Microsoft Word - ETASR_V11_N2_pp7060-7067 Engineering, Technology & Applied Science Research Vol. 11, No. 2, 2021, 7060-7067 7060 www.etasr.com Behih & Attoui: Backstepping Terminal Sliding Mode MPPT Controller for Photovoltaic Systems Backstepping Terminal Sliding Mode MPPT Controller for Photovoltaic Systems Khalissa Behih Department of Electrical Engineering LSI Laboratory Ferhat Abbas Sétif 1 University Sétif, Algeria khalissabehih@univ-setif.dz Hadjira Attoui Department of Electrical Engineering QUERE Laboratory Ferhat Abbas Sétif 1 University Sétif, Algeria attoui_hadjira@univ-setif.dz Abstract-In this paper, a new Maximum Power Point Tracking (MPPT) control for a Photovoltaic (PV) system is developed based on both backstepping and terminal sliding mode approaches. This system is composed of a solar array, a DC/DC boost converter, an MPPT controller, and an output load. The Backstepping Terminal Sliding Mode Controller (BTSMC) is used via a DC-DC boost converter to achieve maximum power output. The stability of the closed-loop system is guaranteed using the Lyapunov method. This novel approach provides good transient response, low tracking error, and very fast reaction against solar radiation and PV cell temperature variations. Furthermore, chattering, which constitutes the main disadvantage of the classic sliding mode technique is eliminated. To show the effectiveness and robustness of the proposed control, different simulations under different atmospheric conditions are conducted in Matlab/Simulink. Keywords-backstepping; terminal sliding mode control; Lyapunov stability; maximum power point tracking; photovoltaic system I. INTRODUCTION Renewable energy sources are nowadays an important part of power generation. Photovoltaic (PV) generation is one of the most promising renewable sources since it exhibits many merits such as availability, cleanness, little maintenance, and no noise pollution. However, all PV systems have two problems: very low electric-power generation efficiency, especially under low-irradiation states and the interdependence of the amount of the electric power generated by solar arrays and the weather conditions. Load mismatch can occur under these weather varying conditions and maximum power may not be extracted and delivered to the load. This issue constitutes the so-called Maximum Power Point Tracking (MPPT) problem [1-4]. Many methods have been developed to determine the Maximum Power Point (MPP) under varying conditions [5-7]. Some of them are based on the well-known principle of perturb and observe (P&O) [8], others are based on sliding mode control [9-12], on artificial neural networks, or on fuzzy logic algorithms [1, 2, 7]. In [12-14], Maximum Power Voltage (MPV) based approaches are developed using a two-loop MPPT control scheme. The first loop is to determine the MPV reference of the PV array and the second loop is to regulate the PV array voltage to the reference voltage. The procedure repeats the MPV reference searching and the PV voltage tracking until maximum power is reached. To track MPP more efficiently a hybrid method consisting of two loops is proposed in [15]. In the first loop, the MPP is estimated using an incremental conductance method, and in the second loop a terminal sliding mode controller is developed to drive the system to the searched reference MPP. Authors in [16] proposed the use of backstepping sliding mode control for the second loop. The backstepping sliding mode control law is based on the asymptotic stability analysis whilst the system trajectories evolve to a specified attractor reaching the equilibrium in an infinite time. Many authors have proposed an alternative way to get a finite time convergence based on terminal attractor techniques [15-18], providing high-precision performance besides disturbance attenuation. Moreover, chattering in BSMC remains the problem that has to be overcome. In order to avoid chattering, the major disadvantage in the sliding mode methodology, various methods have been proposed. One of them consists in replacing the sign function by a continuous approximation in the vicinity of the sliding surface. Saturation function or sigmoid function was used in fuzzy logic to build the transition band [9, 21, 22]. The authors of [22] proposed to vary the sliding gain using a fuzzy system which adjusts the distance between the system and the sliding surface. Thus, its value decreases as the system state approaches the sliding surface. However, the ultimate accuracy and robustness of the sliding mode are partially lost. In this paper, a Backstepping Terminal Sliding Mode Controller (BTSMC) is developed for MPPT. By using a DC/DC boost converter in the power control circuit, the BTSMC is proposed