Simulated Annealing Modeling and Analog MPPT …Simulated Annealing Modeling and Analog MPPT Simulation for Standalone Photovoltaic Arrays G.El-Saady, El-NobiA.Ibrahim, Mohamed EL-Hendawi

International Journal on Power Engineering and Energy (IJPEE) Vol. (4) – No. (1)ISSN Print (2314 – 7318) and Online (2314 – 730X) January 2013

Reference Number: W13-P-0035 353

Simulated Annealing Modeling and Analog MPPTSimulation for Standalone Photovoltaic Arrays

G.El-Saady, El-NobiA.Ibrahim, Mohamed EL-HendawiElectrical Engineering Department, Faculty of Engineering, Assiut University

Abstract - This paper proposes a method formodelling andsimulation of photovoltaic arrays. The method is used to obtainthe parameters of the array model using its datasheet information.To reduce computational time, the input parameters are reducedto four and the values of shunt resistance Rp and series resistanceRs are estimated by simulated annealing optimization method.Then we draw I-V and P-V curves at different irradiance levels.Lowcomplexityanalogue MPPT circuit can be developedbyusingtwo voltage approximation lines (VALs) that approximatethe maximum power point (MPP) locus.In this paper, a fast andlow cost analog MPPT method for low power PVsystems isproposed.The Simulation results coincide with experimentalresults at different PV systems to validate the powerful of theproposed method.

Index Terms. PV module, simulated annealing, MPP, VAL.

I. INTRODUCTION

Large and small scale PV power systems have beencommercialized in many countries due to their potential longterm benefits. In PV power generation, due to the high cost ofmodules, optimal utilization of the available solar energy has tobe ensured. [1].A photovoltaic system converts sunlight into electricity. Thebasic device of a photovoltaic system is the photovoltaic cell.Cells may be grouped to form panels or modules. Panels can begrouped to form large photovoltaic arrays. The term array isusually employed to describe a photovoltaic panel (with severalcells connected in series and/or parallel) or a group of panels.[2].The most important component that affects the accuracy of asimulation is the PV cell modeling, which primarily involvesthe estimation of the non-linear I-V and P-V characteristicscurves. The simplest model of a PV cell is shown as anequivalent circuit below that consists of an ideal current sourcein parallel with an ideal diode as shown in fig.1. The currentsource represents the current generated by photons, and itsoutput is constant under constant temperature and constantincident radiation of light. It only requires three parameters,namely the short-circuit current (Isc), the open circuit voltage(Voc) and the diode ideality factor (a). This model is improvedby the inclusion of one series resistance Rs [3,4 and 5]. Anextension of the model which includes an additionalShuntresistance Rp is shown in Fig.1 [2 and 6]. The Rp resistanceexists mainly due to the leakage current of the p-n junction anddepends on the fabrication method of the photovoltaic cell. The

value of Rp isgenerally high and some authors neglect thisresistance to simplify the model. The value of Rs is very lowand sometimes this parameter is neglected too [2].Although a significant improvement is achieved, this modeldemands significant computational effort.For more accuracy the recombination in the depletion region ofPV cells provides non-ohmic current paths in parallel with theintrinsic PV cell [1]. This can be represented by the seconddiode (D2) in the equivalent circuit.

Fig.1 single diode model

In this paper we deal with single diode model as in fig.1. Thesingle diode models were based on the assumption that therecombination loss in the depletion region is absent.There exist two main problemswhen operating a PV generationsystem – the conversionefficiency is very low, especially underlow irradiation, andthe amount of the electric power generatedby solar cells varieswith weather conditions, i.e., the solarisolation andpanel temperature. To overcome these problems, amaximumpower point tracking (MPPT) method, which hasquickresponse and is able to make good use of the electricpowergenerated in both high and low irradiation levels, isrequired.[7]After modeling PV array and get unknown parameters we canpropose MPPT method for PV array.Due to the complexity ofthe required mathematicaloperations, a digital signal processor(DSP) or a relativelypowerful microcontroller (µC) is typicallyneeded,which increases the cost of the system. However, inlowpower PV systems (from a few watts up to a few hundredsof watt) which are frequently used as stand-alone poweranalogconditioningcircuit may not be cost-effective.



II. MODELING OF PV DEVICESA. Ideal PV CellFig. 1 shows the equivalent circuit of the ideal PV cell. Thebasic equation from the theory of semiconductors thatmathematically describes the I–V characteristic of the ideal PVcell is

(1)

Where:• IPVcell is the current generated by the incident light.• Id is the Shockley diode equation.• I0,cell is the reverse saturation or leakage current of the

diode.• q is the electron charge [1.60217646 ×10-19 C].

