energies Article Chattering Free Adaptive Sliding Mode Controller for Photovoltaic Panels with Maximum Power Point Tracking † Hina Gohar Ali 1,2, * and Ramon Vilanova Arbos 1 1 Department Telecommunications and Systems Engineering, School of Engineering, Universitat Autonoma de Barcelona, Bellaterra, 08193 Cerdanyola del Vallés, Barcelona, Spain; ramon.vilanova@uab.cat 2 School of Electrical Engineering and Computer Science, National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan * Correspondence: hina.goharali@e-campus.uab.cat † This paper is an extended version of our paper published in 2020 IEEE 20th International Conference on Environmental and Electrical Engineering (EEEIC), Madrid, Spain, June 2020.  Received: 26 September 2020; Accepted: 28 October 2020; Published: 30 October 2020  Abstract: Photovoltaic system is utilized to generate energy that relies upon the ecological conditions, for example, temperature, irradiance, and the load associated with it. Considering the non-linear component of photovoltaic (PV) array and the issue of low effectiveness because of the variable natural conditions, the Maximum Power Point Tracking (MPPT) method is required to extract the maximum power from the PV system. The adopted control is executed utilizing an Adaptive Sliding Mode Controller (ASMC) and the enhancement is actualized utilizing an Improved Pattern Search Method (IPSM). This work employs IPSM based optimization approach in order to command the underlying ASMC controller. The upper level decision determines the sliding surface for the adaptive controller. As a non-linear strategy, the stability of the adaptive controller is guaranteed by conducting a Liapunov analysis. On the practical side, MATLAB/Simulink is used as simulator for the controller implementation and coupling with PSIM in order to connect it with the PV system object of control. The simulation results validate that the proposed controller effectively improves the voltage tracking, system power with reduced chattering effect and steady-state error. The performance of the proposed control architectures is validated by comparing the proposals with that of the well-known and widely used Proportional Integral Derivative (PID) controller. That operated as a lower level controller for a Perturb & Observe (P&O) and Particle Swarm Optimization (PSO). Keywords: photovoltaic (PV); maximum power point tracking (MPPT); adaptive sliding mode controller (ASMC); improved pattern search method (IPSM); particle swarm optimization (PSO) 1. Introduction Energy is currently recognized as the most demanded resource in our daily lives, being the essential part that determines the development of economy as well social growth. At the global level, energy crises are highly present, and can be reduced by the optimum utilization of sustainable energy. Solar energy is the most commonly available free energy renewable resource across the world, which is clean, sustainable, and environmentally friendly [1]. Photovoltaic technology is used to obtain electrical energy from solar energy by using PV panel. PV panel is made up of several PV solar cells in series and parallel combinations. The behavior of the desired PV output is of non-linear type. This is what makes its operation difficult. The main figure of interest is the Maximum Power Point (MPP) which can be altered because of variable environmental conditions (i.e., solar irradiance and temperature) at different operating points. The current-voltage (I-V) and power-voltage (P-V) characteristics will Energies 2020, 13, 5678; doi:10.3390/en13215678 www.mdpi.com/journal/energies Energies 2020, 13, 5678 2 of 18 also be altered because of such changing operating conditions. Therefore, to operate the PV system at particular MPP under the given meteorological conditions control strategies are needed to formulate in order to extract and deliver the maximum possible power from the PV which improves the overall efficiency of the PV system and minimize power losses. The operation of the PV output characteristics in order to extract the MPP and maximize the PV operation benefits, a number of operation and control algorithms have been proposed in the literature. Such algorithms can be distinguished among them on the basis of features such as complexity, implementation, and speed of convergence, among others [2]. Generally, these algorithm techniques are divided into Conventional Techniques (CTs), Soft Computing Technique (SCTs), and linear and nonlinear control techniques [3]. In conventional algorithms, Perturb and Observe (P&O) [4] and Incremental Conductance (INC) [5] are the main basic algorithms. These proposed CTs are simple, easy in implementation and have the capacity of tracking the MPP efficiently at present ecological conditions, but the drawback of these CTs is the fluctuations around MPP, which influence the accuracy rapidity of the system, resulting in a loss of useful power [6]. Soft-computing based techniques have proven to be powerful to deal with the MPPT optimization problem as per comparison with the classical ones [7]. SCTs techniques consist of Artificial Intelligence Techniques (AITs) [8] and Bio-Inspired Techniques (BITs) [9]. Fuzzy logic controller [10], artificial neural network [11], and genetic algorithms [12] comes in the category of AITs. These methods require extensive high computation when dealing with the nonlinear characteristics of the I-V curves, although AITs methods are generally effective. Along with this, the PV system operating conditions change continuously with time; therefore, MPPT has to respond in real time to the environmental condition variations (insolation and