Photovoltaic Panel Modelling Using a Stochastic Approach in MATLAB &Simulink

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1 hotovolti nel Modelling Using Stohsti Approh in MATLAB &Simulink KAREL ZALATILEK, JAN LEUCHTER eprtment of Eletril Engineering University of efene Kouniov 65, 61 City of Brno CZECH REUBLIC Astrt: - The topi of this pper is development of mthemtil model of rel photovolti pnel, sed upon long term mesurements, using stohsti pproh The input is the dt of typil power-voltge hrteristi mesured on the String inverter The output is n integrted prmetri model whih n ontrol the pnel s operting point with the use of the solr irrdition The rtile expnds the originl ide of the impliit pproximtion pulished in [1] with the possiility of the prmetri ontrol The mthemtil model developed in MATLAB is ompleted in the form of funtionl lok model in Simulink s hierrhil model The dvntge is n esy hnge of the pnel y rewriting severl onstnts nd lso inluding the mesures of temperture, if ville The enefit of this pproh is the inlusion of ll the influenes on the pnel, suh s losses, ging, rndom errors, et Key-Words: - impliit pproximtion, MATLAB &Simulink, photovolti pnel modelling, stohsti pproh 1 Introdution The previous pper [1] ontins the originl method of the pproximtion of long term mesurements of rel photovolti pnel p/v hrteristi, sed on n impliit irle eqution The eqution oeffiients long with the pproximtion intervls of power nd voltge re the output of the lgorithm The impliit irle eqution in the quoted prmeter is derived with the use of the symoli mthemtis in the MATLAB environment The disussed pproximtion lgorithm is fully usele; however, it does not inlude these importnt onditions nd possiilities: rmetri ontrol of the operting point with the solr irrdition Numeril lgorithm for the lultion of power nd voltge Blok form of the model for further experiments The essene of this rtile is the innovtion of the originl pproximtion method with the three mentioned hrteristis of the model The min output, mong other, is fully funtionl prmetri model of rel pnel in the Simulink environment The originl sript for the desription of its essentil hrteristis ws developed in MATLAB whih is well suited for oth input of the p/v hrteristi mesurements nd other hrteristis desried elow Impliit pproximtion of p/v hrteristis This hpter riefly introdues the min priniples nd outputs of the pproximtion lgorithm desried in [1] The lgorithm inputs re: Long term mesurements of the pnel s p/v hrteristi Three points on the hrteristi hosen either mnully or utomtilly The typil outputs re: An impliit irle eqution pproximting the given ourse A rnge of the pproximtion intervl of power nd voltge The Figure 1 shows typil result of long term p/v hrteristi mesurement nd the ourse of the pproximtion irle It is stohsti pproh nd the ISBN:

2 pnel works lose to the MT mode (Mximum ower oint Trking) [] Every point of the hrteristi is influened y the solr irrdition t given time nd represents n operting point t tht time ower (W) Mesured /V hrteristi nd pproximting irle r,1, whih is more suitle for the modelling purposes The disussed model n work with oth solute nd reltive vlues of irrdition ue to the impliit hrter of the pproximtion irle ording to the Figure, the following proedure ws hosen: Approximtion of the ourse p=f( r ) Clultion of speifi power for speified irrdition r Clultion of voltge V from the known power ording to the impliit eqution (qudrti eqution solution) The lgorithm is lerly desried y the lok sheme shown in Figure Voltge (V) Fig1 Long-term mesured p/v hrteristis nd its pproximtion [1] The Figure shows typil output of the pproximtion lgorithm, whih is n impliit eqution of the pproximtion irle nd rnge of the power nd voltge intervls The numer of deiml ples is redued for the in order to sve spe K1, K, K3, K4, K5 ower lultion on the sis Voltge V lultion on the sis Operting point drwing in p/v Input onstnts pproximtion of p=f( r ) Qudrti eqution solution Fig3 Blok digrm of operting point ontrol definition Fig Typil pproximting lgorithm output in MATLAB 3 rmetri operting point ontrol The min ojetive of our originl method is to omplete the prmetri ontrol of the pproximtion urve in the Figure 1 The min prmeter in prtie is the irrdition of the pnel (Wm - ), or the reltive irrdition For the possiility of ontrol of the operting point with the irrdition, defult liner dependene etween power nd reltive irrdition p=f( r ) ws set ording to the formul: p = k + r q ( W ), (1) where k nd q re the slope of the pproximtion line nd its shift The onstnts k nd q n e esily lulted from the input onstnts in Figure 3: mx min k = ( W), q = min (W) () r mx r min If the lulted power is known, then it is neessry to lulte the power on the horizontl xis of the grph ISBN:

in Figure 1 To do tht, the derived impliit eqution nd its oeffiients hve to e used Sustituting the known power to the impliit eqution, the eqution is simplified to this generl form: v + v + = (3) For

