Fuzzy Logic Approach for Maximum Power Point Tracking Implemented in a Real Time Photovoltaic System

applied sciences Article Fuzzy Logic Approach for Maximum Power Point Tracking Implemented in a Real Time Photovoltaic System Cristian Napole * and Mohamed Derbeli and Oscar Barambones   Citation: Napole, C.; Derbeli, M.; Barambones, O. Fuzzy Logic Approach for Maximum Power Point Tracking Implemented in a Real Time Photovoltaic System. Appl. Sci. 2021, 11, 5927. https://doi.org/10.3390/ app11135927 Academic Editor: Ludmila Dymova Received: 10 June 2021 Accepted: 23 June 2021 Published: 25 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). System Engineering and Automation Deparment, Faculty of Engineering of Vitoria-Gasteiz, Basque Country University (UPV/EHU), 01006 Vitoria-Gasteiz, Spain; [email protected] (M.D.); oscar[email protected] (O.B.) *Correspondence: [email protected] Abstract: Photovoltaic (PV) panels are devices capable of converting solar energy to electrical without emissions generation, and can last for several years as there are no moving parts involved. The best performance can be achieved through maximum power point tracking (MPPT), which is challenging because it requires a sophisticated design, since the solar energy fluctuates throughout the day. The PV used in this research provided a low output voltage and, therefore, a boost-converter with a non-linear control law was implemented to reach a suitable end-used voltage. The main contribution of this research is a novel MPPT method based on a voltage reference estimator (VRE) combined with a fuzzy logic controller (FLC) in order to obtain the maximum power from the PV panel. This structure was implemented in a dSpace 1104 board for a commercial PV panel, PEIMAR SG340P. The scheme was compared with a conventional perturbation and observation (P&O) and with a sliding mode controller (SMC), where the outcomes demonstrated the superiority of the proposed advanced method. Keywords: FLC; PV system; MPPT; P&O; nonlinear control; voltage reference estimator; boost converter 1. Introduction The increasing degree of pollution throughout the last decades made a change of direction in the policies of energy production, where renewables are preferred over the conventional ones. Actually, it an increment of 25% in the world energy consumption is expected for 2040, and the target is that clean ones can provide 40% of the whole production [ 1 ]. Researchers also forecast that solar PV panels could generate 15% of the global demand in 2050 [2]. Despite PV panels being highly dependent on sun irradiation (which fluctuates sufficiently depending on the geographical location), major advantages include the low maintenance and a large life-span service [ 3 ]. In several applications where a PV output voltage is unsuitable, DC–DC boost converters are used to step-up this variable, thus increasing the efficiency of the whole system. The voltage growth is carried out through a switching of electric circuits which indicates that the end-user voltage is dependent on a duty cycle [ 4 ]. The switching signal can be managed by a pulse-width-modulation (PWM) generator; this implies that a suitable control law can be designed with the target of maximizing the performance of the MPPT. Linear strategies can be a suitable first option for MPPT control. Despite the conventionality of proportional–integral–derivative (PID) controllers, they have been widely used in PV power systems. For instance, the author of [ 5 ] produced a linear simulation of a DC–DC converter with a PV panel; despite the controller being achieved through classic Bode analysis, the results reported a reduction of overshoot and settling time. Likewise, an advanced linear quadratic regulator (LQR) has been developed for boost-converters [ 6 ]; although the measurement of the performance of this algorithm needs experimental validation, the simulation outcomes revealed increments in robustness in comparison with similar Appl. Sci. 2021,11, 5927. https://doi.org/10.3390/app11135927 https://www.mdpi.com/journal/applsci Appl. Sci. 2021,11, 5927 2 of 18 strategies. However, linear controllers produce certain issues for real boost converters due to inconsistencies such as the intrinsic non-minimum phase [ 7 ]. Additionally, there are nonlinearities, such as solar energy, that depend on everyday weather; panels have assorted voltage-current oscillations and boost converters have a discontinuous action due to the switching [8,9]. Nonlinear controllers are known not only for the performance improvement of boost converters but also for their practical implementation [ 10 ]. The P&O algorithm is a reliable nonlinear algorithm