processes Article Non-Linear Sliding Mode Controller for Photovoltaic Panels with Maximum Power Point Tracking Hina Gohar Ali 1,2, * , Ramon Vilanova Arbos 1 , Jorge Herrera 3 , Andrés Tobón 4 and Julián Peláez-Restrepo 4 1 Departament de Telecomunicació i d’Enginyeria de Sistemes, Escola d’Enginyeria Universitat Autònoma de Barcelona (UAB), Bellaterra, Cerdanyola del Vallés, 08193 Barcelona, Spain; ramon.vilanova@uab.cat 2 School of Electrical Engineering and Computer Science, National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan 3 Departamento de Ingeniería, Facultad de Ciencias Naturales e Ingeniería, Universidad de Bogotá Jorge Tadeo Lozano, Bogotá, Distrito Capital 110311, Colombia; jorgea.herrerac@utadeo.edu.co 4 Departamento de Electrónica y Telecomunicaciones, Facultad de Ingenierías, Instituto Tecnológico Metropolitano, Calle 54 A #30-01, Medellín, Antioquia, Colombia; andrestobon@itm.edu.co (A.T.); julianpelaez@itm.edu.co (J.P.-R.) * Correspondence: hina.goharali@e-campus.uab.cat  Received: 11 November 2019; Accepted: 8 January 2020; Published: 14 January 2020  Abstract: In this paper, nonlinear sliding mode control (SMC) techniques formulated for extracting maximum power from a solar photovoltaic (PV) system under variable environmental conditions employing the perturb and observe (P and O) maximum power point tracking (MPPT) technique are discussed. The PV system is connected with load through the boost converter. A mathematical model of the boost converter is derived first, and based on the derived model, a SMC is formulated to control the gating pulses of the boost converter switch. The closed loop system stability is verified through the Lyapunov stability theorem. The presented control scheme along with the solar PV system is simulated in MATLAB (matric laboratory) (SMC controller and PWM (Pulse Width Modulation) part) and PSIM (Power electronics simulations) (solar PV and MPPT algorithm) environments using the Simcoupler tool. The simulation results of the proposed controller (SMC) are compared with the classical proportional integral derivative (PID) control scheme, keeping system parameters and environmental parameters the same. Keywords: integer order SMC; maximum power point tracking; photovoltaic panel; perturb and observe algorithm 1. Introduction The current global energy demand of the world has been continuously tremendously increasing due to various reasons, such as population growth, general economic growth, and industrial growth. The majority of energy needs have been fulfilled over the centuries by fossil fuels. Major concerns associated with fossil fuels are ever-increasing prices and adverse effects on nature, which results in a global energy crisis due to limited supply. These fuels cannot be renewed at the rate of their consumption, so these are termed as non-renewable energy sources [1]. A solution to these issues is to use renewable energy sources which are inexhaustible and cause less pollution when compared to fossil fuels. There are different sources of renewable energy, such as solar energy, wind energy, biomass energy, ocean energy, geothermal energy, hydropower, and biofuel [2], among others. Some other energy adequacy has been discussed in detail in Reference [3]. Among several renewable energy resources, solar energy is one of the most sustainable energy sources [4] because of the fact that it is clean, inexhaustible, free, and has a long-life expectancy. The energy which is Processes 2020, 8, 108; doi:10.3390/pr8010108 www.mdpi.com/journal/processes Processes 2020, 8, 108 2 of 14 consumed on earth is almost ten thousand times less than the sun energy imparted upon us. Therefore, it is necessary to develop instruments which will utilize the unrestricted energy sources by using a photovoltaic (PV) system. PV panels are devices that convert sunlight directly into electricity by exploiting a photoelectric effect. It is a group of solar cells, which is the basic unit of the solar system. Stand-alone systems and grid-connected systems are the two main classifications of photovoltaic systems. Stand-alone PV systems operate independently from the utility grid [5] and are generally designed for supplying DC or AC electrical loads. For example, in Reference [6], the design of a stand-alone photovoltaic system for footbridge lighting has been analyzed for the AC loads. On the other hand, grid-connected systems are connected to the utility grid [7] which is composed of grid-connected equipment, a power conditioning unit, an inverter, and a PV array. The PV system has exhibited a nonlinear current-voltage (I-V) and power-voltage (P-V) characteristics which vary with the solar irradiance and temperature of the cell. Efficiency becomes low in PV due to the energy transformation from electrical to solar, which causes the main obstacles in the maximum solar energy utilization. Consequently, it is of great importance to obtain the maximum efficiency of PV systems. This is achieved by making an optimal follow-up of the maximum power point (MPP), which means keeping the system working at the operation point where the extraction of power is maximum. Therefore, maximum power point tracking (MPPT) techniques are introduced to extract maximum power from PV panels to significantly use the PV panel power [8,9]. Numerous algorithms have been proposed in the literature to accomplish the goal of MPPT [10] and can be distinguished from one another based on different features, such as complexity, convergence speed, implementation, effectiveness range, and various other aspects [11]. The perturb and observe (P and O) technique is the most used due to its ease of implementation and low cost [12]. In P and O, the perturbation is made in