Inter national J our nal of P o wer Electr onics and Dri v e System (IJPEDS) V ol. 11, No. 2, June 2020, pp. 942 952 ISSN: 2088-8694, DOI: 10.11591/ijpeds.v11.i2.pp942-952 r 942 A no v el fast MPPT strategy used f or grid-connected r esidential PV system applied in mor occo Sana Sahbani 1 , Hassane Mahmoudi 2 , Abdennebi Hasnaoui 3 , Mustapha Kchikach 4 , Hanane Benchraa 5 1,2,5 Electronics Po wer and Control T eam,Department of Electrical Engineering,Mohammadia School of Engineers, Mohammed V Uni v ersity , Rabat, Morocco 1,3,4 Electromechanical Department, Higher National School of Mines, Rabat, Morocco Article Inf o Article history: Recei v ed Jun 26, 2019 Re vised Oct 24, 2019 Accepted No v 8, 2019 K eyw ords: Maximum po wer point tracking Photo v oltaic system Po wer f actor correction Predicti v e current control ABSTRA CT Re g ardless its significant potential for generating rene w able ener gy , Moroccan go v ern- ment prohibited the inj ection of production surplus into the lo w v ol tage (L V) netw ork because it still lack the implementing decreases, that represents one of the princi- pal challenges for residential self-production in the country . The focus of this paper w ork is to introduce and analyze a no v el f ast MPPT strate gy applied in an impro v ed grid-connected Residential PV system respecting the current le gislati v e frame w ork in Morocco, which allo w t o the consumer being an actor in the ener gy transition to w ards a lo w-carbon socie ty by reducing his dependence to the elect rical grid and managing his o wn ener gy consumption ef ficiently by a good switching between photo- v oltaic (P V) source and the grid and therefore making a frame w ork of smart residence management system. The o v erall system is designed to impro v e the ener gy control performance with tw o techniques: the first one uses a no v el high performance con- troller to track the maximum po wer point (MPP) of a photo v oltaic array under f ast irradiation and load changes. Among the adv antages of this proposed controller is the stability of its output v oltage with f ast response speed to the required parameters. The second one uses a Po wer F actor Correction (PFC) circuit to ensure the po wer quality re gulation in the grid side via a predicti v e current control method. Finally , the stability of a closed-loop syste m is simulated and analyzed using commercial softw are of fering suf ficient condi- tions to v alidate a practical stability and rob ustness of the proposed o v erall designed system. This is an open access article under the CC BY -SA license . Corresponding A uthor: Sana Sahbani, Electronics Po wer and Control T eam, Department of Electrical Engineering, Mohammadia School of Engineers, Mohammed V Uni v ersity , Rabat, Morocco. E-mail:sana.sahbani@gmail.com 1. INTR ODUCTION As a result of the demographic dynamics added to human de v elopment and economic gro wth, ener gy consumption in Morocco may lead to an increase a v erage which put the country’ s natural resources under pressure. In order to confront this challenge, the go v ernment has embark ed on series of strate gies and policies to preserv e the e xhaustion of it s finite natural resources to b uild a sustainable economy and ensure access to af fordable, reliable, sustainable and modern ener gy for human well-being. According to the IEA [1], the b uilding sector is the lar gest ener gy consumer with 25% share of total ener gy consumption in Morocco, J ournal homepage: http://ijpeds.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 r 943 including 18% for residential a rea. This ener gy consumption is e xpected to increase quickly in the coming years re g arding considerable ef forts achie v ed to impro v e the population’ s standard of li ving and prospects with multiples acti vities: significant b uilding programs de v elopment; human de v elopment initiati v e; global rural electrification program for e xtending access to electricity and the program to impro v e access to health care and education added to the significant increase and lo wer prices in the le v el of households equipment (w ater heating, refrigeration, . . . etc.) [2]. This accelerated consumption trend can only be met by increasing supply and controlling ener gy con- sumption, Morocco has tak en therefore a global leadership position on climate change mitig ation by setting dif ferent acts and la w of ener gy ef ficienc y and rene w able ener gy for dif ferent sectors and especially for b uild- ing sector [3] such as: La w 47-09 of No v ember 2011 relating to ener gy ef ficienc y in