temperature). Hence, a large memory size and computing requirements are usually required. One of the features that characterize some of the BITs proposals that can be found in the literature is its ability for optimal searching in the search space but with moderate computational effort. These methods have the tendency to converge quickly to a global maximum; thus, they can save power loss even in a partially shaded environment. Cuckoo search algorithm [13], ant colony optimization [14], particle swarm optimization [15], and evolutionary algorithm [16] are the proposed latest techniques developed in the class of BITs. Despite their usefulness in various environmental conditions, these techniques are inefficient because their slow convergence obstructs their practical usage as on-line solutions. Recently, a MPPT improvement approach dependent on Pattern Search was proposed in [17]. The strategy introduced depends on Generalized Pattern Search Method (GPSM). The GPSM was proposed in [18] for subsidiary free unconstrained enhancement of constantly differentiable convex function and has been utilized from that point forward in various control approaches. Hence, in this paper, the Improved Pattern Search Method (IPSM) optimization algorithm is used, which was introduced in [19]. The operational configuration can also be built up based upon linear controllers that will operate as voltage controllers, obeying the reference voltage generated by a suitable MPPT algorithm as well as trying to minimize the effect of environmental perturbations [20–22]. The linear controller option, however, needs a linear model to be designed. That linear model is usually a linearization of the non-linear PV model. As is well known, this representation may work well on the required operating point but loses representative power in other PV working range. As an alternative to the need of a linearized model, other controllers have been proposed. Most of those controllers, in order to guarantee good performance in all operating ranges, do include adaptive laws [23] and energy balance [24]. In the MPPT literature, different non-linear operation configurations can be found as good alternatives to deal with the non-linear dynamics of the PV as well as power converters [25]. The presented scenario has motivated the introduction of a Sliding-Mode Control MPPT (SMC-MPPT as a robust controller because of the inherent robustness as well as the stability Energies 2020, 13, 5678 3 of 18 characteristics of SMC controllers. In SMC-MPPT, the tracking error is considered as a sliding surface [26]. In SMC, the control scheme is intended to drive and, afterward, hold the system states within the limits of the switching function. It can be found in the literature that the SMC has been widely used as a good option for controlling non-linear processes. Among them, DC–DC converters that operate in PV systems [27]. Two-loop MPPT control approaches were tended to in [28,29], which require either a current reference or voltage reference. This control approach based on terminal sliding mode control. The chattering was addressed in [30,31], which is the main drawback of the traditional sliding mode control. This strategy is robust in terms of load variations and system uncertainties. The chattering effect being the main drawback that classical sliding model control exhibits, the main proposal in this work is to reduce it and, as a consequence, reduce high frequency oscillations. In this paper, an Adaptive Sliding Mode Controller (ASMC) [32] is applied with a two-loop control approach with the purpose of extracting the maximum power from a PV panel under non ideal/constant conditions. The study uses an IPSM-based MPPT algorithm to generate the commanded reference voltages for the voltage control loop. This will be done by suitable definition of the sliding surface. The layout of the system to be controlled is built up by the interconnection of the PV panel and a DC load that receives power extracted from the panel by using a boost converter. The ASMC controller is derived based on the idea proposed in [33]. System stability is ensured by applying Lyapunov candidate function. Simulation platforms used in this work are MATLAB/Simulink and PSIM. Whereas the boost converter, the PV panel, and the MPPT algorithm are implemented in PSIM, the voltage, lower level, and controller are deployed by using MATLAB/Simulink. In order to evaluate the performance of the proposed PV operation configurations, we need to evaluate the capabilities for voltage following as well as extracted power. Results are to be compared with the ones obtained by a PID controller. The performance comparison is based on usual figures of merit such as steady state error, oscillations, etc. As the operational architecture is composed of two levels of operation (being the PID at the lower level), the comparison also includes two other options for the upper level. These two options are P&O and PSO as widely used MPPT algorithms. This work follows previous studies proposed by the author in [34], where an integer order SMC controller was modelled for extraction of maximum power from PV. Classical SMC generally suffer from the problem of ‘chattering’, which is a very high frequency oscillation of the sliding variable around the sliding manifold. In this study, the authors have introduced an adaptive version of SMC that reduces the chattering phenomenon and limits high frequency oscillations that were present in [34]. Along with this, the authors have implemented two more MPPT algorithms (PSO, IPSM) with the proposed controller that was conducted in the previous studies [33,34] with only conventional