the operating point until maximum power is achieved. It operates by periodically perturbing the control variable and comparing the instantaneous PV powers before and after the perturbation. This algorithm is composed of two critical parameters: the sampling interval (Ta), in which the algorithm perturbs the control variable, and the amplitude of such perturbation (∆Vref ). Due to its simple implementation, the P and O is adopted to generate reference voltage (∆Vref ) [13,14]. Numerous linear controllers can also be used along with different algorithms for MPPT, which guarantee a proper tracking of the reference voltage generated by the MPPT algorithm to mitigate the perturbations [15]. The main problem associated with these kinds of controllers is that they are based on a linearized model of the PV system around a given operating point, which does not ensure the same performances in all of the PV operation range. Other types of controllers have been proposed in the literature to ensure a correct behavior of the system without requiring a linearization process [16]. Some of those controllers are based on adaptive laws [17] and energy balance [18]. Due to the nonlinear feature of PV arrays and power converters, applying non-linear controllers presents a good solution. A non-linear backstepping and integral backstepping controller is proposed in References [19,20] to track the MPP of PV. In Reference [21], a non-linear, robust integral backstepping-based MPPT control scheme is proposed for MPP tracking of the PV array. The sliding mode controller (SMC) is a non-linear control strategy derived from variable structure system (VSS) theory, which was originally introduced in References [22,23]. The switched-mode (DC-DC) converters used in PV system applications are the ideal target of this kind of controller. In SMC, the control scheme is designed to drive and then retain the system states within the limits of the switching function. This approach offers two main advantages. First, the dynamic behavior of the system may be tailored by the specific choice of switching function. Secondly, the closed-loop system response becomes insensitive to a particular class of uncertainty. This property makes the SMC a proper candidate for robust control. In addition, the ability to specify performance directly makes sliding mode control attractive from a design perspective. The classical SMC consists of two components. The first component comprises the design of a switching function, so that the sliding Processes 2020, 8, 108 3 of 14 motion achieves the design specifications. The second component is associated with the selection of a Processes 2020, 8, x FOR PEER REVIEW 3 of 14 control law that will make the switching function attractive to the system state [24]. This is not always true for a control selection of alaw to be control lawdiscontinuous that will make the in nature. switching The most attractive function eminent to feature of SMC the system stateis that [24]. it is This completely insensitive to parametric uncertainty and external disturbances is not always true for a control law to be discontinuous in nature. The most eminent feature of SMC during the sliding mode. In particular, is that ittheis sliding completely mode approachtooffers insensitive stability parametric and robustness uncertainty againstdisturbances and external parameters,during input,the and load uncertainties, sliding mode. which are common In particular, in PVmode the sliding systems. Moreover, approach offers SMC is simpler stability to implement and robustness againstin comparison with other parameters, input,types and of nonlinear load controllers uncertainties, which[25]. are The commonsliding in mode controlMoreover, PV systems. has received SMC muchis simpler to implement in comparison with other attention because of its benefits of a quick response and robustness. types of nonlinear controllers [25]. The sliding mode Incontrol has received this article, an integermuchorderattention SMC because of its benefits is proposed for theofextraction a quick response of maximum and robustness. power from a In this article, an integer order SMC is proposed for the PV panel under varying radiation and temperature. This is to highlight that the proposed extraction of maximum power from system a PV panel under varying radiation and temperature. This is to highlight that the proposed system is is controlled by the sliding mode controller formulated in References [16,23], i.e., a design of stable controlled by the sliding mode controller formulated in References [16,23], i.e., a design of stable SMC SMC to track the reference provided by the P and O MPPT algorithm. The overall system consists to track the reference provided by the P and O MPPT algorithm. The overall system consists of a PV of a PV panel connected to a boost converter, which in turns supplies power to a DC load. The P panel connected to a boost converter, which in turns supplies power to a DC load. The P and O MPPT and O algorithm MPPT algorithmis employed is employed to generateto generate the referencethe reference PV voltagePV voltage with a boost with a boost for converter converter the SMC for the SMCcontroller. The SMC controller is derived based on the nonlinear mathematical model of a PV panel a controller. The SMC controller is derived based on the nonlinear mathematical model of PV panel withwith a boost a boost converter. converter. A classical A classical integer integer order order slidingsliding surfacesurface is chosen is chosen and then and then law control control is law is derived, derived,such such that that thethe overall overall closed closed loop system loop system should should strictly strictly track the track