Maximum power point tracking of PV system under partial shading conditions through flower pollination algorithm

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1 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Protection nd Control of Modern Power Systems ORIGINAL RESEARCH Mximum power point trcking of PV system under prtil shding conditions through flower pollintion lgorithm Liqun Shng *, Weiwei Zhu, Pengwei Li nd Hngchen Guo Open Access Astrct For mximum utiliztion of solr energy, photovoltic (PV) power systems should e operted t the mximum power point (MPP) which cn e chieved using mximum power point trcking (MPPT) methods. However, the occurrence of multi-pek on P-V curve of PV rry due to the chnging environmentl conditions such s eing prtilly shded increses the complexity of the trcking process. The glol MPP cnnot lwys e chieved y the conventionl MPPT methods. Therefore novel MPPT method for PV systems using flower pollintion (FP) lgorithm is proposed in this pper nd the Levy flight is used to improve the convergence of FP lgorithm. MPPT model of the PV system is estlished in MATLAB to verify the effectiveness of the proposed method, nd the proposed method is compred with two well estlished MPPT methods. The simultion results indicte tht the proposed MPPT method cn quickly trck the chnges in externl environment nd effectively hndle the prtilly shded condition. Keywords: Photovoltic (PV), mximum power point trcking (MPPT), prtilly shded condition, flower pollintion (FP) 1 Introduction With the energy crisis nd environmentl pollution ecoming more nd more serious, there hve een significnt efforts in exploring new nd green energy. As kind of green energy solr energy is highly vlued for its dvntges of zero pollution, no regionl restriction nd convenient utiliztion [1]. Photovoltic (PV) power genertion is the most common form of solr energy utiliztion. Since the output power of single solr cell is low, it is necessry to connect multiple solr cells in series nd in prllel to estlish sic unit of PV module. In prctice, multiple PV modules re connected in series nd in prllel to form PV rry ccording to the requirements of voltge nd power, nd the PV rry is then converted to pproprite voltge y the power electronic conversion device to supply lods [2]. In order to improve the efficiency of PV power genertion, PV is expected to work t the mximum power point (MPP) ll the time. The most widely used methods of mximum power point trcking (MPPT) t present re pertur nd oserve (P&O) [3, * Correspondence: shnglq@xust.edu.cn Xi n University of Science & Technology, Xi n, Chin 4], hill climing (HC) [5, 6] nd incrementl conductnce (INC) [7]. Under uniform irrdition condition, the power-voltge (P-V) chrcteristic of PV rry hs only one pek point, nd the MPP of PV rry cn e trcked ccurtely y using the ove conventionl methods. However, in prctice, due to the chnging environments such s the prtil shding of clouds, trees, uildings nd dust covering, the P-V curve of PV rry hs multimodl chrcteristic. Using the trditionl MPPT methods, MPP trcking cn esily fll into locl pek point nd result in the reduction of solr energy utiliztion. Therefore, how to void flling into the locl optimum nd to find the glol MPP efficiently is prticulrly importnt [8]. Reference [9] dopted dul-lgorithm MPPT control model comining glol prticle swrm optimiztion (PSO) nd locl HC mode to serch the glol MPP ccurtely. Reference [10] comined differentil evolution nd PSO lgorithm to etter dpt to sttic nd dynmic environments for MPP trcking. Reference [11] proposed n improved dynmic multi-pek MPPT method. It comines the three-point method with the PSO lgorithm, nd dopts closed-loop power control to trck The Author(s) Open Access This rticle is distriuted under the terms of the Cretive Commons Attriution 4.0 Interntionl License ( which permits unrestricted use, distriution, nd reproduction in ny medium, provided you give pproprite credit to the originl uthor(s) nd the source, provide link to the Cretive Commons license, nd indicte if chnges were mde.