to drive the system to the MPV reference in the second loop. Using this approach, finite time convergence of the error is guaranteed and the chattering effect is eliminated without losing robustness. II. PV SYSTEM MODELING A DC-DC boost converter constituting the heart of the MPPT is inserted between the PV module and its load to achieve optimum power transfer, as can be seen in Figure1. Corresponding author: Khalissa Behih Engineering, Technology & Applied Science Research Vol. 11, No. 2, 2021, 7060-7067 7061 www.etasr.com Behih & Attoui: Backstepping Terminal Sliding Mode MPPT Controller for Photovoltaic Systems Fig. 1. Structure of the PV system. The converter is used to regulate the PV module output voltage Vpv in order to extract as much power as possible from the PV module. Referring to [15], the dynamics of the boost converter are given by: ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1 2 2 1 11 1 1 1 1 1 1 1 pv pv L CL pv L c Dc C c C L C c c dV I I dt C R ddI V I Rdt L L R d V dR V L R R L dV d I V Rdt C R R C R    = −   − = −   +      − −   + − −   +   − = − +   +     (1) where the three states variables pvV , LI and 2CV are respectively the output voltage of the PV module, the inductor current and the voltage of the capacitor 2C (i.e. the voltage across the load). DV is the forward voltage of the power diode, d is the duty ratio of the PWM control input signal, and R is the resistive load. By taking ( ) ( ) ( ) ( ) 2 T pv L Cx t V t I t V t =   , the set of equations in (1) can be written in the following form [15]: ( ) ( ) ( ) ( ) ( )2 1 1 1 2 2 1pv pv L L C dV I I dt C dI f x g x d dt dV f x g x d dt  = −   = +   = +  (2) where: ( ) 21 1 1 1 1 C c D pv L C c c R R V f x V I V RL L R R L L R   = − + − −  +   +    ( ) ( ) 22 2 2 1 1 1 L C c c f x I V R C R R C R = − +  +    ( ) 21 1 1 1 c c D L C c c R R V g x I V R L R R L L R   = − − +  +   +    ( )2 2 1 1 1 L c g x I RL C R = −   +    III. DESIGN OF THE BACKSTEPPING TERMINAL SLIDING MODE MPPT CONTROLLER The overall control structure is illustrated in Figure 2. Here, ipv and Vpv are measured from the PV array and transmitted to the MPP searching algorithm, which generates the reference maximum power voltage Vref. Then, the reference voltage is given to the MPV based BTSM controller for maximum power tracking. A. MPP Searching Algorithm To seek the MPP voltage Vref, we use an incremental conductance method [1, 15]. The power slope pv pvdP dV can be expressed as: pv pv pv pv pv pv dP dI I V dV dV = + (3) When the power slope 0, pv pv dP dV = i.e pv pv pv pv dI I dV V = − , the PV system operates at maximum power generation. Therefore, the update law for Vref is given by the following rules [1, 15]: ( ) ( ) 1 , 1 ,  = − + ∆ > −    = − − ∆ < −  pv pv ref ref pv pv pv pv ref ref pv pv dI I V V k V for dV V dI I V V k V for dV V (4) B. Backstepping Terminal Sliding Model Controller The backstepping terminal sliding mode controller is designed to extract maximum power from a PV panel. The objective of the controller is to let the panel PV voltage Vpv track the reference maximum power voltage Vref by acting on the duty cycle d(t) of the boost converter switch. The recursive nature of the proposed control design is similar to the standard backstepping methodology. However, the proposed control design uses backstepping to design controllers with a terminal sliding surface at the last step [22-23]. The design proceeds as follows: For the first step we consider a zero-order sliding surface: 1 1 refe x V= − (5) Considering an auxiliary tracking error variable: Engineering, Technology & Applied Science Research Vol. 11, No. 2, 2021, 7060-7067 7062 www.etasr.com Behih & Attoui: Backstepping Terminal Sliding Mode MPPT Controller for Photovoltaic Systems 2 1 1e e α= +& (6) Let the first Lyapunov function candidate is: 2 1 1 1 2 V e= (7) The time derivation of (7) is given by: ( ) 1 1 1 1 2 1 2 1 1 1 2 V e e e e e e e α λ = = − = − + & & (8) The stabilization of 1e can be obtained by introducing a new virtual control 1α , such that: 1 1 1 1, 0eα λ λ= > (9) where � � is a positive feedback gain, such that 1α can be chosen in order to eliminate the nonlinearity and getting ( )1 0<&V x . Equation (8) shows that, if the designed control law makes 2e converge, then ( )1 0V x <& which guarantees global stability. In order to make 2e converge in finite time and improve the convergence rate and the steady-state tracking accuracy of the system, the higher-order non-singular terminal sliding mode surface is designed for 2e as follows: 2 2 , 1 2, 0 p q s e e p qγ γ= + < < >& (10) where γ>0 is a positive constant that contributes to force the error 2e to converge to zero while p and q are positive impair constants such that 1 2<