reference thevoltage reference voltage generated generated through through the MPPT the MPPT algorithm algorithm and theand the response response should should remain remain insensitive insensitive to parametric to variations. parametric variations. The stability of the proposed SMC is proved by selecting the integer order candidate The stability of the proposed SMC is proved by selecting the integer order Lyapunov Lyapunov function. candidate PV, along function. PV, with alongthe boost with theconverter and MPPTand boost converter algorithm, MPPT is modeled inisPSIM, algorithm, modeledwhereas the in PSIM, SMC controller is implemented in MATLAB/Simulink. The SMC whereas the SMC controller is implemented in MATLAB/Simulink. The SMC controller is coupled controller is coupled through the Simcoupler interface between PSIM and MATLAB/Simulink. In order through the Simcoupler interface between PSIM and MATLAB/Simulink. In order to test the superiority to test the superiority of the proposed controller, the simulation results are compared with the classical proportional integral of the proposed controller, the simulation results are compared with the classical proportional integral derivative (PID) controller. derivative (PID) controller. The overall paper is structured as follows: In Section 2, related work is discussed. Section 3 The overall paper is structured as follows: In Section 2, related work is discussed. Section 3 introduces the system model used in this work and the proposed control scheme is defined. introduces the system Simulation results model used in this are presented in work Section and4. the proposed Finally, Section control scheme isthe 5 summarizes defined. Simulation conclusions and resultsfuture are presented work. in Section 4. Finally, Section 5 summarizes the conclusions and future work. 2. Related Work/Background 2. Related Work/Background Figure 1 presents a typical control structure for the PV system aimed at regulating the PV voltage Figure to a reference 1 presents given by thea MPPT typical control structure algorithm and for the PV system to mitigate aimed at regulating the oscillations in the the PV voltage environmental to a reference given by the MPPT algorithm and to mitigate the oscillations in the environmental conditions. The PID controller is designed from the linearization of the PV system around a specific conditions. The PID controller is designed from the linearization of the PV system around a specific operating point, e.g., the MPP at the lowest irradiance for a stand-alone system, as in Reference [13]. operating point, e.g., the MPP at the lowest irradiance for a stand-alone system, as in Reference [13]. Therefore, to guarantee the same performance in all of the operation range, it is necessary to design Therefore, to guarantee the same performance in all of the operation range, it is necessary to design non-linear controllers non-linear that do controllers thatnot do depend not dependon linearized models. on linearized models. Figure 1. System scheme based on a classical proportional integral derivative (PID) control. Figure 1. System scheme based on a classical proportional integral derivative (PID) control. Processes Processes2020, 2020,8,8,x108 FOR PEER REVIEW 4 4ofof14 14 Processes Sliding 2020, 8, x FOR mode PEER REVIEW control (SMC) has been proposed in the literature to ensure correct behavior 4 of 14 withoutSliding modeofcontrol the need (SMC) has linearization. been This work proposed is based in the literature on the ideas to ensure correct published behavior[26–28], in References without the needSliding of mode linearization. control This (SMC) work is has based been on proposed the ideas in the published literature which apply the sliding mode technique to regulate the PV voltage and to mitigate the oscillations. in Referencesto ensure [26–28],correct which behavior apply The without the proposed the sliding mode need of technique scheme linearization. implementedto regulate This work thework in this is PV voltagebased on and toin is presented the ideas mitigate Figure 2. published in theInoscillations. References [26–28], The proposed this implementation, the which schemeand voltage apply implemented the sliding current of the in this mode technique work are PV array is presented to provided inregulate to Figure the a P and2.OInPV voltage and this implementation, algorithm, to mitigate which defines the the oscillations. voltage the and reference to the SMC controller to provide reference peak power voltage, which can be tracked by the proposedthe The current proposed of the PV scheme array implemented are provided toina this P andwork O is presented algorithm, in which Figure defines 2. In the this implementation, reference to the SMC voltage to controller non-linear and currentreference provide controller. of the The PVpeak array controller are provided power has voltage, been derivedto a Pusing which and can Obe algorithm, thetracked bywhich mathematical defines the proposed model of the areference non-linear non- to the controller.SMC The controller controller to provide has been reference derived peak using power the voltage, mathematical which inverting boost converter and generates an output signal µ, which controls the duty ratio of the PWM model can be of atracked by non-invertingthe proposed boost non-linear converter signal andcontroller. provided generates The an to the converter controller output signal has switches. beencontrols µ, which derivedthe using dutythe ratio mathematical of the PWM signal modelprovided of a non- inverting to the Theconverterboost MPPT-based converter switches.P and O generates the reference voltage Vref, which is compared withthe and generates an output signal