residential and commercial b uildings. It introduces ener gy performance ratings for b uildings, equipment and appliances. The decree no 2-13-874 of No v ember 2015 is about the Thermal Re gulation for Construction in Morocco (TRCM) aiming to optimize heating and cooling necessities in ne w b uilding by impro ving the thermal performances of the en v elope while impro ving thermal comfort and reducing the ener gy cons umption. These la ws, along with a number of other pro visions, are the crucial first steps in the process. The geographical location of Morocco promotes the use of distrib uted rene w able ener gy systems especially photo v oltaic source, that requires further liberalization, particularly increased access to L V netw ork. Then within the implementation frame w ork for the photo v oltaic ener gy de v elopment, the la w No 58-15 amending and supplementing la w No 13-09 on rene w able ener gy w as adopted on December 2015. F or the opening up of the L V netw ork to decentralized producers, the implementing Decree is still being prepared and until this time, no date had yet been fix ed for these pro vi- sions to become ef fecti v e. W ith the e xisting Moroccan re gulatory c o ndi tions, the indi vidual producer is not allo wed to i nject e xcess po wer produced from his rene w able source system in the L V netw ork and cannot become a share- holder in the ener gy sector by selling surplus production to the grid operator neither can intrinsica lly reduce his dependence on po wer generation plants. In the literature, most issues car ried out about b uilding inte grated photo v oltaic (PV) system with bidirectional po wer flo w capability based on in v erter circuit for grid synchro- nization control adding to the maximum po wer point tracking (M PPT) functions [4, 5, 6] and the impact of interconnecting PV to grid re g arding the standardized po wer quality , the po wer grid stability and the safety of equipment [7]. This paper e xamine an impro v ed model designed for grid connected P V , respecting the actual Moroccan re gulatory requirements by k eeping only one direction po wer flo w , starting from generator source to households appliances based on a proposed no v el Maximum Po wer Point T racking (MPPT) technique with higher speed response and stable output v oltage w a v eform of photo v oltaic (PV) systems as well as a good load follo wer . The o v erall system configuration is designed and analyzed using time scale domain simulation of electrical characteristics, sho wing the stability of DC link output v oltage a n d load po wer . The performance of the proposed MPPT control technique and PFC controller circuit are sho wn and e xamined. 2. GRID-CONNECTED PHO T O V OL T AIC SYSTEM Figure 1 i llustrates the general topology of the designed model; it consists of the main follo wing components: the PV array , which generates po wer directly from solar radiation, the boost con v erter , whose switch is operated by the control scheme of the MPPT controller to supply 400V DC distrib ution netw orks. Due to the f act that PV array ef ficienc y mainly depends on irradiance and temperature [8], so that the required v oltage and current are not fed to the loads e v ery time, therefore the L V grid co v er the po wer dif ference between load and PV , follo wed by a single phase diode bridge rectifier , pro viding constant and one w ay po wer flo w for DC-link, from the grid to the load according to Moroccan re gulatory , and then the boost con v erter controller , which is applied to pro vide a po wer f actor correction for rectified current w a v eform. 2.1. PV array The output po wer from a single PV cell is relati v ely small. So the required electri cal ener gy is pro- duced by grouping the PV cells in series and parallel forming the modules. The PV panels are connected together to b uild up the entire PV array and an y desired current v oltage characteristics could be generated [9, 10]. The po wer -v oltage ( P-V) and Current-V oltage (I-V) curv es of the PV array are illustrated in Figure 2. The manuf acturing characteristics measured with the Standard T est Conditions (STC) used in this paper w ork are gi v en in T able 1. A no vel fast MPPT str ate gy used for grid-connected r esidential PV system... (Sana Sahbani) Evaluation Warning : The document was created with Spire.PDF for Python.