2 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Pge 2 of 7 the glol MPP nd optimize the dynmic chrcteristics effectively during continuous irrdince chnge. The convergence time nd optiml vlue precision of the ove three methods were improved through etter PSO lgorithms, ut the convergence time is still reltively long, nd setting the initil position of prticles is difficult. Other methods such s fuzzy logic control (FLC) [12], rtificil ee colony (ABC) [13], neurl network (NN) [14] nd nt-colony optimiztion (ACO) [15] were used for glol optimiztion nd hve proved to e le to chieve good results. In this pper, novel MPPT method using flower pollintion (FP) lgorithm is proposed. An effective itertive termintion strtegy is developed to reduce the power oscilltion of the system when the system hs reched stle point. Simultion results show tht the proposed MPPT method cn trck the glol MPP rpidly nd ccurtely under irrdince chnge nd prtilly shded conditions. 2 Modeling of PV module The single diode equivlent circuit for the most common monocrystlline silicon PV cells is shown in Fig. 1. The output current of Fig. 1 cn e written s, I pv ¼ I ph I 0 exp qu pv þ R s I 1 U pv þ R s I AKT R p ð1þ where I pv is the PV cell output current, I ph is the photocurrent, nd I 0 is the reverse sturtion current. q is the chrge of n electron nd U pv is the PV cell work voltge. A is the idelity fctor, K is the Boltzmnn s constnt, T is the cell temperture, R s nd R p re the equlized series nd prllel resistnces, respectively [16]. The PV cell pnel chosen in this pper is the EGing-50 W. Its prmeters under stndrd test conditions re shown in Tle 1, nd the output chrcteristics of the PV rry composed of this type of pnels in series nd prllel re shown in Fig. 2. It cn e seen from Fig. 2 tht the output curve of the PV rry ppers nonliner nd shows unimodl chrcteristics. Tle 1 Prmeters of the EGing-50 W Model Prmeters Vrile Vlue Short circuit current I sc 3A Open circuit voltge V oc 22 V Current of P mx I MPP 2.77A Voltge of P mx V MPP V Mximum power P MPP 50 W V oc cof. of temperture K v 0.33%V/ C I sc cof. of temperture K i 0.04%A/ C No. of modules in series (per string) N s 36 3 Flower pollintion lgorithm Flower pollintion lgorithm ws firstly proposed y Yng et l. in 2012 [17], nd hs een proved to e effective in serching for glol optiml solutions within short period. In recent yers, it hs een widely used to solve nonliner optimiztion prolems. FP lgorithm cn lso e esily djusted nd hs fewer prmeters thn other methods. The dynmic conversion etween glol serch nd locl serch cn e implemented y using the conversion proility prmeter, nd therefore the lnce etween glol serch nd locl serch is well solved. In ddition, FP lgorithm lso dopts Levy Fig. 1 The single-diode model of solr cells Fig. 2 Output chrcteristics of solr cells given in Tle 1. Under different irrdince. Under different temperture

3 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Pge 3 of 7 flight mechnism, which mkes its glol optimiztion ility much stronger. It is lso etter thn PSO in convergence speed. According to Yng et l., nturl flower pollintion cn e divided into two sic forms of iologicl cross pollintion nd non-iologicl self-pollintion. The following four rules re proposed ccording to the constncy nd pollintion ehvior of flowers: 1) Biologicl cross pollintion is considered s the glol serch ehvior of FP lgorithm, nd pollintion is crried out y pollintor through Levy flight mechnism. 2) Non-iologicl self-pollintion is regrded s the locl serch ehvior of FP lgorithm, or locl pollintion. 3) The constncy of flowers cn e considered s the proility of reproduction, which is positively proportionl to the similrity of two flowers involved in pollintion. 4) The glol pollintion nd locl pollintion of flowers re regulted y conversion proility p [0, 1]. Due to the influence of physicl proximity, wind nd other fctors, the conversion proility p is very importnt prmeter in the whole pollintion process. Normlly, p = 0.8 is considered to e more conducive to lgorithm optimiztion ccording to the experimentl study in [17]. 