µ, which controls the duty ratio of PWM panel signal The provided MPPT-based to to generate P the converter anand switches. O generates the is reference to the V voltage voltage VPV error signal, which supplied ref , whichsliding improved is compared with panel mode controller. voltage The The controller MPPT-based VPV togenerates generate the P and an error O generates signal, control inputwhich the reference is supplied µ, which voltage controlstothe thePWM V ref, which is compared with panel improved signalsliding widthmode controller. and drives the Thevoltage converter toVPV controller to track generate generates the reference an control the error signal, input voltage. which µ, which Hence, is supplied controls operating theto the PV thePWM improved module signal on thissliding width mode and reference controller. drives the voltage The convertercontroller to track generates the reference the control voltage. will ensure that maximum power is generated by the system. input Hence, µ, which operating controls the PV the module PWM on signal this width reference and drives voltage the will converter to track the reference voltage. ensure that maximum power is generated by the system. Hence, operating the PV module on this reference voltage will ensure that maximum power is generated by the system. Figure 2. System scheme based on the improved sliding mode controller (SMC). Figure 2. System scheme based on the improved sliding mode controller (SMC). 3. System Modeling Figure 2. System scheme based on the improved sliding mode controller (SMC). 3. System Modeling 3.1.3.Photovoltaic System Modeling (PV) Model 3.1. Photovoltaic (PV) Model Mathematical 3.1. models Photovoltaic (PV) are used to describe the operation and behavior of the PV panels in the Model Mathematical calculation models are used of the current-voltage to describe the characteristic. The operation current and behavior voltage of the PVmathematical (I-V relation) panels in the equation of the solar cell is implicit and non-linear. For precise PV cell modeling and betterpanels Mathematical calculation of the models are current-voltage used to describe characteristic. the The operation current and voltagebehavior (I-V of the relation) PV mathematical accuracy,in the in calculation equation this work,of the of the we solar current-voltage use acell twoisdiode implicit PVandcharacteristic. non-linear. model The current For precise which involves voltage (I-V PV cell modeling identification relation) of moreand mathematical better accuracy, parameters at the in equation expense of of this work, the solar we longer use acell twoisdiode implicit computational PVand time non-linear. model and iswhich known For precise involves as PVa cell modeling identification being andparameters of more seven-parameter better modelaccuracy, [29].at thein this work, expense of we use longer a two diode computational PV model time and which is involves known as identification being a of more seven-parameter Simulations are based on the double-diode model, since their estimation is more useful with other parameters model at the [29]. expense Simulations models of longer are based (i.e., single computational diodeon time the double-diode model) and [30]. The PV model, is known sinceon panel based as their being a the estimation seven-parameter is moreisuseful two diode model model shownwith other in Figure [29]. Simulations are based on the double-diode model, since their estimation is more 3.models (i.e., single diode model) [30]. The PV panel based on the two diode model is shown in Figure 3. useful with other models (i.e., single diode model) [30]. The PV panel based on the two diode model is shown in Figure 3. Figure 3. Photovoltaic (PV) panel double-diode model representation. Figure 3. Photovoltaic (PV) panel double-diode model representation. Figure 3. Photovoltaic (PV) panel double-diode model representation. Processes 2020, 8, 108 5 of 14 Processes 2020, 8, x FOR PEER REVIEW 5 of 14 To operate the PV panel at MPP, a DC-DC converter controlled by the MPPT is inserted between the PV panel andand the the load. load. DC-DC DC-DCconverters converters areare used used widely widely for for the theefficient efficient management management of of energy energy in PV systems. The boost converter has The boost converter has been been chosen for this work [31], as shown in Figure 2. To extract the maximum possible power of the panel, the the P and O algorithm algorithm is is implemented, implemented, which is the most widely widely used used MPP MPP tracking tracking method. method. P and O O generates generates thethe reference reference voltage voltage V Vref ref after measurement measurement of of the thepanel panelpower. power.IfIfthe themeasured measured power power is is greater greater than than thethe previous previous power, power, the the reference reference voltage voltage is steadily is steadily incremented incremented in theproportion, in the same same proportion, otherwise, otherwise, if not, then if not, then it is it is decreased. decreased. Figure the Figure 4 presents 4 presents P and Othe P and Oflow algorithm algorithm diagram, flowwhich diagram, which is implemented is implemented with PSIM with PSIM simulation simulation tools. This tools. This method findsmethod finds thepower the maximum maximum power of point (MPP) point (MPP) ofby PV modules PV modulesperturbing iteratively by iterativelythe perturbing the reference reference voltage and observingvoltageandand observing comparing theand powercomparing generatedthe bypower the PV generated module at any by the PV instant module with the at any instant previous power. with Thethe previous voltage power. The perturbation voltagethrough is achieved perturbation is achieved the change through in reference the voltage, ∆Vref . The change in increment reference voltage, ΔVref.ofThe or decrement the increment or decrement reference voltage in everyof the reference sampling period voltage in every is determined by sampling periodofisthe the comparison determined power atby thethe comparison present time andof the powertime. previous at theThe present sign oftime theand ∆P(k) =time. previous error, P(k) The − P(ksign ofisthe − 1), error, used ΔP(k) = P(k) to determine the− direction P(k − 1), isofused to determine perturbation. the If the direction ofpower, incremental ∆P(k) > If perturbation. 