3 in Figure 1 To do tht, the derived impliit eqution nd its oeffiients hve to e used Sustituting the known power to the impliit eqution, the eqution is simplified to this generl form: v + v + = (3) For the lultion of voltge ording to (3) it is neessry to define the onstnts, nd By ompring with the originl impliit eqution nd the expression (3) they n e defined s follows: = K5; = K 4; = K3 + K + K1 (4) The next step is the solution to the qudrti eqution (3) for the known vlues of the onstnts,, nd This is solved with well-known formul: ± V1, =, = 4 (5) The numeril lultion shows tht only the seond root for whih pplies tht V > is physilly suitle If the numeril vlues of power nd voltge V re known for the defined reltive irrdition r, the speified operting point of the p/v hrteristi n e drwn 4 rtil exmple Let us onsider rel photovolti pnel with nominl power n =1 W tht opertes in our deprtment nd for whih the mesured dt in Figure 1 re vlid The oeffiients of n impliit pproximtion irle for this pnel were lulted ording to Figure It is true tht: mx r mx = 1158 W, = 1, = r min min = W Let us hve speified reltive irrdition r =45 Aording to (), the slope nd the shift of the pproximtion line p/ r n e lulted: 1158 k = = 8158 W, q = W 1 Aording to (1) the vlue of power is =56711W Aording to (4) nd (5), the vlues of the uxiliry onstnts nd the disriminnt re lulted The resulting voltge ording to the first prt of the eqution (5) is: V = 1541V The Figure 4 shows the lulted operting point long with its oordintes With the speifition of reltive solr irrdition; the whole p/v urve is drwn It should e emphsized tht users n lso use other rnge of the reltive irrdition vetor ording to their needs ower (W) Simulted /V hrteristi ower (W): Voltge (V): 1541 r (-): Voltge (V) Fig4 Operting point lultion for required vlues In tht se the prmeters of the pproximtion line will hnge ordingly (1) nd () The limits of the vetors of power nd voltge re inluded in the Figure The Figure 5 shows the experimentl lortory for the long term mesurements nd dt proessing from rel photovolti pnel, see lso the Figure 1 The red devie in the upper left orner is String inverter SUNNY BOY 11, with whih the dt were olleted The mesured pnel is professionl photovolti system Shüo ME S 5 Serie Fig5 Workple for photovolti pnel mesurement nd simultion ISBN:

5 Soure ode in MATLAB The min prts of the lultion were relized t first in MATLAB s sript The Figure 6 shows seleted key prts of the soure ode with desription Some of the formtting ommnds were omitted

whih fully orresponds to the Figure 1, see the Figure 7 It should e noted tht the lultion of the key prmeters is solved numerilly, prt from the proedure desried in [1], where the symoli mthemtis of

funtionl model of pnel in Simulink The Figure 8 shows the resulting model where the tul pnel is presented in the form of susystem The ontrolling reltive irrdition is presented s onstnt (mnul input)

4 5 Soure ode in MATLAB The min prts of the lultion were relized t first in MATLAB s sript The Figure 6 shows seleted key prts of the soure ode with desription Some of the formtting ommnds were omitted due to the lk of spe The soure ode is supposed to e ler nd understndle nd is in the full ompline with the presented theoretil desription One of the lgorithm outputs is the ourse of the p/v hrteristi whih fully orresponds to the Figure 1, see the Figure 7 It should e noted tht the lultion of the key prmeters is solved numerilly, prt from the proedure desried in [1], where the symoli mthemtis of MATLAB environment ws used for the derivtion of the oeffiients of the impliit irle eqution Fig7 Simulted p/v hrteristis s typil lgorithm output 6 Blok model in Simulink The min ojetive ws to set up funtionl model of pnel in Simulink The Figure 8 shows the resulting model where the tul pnel is presented in the form of susystem The ontrolling reltive irrdition is presented s onstnt (mnul input) or s hrmoni genertor Fig6 MATLAB soure ode of lgorithm key prt The numeril pproh ws hosen deliertely for the purposes of the implementtion in the Simulink environment, see elow Fig8 Resulting lok model in Simulink ISBN:

The pnel n e ontrolled in ny other wy, e g the dt from disk or mesuring rd, or y rndom genertor The lulted prmeters orrespond to the results in the hpter 4 Rel photovolti pnel model sed on long-term

5 The pnel n e ontrolled in ny other wy, e g the dt from disk or mesuring rd, or y rndom genertor The lulted prmeters orrespond to the results in the hpter 4 Rel photovolti pnel model sed on long-term mesurement Sine Irrdition ( -1) Step 1 onstnts definition Swith [1] [] [hi1] [hi] [hi] hi1 45 [hi] hi [K4] [] 5671 Output power Constnts Voltge1 [1] [] [hi1] [hi] Step power lultion [] ower [] [K3] [K] [K1] Step 4 disriminnt lultion [K4] 154 Output voltge1 [] ower1 [hi] 45 hi mx min himx himin ower nd hi limits mx min himx himin hi ower =^-4 isriminnt [] Input irrdition [] Voltge [] ower Constnts K1 K K3 K4 K5 Impliit oeffiients K3 K K1 Clultion of onstnt V Voltge [K1] [K] [K3] [K4] Step 3 lultion of "" [] 1 Step 5 voltge lultion Output voltge =f(v) Fig9 etiled internl struture of the Simulink lok model The Figure 9 shows the model of the whole pnel in more detil It lso presents the proedurl steps in ompline with the theoretil proedure mentioned ove in Figure 3 The lultions of the power, the disriminnt nd the resulting voltge orrespond to the equtions (1) to (5) The numeril outputs were kept to hek the ove mentioned numeril exmple The min output of the lok model in the Figure 9 is the grph of the p/v hrteristi By setting the mnul swith to the hrmoni ourse of the reltive irrdition the whole simulted hrteristi p/v is otined ording to Figure 7 The ourse of the reltive irrdition is then defined s: r = 5sin(πFt), F = 1Hz The vlue of the mximum time in the Simulink ws set to T mx =1s Considering the nture of the tsk disrete type solver ws set, nd the mximum step to the vlue 1/5 The inner struture of the susystems in the Figure 9 orresponds to the ove mentioned proedure After liking on the susystem for setting the onstnts it is possile to hnge the type of pnel nd the limits of the reltive irrdition t ny time A lrge numer of works on this topi hs een pulished reently, eg [3], [4] 7 Conlusion This rtile presents the originl lgorithm of development of rel photovolti pnel model The model is sed on the long time mesurements of the p/v hrteristi The presented proedure follows the works pulished in [1] tht ontin the proedure of lultion of the impliit irle eqution oeffiients tht pproximte the mesured dt In this pper, the disussed model ws expnded with the option of prmetril ontrol with reltive solr irrdition nd finlized in the lgorithmi form in the MATLAB environment nd the Simulink lok model The experimentl nd simultion works fully justify the legitimy of the model Aknowledgements MATLAB nd Simulink re registered trdemrks of The MthWorks, In Referenes: [1] K Zpltilek, J Leuhter, Impliit Approximtion of hotovolti nel Chrteristis Using Stohsti Approh, Advnes in Eletril nd Computer Engineering, 1, vol 1, no 4, pp [] J Leuhter, V Reruh, A F Zo, Mthemtil modeling of photovolti systems, in ro 14th ower Eletronis nd Motion Control Conferene (EE-EMC 1), Ohrid (Medoni), 1, pp 4-47 [3] R M d Silv, J L M Fernndes, Hyrid hotovolti/therml (V/T) Solr Systems Simultion with Simulink &MATLAB, Solr Energy, 1, Vol 84, Issue 1, pp [4] S Llouni, Rekiou, Modeling nd Simultion of hotovolti System Using Fuzzy Logi Controller, in ro nd Interntionl Conferene on evelopments in Systems Engineering, Au hi, Ar Emirtes, 9, pp 3-8 ISBN:

Duality in linear interval equations

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