4 MPPT using FP lgorithm 4.1 MPPT Serching Pth In order to serch the entire power-duty cycle curve (P-D curve), the initil pollens need to e distriuted in the entire duty cycle rnge. The choice of pollen numer m is importnt for the glol serch. Lrger numer m improves the proility of finding the glol optiml solution ut leds to longer convergence time. Lrge numers of simultions hve shown tht FP lgorithm cn ccurtely find the glol optiml solution when the popultion numer is three. Therefore, three pollens re dopted in this pper. Figure 3() shows the serch pth of FP lgorithm under the uniform irrdince, where vriles A, B nd C represent three pollens, nd the upper lels of vriles represent the numer of itertions. During the first itertion, B 0 is the closest to the MPP, so pollen B is considered to e the optiml fitness vlue. The itertive step of pollen depends on the distnce etween the current pollen nd the optiml pollen, nd therefore, pollen A 0 nd C 0 re forced to move to B 0. Becuse of the Levy flight in FP lgorithm, the pollen cn serch glol optimum from oth sides of the optiml solution, which mkes the pollens esy to jump out of the locl peks In prctice, ech flowering plnt hs mny flowers, nd ech flower hs thousnds of flower gmetes. For implementing the lgorithm, it is normlly ssumed tht ech flowering plnt hs only one flower, nd ech flower contins only one gmete. Therefore, ech gmete is considered s cndidte solution in the solution spce s x tþ1 i ¼ x t i þ Lxest x t i ( x tþ1 i ¼ x t i þ ξ xt j xt k ξ Uð0; 1Þ ð2þ ð3þ In (3), x tþ1 i nd x t i re cndidte solutions for the t nd t + 1 genertions, respectively. x t j nd x t k re different pollen gmetes of the sme plnt species. x est refers to the current est solution, ξ is the locl pollintion coefficient, nd L is the flying step nd is suject to uniform distriution s. L λγ ð λ Þ sin ð πλ=2 Þ π 1 s 1þλ s s 0 > 0 ð4þ where Γ(λ) is the gmm constnt, s 0 is the minimum step size, nd λ is chosen s 1.5. In this pper, Mntegn s lgorithm is used to generte Levy flight step size L. Fig. 3 The MPP serching pth y FP lgorithm. Uniform irrdince. Prtilly shded condition

4 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Pge 4 of 7 nd rech the glol optimum effectively. The convergence rte is lso improved. When pollen gets closer to the MPP, the itertive step ecomes smller, s shown in (2). When ll pollens converge to the MPP, the step size decreses to zero. The serching pth of FP lgorithm in prtilly shded conditions is shown in Fig. 3(). At the eginning, ll pollens re distriuted t vrious loctions of the P-D curve. During the first itertion, pollen B 0 is in the optiml position, nd thus pollen A 0 nd C 0 re forced to leve their initil positions nd move to B 0. In the second itertion, C 2 ecomes the optiml pollen nd thus other two pollens move to C 2. As seen from Fig. 3(), the glol pek is locted on the right of C 2. Since Levy flight llows pollens to pss through the optiml position, pollen A nd B cn cross C 2 nd rech the glol MPP. 4.2 Implementtion of FP Algorithm FP is new metheuristic intelligent lgorithm, nd the steps of implementing FP lgorithm in MPPT re descried s follows. 1) Initiliztion of prmeters. The mximum numer of itertions (N), pollen popultion numer (m), duty cycle limittion (D min nd D mx ), nd conversion proility (p) re set s 15, 3, 0.2, 0.8, nd 0.8, respectively. 2) Clcultion of the fitness vlue of ech pollen, nd the optiml duty cycle nd optiml power t the time. 3) If the condition of trnsformtion proility p > rnd is true, the duty cycle is updted ccording to (2). 4) If the condition of trnsformtion proility p < rnd is true, the duty cycle is updted ccording to (3). 