0, the incremental power,beΔP(k) duty cycle should > 0, the increased in duty ordercycle to make ∆Vref should be>increased 0. On thein order other to make hand, if ∆P(k) ΔVref<>0,0.then On the other hand, reference if ΔP(k) voltage < 0, thento is reduced the ∆Vref voltage reference make < 0. is reduced to make ΔVref < 0. Figure 4. Perturb and observe (P and O) algorithm. Figure 4. Perturb and observe (P and O) algorithm. 3.2. Control Scheme 3.2. Control Scheme 3.2.1. DC-DC Converter Model 3.1.1. DC-DC Converter Model Power electronic converters (DC-DC) are used in photovoltaic systems as an adaptation stage Power between theelectronic converters PV panel and the load. (DC-DC) are used The DC-DC powerin photovoltaic systems as converter is connected toan adaptation adjust stage the PV panel between the PV panel and the load. The DC-DC power converter is connected to adjust output voltage to maximize the solar power generation. In this work, we adapt a boost converter the PV panel output voltage which steps to maximize up voltage theinput from its solar(PV power generation. array) In this to its output work, (load), we adapt in order a boost to operate theconverter PV panel which steps Itupisvoltage at the MPP. assumedfrom thatits input the (PV array) converter to its output is operating (load), in conduction in continuous order to operate mode.the PV panel at the MPP. It is assumed that the converter is operating in continuous conduction mode. 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 Reference [28], the dynamics of the boost converter is given by: Processes 2020, 8, 108 6 of 14 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 Reference [28], the dynamics of the boost converter is given by: dVpv Icin = Cin = Ipv − IL (1) dt dIL VL = L = VPV − Vb (1 − u) (2) dt where Icin , PV , Vb , Cin , VL , L , and L represent capacitor current, PV current, battery voltage, input capacitor capacitance, voltage across inductor, inductor current, and inductor inductance, respectively. Rearranging Equations (1) and (2), we have: . IL I V PV = − + PV (3) Cin Cin VPV Vb . V − + bu IL = (4) L L L Equations (3) and (4) can be written in state space form as:  .  " −1 #" #  IPV " # " #  V PV  = 0  Cin VPV  Cin 0  1 0  . 1 +  −Vb + Vb u (5) IL 0   IL  L 0 L 0 L Equation (5) can be re-written in generalized form as: . X = f (X, t) + J (X, t) + h(X, t)u (6) h iT h iT Here, X = x1 x2 = VPV IL represents PV panel voltage and inductor current, J(X, t) and h(X, t) represent nominal system inputs, and u represents the control excitation. " −1 # 0 Cin f (X, t) = 1 (7) L 0  IPV   Cin 0  J (X, t) =  −Vb  (8) L 0 " # 0 h(X, t) = Vb (9) L 3.2.2. Controller Formulation The objective of the closed loop control system is that panel voltage, *VPV , must strictly follow the VPV-ref generated by the MPPT algorithm so that maximum power can be extracted from the PV panel under varying sunlight and temperature. The reference signal generated by the MPPT algorithm can be written as: h . iT h . iT Xd = xd xd = VPV−re f V PV−re f (10) The tracking error can be defined as:     e1 = x1 − xd     .     e2 = e1   (11)   . e2 = x2 − xd       . . ..      e2 = x2 − x    d Processes 2020, 8, 108 7 of 14 Sliding surface is chosen as: s = k1 e1 + e2 (12) Here, k1 > 0 is the design parameter. Differentiating Equation (12), on both sides: . . s = k1 e2 + e2 (13) By combining Equations (6) and (13) one can obtain: . .. s = c1 e2 + f (X, t) + J (X, t) + h(X, t)u − xd (14) . To derive the control set s = 0, the desired response can be achieved by choosing the control law as:    u = ueq + us ..  ueq = h(X, t)−1 [xd − f (X, t) − J (X, t) − c1 e2 ]  (15)     us = −h(X, t)−1 ks sgn(s)   where ueq is the equivalent control item to drive the nominal part of the system, us is the robust switching control term, and ks is switching gain, and sgn(.) is the signum function, defined as: s > 0     +1 if sgn(s) =  0 if s = 0 (16)   s < 0   −1 if 3.2.3. Stability Proof of the Proposed Controller The stability of the proposed control scheme can be proved by choosing the Lyapunov candidate function as: 1 V = S2 (17) 2 where ‘S’ represents the sliding surface chosen in Equation (12). According to Lyapunov, the control system will be stable if the derivative of the Lyapunov candidate is negative along the closed-loop system trajectories. Thus, by taking the derivative of Equation (17), we get: . . V = SS (18) Putting ‘S’ from Equation (14) into Equation (18), we get: . .. V = S(c1 e2 + f (X, t) + J (X, t) + h(X, t)u − xd ) (19) Putting the value of ‘u’ from Equation (15) into Equation (19) and simplifying, we obtain: . V = S(−ks sgn(S)) ≤ (−ks |S|) ≤ 0 (20) . It can be shown that V ≤ 0 if the switching gain ks > 0 and the closed loop system is stable. 