P&O MPPT. It has been observed that the IPSM optimization method is computationally efficient and offers the best solution than the other optimization algorithms PSO and P&O. This study is developed to reduce the chattering effect and high frequency oscillations that were present in [34] behavior. The conducted methodology presented initially in [33] is used to nullify the chattering effect and improve tracking response and power losses to enhance overall efficiency of the stand-alone PV system, which is shown by estimating numerical analysis in form of overshoot, settling time, and losses. The overall paper is organized as follows: in Section 2, interrelated work is deliberated. Section 3 presents the system model for this work and the derivation of proposed control scheme is shown. Simulation results are described in Section 4. Lastly, Section 5 sums up the conclusion and the possible future work. 2. Problem Formulation Figure 1 shows the topology of the implemented work in this study. Stand-alone PV system is used which consists of a PV panel, DC-DC boost converter, a load and a control loop that produces PWM signal to the step-up converter for MPPT process. This work is established on the concepts published in [33], which apply the adaptive sliding mode technique to adjust the PV voltage and to Energies 2019, 12, x FOR PEER REVIEW 4 of 18 alleviate the chattering effect. The description of the work is explained in work published in [33] that Energies 2020, 13, 5678 4 of 18 guarantees the maximum power is produced successfully by the proposed control methodology. Energies 2019, 12, x FOR PEER REVIEW 4 of 18 alleviate the alleviate the chattering chattering effect. effect. The The description description of of the the work work is is explained explained in in work work published published in in [33] [33] that that guarantees the maximum power is produced successfully by the proposed control guarantees the maximum power is produced successfully by the proposed control methodology. methodology. Figure 1. Block diagram of the system scheme based on adaptive sliding mode control. 3. System Model Figure The 1. Block schematic Figure diagram circuit 1. Block of of diagram thethe diagram system of the scheme system PV system scheme based used based onin on adaptive this study adaptive sliding mode is appeared sliding mode control. in Figure 2, which control. is made out of a PV module and a power electronic converter. A two‐diode model representation of 3. System 3. SystemModelModel PV cell is chosen that involves identification of more system parameters and better proficiency. This The schematic schematic provides representation The circuit diagram circuit of of the the PV more accurate diagram system PVoutput systemPV used in inthis thisstudy characteristic used study isisappeared curves, ininFigure i.e., I‐V appeared and 2,2, P‐V Figure which whichis [35]. made out of a PV module and a power electronic converter. A two-diode is made out of a PV module and a power electronic converter. A two‐diode model representation of As In order to appropriately operate the PV panel power extraction, amodel converterrepresentation is needed. of PV PV cellcell shown is in chosen is chosenFigure that that2, involves here involves willidentification weidentification use a DC–DC of more converter of more systemsystem that parameters operates parameters and the between and better better proficiency. panel andThis proficiency. the load This representation [36]. In this work,provides the more boost accurate converter output will be PV characteristic utilized [34]. curves, representation provides more accurate output PV characteristic curves, i.e., I‐V and P‐V [35]. i.e., I-V and P-V [35]. In order to appropriately operate the PV panel power extraction, a converter is needed. As shown in Figure 2, here we will use a DC–DC converter that operates between the panel and the load [36]. In this work, the boost converter will be utilized [34]. Figure 2. Circuit diagram the proposed PV system. In order to appropriately operate the Figure 2. PV panel Circuit power diagram the extraction, proposed PV a system. converter is needed. As shown in Figure 2, here we will use a DC–DC converter that operates between the panel and the load [36]. 3.1.work, In this MPPTtheAlgorithms boost converter will be utilized [34]. Figure 2. Circuit diagram the proposed PV system. 3.1. 3.1.1. MPPTMPPT Algorithms Algorithm Based on P&O 3.1. MPPT 3.1.1. MPPTAlgorithms The P&O MPPT Algorithm algorithm Based on P&Ois based on managing either the voltage command or the boost converter input current. Subsequently, the measure of power converted from the panel is estimated. The 3.1.1.The MPPTP&O MPPT algorithm is based on managing either the voltage command or the boost P&OAlgorithm algorithmBased on P&O adopted methodology description is explained in [36], in which an integer order converter input current. Subsequently, the measure of power converted from the panel is estimated. sliding The P&O mode MPPTcontroller had is algorithm been proposed based for the either on managing two‐diode model‐based the voltage PV system. command The P&O or the boost The P&O algorithm adopted methodology description is explained in [36], in which an integer order MPPT algorithm had been used in [34] in order to be able to extract the maximum power converter input current. Subsequently, the measure of power converted from the panel is estimated. from the sliding mode controller had been proposed for the two-diode model-based PV system. The P&O MPPT The P&O algorithm adopted methodology description is explained in [36], in which an integer order algorithm had been used