for MPPT that compares previous power measurements to current ones to find the MPP, using the duty cycle as a variable [ 11 ]. In the field of PV panels, this algorithm has even been studied in advanced and complex systems, such as PVs in space applications, as the authors of [ 12 ] explained in their research. The combination of this algorithm with a solar tracker provided suitable results. Due to its properties, it has also been used in assorted renewable systems such as wave energy generators [ 13 ], PV based microgrids [ 14 ], wind generators [ 15 ], and so forth. Despite its robustness and practicality, the downsides of P&O are related to the generated perturbations or partial shadow cases, which can produce, respectively, oscillations around the MPP or fall to a local maximum, which produces a reduction in accuracy [16,17]. Another classic nonlinear structure is SMC, which not only enhances the dynamics of a system but also reduces the effects of disturbances and uncertainties [ 18 ]. For instance, Derbeli et al. [ 19 ] proposed SMC for a boost-converter used in a fuel cell. The outcomes showed that one of the primary disadvantages of these structures is the chattering, which causes extra energy consumption. Even though the chattering can be reduced by using high order sliding modes—which have been implemented in the past [ 20 ]—it is impossible to eliminate this phenomenon since there are always unmodeled dynamics involved with control digitalization [ 21 ]. Backstepping depicts another nonlinear structure, known for its robustness in terms of unmodeled dynamics and uncertainties, based on a Lyapunov approach by splitting the main system into subdivisions to achieve a suitable design [ 22 ]. In practical terms, backstepping has been implemented in a boost converter by the authors of [ 23 ], where the robustness and settling time have been improved; nevertheless, one of the main drawbacks of the backstepping is the complex design of the control law. Another non-linear technique is FLC, a practical, ruled-based approach in which the configuration is dependent on the operator knowledge with regards to the main system [ 24 , 25 ]. FLC has been used in adaptive experimental DC–DC boost converters, where the inductor features changed to achieve high efficiencies and the outcomes showed significant enhancements [ 26 ]. In terms of PV, the research conducted by the authors of [ 27 ] was based on an analysis of the power forecast over a year, where they employed an adaptive neural fuzzy inference system and accurate results were achieved. Concerning MPPT for PV systems linked with boost converters, FLC was used by the authors of [ 28 ], where they showed that the outcomes developed a fast dynamic response and ensured the robustness. FLC has also been embedded for a PV battery system in a study based on an optimisation [ 29 ]; in this case, the state of charge and consumption were studied and the results revealed significant improvements. This research is focused on a type-1 FLC, which is known for its higher performance compared to conventional controllers due to its capability to manage uncertainties through rules [ 30 , 31 ]. A VRE was designed with real data from the PV panel and was assembled with a type-1 FLC, an error-based controller used for tracking. The first comparison was performed against a P&O, as it is commonly used for the comparison of new MPPT controllers [ 32 , 33 ]. The second contrast was executed with an SMC combined with the VRE to highlight the benefits of the proposed FLC. The drawbacks are related to sudden fluctuations around the maximum power point (MPP) due to sudden fluctuations in the irradiation or under partial shadowing conditions [33,34]. This research paper is structured as follows: Section 2describes the hardware used and its interconnection, and presents a theoretical explanation of the models applied for the PV and the boost converter with further details about the controllers handled for the MPPT Appl. Sci. 2021,11, 5927 3 of 18 tracking. Section 3presents an experimental analysis of the PV features such as voltage– current and voltage–power curves, which are significant for generating a VRE. This section also concludes with the outcomes gathered with the implemented controllers. Finally, Section 4comprises a summary of the highlights accomplished throughout this research. 