• k is the Boltzmann constant [1.3806503 × 10-23 J/K].• t is the temperature of the p-n junction.

• is the diode ideality constant which lies between 1and 2 for mono crystalline silicon [8].

Fig. 3 Characteristic I-V, P-V curve of a practical photovoltaic device B. Modeling the photovoltaic arrayThe basic equation (1) of the elementary photovoltaic cell doesnot represent the I-V characteristic of a practical photovoltaicarray. Practical arrays are composed of several connectedphotovoltaic cells and the observation of the characteristics atthe terminals of the photovoltaic array requires the inclusion ofadditional parameters to the basic equation. [2]

(2) Where, RS and Rp are the equivalent series and parallelresistances, respectively. Ipv and Io are the photovoltaic andsaturation currents of the array and Vt = Nskt/q is the thermalvoltage of the array with Ns cells connected in series. Cellsconnected in parallel increase the current and cells connectedin series provide greater output voltages. If the array iscomposed of Np parallel connections of cells the photovoltaic

and saturation currents may be expressed as: Ipv=Ipv,cellNp,I0=I0,cellNp . This model yields more accurate result than the Rs-model, but at the expense of longer computational time [9].C. Improved computational methodThe equation for the PV current as a function of temperatureand irradiance can be written as:`

(3)Where Ipvn is the light generated current under Standard Test

Conditions (STC), T = T –Tn ( Tn=25o C), G is the surfaceirradiance of the cell and Gn (1000W/m2) is the irradianceunder STC. The constant KI is the short circuit currentcoefficient, normally provided by the manufacturer.

The temperature dependence of diode saturation current Io canbe expressed as:

Where Eg is the band gap energy of the semiconductor (Eg≈1.12 ev for the polycrystalline Si at 25oC), and I0,nis thenominal saturation current[2][8].In this paper the nominal saturation current Io,n is indirectlyobtained from the experimental data through (5), which isobtained by evaluating (2) at the nominal open-circuitcondition, with V = Voc,n , I = 0, and Ipv,n ≈ Isc,n.From (4) and (5) Io can be expressed as :

Where VOC,nis open circuit voltage,ISC,nis the short circuitcurrent , constant KI is the short circuit current coefficient ,is the open circuit voltage coefficient

D. Simulated annealing algorithmSA was first introduced as an intriguing technique foroptimizing functions of various variables. It is a heuristicstrategy that provides a means for optimization of completeproblems for which an exponentially number of steps isrequired to generate an exact answer.SA is based on an analogy to the cooling of heated metals. Thebasic algorithm of SA may be described as follows:Successively, a candidate move is randomly selected; thismove is accepted if it leads to a solution with a better objectivefunction value f than the current solution x. Otherwise themove is accepted with a probability that depends on thedeterioration Δfof the objective function value. The probability



of acceptance is usually computed as , using atemperature t as control parameter and Δf = fi+1(x)-fi(x).Thistemperature t is gradually reduced according to some coolingschedule, so that the probability of accepting deterioratingmoves decreases in the course of the annealing process. From atheoretical point of view, a SA process may converge to anoptimal solution if some conditions are met for instance, withan appropriate cooling schedule and a neighborhood whichleads to a connected solution space [10].Suppose that we have the current iteration point x where

Xmin<X<Xmax

And the next iteration point is:

(7)Where r is random number between[0,1]. The point y isaccepted as the next iteration point if it is better than thecurrent iteration point, in other words, f(yi) < f(xi) or if it isworse than the current iteration point then, Metropoliscriterion is valid:

>r (8)where r is a uniformly distributed random number from (0, 1).And i is the iteration number. If Eq. (7) is ensured then theworse candidate is accepted. Here, the parameter t > 0 is a so-called temperature and it is decreased during the algorithm.[10]

E. Numerical solution for modeling PV arrayTwo parameters remain unknown in (2), which are Rs and Rp.A few authors have proposed ways to mathematicallydetermine these resistances. Some authors propose varying Rsin an iterative process, incrementing Rs until the I-V curvevisually fits the experimental data and then vary Rp in the samefashion. This is a quite poor and inaccurate fitting method,mainly because Rs and Rp may not be adjusted separately if agood I-V model is desired.Some authors use optimization solutions like GeneticAlgorism, Particle Swarm Optimization to update the values ofmodel parameters [11].Her Rp and Rs are calculated simultaneously. we proposes amethod for adjusting Rs and Rp based on the fact that there isan only pair {Rs,Rp} that warranties that the mathematicalmaximum power Pmax,m= experimental maximum power Pmax,e=VmpImp at the (PV output voltage at maximum power Vmp, PVoutput current at maximum power Imp) point of the I-V curve,i.e. the maximum power calculated by the I-V model of (2),Pmax,m, is equal to the maximum experimental power from thedatasheet, Pmax,e, at the maximum power point (MPP).In this paper we will use simulated annealing optimization tocalculate Rp and Rs to reach to Pmax,m= Pmax,e

The relation between Rs and Rp, the only unknowns of (2), maybe found by making Pmax,m= Pmax,e, asshown in (9) and (10).