4. Simulation Results Matlab/Simulink is used to model and simulate the proposed controller’s technique. While the PV panel along with the boost converter and MPPT algorithm simulations are performed in PSIM (PowerSim), Simcoupler is used as an interface to couple Simulink and PSIM co-simulation. The parameters of the PV array that are used in this work are mentioned in Table 1. From Table 1, the short circuit current, open circuit voltage, and maximum power point tracking voltage of a single PV panel is given, for which a single DC-DC boost converter is selected. The parameters of the input Processes 2020, 8, 108 8 of 14 capacitor and the inductor are selected such that the inductor current ripple equals to 1. A physical model of a PV panel is used according to the renewable energy module of PSIM [32], with parameters corresponding to the PV module of type MSX-60 [33]. Table 1. Parameters of the PV array [33]. Symbol Parameter Value Isc Open circuit current 3.8 A Voc Open circuit voltage 21.1 V Imp Maximum panel current 3.5 A Vmp Maximum panel voltage 17.1 V Is1 = s2 Saturation currents 4.704 × 10−10 Ipv Panel current 3.8 A Rsh Shunt resistance 176.4 Ω Rs Series resistance 0.35 Ω Similarly, the parameters of the controller and converter are arranged in Table 2. The design parameters of controllers are selected using Matlab optimization tools which are given in this Table. Table 2. Parameters of controller, converter, and maximum power point tracking (MPPT). Parameter Value L 22 µF C 100 µF Vo 24 V fsho 49.9 kHz Kp 0.1 Kd 0.1 Ki 50 Ks (MPPT) 14.53 Ta 400 µs ∆Vo IV (P and O) LPF 20 kHz LPF (low pass filter). Simulations of the proposed controller are performed in PSIM and MATLAB/Simulink to verify its performance. The system is perturbed with an irradiance step of 1000 W/m2 in the instant 0 and after 50 ms, the irradiance is decreased by 50%. The irradiance is varied to validate the robustness of the proposed MPPT technique and temperature is kept constant at 25 ◦ C. The relationship coefficient of the Solar Panel MSX-60 used in the paper is ±0.05 ◦ C m2 /W. This means that for an environment temperature of 25 ◦ C, the PV panel will operate up to 40 ◦ C if irradiance is 1000 W/m2 , and 32.5 ◦ C if irradiance is 500 W/m2 . Similarly, the temperature coefficient of power is −(0.5 ± 0.15)%/◦ C, which implies that maximum output power will be reduced to half if the irradiance level varies from maximum to half. The same effect is simulated in the paper, and the irradiance level has been instantly reduced to 50% after 50 ms. 4.1. Response Using the Proportional Integral Derivative (PID) Controller To show the performance of the proposed SMC controller, it is compared with a conventional PID controller. The conventional controller response based on the P and O MPPT algorithm can be seen in Figure 5a–c, with a P and O perturbation amplitude of 1 V. The voltage tracking of the conventional controller is shown in Figure 5a. Reference ‘Vref ’ of the peak power voltage generated by P and O MPPT is successfully tracked by the PID controller. ‘VPV ’ reaches the desired set point ‘Vref ’ in a settling time of 5 ms. Figure 5b shows the tracking error of the conventional controller with high ripples and oscillation. PV array output power along with the reference power curve is shown in Figure 5c. It can Processes 2020, 8, 108 9 of 14 be observed that MPP is achieved by the conventional PID controller within 5 ms; however, it can be observed that the controller successfully tracks the reference but displays large ripples in the voltage waveform along with an overshoot. The zoomed views are provided in voltage and power curves to see the 2020, Processes comparative 8, 108 behavior with reference voltage and power. 9 of 14 (a) (b) (c) Figure Figure 5. 5. (a) (a) Profile Profile of of the the PV PV panel panel voltage, voltage, (b) (b) tracking tracking response response of of the the proposed proposed PID PID controller, controller, and and (c) profile of (c) profile of the the PV PV power power extraction. extraction. Processes 2020, 8, 108 10 of 14 Processes 2020, 8, 108 10 of 14 4.2. Response Using 4.2. Response Usingthe theSliding SlidingMode ModeController (SMC) Controller (SMC) The output of The output of the thePPandandO-based O-basedMPPT MPPTis is a voltage a voltage reference reference which which needs needs to tracked to be be tracked by by the the controller. The controller is used to keep track of the panel voltage controller. The controller is used to keep track of the panel voltage with the reference voltage with the reference voltage generated generated by by PP and and O and ensuring O and ensuring aa tracking tracking error error around around ‘zero’ ‘zero’ for for the the desired desired performance performance of of the the proposed controller. proposed controller. Figure 6a–c shows Figure 6a–c showsthe theperformance performanceofof thethe SMC SMC controller controller based based on P on the theand P and O algorithm O algorithm with with a perturbation amplitude of 1 V under variable irradiance. It can be a perturbation amplitude of 1 V under variable irradiance. It can be seen in Figure 6a that the panel seen in Figure 6a that the panel voltage ‘V pv ’ starts following the reference generated voltage ‘Vpv’ starts following the reference generated voltage ‘Vpv-ref’ once voltage ‘V ’ once it has reached it has reached the steady- pv-ref the steady-state after transient behavior and successfully tracked the reference voltage. state after transient behavior and successfully tracked the reference voltage. It is highlighted from the It is highlighted from trackingthe tracking responseresponse curve in curve in Figure Figure 6b that6b that the the proposed proposed controllerclearly controller clearlyoutperforms outperforms the the conventional controller with little oscillation. During the abrupt variation conventional controller with little oscillation. During the abrupt variation of irradiance at of irradiance at 0.05 0.05 s, s, the the controller controller performed performed well, well, showing