5) Clcultion of the corresponding fitness vlue of the new duty cycle from step 3) or step 4). If the fitness of the new duty cycle is etter, the current duty cycle nd the current fitness vlue re replced with the new duty cycle nd the corresponding fitness vlue, respectively. 6) If the corresponding fitness of the new duty cycle is etter thn the glol optiml vlue, the glol optiml duty cycle nd glol optiml power re updted. 7) Judgment of the termintion condition. If the condition is stisfied, the progrm exits nd outputs the optiml power nd optiml duty cycle, otherwise switches to step 3). The repeted itertion leds to power fluctution for considerle time. Thus, termintion strtegy is proposed in this pper to quickly stilize the power t the MPP nd to reduce power fluctution t system stle point. Becuse the initil pollen positions re dispersed, when pollen positions ecome concentrted, the MPP cn e considered s eing reched. So in the proposed strtegy, when the difference of mximum duty cycle is less thn 0.5%, the itertion stops. When the prtil shding or irrdince conditions chnge, the output power of the PV rry will chnge ccordingly. Therefore, it is necessry to restrt the FP lgorithm to ensure the system works stly in the new MPP. The power chnge rte Δp is expressed s: Δp ¼ j P P m j P m ð5þ where P is the ctul output power of the PV rry operting t point D m. In this pper, two restrt conditions re set, i.e., nturl restrt nd muttion restrt. It is found tht irrdince does not chnge more thn 10 W/ m 2 /s under stle nturl conditions, nd the corresponding output power conversion rte of the rry Δp is Thus, the nturl restrt condition is set to 2 min. Simultion results lso show tht the power chnge rte Δp is greter thn 0.15 during shrp chnge of the prtilly shded condition. Therefore, the muttion restrt condition is set s Δp > Simultion result In this pper, system simultions re crried out using MATLAB The dt of the EGing-50 W PV cell module is used for modeling, nd the simultion model of the PV system with the proposed MPPT method is shown in Fig. 4. The min prmeters for the oost converter circuit re: C 1 =470μF, C 2 =470μF, L = 0.3 mh, f = 50 k Hz, nd R =187Ω. Tle 2 shows the sic prmeters of P&O, PSO nd FP lgorithms. The smpling intervl for the MPPT controller is chosen s 0.03 s. FP lgorithm is compred with two conventionl P&O nd PSO lgorithms to evlute the performnce. The following three tests re conducted: (1) strt-up test; (2) Fig. 4 PV system structure with MPPT control in MATLAB

5 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Pge 5 of 7 Tle 2 Prmeters of P&O, PSO nd FP lgorithm Prmeter P&O PSO FP Initil duty cycle 40% 25%, 45%, 70% Rndom duty cycle etween 20% nd 80% m 3 3 C 1mx 1.4 C 1min 1 C 2mx 1.8 C 2min 1 W mx 1 W min 0.1 d 1% irrdince step chnge test; nd (3) ility test to del with prtil shding. 5.1 Strt-up Test This test is designed to evlute the performnce of FP lgorithm t strt-up. Due to low power genertion of the PV system t night, the PV system needs to e strted every morning. The strt-up test condition is set s the irrdince step chnges from 0 W/m 2 to 1000 W/ m 2, nd the simultion wveforms of the three methods re shown in Fig. 5. It cn e oserved tht the MPP serching time is 0.24 s for FP lgorithm, compred to 0.36 s nd 0.45 s for P&O nd PSO lgorithms, respectively. In ddition, P&O lgorithm hs out 4 W power fluctution t the MPP, which reduces the verge efficiency of the PV system. c 5.2 Irrdince step chnge test When clouds or irds pss through the PV rry t high speed, the irrdince will undergo step chnge. In order to evlute the performnce of the proposed lgorithm under this condition, set of irrdince step chnges re pplied to the PV rry, s shown in Tle 3. Becuse the influence of temperture on the output power of the PV rry is smll, mient temperture is kept constnt t 25 C during the whole testing process. The power wveforms of P&O nd FP lgorithms re shown in Fig. 6. It cn e seen tht the stedy stte power loss is out 3 W for P&O lgorithm when itertion converged to the MPP, while the stedy stte power loss is round 0 W for FP lgorithm. The duty cycle of FP lgorithm is lwys stle round P MPP. The power wveforms of PSO nd PF lgorithms re shown in Fig. 7. Since Levy flight in FP lgorithm, it cn e seen tht during ech irrdince step chnge, PF tkes round 60 ms less time to converge to the MPP thn tht of PSO. In stedy stte, oth lgorithms cn trck the MPP perfectly. Fig. 5 Simultion results of the three methods for strt-up test. P&O. PSO nd (c) proposed lgorithm Tle 3 Simulted conditions for step vries in irrdince Time(s) G(W/m 2 ) P MPP (W)