2. Materials and Methods 2.1. Hardware Description Figure 1shows the workflow of the hardware involved in the experiments. The PV panel used was a PEIMAR SG340P, the modules of which were produced from polycrystalline silicon, which represents suitable versatility and efficiency. These panels are frequently employed in commercial, residential and industrial installations. Since the structural design is focused on the lightness and robustness, it has high stiffness and a feasible installation. Supplementary technical information about this device is detailed in Table 1. Figure 1. Software–hardware workflow diagram. Table 1. Peimar SG340P Specifications. Properties Values Units Dimensions 156 ×156 mm Maximum power 340 W Open circuit voltage 45.2 V Max power voltage 36.7 V Max power current 9.28 A Number of cells in series 6 unit Number of cells in parallel 12 units Isc 9.9 A The temperature and irradiation were measured with a silicon external sensor from the manufacturer Ingenieurbüro Si-V-10TC-T, which is reliable for PV variables monitoring. This module is formed of a monocrystalline silicon solar cell that is connected to a shunt. It is also capable of correcting the measurements due to an active temperature compensator, Appl. Sci. 2021,11, 5927 4 of 18 which works through a sensor that is laminated to the back surface of the module. As a consequence of this action, it provides additional information about the temperature. Both measured signals are transmitted as voltage variations in the range of 0–10 V. Further details are provided in Table 2. Table 2. Ingenieurbüro Si-V-10TC-T Specifications. Properties Values Units Voltage supply 12 to 28 VDC Irradiance measurement range Up to 1500 W/m2 Temperature measurement range −40 to 90 ◦C Regarding the boost converter, a TEP-192 produced by the research group of Huelva University (Spain) was implemented in this case. This device has a PWM switching input of 20 kHz for the control process and works with input/output signals of 0–10 V. The module has two Schottky diodes MURF1560 GT, 2 TK capacitances (1500 µ F and 3000 µ F), six PVC2-564-08 inductances and an HGT40N60B3 IGBT. Voltage and current lectures are provided in signals from 0 to 10 V. Additional technical data on this converter are described in Table 3. Table 3. TEP-192 Details. Properties Values Units Switching frequency 20 kHz Maximum input voltage 60 V Maximum input current 30 A Maximum output voltage 250 V Maximum output current 30 A To close the electric circuit, an 8500B by BK Precision was used since it is a DC programmable load with wide flexibility and it is suitable for testing and evaluating DC power sources such as DC–DC boost converters, batteries, chargers and especially for PV panels. This programmable resistance includes reverse polarity protection to protect the system from temperature, power, voltage and current overruns. The technical specifications are presented in Table 4. Table 4. BK 8500B Specifications. Properties Values Units Power 300 Rated Voltage 500 V Rated Current 15 A Input Voltage 0–150 V Input Current 0–15 A A Resistance range 0.05–10 Ω In the acquisition and control signal generation, a dSpace DSP1104 was linked because it is convenient hardware for collecting and generating analog signals, which vary between 0 and 10 V. Additionally, external software designed in Simulink can be embedded for control purposes. This platform also supports Real-Time-Interface (RTI) and ControlDesk, where the latter is the software used for observing data in real time. All the experiments were carried out with a sampling frequency of 10 kHz as this satisfies the requirements for the quality of the data acquired and the hardware limitations. Appl. Sci. 2021,11, 5927 5 of 18 2.2. PV Model The single diode model was considered for this study since it provides accuracy and simplicity [ 35 ]. This theory suggests that PV should be considered as a DC source of an electric circuit, as shown in Figure 2, which produces a current Iph , generated by the irradiation of the sun. In addition, two resistances are involved, where Rsh is related to the leakage current of the diode of the p-n interface [ 36 ] and Rs represents the resistance athwart the PV [ 37 ]; the latter causes a detrimental phenomenon in terms of the maximum power of the system [38]. Figure 2. PV Model. The Kirchoff current law provides Equation (1) , where the Ish and Ic are defined according to the research of [39]. Ic=Iph −Id−Ish (1) Ic=Iph −Ioeq(V+RsIc) αKTc−1−V+RsIc Rsh , (2) where Io ,K,qand Tc are the reverse saturation current, Boltzmann constant, elementary charge and the operating temperature, respectively [ 40 ]. The generated current from the PV panel is also expressed as Equation (3) , where G/GSRC represents the relation of the solar radiance measured and the radiance at standard rating conditions (SRC); the Isc_re f is the short circuit current of the PV and Tre f is the PV temperature, both variables at SRC [ 41 ]. The term kI_re f comprises a thermal