showing the the robustness robustness of of the the controller. controller. The The proposed proposed controller controller is is not not only only robust, robust, but but the the ripples ripples are are also also negligible. Similarly, the negligible. Similarly, the PV PV panel panel output output powerpower alongalong with with the the reference power curve is shown in Figure 6c. It is observed reference power curve is shown in Figure 6c. It is observed that panel power ‘Ppvthat panel power ‘P ’ and reference pv’ and reference power power ‘P ‘Ppv-ref ’ are following each other faster once they have reached the MPP. pv-ref’ are following each other faster once they have reached the MPP. The The efficiency efficiencyofofthe thesystem system is greatly is greatlyenhanced enhanced when the proposed when controller the proposed is used.is The controller results used. The that results that are obtained by using an improved SMC controller are free of ripples and overshoot,PID, are obtained by using an improved SMC controller are free of ripples and overshoot, but with but both of them are high and visible. with PID, both of them are high and visible. (a) (b) Figure 6. Cont. Processes 2020, 8, 108 11 of 14 Processes 2020, 8, 108 11 of 14 Processes 2020, 8, x FOR PEER REVIEW 11 of 14 (c) Figure 6. Figure 6. (a) (a) Profile Profileofofthe thePV PVpanel panelvoltage, voltage,(b)(b) tracking tracking response response of the of the proposed proposed SMCSMC controller, controller, and andprofile (c) (c) profile of power of power extraction. extraction. (c) 4.3. Comparative FigureAnalysis 4.3. Comparative 6.Analysis (a) Profile of the PV panel voltage, (b) tracking response of the proposed SMC controller, and (c) profile of power extraction. Table Table 33 shows shows that that the the overshoot overshoot characteristics, characteristics, response response time, time, and and power power losses losses havehave been been explained. explained. It is It is possible possible 4.3. Comparative to deduct to Analysis deduct fromfrom Table Table 33 that that the the performance performance characteristic characteristic parameters parameters of of the the SMC controller SMC controller in Tablein comparison comparison 3 shows with that thewith the PID the PID overshoot controller for controller response characteristics, the proposed for the proposed PV system PV system time, and power have losseshave successfully have successfully been improved. improved. The comparison The explained. comparison It is possible to ofdeduct of the proposed the from TableSMC proposed 3 thatcontroller SMC controller the performance is is done done in in Figures Figures characteristic 7–9. 7–9. In parameters In Figure of the 7, Figure 7, the the comparison SMC of the proposed controller in controller comparison with voltage the PID curve is controller done for the with the proposed comparison of the proposed controller voltage curve is done with the reference signal and reference PV system signal have and conventional successfully improved. controller conventionalvoltage The comparison signal. controller ofsignal. the proposed Both controllers voltage track Both SMC the controller reference controllers track issuccessfully, done in Figures the reference and 7–9. In Figure there is high successfully, 7,and the oscillation there is in comparison the oscillation PID controller of the proposed behavior. controller Similarly, Figure voltage curve 8 highlights is done theFigurewith comparativethe reference behaviorthesignal of the andproposed high in the PID controller behavior. Similarly, 8 highlights comparative conventional controller voltage signal. Both controllers track the reference successfully, and there is controller behavior panel of the power proposed with referencepanel signalpower powerwith and reference conventional controller power. It can be high oscillation in the controller PID controller behavior. Similarly, Figure 8 signal highlightspower and conventional the comparative observed controller that power. behavior MPP of theItis proposed successfully can be observed achieved controller that by panel MPPthe is power proposed successfully with referenceSMC controller achieved signal power by with and thealmost proposed conventional negligible SMC ripples compared controller with almost controller to the power. It PID controller, negligible can be rippleswhich observed compared that MPPhasislarge to theripples in correspondence PID controller, successfully achieved bywhich hasto the proposed the largeSMC reference ripples in signal. The zoomed controller with views almost are also negligible shown ripples to clearly compared to observe the PID the comparison. controller, correspondence to the reference signal. The zoomed views are also shown to clearly observe the which has The large tracking ripples in error correspondence to the reference signal. The zoomed viewsoscillations comparative comparison. plot tracking The is shown in Figure error 9, which comparative shows plot high is shown inareFigure also shown 9, in to clearly the which showsobserve conventional the controller high oscillations comparison. The tracking error comparative plot is shown in Figure 9, which shows high oscillations response as compared to the proposed SMC controller which has little in the conventional controller response as compared to the proposed SMC controller which has little oscillations. in the conventional controller response as compared to the proposed SMC controller which has little oscillations. oscillations. Table 3. Performance characteristics of the conventional PID and the proposed SMC controller. Table Table 3. 