944 r ISSN: 2088-8694 Figure 1. The o v erall grid connected PV system configuration scheme Figure 2. P-V and I-V characteristics of the PV array T able 1. Specifications of the photo v oltaic array PV panel parameters V alue Maximum po wer rating Pmax 3254,2 (W) Short circuit current (Isc) 12,18 (A) Open circuit v oltage (V oc) 341.2 (V) V oltage at maximum po wer point Vmp 291,6 (V) Current at maximum po wer point Imp 11.16 (A) 2.2. Maximum po wer point tracking The maximum po wer point sho wn in Figure 2 v aries according to the weather conditions. The ba- sic principle of maximum po wer point tracking (MPPT) algorithm depends on the e xploitation of v oltage and current v ariations caused due to the pulsations of instantaneous po wer . Analyzing these v ariations allo ws us to obtain po wer gradient e xpressed in the (1) and e v aluate whether the solar PV system operates close to the maximum po wer point [11]: @ P P V @ V P V = @ ( V P V I P V ) @ V P V = I P V + V P V @ I P V @ V P V (1) At the maximum po wer point Pmax, the deri v ate of po wer with respect to v oltage is equal to zero, which yields to (2): I P V M = V P V M 4 I P V 4 V P V (2) Int J Po w Elec & Dri Syst, V ol. 11, No. 2, June 2020 : 942 952 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 r 945 Where I P V M and V P V M are respecti v ely the optimal operation current and v oltage of PV array at the condition of maximum po wer output. In addition, the solar cell e xhibi ts non-linear V -I characteristics as sho wn in Figure 2 , therefore the MPPT controller must track the maximum po wer and match the current en vironmental changes [12]. 2.3. MPPT contr oller con v erter The MPPT is achie v ed by using DC-DC Boost con v erter between PV array and the DC output v oltage. It’ s considered as the heart of MPPT hardw are for solar PV applications [13]. From the measured v oltage and current, the MPPT algorithm generates the optimal duty ratio to maintain the electrical quantities at v alues corresponding to the desired parameters [14]. There are man y MPPT methods a v ailable in the literature; the most widely-used techniques are described in [15], the incon v enient of these techniques is the v oltage-ripple emer ging during attempts to identify maximum po wer point. F or instance, con v entional Perturb Observ e (PO) algorithm causes the ripples (oscillations) e v en if it reaches maximum po wer point because of its structure [16]. This dif ficulty increases the po wer losse s and hardens the control actions. Hence, some calculation procedures of con v entional PO algorithm w as modified and the ripples were corrected [17]. The basic circuit diagram of boost con v erter is sho wn in Figure 3, it mainly consi sts of an Inductor L, capacitor C 2 , controllable semiconductor switch S, diode D and load . V D C is the 400V -DC distrib ution netw ork. Figure 3. Boost con v erter circuit Considering the electrical mesh la w of the boost con v erter circuit sho wn abo v e, we obtain the fol lo w- ing equation: V P V L dI P V dt = d V D C (3) Moreo v er , by calculation the a v erage v alue of this equation (3) o v er the switching period interv al [0 ; T ] , it yields to the follo wing (4): 1 T Z T 0 V P V L T Z T 0 dI P V dt = V D C Z T 0 d (4) Where V r ef is the reference v oltage that control directly the switching duty c ycle ratio . Thus: V r ef = Z T 0 d (5) At t = T : The predicted inductor current will be equal to I r ef , which is the internal reference current that will determine the PV output current: V P V 0 L T ( I P V ( t = T ) I P V ( t =0) ) = V D C V r ef (6) Therefore, the operation point of the con v erter by controlling reference v oltage calculated in the fol- lo wing (7); the control of V r ef is formulated as a reference current re gulation I r ef : A no vel fast MPPT str ate gy used for grid-connected r esidential PV system... (Sana Sahbani) Evaluation Warning : The document was created with Spire.PDF for Python.
946 r ISSN: 2088-8694 V r ef = V P V 0 L T ( I r ef I P V 0 ) V D C (7) As e xplained in the flo wchart illustrated in the Figure 4, the reference v alue that the PV will pro vide depends on current needed for residential loads. While the load typically v aries with unkno wn w ay because of the v ari- ability of residents acti vities [18]. The MPPT controller system requires an instantaneous measurement of the load current I Load , which will check whether this measured v alue is higher than the maximum output current I max of the PV array as gi v en v alue, therefore the controller will track the MPP and yields to the follo wing results: I r ef = I P V M (8) Where I P V M is the current calculated in the equation (2). If it is not higher than the maximum output current, the predicted reference current I r ef that the PV controller will trac k will be equal to the load current v alue I Load . Then, the predicted reference v oltage V r ef can be calculated from a predicted reference current I r ef as gi v en in the equation (2) and will increase or decrease the PWM duty c ycle ratio (D) of the switching de vice. Figure 4. Predicti v e control algorithm. 