in [34] in order to be able to extract the maximum power from the panel sliding mode controller had been proposed for the two‐diode model‐based PV system. The P&O MPPT algorithm had been used in [34] in order to be able to extract the maximum power from the Energies 2020, 13, 5678 5 of 18 Energies 2019, 12, x FOR PEER REVIEW 5 of 18 panel and providing and providing the reference the reference voltagevoltage to the mode to the sliding slidingcontroller mode controller acting asacting as aloop a voltage voltage loop controller. controller. Here, the controller Here, the controller is by is modified modified by Adaptive Adaptive SMC tothe SMC to address address the chattering chattering phenomenon phenomenon that was that wasin present present in [34]. [34]. The P&O The P&O algorithm algorithm flow diagram flow diagram is shownis shown in Figure in Figure 3, which 3, which is executed is executed in in PSIM PSIM simulation simulation tools. tools. Figure Figure 3. 3. Perturband Perturb andobserve observe (P&O) (P&O)algorithm. algorithm. 3.1.2. MPPT Algorithm Based on PSO 3.1.2. MPPT Algorithm Based on PSO Particles Swarm Optimization (PSO) [34,37] algorithms are strategies based on a heuristic search Particles Swarm Optimization (PSO) [34,37] algorithms are strategies based on a heuristic search that use a population, characterized with stochastic features, which are motivated by swarms. Each one that use a population, characterized with stochastic features, which are motivated by swarms. Each of such particles constitutes a candidate solution. PSO calculations produce new particles positions one of such particles constitutes a candidate solution. PSO calculations produce new particles and features on the basis of its interaction with the rest. For example, for what matters to the particle positions and features on the basis of its interaction with the rest. For example, for what matters to position, it is determined on the basis of particles in a superior situation. This superior situation, in our the particle position, it is determined on the basis of particles in a superior situation. This superior case study, corresponds to a reference voltage that generates a more efficient power conversion. As an situation, in our case study, corresponds to a reference voltage that generates a more efficient power iteration-based approach, once a particle with superior characteristics is found, the rest of the particles conversion. As an iteration‐based approach, once a particle with superior characteristics is found, the will be affected by this. This wining particle will constitute the output of the algorithm. The flow rest of the particles will be affected by this. This wining particle will constitute the output of the diagram of the PSO algorithm is depicted in Figure 4. algorithm. The flow diagram of the PSO algorithm is depicted in Figure 4. Energies 2020, 13, 5678 6 of 18 Energies 2019, 12, x FOR PEER REVIEW 6 of 18 Figure 4. Particle Swarm Optimization (PSO) algorithm. Figure 4. Particle Swarm Optimization (PSO) algorithm. 3.1.3. MPPT Algorithm Based on IPSM 3.1.3. MPPT Algorithm Based on IPSM In this case, IPSM is an improvement with respect to the Pattern Search Method (PSM) from [38]. PatternIn Search this case, IPSM is anare algorithms improvement defined along with respect two maintoconstitutive the Pattern parts: Searchfirst, Method (PSM) from [38]. an arrangement of Pattern Search algorithms are defined along two main constitutive parts: mesh definitions and, second, a list of polling conditions. Every component of the mesh first, an arrangement is a solution of mesh definitions candidate. Pattern and, second, Searches a list are methods of polling conditions. also iterative Every methods. component Therefore, of the at each mesh is iteration, a solution the meshes move towards the best position, according to a convergence condition. In this case, the search the candidate. Pattern Searches methods are also iterative methods. Therefore, at each iteration, is meshes move actualized withtowards respectthe bestone to the position, in [17]according to a convergence by also introducing a searchcondition. In this case, at the adjoining the search members to is actualized the one that iswith respect defined to thethe as with onebest in [17] by alsoThis position. introducing a search update, for at the the case adjoining at hand, members introduces theto the one that is defined as with the best position. This update, for the case at hand, possibility to guarantee appropriate convergence even in cases of radiation or partial shading. Figure 5introduces the possibility shows to guarantee the algorithm appropriate as applied convergence here for even in cases power conversion of theofPV radiation panel. or partial shading. Figure 5 shows the algorithm as applied here for power conversion of the PV panel. Energies 2020, 13, 5678 7 of 18 Energies 2019, 12, x FOR PEER REVIEW 7 of 18 Proposed IPSM Figure5.5.Proposed Figure IPSMalgorithm. algorithm. 