6 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Pge 6 of 7 Fig. 6 Response of P&O nd the proposed lgorithm under step chnge 5.3 Aility test to del with prtil shding When multiple tteries in the PV rry re locked in different degrees, there will inevitly hve multiple knee points on the V-I chrcteristic curve of the whole PV rry. This mens tht there will e multiple pek points on the corresponding P-D chrcteristic curve including glol pek nd multiple locl peks. The conventionl MPPT lgorithms such s P&O nd HC lgorithms my not e le to distinguish these points, nd in most cses, trditionl lgorithms my fll into locl point, cusing lrge mount of power loss. Since FP is glol serch lgorithm, it is esy to del with prtil shding. Initilly, the entire rry is exposed to n unshded condition with n irrdince of 800 W/m 2, s shown in curve 1 of Fig. 8(). The entire rry hs only one glol pek. After 1 s, the PV rry is under prtil shding with the irrdince of 1000 W/m 2, 800 W/m 2 nd 400 W/m 2 respectively, s shown in curve 2 of Fig. 8 (). The P-D curve of the PV rry then hs three pek points including glol pek nd two locl peks. When the PV rry is under the prtilly shded condition, ll operting points switched from curve 1 to curve 2. If the Fig. 7 Response of PSO nd the proposed lgorithm under step chnge Fig. 8 P-D chrcteristics for MPP trcking under prtilly shded conditions. P&O nd () the proposed lgorithm conventionl P&O method is used t this point, the operting point is moved to the nerest pek point s indicted y the rrow in Fig. 8(). Oviously, this point is the locl pek, which leds to lrge mount of power loss nd reduced system efficiency. When PF lgorithm serches the glol MPP, the new pollen is dispersed to the entire duty cycle intervl. Since the new duty cycle is locted t vrious positions of the P-D curve, FP lgorithm will not fll into ny locl peks. After multiple itertions, PF lgorithm reches for the glol MPP, s shown in Fig. 8(). In the cse of prtil shding, the simultion wveforms of P&O nd FP lgorithms re shown in Fig. 9. It cn e seen tht when prtil shding occurs, the locl pek with power of 66.4 W is serched in reltively short time y P&O lgorithm. This result is consistent with the P-D curve in Fig. 8 (). On the other hnd, FP lgorithm converges to the glol MPP of 81.5 W fter 0.21 s. In the serching process of FP lgorithm, it cn e oserved tht the output power hs lrge fluctution efore converged to the glol point, which is cused y the rndomness of FP lgorithm nd Levy flight trjectory. However, such trnsient ehvior hs little impct on the PV power genertion system in prctice, ecuse the trnsient durtion is lmost negligile compred with the stedy stte durtion.

7 Shng et l. Protection nd Control of Modern Power Systems (2018) 3:38 Pge 7 of 7 Authors contriutions Zhu nlyzed nd interpreted the simultion results. Li nd Guo performed the simultion exmintion. Shng designed nd supervised the experiment, prepred nd revised the mnuscript. All uthors red nd pproved the finl mnuscript. Competing interests The uthors declre tht they hve no competing interests. Received: 11 August 2018 Accepted: 21 Novemer 2018 Fig. 9 Trcking performnce y P&O nd proposed lgorithm under prtilly shded conditions. 