2.4. Grid connected to DC-link utility con v ersion The single-phase diode bridge rectifier used in the proposed configuration is widely used in lo w v olt- age distrib ution systems. Ho we v er , this classical con v erter dra w non-sinusoidal ac input currents, leading to lo w po wer f actors and injection of current harmonics into the utility lines [19]. Therefore, it i s essential to predict the current harmonic le v els produced by these con v erters [20] by associating them with Po wer F ac- tor Correction (PFC) stage based on boost topology with a high switching frequenc y po wer con v ersion. The Int J Po w Elec & Dri Syst, V ol. 11, No. 2, June 2020 : 942 952 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 r 947 major control challenge required of this correcting topology is the capability to follo w precisely a rectified si- nusoidal current reference. The current control techniques ha v e g ained importance in A C-DC con v ersion used for high performance ut ilizations, where the f ast response and high ef ficienc y are important. V arious current control methods ha v e been proposed in PFC circuits, the most commonly studied are : linear control [21], h ysteresis control [22] and predicti v e control [23], a comparati v e study gi v en by [24] sho ws that the predicti v e control of fers a good performances re g arding to the others proposed control methods in terms of input current harmonic content and po wer quality . Therefore this technique mak es an e xtremely attracti v e choice for our proposed model. The circuit scheme considered in the paper w ork is illustrated in Figure 5. It’ s realized by cascading single-phase diode bridge rectifier and boost con v erter with a PFC controller based on predicti v e current control. Figure 5. Boost con v erter with predicti v e control. The switch v oltage reference V sw r ef at ( k + 1) th instant is predicted at ( k ) th instant itself for the circuit sho wn in Figure 5 by means of equation (9): V sw r ef = V R ( t ) L T ( i L ( t ) i L ( t ) ) (9) Where: V R : Rectified v oltage. i L : Inductor current. i L : The reference current that the inductor current i L should follo w which is proportional to t he rectified v oltage. T : Modulation period (in v erse of switching frequenc y). As it will be sho wn in simulation results, this technique mak es it possible to obtain good performa n c es such as the stability of the system, precise beha vior of the currents, input and output v oltage. 3. O VERALL SYSTEM CONCEPTION The o v erall system design of grid-connected PV using commercial softw are is gi v en in Figure 6. The grid-connected PV system consists of a 3kW PV array connected to a 400V DC-link for supplying po wer to residential load R D C through a boost con v erter controlling the po wer deli v ered from the PV using a no v el MPPT controller . On the right side of the system scheme, the 220V A C source pro vided from single phase grid ensure local supply continuity when there is a lack of irradiation, the deli v ered po wer is con v erted and stepped up to 400V DC via diode bridge rectifier associated to the boost con v erter with a PFC controller . The specifications and the components used in the proposed design are illustrated in T able 2: A no vel fast MPPT str ate gy used for grid-connected r esidential PV system... (Sana Sahbani) Evaluation Warning : The document was created with Spire.PDF for Python.
948 r ISSN: 2088-8694 Figure 6. The o v erall grid connected PV system scheme. T able 2. Specifications of the circuit components Circuit parameters V alue Stray capacitance C1 1 mF Boost inductor L 5 mH DC link capacitance (C2) 10 F DC link Full Load R D C 48 DC link P artial Load R D C 88 MPPT Boost con v erter switching frequenc y 10 K hz DC link V oltage 400 V Grid nominal v oltage 220 V r ms PFC Boost con v etrer switching frequenc y 10 K hz Boost inductor L1 5 mH Stray capacitance Cin 10 nF Output Capacitor C 10 mF T ime step simulation Ts 1 s 4. SIMULA TION RESUL TS AND AN AL YSIS The aim of these simulations results is to v erify the performance of the proposed controllers designed in pre vious sections as the proposed MPPT strate gy performances re g arding v oltage stability and response speed and the good fol lo wing of the reference. And also the PFC con v erter