3.2. Control Scheme 3.2. Control Scheme Control Law 3.2.1. Control Law The work is based on the published work in [33,34]. Figure 6 shows the schematic circuital The work is based on the published work in [33,34]. Figure 6 shows the schematic circuital representation of the proposed adaptive SMC controller PV system. The operation of the work has representation of the proposed adaptive SMC controller PV system. The operation of the work has been described in detail in [34]. Therefore, referring to the published work [33] the dynamics of the been described in detail in [34]. Therefore, referring to the published work [33] the dynamics of the DC–DC boost converter is given by: DC–DC boost converter is given by: dVpv Icin =I (C  (C +∆CCin))dVpv  I=  Ipv − IL (1) dt pv IL in (1) cin in in dt dIdI L VL = V(LL+( L∆L  )L ) L= VPV − V (1 − u) (2) dtdt  VPV  Vb (1 b u ) (2) The above parameters definition can be read in [34]. ∆ is the uncertainty term. The above parameters definition can be read in [34]. Δ is the uncertainty term. Rearranging Rearranging Equations (1) and (2) we have Equations (1) and (2) we have . IL IPV V PV = − + (3) (3) Cin + ∆Cin Cin + ∆Cin . VPV Vb Vb IL = − + u (4) (4) L + ∆L L + ∆L L + ∆L Equations Equations (3) (3) and and (4) (4) can can be be written written in in state state space space form form as:as: #   I PV IPV0     .  −1 1 "   0 "  #      0& 0 0 0  V.PV   VPV    V VPV PV  Cin+ ∆C1in   1 Cin Cin     1&    C1in + ∆C       Vb   =   Cin    + Cin in u +  u     ILL    Vb −Vb 0    0 V b (5) (5) IL   IL   L + ∆L  L  L 0 0  0L  L      L  L 0 L + ∆L L + ∆L  Energies 2020, 13, 5678 8 of 18 Energies 2019, 12, x FOR PEER REVIEW 8 of 18 Figure 6. System circuital scheme based on Adaptive sliding mode control. Figure 6. System circuital scheme based on Adaptive sliding mode control. Equation Equation (5)(5) can can bebe re‐written re-written inin generalized generalized form form as:as: . X& f ( X , t )  J ( X , t )  h( X , t ) u   f ( X , t )  J ( X , t )  h( X , t )u  d ( X , t ) (6) X = f (X, t) + J (X, t) + h(X, t) u + ∆ f (X, t) + ∆J (X, t) + ∆h(X, t)u + d(X, t) (6) All above shown parameters are defined in published work [33]. where, All above shown parameters are defined in published work [33]. where, 0 1  f ( X , t)   1 C in   (7)  0 L −1   0   f (X, t) =  1 Cin  (7)   L I PV 0 0    C  J ( X , t)   in  (8) I  PV V   C b 00    inL  J (X, t) =   (8)  −Vb    0 0  L  h ( X , t )  Vb  (9)    0 L  h(X, t) =  Vb  (9) 0 L 1     f ( X , t)  1   C in   (10)   0  L 0−1   ∆ f (X, t) =  1 ∆Cin  (10)   ∆L I PV 00     C  J ( X , t)  IPV in  (11)   Vb 0   ∆C  0  ∆J (X, t) =   inL  (11)  −Vb  0   0   ∆L  h ( X , t )  Vb  (12)  0     L ∆h(X, t) =  V (12)  b   Equation (6) can also be given the following generic form ∆L Equation (6) can also be given the following generic form (13) . X = f (X, t) + J (X, t) + h(X, t) u + D(X, t) (13) where D( X , t )   f ( X , t )   J ( X , t )   h( X , t )u  d ( X , t ) (14) where The MPPT algorithmD(X,will ∆ f (X, t) a+command t) =generate ∆ J (X, t) +signal ∆ h(X,for t)u the + d(lower X, t) level control loop. (14) Such command is given by: (15) The tracking error can be defined as: Energies 2020, 13, 5678 9 of 18 The MPPT algorithm will generate a command signal for the lower level control loop. Such command is given by: h . iT h . iT Xd = xd xd = VPV−re f V PV−re f (15) The tracking error can be defined as:    e1 = x1 − xd   .  e2 = e1   . (16) e2 = x2 − xd    . . ..    e2 = x2 − x  d The sliding surface can be chosen as: s = k1 e1 + e2 (17) here k1 > 0 is the design parameter. Differentiating Equation (17) on both sides . . s = k1 e2 + e2 (18) By combining (13) and (18) one can obtain . .. s = c1 e2 + f (X, t) + J (X, t) + h(X, t)u + D(X, t) − xd (19) The controller that achieves the desired output is:     u = ua + us ..  ua = h(X, t)−1 [xd − f (X, t) − J (X, t) − c1 e2 − D̂(X, t)]  (20)      us = −h(X, t)−1 ks sgn(s)   The obtained derived parameters definition can be read in [33]. Signum function sgn(.) can be defined as: +1 i f s > 0      sgn(s) =  0 if s = 0 (21)     −1 i f s < 0  The stability of the proposed control scheme has been proved and checked in [33] by the Lyapunov candidate function. It has been analyzed that the close loop system is stable. 4. Simulation Results and Discussion In this section, the results for each one of the three MPPT implemented algorithms are shown. First of all, the description of the irradiance experiment as well as parameters for the PV system as well as MPPT and controller parameters are provided. Next, a separate subsection for each MPPT algorithm provides the corresponding results and evaluation. The section ends with a comparative summary. MATLAB/Simulink is utilized to model and perform simulations of the proposed controllers’ methods. The simulations of PV module and power electronic converter with MPPT controller are performed in PSIM (PowerSim). To perform co-simulations between MATLAB/Simulink and PSIM, Simcoupler is used. The parameters of PV that are utilized in this study can be found in Table 1. In PSIM physical model [39] of a PV board is available that is used in simulations, with parameters comparing to the PV module of type MXS-60 [40]. Energies 2020, 13, 5678 10 of 18 Table 1. Parameters of PV Array [37]. Symbol Parameter Value ISC Short-circuit current 3.8 A VOC Open-circuit voltage 21.1 V Imp Maximum panel current 3.5 A VPV Maximum panel voltage 17.1 V IS1 = IS2 Saturation currents 4.704 × 10−10 IPV Panel current 3.8 A Rsh Shunt resistance 176.4 Ω Rs Series resistance 0.35 Ω. Table 2 provides the parameters of converter and controller that are used in this work. MATLAB optimization tools are used to obtain the design parameters of controllers, which are displayed additionally in this table. The experimental conditions that will be simulated consists of an initial irradiance step of 1000 W/m2 followed by a 50% decrease of irradiance. The working temperature is 25 ◦ C. Table 2. Parameters of controller, converter and MPPT. Parameters Value L 22 µF C 100 µF Vo 24 V f sw0 (controller) 49.2 kHz KP 0.1 KI 50 Kd 0.1 K1 4.3 KA 55.5 Ta 400 µs ∆Vo 1 V (P&O) ∆Vo 0.2 V (40 p.) ∆Vo 0.8 V (10 p.) LPF 20 kHz 4.1. Simulation Results 4.1.1. Response Using P&O In this section we will compare the performance of the ASMC with that one of the PID controller. Both operating