3. Performance Performance characteristicsofofthe characteristics the conventional conventional PID andand PID the the proposed SMC controller. proposed SMC controller. Controller Over/Undershoot (%) Settling Time (s) Power Losses (Watt) Controller Over/Undershoot Controller Over/Undershoot(%)(%) Settling SettlingTime (s) Power LossesLosses (Watt) (Watt) PID 2.61 5Time ms (s) Power 3 PID 2.61 5 ms 3 PID SMC 2.61 0.6 5 0.3 msms 3 SMC 0.6 0.3 ms 0.68 0.68 SMC 0.6 0.3 ms 0.68 Figure 7. Reference, PID, and SMC PV voltage curve. Processes 2020, 8, x FOR PEER REVIEW 12 of 14 Processes 2020, 8, x FOR PEER REVIEW 12 of 14 Figure 7. Reference, PID, and SMC PV voltage curve. Processes 2020, 8, 108 12 of 14 Figure 7. Reference, PID, and SMC PV voltage curve. Figure 8. Reference, PID, and SMC PV power curve. Figure 8. Reference, PID, and SMC PV power curve. Figure 8. Reference, PID, and SMC PV power curve. Figure 9. PID and SMC PV tracking error curve. Figure 9. PID and SMC PV tracking error curve. 5. Conclusions Figure 9. PID and SMC PV tracking error curve. 5. Conclusions In this paper, a nonlinear sliding mode controller (SMC) based on a mathematical model of a 5. Conclusions In this paper, boost converter hasa been nonlinear derivedsliding for amode controllersystem. photovoltaic (SMC) based on a mathematical The perturb and observe model maximum of a boost In converter this paper, hasa been derived nonlinear for sliding a modephotovoltaic controller system. (SMC) The based perturb on power point tracking technique has been used to generate a voltage reference for the SMC controller. a and observe mathematical maximum model of a power boost The pointloop closed tracking converter technique has been system derived stability has been for is shown used to betoguaranteed a photovoltaic generate a by system.voltage The reference using perturb for the and the Lyapounov SMC maximum observe controller. stability criteria. The power closed pointloop system tracking stability technique is has shown been to used be guaranteed to generate a by using voltage the Lyapounov reference The proposed control scheme is tested under varying irradiance levels and the simulation results are for the stability SMC criteria. controller. The proposed closed compared loopcontrol with asystem scheme classical stabilityis is tested shown PID controller. under to bevarying From guaranteed the irradiance simulation levels byresults, using the and it is the simulation Lyapounov concluded theresults stability that are criteria. proposed compared The SMCproposed controlwith a classical control scheme schemePID overcomes controller. is tested the underFrom nonlinear varying dynamicstheirradiance simulation results, of the PVlevels system andand it offers the issimulation concluded a faster that are results the transient proposed compared SMC with control a scheme classical PID overcomes controller. the nonlinear From the dynamics simulation response with negligible power losses and minimum voltage ripples in comparison with the PID of the results,PV system it is and concludedoffers a thatfaster the transient controller.response proposed SMC nextwith As acontrol negligible scheme step, power overcomes the authors lookthelosses and nonlinear forward to minimum andynamics voltage experimental ripples of thevalidation PV system inofand comparison theoffers results. with a faster the PID controller. transient response with As anegligible next step,powerthe authors losses look forward tovoltage and minimum an experimental validation ofwith ripples in comparison the Author controller. AsH.G.A., PIDContributions: results. the a next R.V.A. step, theandauthors J.H. conceived and designed look forward to an the experiments; experimental H.G.A. and validation of A.T. the performed the simulations; J.P.-R. provided the PSIM simulation tools and access to laboratory; writing-review results. and editing, H.G.A., R.V.A., and J.H.; supervision, R.V.A.; H.G.A. wrote the paper. All authors have read and Author agreed to the published H.G.A., Contributions: version ofR.V.A. and J.H. conceived and designed the experiments; H.G.A. and the manuscript. A.T. performed Author the simulations; Contributions: H.G.A., R.V.A. J.P.-R.andprovided the PSIM J.H. conceived simulation and designedtools and access toH.G.A. the experiments; laboratory; and Funding: This research was funded by the Spanish MINECO/FEDER grant DPI 2016-77271 And the APC was writing-review A.T. performed and the funded from this project. editing, simulations; H.G.A., J.P.-R.R.V.A., providedand J.H.; the PSIMsupervision, simulation R.V.A.; tools H.G.A. and wrote access to the paper. laboratory; All authors haveand writing-review read and agreed editing, H.G.A., to the published R.V.A., and J.H.; version of the manuscript. supervision, R.V.A.; H.G.A. wrote the paper. Acknowledgments: This work was supported by the Spanish MINECO/FEDER grant DPI 2016-77271. The authors All authors thank Santander have read and bank aswas agreed wellfunded to the as the National published Universityversion of the manuscript. of Science and Technology, Islamabad, And Pakistan, Funding: This research by the Spanish MINECO/FEDER grant DPI 2016-77271 the for financial support during the completion of this research work. APC wasThis Funding: funded from was research this project. funded by the Spanish MINECO/FEDER grant DPI 2016-77271 And the Conflicts of Interest: The authors declare no conflict of interest. APC was funded from this project. Processes 2020, 8, 108 13 of 14 References 1. Ekins, P.; Bradshaw, M.J.; Watson, J. Global Energy: Issues, Potentials, and Policy Implications; Oxford University Press: Londong, UK, 2015. 2. Growth of Renewable Energy Sources Generating ‘New World’: IRENA: Tüm Kaynaklar. 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