performances in forcing the input current to follo w the w a v e shape of the rectified input v oltage added to the automatic switching between grid and PV for pro viding stable po wer to the loads when the en vironmental conditions are changing. Therefore; the system is analyzed for dif ferent scenarios considering irradiation and load changes: 4.1. Ov erall grid connected system operating with full-load and irradiation change The controllers capability is tested wit h a full residential load under solar irradiation change condi- tions. As sho wn by Figure 7; the system w as initially subjected to a sun irradiation condit ion of 500 W =m 2 until the time t = 5 s when it jump to 1000 W =m 2 (using step change), simultaneously the output current, v oltage and po wer w a v eforms of the PV array are displayed . It can be seen from the diagram that the po wer supplied by the PV array v aries according to the intensity of the en vironment’ s light. At 1000W/m2 of irradia- tion with full-load condition, the controller is able to track the hi g he st MPP v oltage and current v alues of 290 V and 11 A , resulting in a po wer of 3200 W with the least MPP tracking time equal to 0 : 02 s and non-oscillatory response around the MPPT . Once the system reached its steady state, it pro v es the sta bility and the v elocity of the proposed MPPT strate gy . W ith the same conditions mentioned abo v e; the DC-link system simulation results with the proposed MPPT controll er are sho wn in Figure 8. it can be seen that despite the decresase of PV P anel po wer generated at times when irradiation le v el is weak ( 500 W =m 2 ) , the response obtained sho ws the stability of the DC-link output v oltage, which is close to 400 V . This v oltage v alue ensures the good switching between A C grid and PV panel in pro viding stable po wer to residential load. Int J Po w Elec & Dri Syst, V ol. 11, No. 2, June 2020 : 942 952 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 r 949 Figure 7. (a) Solar irradiation change, (b) The output current, v oltage and po wer of the PV array for full-load Figure 8. Output v oltage, current and po wer in DC link for full-load In another hand, fr om the PFC performances sho wn in Figure 9, the load is supplied by the A C grid because of the lo w irradiation le v el and the resulting w a v eforms sho ws that the rectified current follo ws the rectified v oltage w a v e shape and are in phase, which, e xplain the good tracking capabilities of the Predicti v e Current Control method when the irradiation conditions change quickly to the optimal condition of sun irra- diation. The de vice find the maximum po wer point of the PV panel then the rectified grid current tends to be zero, e xplaining that in this duration, the electrical grid becomes idle and the po wer source is switched to the PV generator . A no vel fast MPPT str ate gy used for grid-connected r esidential PV system... (Sana Sahbani) Evaluation Warning : The document was created with Spire.PDF for Python.
950 r ISSN: 2088-8694 Figure 9. Rectified v oltage and current w a v eforms. 4.2. Ov erall grid connected system operating with partial load considering optimal irradiation condi- tion As illustrated by Figure 4 in the pre vious paragraph, the proposed MPPT controller complies with both full load and partial load. W ith standard test condi tions ( 1000 W =m 2 solar irradiation) we use a partial load of 88 , so the needed current for a fix ed DC-v oltage of 400 V is 4 : 5 A , which is smaller than 8 A the maximum output current of the PV . In Fi gure 10, the DC load dra ws a ne w smaller po wer v alue from the PV array (the PV no w is not w orking at MPP as there’ s no where for the e xcess po wer to go). Therefore,the MPPT controller will adjust the duty c ycle of the con v erter to meet the required load at constant output v oltage, then the PV automatically becomes a load follo wer and operate at the point where the output po wer matches the load, in this e xample the output po wer is close to 1800 W . Figure 10. (a) Output current for partial-load,(b)the PV array current, v oltage and po wer . Int J Po w Elec & Dri Syst, V ol. 11, No. 2, June 2020 : 942 952 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Po w Elec & Dri Syst ISSN: 2088-8694 r 951 5. CONCLUSION AND PERSPECTIVE In this paper , we ha v e de v eloped a circuit design of a single-phase grid connected PV for home en- er gy management system within the Moroccan conte xt of rene w able ener gy inte gration, that enables users to economies ener gy consumption and reduce their dependence on fossil fuel. This