under the voltage reference generation by using P&O. PID controller tuning parameters have been obtained by using MATLAB/Simulink optimization tools. To show the performance of the proposed chattering-free ASMC controller, first, the conventional technique PID with P&O MPPT is compared with the proposed ASMC controller with P&O under the same system parameters and environmental parameters. Figure 7a–d shows the comparative behavior of both controllers using P&O MPPT with a P&O perturbation amplitude of 1 V. The output of P&O MPPT is a voltage reference signal that is supposed to be tracked by the PID controller to ensure tracking error as close as possible to zero. Figure 7a is the PV panel voltage, which is tracked by controller with reference voltage. Energies 2020, 13, 5678 11 of 18 Vpv successfully tracks Vref . The PV voltage of PID deviates from Vref while there is no deviation in the proposed controller PV voltage. The tracking error comparative plot of PID and ASMC with P&O is shown in Figure 7b. There are high ripples and oscillations in PID tracking error behavior and fewer oscillations in ASMC. The implemented controller plainly overtakes the conventional controller with slight oscillation. PV panel output power curve is shown in Figure 7c. From power curve it can be seen that MPP is achieved successfully Energies 2019, and 12, x FOR PEER the controllers track the reference voltage in the voltage curve but11displays REVIEW of 18 large ripples in the voltage waveform along with an overshoot in PID. It is clear that MPP is achieved by ASMCTablewith 3. Performance reduced characteristics of the conventional oscillations compared to PID.controller and that The results the proposed ASMCby are obtained controller using ASMC based are free on P&O of high MPPT. oscillations. Figure 7d depicts performance index IAE (Integral Absolute frequency Error) of the PV system. The performance of the proposed Over/Undershoot Settling controller Time has beenLosses Power verified based on this performanceController index. (%) (Second) (Watt) As a resume PIDquantitative comparison, 2.8 Table 3 shows the different considered 5.3 ms 3.2 figures of merit. It can be observed ASMC that the performance 0.6 has been improved 0.15 msby using the ASMC. 0.68 Figure 7. PID & ASMC Figure 7. ASMC basd on P&O MPPT (a) Profile Profile of of the the PV PV panel panel voltage voltage (b) (b) Tracking Tracking response response (c) Profile of the (c) Profile PV PV of the power extraction power (d)(d) extraction IAE. IAE. Table 3. Performance characteristics of the conventional controller and the proposed ASMC controller 4.1.2. Response Using PSO based on P&O MPPT. The combined response using conventional controller and the proposed ASMC controller based on PSO MPPT Controller can be seenOver/Undershoot in Figures 8a–d(%) Settling and 9a–d. As aTime (Second) stochastic PowerPSO algorithm, Losses does(Watt) not always guarantee thePID same exact location2.8for the best positioned5.3 ms particle (optimal solution).3.2 Therefore, two sets of 10 simulations ASMC each has been0.6 conducted. A first simulation 0.15 ms set using 10 particles 0.68 and a second one using 40 particles. 4.1.2. From PSO with 10 particles comparative plot, it can be observed that the controllers track the Response Using PSO reference Vref in the voltage curves in Figure 8a, the panel voltage is tracked by the controller with the The combined reference response voltage Vpv‐ref using conventional . The tracking controller error response and theinproposed that is shown Figure 8bASMC controller with less based oscillations on andPSO MPPT ripples as can be seentoinP&O compared Figures 8a–d and 9a–d. MPPT‐based resultsAs anda stochastic algorithm, MPP is achieved PSO in the does curves power not always in guarantee Figure 8c. the PSOsamewithexact locationshows 10 particles for thethe best positioned average particle response, and(optimal solution). the algorithm Therefore, reached the MPP two sets of 10 before thesimulations each has simulation ended. been conducted. However, A first the behavior simulation using ASMC showsset using 10 particles limited andand oscillations a second less one using ripples in 40 particles. of PID. comparison On the other hand, the response of PSO algorithm with 40 particles in Figure 9a–c never reached the steady state unlike the response based on PSO with 10 particles and always keeps moving around the search‐space. However, with adaptive SMC the oscillations reduced in the performance of PSO with 40 particles, which are significant in PID. As a result, it can be seen that, as a MPPT algorithm, PSO generated reference voltages with large oscillations, therefore energy losses, and, in some situations, difficulties to appropriately reach the steady state. The performance index of PV system Energies 2020, 13, 5678 12 of 18 Energies2019, Energies 2019,12, 12,xxFOR FORPEER PEERREVIEW REVIEW 1212ofof1818 Figure8. Figure Figure 8.8.PID PID&& PID &ASMC ASMCbased ASMC based basedinin in PSO PSO PSO MPPT MPPT MPPT with with 10particles 10 with particles 10 (a)Profile (a) particles Profile (a) ofofthe Profile the PVpanel of PV the panel PV voltage. voltage. panel (b) (b) voltage. Tracking Tracking (b) Tracking response response (c) response Profile (c) (c) Profile of the of the Profile PV power PV PV of the power extraction extraction power (d) IAE. (d) IAE. extraction (d) IAE. Figure9. Figure Figure 9.9.PID PID&& PID &ASMC ASMCbasedbased basedinin in PSO PSO PSO MPPT MPPT MPPT with with 40particles 40 with particles 40 (a)Profile (a) particles Profile (a) ofofthe Profile the PVpanel of PV the panel PV voltage. voltage. panel (b) (b) voltage. Tracking Tracking (b) Tracking response response (c)(c) (c) response Profile Profile ofofthe Profile thethe of PVPV PV power power extraction extraction power (d)IAE. (d) extraction IAE. (d) IAE. From TablePSO Table with 10 particles 4.4.Performance Performance comparative characteristics characteristics ofofthe plot, it can theconventional conventional be observed controller controller andthe and that theASMC theproposed proposed controllers track the ASMCcontroller controller based reference on basedVon ref inPSO PSOthe10 particles. 