varying irradiance compared to other methods.

Fig. 11 .Figure 12

 1112 Figure 12 depicts the experimental setup of the proposed MPPT technique. The experimental tests were conducted using the PV array already introduced and whose experimental I-V characteristic is presented above. The PV array was connected to the DC load (12V-120Ah batteries wired in series) via the boost converter with the parameters given in Table II. A dSPACE DS1104 platform is used to implement the proposed MPPT controller, which facilitates the real-time testing. The DS1104SL-DSP-PWM block is utilized to generate the desired PWM signal for the converter that is fed through the gate driver (IR2110) circuit. Voltages and currents are measured by employing resistor dividers and LA 25-NP sensors and then converted to digital signals using ADC interfaces of DSP that vary under a voltage range between -10V and +10V. PWM generation and instantaneous power schemes for the proposed MPPT controller in the dSPACE are illustrated in Fig.13. To get rid of high-frequency noise signals, the A/D channel output is passed through an analog filter. Before this block, a gain scale of 10 is added for dSPACE adaptation. The instantaneous power was calculated by multiplying the instant array current and voltage. The instantaneous array voltage and current, inductor current, and output voltage are provided to the input of the implemented MPPT algorithm to produce a duty cycle for the boost converter. It must be noted that the switching frequency chosen in this study was set depending on the interface DSP board limitation. It is generally recommended that the time-step used by the board (1µs in our case) be approximately 40 times smaller than the switching period of the converter, to ensure good precision and keep the results accurate [28].

Fig. 12 . 2 . 2 .

 1222 Fig.12. Laboratory experimental setup to implement the proposed MPPT technique

Fig. 13 .

 13 Fig. 13. dSPACE implementation scheme of MPPT algorithm (a) parameters measurement (b) PWM generation

Fig. 15 .Fig. 14 .

 1514 Fig. 15. Measured converter output voltage waveform

Fig. 17 .Fig. 16 .

 1716 Fig. 17. Power tracking ability in low sun irradiance profile (a) Sun irradiance profile (b) generated power by the PV array

Fig. 18 .

 18 Fig. 18. Comparison of behavior of backstepping control and integral backstepping control (a) PV array voltage compared to reference voltage ref pv V (b) generated power by the PV module

Fig. 19 .

 19 Fig. 19. P&O algorithm (a) under steady-state conditions (at 11:45am on March 08, 2020 in Marrakech city) (b) dynamic behavior under sudden variations of solar irradiance

Table I :

 I Electrical characteristics of the used PV module

	Parameters	Value
	Maximum power Pmpp	62W
	Output power tolerance	±5%
	Voltage at maximum power point Vmpp	13.23 V
	Open circuit voltage Voc	19.0 V
	Short circuit current Isc	5.8 A
	Current at maximum power point Impp	4.68 A
	No. of cells and connections	36 (4x9)

Table II :

 II Boost converter specifications

Table III :

 III Average dynamic MPPT tracking efficiency

	Irradiance variation	η	, dyn MPPT	(%)
	10% to 50%		99.42
	30% to 100%		99.57
	1% to 10%		98.96

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Acknowledgments

This research work was financially supported by the PHC Toubkal project (20/103-N°43692PB) and the CNRST Morocco.