paper has presented the mod- eling and control design of tw o-stage: PV system based on a boost con v erter with the proposition of a no v el MPPT technique, with a constant PV output v oltage based on predicti v e control method, to track e v en the MPP of a PV or another operating point depending on load change and a single-phase grid connected diode rectifier with PFC controller for re gulating the DC link v oltage and the rectified current w a v eform with a good track of the reference. The tw o stages are connected to a residential load and depending on meteorologica l conditions the y ensure a good switching between them in pro viding po wer supplying load. Based on the abo v e analysis of the simulation results, the controllers designed in each stage of this paper of fers good performances in term of speed of con v er gence to the required operating v oltage and current parameters added the stability of their w a v eforms under v arious atmospheric and operating conditions with minimum tracking time. Hence, this de- signed system can promote the de v elopment of dis trib uted photo v oltaic po wer generation in Morocco and the residential user can forecast his electrical ener gy consumption and therefore reduce his electrical bill and be an actor in sa ving the en vironment. As a future w ork, controlling the use of households will be proposed in order to use ef ficiently the PV generator when we ha v e f a v orable meteorol o gi cal conditions by e xploiting the Maximum Po wer T racking, and use only necessary loads at night. T o enhance the reliability and stability of DC-link v oltage, the battery system can be added to this model in order to maintain the DC link v oltage when occurs a po wer grid outages. REFERENCES [1] IEA [Online]. a v ailible ”www .iea.or g. [2] ONEE National Of fice of Electricity and W ater [Online]. a v ailible ”www .onee.or g.ma. [3] The Ministry of Ener gy , Mines and Sustainable De v elopment [Online]. a v ailible ”www .mem.go v .ma. [4] C. Limsakul, R. Songprak orp, A. Sangsw ang and P . P arin ya, ”Impact of photo v oltaic grid-connected po wer fluctuation on system frequenc y de viation in contiguous po wer systems, IECON 2015-41st Annual Conference of the IEEE Industrial Electronics Society , P003236-003241, 2015. [5] A. Chouder , S. Silv estre, N. Sadaoui and L. Rahmani, ”Modeling and simulation of a grid connected PV system based on the e v aluation of main PV module parameters, Simulation Modelling Practice and Theory Else vier , v ol. 20, no. 1, pp. 46-58, 2012. [6] F . Blaabjer g, R. T eodorescu, M. Liserre and A. T imb us, ”Ov ervie w of control and grid synchronization for distrib uted po wer generation systems, IEEE T ransactions on industrial electronics , v ol. 53, no. 5, pp. 1398-1409, 2006. [7] S. B. Kjaer , J. K. Pedersen and F . Blaabjer g, A re vie w of single-phase grid-connected in v erters for photo v oltaic modules, IEEE transactions on industry applications, v ol. 41, no. 5, pp. 1292-1306, 2005. [8] B. V . Chikate and Y . Sada w arte, ”The f actors af fecting the performance of solar cell, International journal of computer applications, v ol. 1, no. 1, pp. 0975-8887, 2015. [9] E. K outroulis and F . B laabjer g, ”A ne w technique for tracking the global maxi mum po wer point of PV arrays operating under partial-shading conditions, IEEE Journal of Photo v oltaics, v ol. 2, no. 2, pp. 184- 190, 2012. [10] D. La Manna, V . L. V igni, E. R.Sanse v erino, V . Di Dio and P . Romano, ”‘Rec o nfi gu r able electrical in- terconnection strate gies for photo v oltaic arrays: A re vie w , Rene w able and Sustainable Ener gy Re vie ws, v ol. 33, pp. 412-426, 2014. [11] D. Casadei, G. Grandi and C. Rossi, ”Single-phase single-stage photo v oltaic generation system based on a ripple correlation control maximum po wer point tracking, IEEE T ransactions on Ener gy Con v ersion, v ol. 21, no. 2, pp. 562-568, 2006. [12] C. L. K uo, C. H. Lin,, H. T . Y au and J. L. Chen, ”Using self-synchronization error dynamics formula- tion based controller for maximum photo v oltaic po wer tracking in micro-grid systems, IEEE Journal on Emer ging and Selected T opics in Circuits and Systems, v ol. 3, no. 3, pp. 459-467, 2013. [13] D. Gaikw ad, M. Cha v an and M. Gaikw ad, ”Hardw are implementation of dc-dc con v erter for mppt in pv applications, IEEE Global Conference on W ireless Computing and Netw orking Proceedings, pp. 16–20, 2014. A no vel fast MPPT str ate gy used for grid-connected r esidential PV system... (Sana Sahbani) Evaluation Warning : The document was created with Spire.PDF for Python.