10voltage particles.curves in Figure 8a, the panel voltage is tracked by the controller with the reference voltage Vpv-ref . The tracking error response that isSettling shown in Figure Power 8b with less oscillations Settling Power and ripples as comparedController Over/Undershoot Over/Undershoot to P&O MPPT-based results and MPP is achieved Controller Time Time Losses in the power curves in Losses (%) (%) Figure 8c. PSO with 10 particles shows the average response, and the algorithm reached the MPP (Second) (Second) (Watt) (Watt) before the simulation ended.PID However, the behavior using ASMC shows limited oscillations and less PID 88 80ms 80 ms 66 ripples in comparison of PID. ASMC 0.85 2.8ms ms 0.95 ASMC 0.85 2.8 0.95 On the other hand, the response of PSO algorithm with 40 particles in Figure 9a–c never reached the steady Tablestate Table unlike the 5.5.Performance Performance response based characteristics characteristics ofofthe on the PSO with controller conventional conventional 10 particles controller and and and always theproposed the proposedkeeps ASMC ASMC moving around controller controller basedon based onPSO PSO40 40particles. particles. Energies 2020, 13, 5678 13 of 18 the search-space. However, with adaptive SMC the oscillations reduced in the performance of PSO with 40 particles, which are significant in PID. As a result, it can be seen that, as a MPPT algorithm, PSO generated reference voltages with large oscillations, therefore energy losses, and, in some situations, difficulties to appropriately reach the steady state. The performance index of PV system (IAE) as shown in Figures 8d and 9d validate the effectiveness of the proposed control scheme with PSO MPPT. The performance characteristic parameters with PSO 10 particles is given in Table 4 and with PSO 40 particles is shown in Table 5. Table 4. Performance characteristics of the conventional controller and the proposed ASMC controller based on PSO 10 particles. Controller Over/Undershoot (%) Settling Time (Second) Power Losses (Watt) PID 8 80 ms 6 ASMC 0.85 2.8 ms 0.95 Table 5. Performance characteristics of the conventional controller and the proposed ASMC controller based on PSO 40 particles. Controller Over/Undershoot (%) Settling Time (Second) Power Losses (Watt) PID 10 120 ms 7.8 ASMC 1 3 ms 1.2 4.1.3. Response Using Improved PSM In this section, the MMPT algorithm based on Improved PSM will be tested. As in the preceding section, because the algorithm is of stochastic nature, two sets of 10 simulations each will be pursued; one with 10 models and a second one with 40 models. Results are shown in Figures 10a–d and 11a–d, respectively. IPSM with 10 and 40 models converge faster than PSO with 10 and 40 particles. The perturbation amplitude is greater when the number of models will be low or vice versa to reach to the optimal solution. It is clear from the comparative plots given below that the proposed ASMC controller based on IPSM MPPT has negligible ripples and no deviation from MPP in obtained voltage and power curves. The PV panel voltage curves Figures 10a and 11a track the reference voltage; PID voltage curve deviates from reference voltage and has great oscillations, while there is negligible deviation in the adaptive SMC voltage curve from reference. The PV array output power are shown in Figures 10b and 11b following the reference power. The main feature to highlight from the IPSM-based MPPT algorithm in comparison with the previously presented ones, is that it takes some more time to get the MPP but it guarantees to reach it. Furthermore, it exhibits less power energy losses than the PSO. The tracking error comparative plots are shown in Figures 10c and 11c, which highlight lower oscillations. From the voltage curves (Figures 10a and 11a) the conventional controller tracks the panel voltage successfully with reference voltage. The power curves achieved the MPP in Figures 10c and 11c. The tracking error curves (Figures 10b and 11b) show minimized tracking error behavior as compared to PSO MPPT tracking response In Figures 10d and 11d the performance index IAE of the PV system is depicted. This aggregated index confirms that this approach provides better performance than the other implemented MPPT techniques. In this manner, the validation of the chattering-free and robustness of the proposed adaptive sliding mode controller based on IPSM MPPT under variable environmental conditions and uncertainties is validated by comparing its performance with conventional controller based on P&O and PSO MPPT algorithms. The performance characteristic parameters are shown in Tables 6 and 7, which describe the overshoot characteristic, response time, and power losses. Energies 2019,13, Energies2020, 12,5678 x FOR PEER REVIEW 14 of 18 14 18 Energies 2019, 12, x FOR PEER REVIEW 14 of 18 Figure 10. PID & ASMC based in IPSM MPPT with 10 particles (a) Profile of the PV panel voltage (b) Figure Figure 10.PID 10. PID&&ASMC ASMCbased basedin inIPSM IPSM MPPT MPPT with 10 particles particles (a) (a) Profile Profileof ofthe thePV PVpanel panelvoltage voltage(b) (b) Tracking Trackingresponse