factor of the short circuit current. Iph =G Gre f Isc_re f +kI_re f (T−Tre f ). (3) A PV panel was built with several modules in parallel ( Np ) and in series ( Ns ), which led to an output current ( Im ) and voltage ( Vm ) of the whole module based on Equation (4) . Therefore, with the previous equations, the output current of the PVG can be expressed as Equation (5). Im=NpIc Vm=NsVc (4) Ic=IphNp−NpIoeq(V+RsIc) αKTc−1−NpV+RsIc Rsh . (5) 2.3. Boost Converter Model In this investigation, a converter was used to transfer the energy from the PV panel to the resistive load. The electrical configuration is a boost type that targets a voltage step up from the source to deliver a suitable end-used voltage. The relationship between the input and output is given by the duty cycle (d) through Equation (6) . This variable is dependent Appl. Sci. 2021,11, 5927 6 of 18 on a PWM signal generator, which is controlled through a physical device, which, in this case, is a metal–oxide–silicon field-effect transistor (MOSFET). Certainly, the value of d was bounded between 0.1 and 0.9 for the continuous conduction mode. Vout =Vin 1−d. (6) The state–space representation of the boost converter is expressed as in Equation (7) , such that x1=Iin and x2=Vout [20].                ˙ x="0dc−1 L 1−dc C −1 RC #"x1 x2#+"1 L 0#Vin y=h0 1i"x1 x2#. (7) 2.4. Type-1 Fuzzy Controller FLC controllers are sterling, as their configuration is based on the designer’s experience rather than knowledge of the system’s mathematical model. The implemented type-1 fuzzy controller (shown in Figure 3) uses normalized rules in its structure and, thus, scale factors Ke and Kd are used for the inputs, which are the error and its derivative. An extra output scale factor Kb was also used to regulate the control signal in terms of the required performance. The fuzzy block includes three consequent modules, which are the fuzzification, inference and defuzzification. The first changes the inputs into fuzzy inputs to designate the degree of the membership; for this case, overlapped triangular and uniformly discretized (between − 1 and 1) functions are based on negative big (NB), negative medium (NM), negative small (NS), zero (Z), positive small (PS), positive medium (PM) and positive big (PB); this resulted in 25 adapted rules, which are shown in Table 5. The inference is the mechanism by which linguistic rules are evaluated according to the results obtained in the previous step of an if–then type [ 42 ]. Finally, the defuzzification comprises the stage at which the linguistic expressions are translated into numerical values for the output; in this case, equidistant and discretized constant outputs were configured in a range between − 1 and 1. Figure 3. Type-1 FLC Structure. Table 5. FLC linguistic rules. E\˙ ENB NS Z PS PB NB NB NM NM NS Z NS NM NM NS Z Z Z NM NS Z PS PM PS Z Z PS PM PM PB Z PS PM PM PB Appl. Sci. 2021,11, 5927 7 of 18 FLC architecture was implemented as in the schematic diagram of Figure 4. The voltage reference estimator will be explained in further sections as it is related to the features gathered from the PV panel. Figure 4. Implementation architecture of FLC controller. 2.5. Perturbation and Observe Algorithm This algorithm is based on an intentional and periodical perturbation on the control command with a following observation and evaluation of the system output [ 43 ]. Applied to the PV system, the perturbation is generated through a change in the voltage Vin(k) and current Iin(k) , such that the power of the PV is measured. This implies that the slope ∆P/∆V can be calculated, which helps with knowing whether the MPP is achieved, as Figure 5shows. Figure 5. Power–Voltage curve with the P&O mechanism to reach the MPP. Based on the previous description and on the detailed logic of Figure 6, the knowledge of Pin(k) and Vin(k) and its delay in k− 1 allows for the calculation of the mentioned slope. Therefore, if the latter mentioned value is positive, the duty cycle d(which modifies the voltage by Equation (6) ) will increase such that the algorithm output u=d+∆d and aims to reach the MPP; on the contrary, when the position is at the right side of the MPP, the control signal decreases through u=d+∆d. Appl. Sci. 2021,11, 5927 8 of 18 Figure 6. Flowchart of P&O algorithm. 