6 Conclusion A MPPT method sed on FP serch lgorithm hs een proposed in this pper. The proposed FP lgorithm ws compred with two well estlished MPPT methods, i.e. P&O nd PSO lgorithms. The following conclusions cn e otined: 1) Compred with trditionl P&O lgorithm, FP lgorithm cn effectively shorten the strt-up time of PV systems, reduce the stedy-stte output power oscilltion fter irrdince step chnge, nd improve the output efficiency. It lso improves the system response speed nd the trcking efficiency during irrdince step chnge. 2) Compred with the trditionl MPPT methods, FP lgorithm requires less prmeters to e djusted, which simplifies the complexity of the method. 3) The proposed lgorithm cn esily del with prtil shding of PV rrys, reduce the power loss cused y misrecognizing the locl point, nd improve the efficiency of PV power genertion. Arevitions ABC: rtificil ee colony; ACO: nt-colony optimiztion; FLZ: fuzzy logic control; FP: Flower pollintion; HC: hill climing; INC: incrementl conductnce; MPP: mximum power point; MPPT: mximum power point trcking; P&O: pertur nd oserve; P-D: Power-duty cycle; PSO: prticle swrm optimiztion; PV: Photovoltic; P-V: power-voltge Acknowledgements Not pplicle References 1. Rm, J. P., Bdu, T. S., & Rjsekr, N. (2017). A comprehensive review on solr PV mximum power point trcking techniques. Renew Sust Energ Rev, 67, Bruendlinger, R., Bletterie, B., Milde, M., et l. (2006). Mximum power point trcking performnce under prtilly shded PV rry conditions. In Proc. 21st EUPVSEC, Germny (pp ). 3. Femi, N., Petrone, G., Spgnuolo, G., et l. (2005). Optimiztion of pertur nd oserve mximum power point trcking method. IEEE Trns Power Electron, 20(4), Li, X., Wen, H., Jing, L., et l. (2016). An improve et method with utoscling fctor for photovoltic system. IEEE Trns Ind Appl, 52(5), Xio, W., & Dunford, W. G. (2014). A modified hill climing MPPT method for photovoltic power systems, IEEE 35th Annu. Power Electron. Spec Conf, 3, Kjr, S. B. (2012). Evlution of the hill climing nd the incrementl conductnce mximum power point trckers for photovoltic power systems. IEEE Trns Energy Convers, 27(4), Sfri, A., & Mekhilef, S. (2011). Simultion nd hrdwre implementtion of incrementl conductnce MPPT with direct control method using Cuk converter. IEEE Trns Ind Electron, 58(4), Ptel, H., & Agrwl, V. (2008). Mximum power point trcking scheme for PV system operting under prtilly shded conditions. IEEE Trns Ind Electron, 55(4), Ishque, K., & Slm, Z. (2013). A deterministic prticle swrm optimiztion mximum power point trcker for photovoltic system under prtil shding condition. IEEE Trns Ind Electron, 60(8), Seyedmhmoudin, M., Rhmni, R., Mekhilef, S., et l. (2015). Simultion nd hrdwre implementtion of new mximum power point trcking technique for prtilly shded PV system using hyrid DEPSO method. IEEE Trns Sustin Energy, 6(3), Zhu, Q., Zhng, X., Li, S., et l. (2016). Reserches nd tests of dynmic multi-pek mximum power point trcking lgorithm sed on power loop. Proceedings of the CSEE, 36(5), Aljmi, B. N., Ahmed, K. H., Finney, S. J., et l. (2013). A mximum power point trcking technique for prtilly shded photovoltic systems in microgrids. IEEE Trns Ind Electron, 60(4), Sundreswrn, K., Snkr, P., Nyk, P. S. R., et l. (2015). Enhnced energy output from PV system under prtil shded conditions through rtificil ee colony. IEEE Trns. Sustin. Energy, 6(1), Boumrf, H., Tlh, A., & Bouhli, O. (2015). A three-phse NPC gridconnected inverter for photovoltic pplictions using neurl network MPPT. Renew Sust Energ Rev, 49, Sundreswrn, K., Vigneshkumr, V., Snkr, P., et l. (2016). Development of n improved P&O lgorithm ssisted through colony of forging nts for MPPT in PV system. IEEE Trns Ind Informt, 12(1), Ding, K., Bin, X., Liu, H., et l. (2012). A MATLAB-simulink-sed PV module model nd its ppliction under conditions of nonuniform irrdince. IEEE Trns. Energy Convers., 27(4), Yng, X., & Krmnoglu, M. (2014). Multi-ojective flower lgorithm for optimiztion. Procedi Comput Sci, 18, Funding Not pplicle Avilility of dt nd mterils The dtsets used nd nlyzed during the current study re ville from the corresponding uthor.