response(c) Profile Profileofof the PV power extraction (d) IAE. IAE. Tracking response (c)(c)Profile ofthe thePV PVpower powerextraction extraction(d) (d)IAE. Figure 11. PID & ASMC based in IPSM. MPPT with 40 particles (a) Profile of the PV panel voltage (b) Figure 11. Figure 11. PID & ASMC based in IPSM. MPPT with 40 particles (a) Profile Profile of the PV panel voltage (b) Tracking response (c) Profile of the PV power extraction (d) IAE. Trackingresponse Tracking response(c) (c)Profile Profileofofthe thePV PVpower powerextraction extraction(d) (d)IAE. IAE. 4.2. Discussion 4.2. Discussion From the previous three scenarios, the IPSM MPPT algorithm provides an overall satisfactory From the previous three scenarios, the IPSM MPPT algorithm provides an overall satisfactory response. This improved approach may need some more time to get the MPP but it guarantees to response. This improved approach may need some more time to get the MPP but it guarantees to reach it. Furthermore, it exhibits less energy losses than the other ones. The aggregated error index, reach it. Furthermore, it exhibits less energy losses than the other ones. The aggregated error index, IAE, shows that this technique is performing better than the ones based on P&O and PSO MPPT IAE, shows that this technique is performing better than the ones based on P&O and PSO MPPT algorithms. Regarding the specific comparison with the other evolutive algorithm, PSO, IPSM with algorithms. Regarding the specific comparison with the other evolutive algorithm, PSO, IPSM with Energies 2020, 13, 5678 15 of 18 Table 6. Performance characteristics of the conventional controller and the proposed ASMC controller based in IPSM with 10 models. Controller Over/Undershoot (%) Settling Time (Second) Power Losses (Watt) PID 5 50 ms 4.8 ASMC 0.40 0.10 ms 0.54 Table 7. Performance characteristics of the conventional controller and the proposed ASMC controller based in IPSM with 40 models. Controller Over/Undershoot (%) Settling Time (Second) Power Losses (Watt) PID 5.8 53 ms 5.2 ASMC 0.41 0.11 ms 0.59 4.2. Discussion From the previous three scenarios, the IPSM MPPT algorithm provides an overall satisfactory response. This improved approach may need some more time to get the MPP but it guarantees to reach it. Furthermore, it exhibits less energy losses than the other ones. The aggregated error index, IAE, shows that this technique is performing better than the ones based on P&O and PSO MPPT algorithms. Regarding the specific comparison with the other evolutive algorithm, PSO, IPSM with 10 and 40 particles converges faster than PSO with 10 and 40 particles. In addition, PSO-based results presents great oscillations, energy losses, and, in some cases, the algorithm cannot obtain the steady state. Therefore, confirming the proposed adaptive sliding mode controller based on IPSM MPPT is better performing by comparing its performance with conventional controller based on P&O and PSO MPPT algorithms. 5. Conclusions In the present work, the design of a non-linear adaptive sliding mode controller (ASMC) based on a mathematical model of a boost converter has been derived for a stand-alone photovoltaic system to address the chattering phenomenon. An IPSM optimization algorithm is used to generate the reference voltage for the proposed controller. Comparison with two other optimization algorithms, namely, P&O and PSO with IPSM for MPPT has been conducted. The presented control scheme is investigated in simulations under variable irradiance and uncertainties in the system parameters. From the simulation results, we conclude that the ASMC controller with P&O MPPT presents constant oscillations around MPP, power losses, and overshoots, although it is the fastest one to obtain the MPP. On the other side, the ASMC controller with PSO MPPT presents great oscillations, the greatest energy losses, and, in some cases, it cannot obtain the MPP. Besides, the ASMC controller with IPSM MPPT is slower to obtain the MPP but presents lower energy losses versus adequate settling time in comparison with the other two algorithms. Clear advantages of the tested optimization based MPPT algorithms over traditional P&O have been shown. In both cases, 10 and 40 particle optimizations have been conducted. Regarding IPSM, as shown in Tables 6 and 7, ASMC results are similar in both cases (10 and 40 particles) and superior in speed of response and power loses to the PSO ones (IPSM shows to be two times faster and exhibits half the power loses). It is worth mentioning that, for the ASMC based P&O MPPT algorithm, it provides reasonable performance indicators, even aligned with the PSO based MPPT but even faster from the settling time point of view (see Tables 3–5). In the case of the IPSM, the settling time is greatly improved with respect to PSO and made overall better results with respect to the original P&O. IPSM, therefore, provides a good alternative to the MPPT algorithm. Energies 2020, 13, 5678 16 of 18 The simulation results are further compared with a classical PID controller to show the robustness of the developed adaptive SMC control scheme. The results obtain using ASMC controller in comparison with PID controller limits the chattering phenomenon and overcomes the high frequency oscillations. As a next step, the authors look forward to an experimental validation of the results. Author Contributions: H.G.A., R.V.A. conceived and designed the experiments; H.G.A. performed the simulations; writing—review and editing, R.V.A.; supervision, R.V.A.; H.G.A wrote the paper. All authors have read and agreed to the published version of the manuscript. 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