2.6. Sliding Mode Controller Considering that the error is defined as Equation (8) , where Vre f is the reference voltage, then an integral sliding surface is established through Equation (9) such that λ>0. e=Vre f −Vin, (8) S=e−λZe·dt. (9) According to Slotine et al. [ 44 ], the control signal is composed of an equivalent ueq and a switching term usw , which is defined in Equation (10) . The first mentioned is gathered through the condition ˙ S= 0 [ 45 ]; the switching, which guarantees robustness, is expressed in Equation (11). u=ueq +usw (10) usw =−K·sign(S). (11) As previously mentioned, obtaining the equivalent control signal implies that the surface derivative should be equal to zero. Therefore, as the error was formerly expressed in Equation (8) , and with the usage of the system in Equation (7) , the equivalent control term is obtained as follows. ueq =−1 x2(Vin +λLe −x2). (12) 3. Results 3.1. Analysis of PV Features and Voltage Reference Estimator The characteristics curves shown in Figure 7were obtained by a considerable value of resistance linked to the PV system; this value was decreased gradually while the data were being recorded. Simultaneously, the environment temperature and irradiation were gathered, which varied, respectively, between 14.6 ◦ C and 36.6 ◦ C and from 64 W/m 2 to 808 W/m2. Figure 7a indicates the relation between the voltage and the current where three sections are distinguished and were labeled in the research conducted by the authors of [ 46 ]. The first is called the current source part, where this feature tends to stay constant; the second one, known as the knee of the I-V curve, is the section where the MPP is achieved; and finally, the voltage source part is where the current–voltage is linearly related. Along the current source section, this tends to stay almost constant between 0 V and 35 V. Appl. Sci. 2021,11, 5927 9 of 18 However, this section is highly dependent on the irradiation, which, ideally, lean these curves upwards, whereas the temperature shifts in a horizontal movement [ 47 ]. The knee and the voltage source part are mostly conditioned by the temperature, which moves the curves to the right hand side of the graph [48]. Figure 7b shows the voltage–power curve where, in this case, the irradiation leans the curves upwards and the slope of the initial linear behaviour ascends. Nevertheless, the temperature influences a diagonal drive of the curves. Therefore, this means that the irradiation moves the MPP on a vertical axis, whereas the temperature moves the curves on an slanted axis. Figure 7. PV panel characteristic curves, where: (a) voltage-current; (b) voltage–power. Formerly, the authors have been working with a current reference estimator in power sources such as proton exchange membrane fuel cells (PEMFC), where the output reference was dependent on the temperature [ 23 , 49 ]. In this case, a VRE was developed by highlighting the MPP points from 790 curves like those in Figure 7b, which varied with the radiation, and then a surface Vre f _MPP =f(P , T) was constructed. This function was attained with the Matlab Curve Fitting Toolbox since it employs an optimized solver to achieve suitable parameters that could reach the best fit quality for curves and surfaces. The framework provided a polynomial surface represented by Equation (13) ; these parameters were obtained through an optimization of performance metrics to acquire a suitable goodness of fitting (GOF); these are the sum of squared errors (SSE), R-square, adjusted R-square and root mean square of the errors (RMSE). Table 6provides the obtained metric values, which are appropriate because the SSE and the RMSE should be minimum whereas the R-square and its adjusted version should be near the unit [ 50 – 52 ]. Furthermore, the coefficients of Equation (13) are also exhibited with 95% confidence bounds. The representation of the surface is shown in Figure 8based on voltage, power and temperature. f(x,y) = p00 +p10 ·x+p01 ·y+p20 ·x2+p11 ·x·y+p30 ·x3+p21 ·x2·y. (13) Appl. Sci. 2021,11, 5927 16 of 18 Abbreviations The following abbreviations are used in this manuscript: PV Photovoltaic MPPT Maximum power point tracking VRE Voltage reference estimator FLC Fuzzy logic controller P&O Perturbation and observation PWM Pulse-width-modulation PID Proportional-integral-derivative LQR Linear quadratic regulator SMC Sliding mode control RTI Real-time-observation SRC Standard rating conditions MOSFET Metal-oxide-silicon field-effect transistor NB Negative Big NM Negative Medium NS Negative Small Z Zero PS Positive Small PM Positive Medium PB Positive Big MPP Maximum power point PEMFC Proton exchange membrane fuel cell GOF Goodness of fitting SSE Sum of the squared errors RMSE Root mean squared of the errors References 1. Garcia, Y.; Dufo-López, R.; Bernal-Agustín, J. Energy Management in Microgrids with Renewable Energy Sources: A Literature Review. Appl. Sci. 2019,9, 3854. [CrossRef] 2. Gielen, D.; Boshell, F.; Saygin, D.; Bazilian, M.D.; Wagner, N.; Gorini, R. 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