(10)The goal is to find the value of Rs (and hence Rp) that makesthe peak of the mathematical P-V curve coincide with the

experimental peak power at the ( , ) point. Thisrequires several iterations until Pmax,m= Pmax,e.In SA method first we put temperature =1000 then we put avalue for Rs in the range of it .The initial conditions for bothresistances are given below:

Rs,min=0 ;Rs,max = ;

Rp,min=From Eq. (7)wecan calculate RsasRs,i=Rs,min+(Rs,max-Rs,min)*r (11)

And then calculate Rp,ifrom (10).Then calculate from

(9) if it equal so Rs and Rp are the optimum value ifnot wecalculate Metropolis criterion:

Where t is the temperature if X>rand (0, 1) so the current valueis the best value. If not so the previous value is the best value.We do this procedure in random iteration. Then we reducetemperature and start the procedure again. This requires severaliterations until Pmax,m= Pmax,e. At the end of this method we getRs and Rp and we can model the pv system.Fig.4 showsthe simplified flowchart of the iterative modelingalgorithm.

F. The Model resultsTable I and II shows the experimental parameters of the arrayobtained from the data sheet and the proposed method resultswith two PV arrays at STC (25 oC, 1000W/m2.)

KC200GT solararraydata sheet information

KC200GT solar arrayModel results

Imp 7.61A Imp 7.61AVmp 26.3V Vmp 26.3VPmax,e 200.143W Pmax,m 200.142935Isc 8.21A Isc 8.21AVoc 32.9V Voc 32.9VKV −1230mV/oC I0,n 9.825 · 10−8 AKI 3.2mA/oC Ipv 8.21ANs 54 Rp 591.1123a 1.0 Rs 0.2277

Table I KC200GT solar array Parametersat 25 oC, 1000W/m2.



Fig.4 flow chart of the method used to adjust the I-V model

BP SolarMSX-60 solararraydata sheet information

BP SolarMSX-60 solararray Model results

Imp 3.5A Imp 3.5AVmp 17.1V Vmp 17.1VPmax,e 59.85 Pmax,m 59.849221Isc 3.8A Isc 3.8AVoc 21.1 Voc 21.1KV -80 mV/oC I0,n 4.70398 e-10AKI 3 mA/oC Ipv 3.8 ANs 36 Rp 173.9089a 1.0 Rs 0.3573

Table II BP Solar MSX-60 solararray Parametersat 25 oC, 1000W/m2.

G. Plotting the P-V and I-V curvesAfter calculating Rs and Rp by SA method, The Plotting of P-Vand I-V curves requires solving (2) for I ∈ [0, Isc,n] and V ∈[0, Voc,n]. Eq. (2) does not have a direct solution becauseI = f(V, I) and V = f (I, V) [2].The Newton-Raphson’s method ischosen for rapid convergence of the answer. The Newton-Raphson method is described as:

Where: = f (V, I) = 0

is the derivative of functionFor a set of V values and the corresponding set of I points canbe obtained [4].Figs.5 and 6 show the I-V and P-V curves ofthe KC200GT photovoltaic array and the MSX60 solar arraydatasheet adjusted with the proposed method. The modelcurves exactly match with the experimental data at the threeremarkable points provided by the datasheet: short circuit,maximum power, and open circuit.

Fig.5 I-V curve adjusted to three remarkable points.

Fig. 6 P-V curve adjusted to three remarkable points.



H. Analog MPPT for low power photovoltaic systems

Low power photovoltaic (PV) systems are commonlyused in stand-alone applications. MPPT methods utilizedin mediumand high power PV systems uses measuredcell characteristics(current, voltage, power) along withan online searchalgorithm to compute the correspondingmaximum powerpoint (MPP). Due to the complexity ofthe required mathematicaloperations, a digital signalprocessor (DSP) or a relativelypowerful microcontroller(µC) is typically needed which increases the cost of thesystem.However, in lowpower PV systemswhich arefrequently used as stand-alone powersuppliesµCs orDSPs may not be cost-effective. Moreover, it consumessignificant portion of the generated power. Therefore, ananalog MPPT circuit with low-cost and fast-trackingfeaturesis essential.Base on the fact that the MPP occurs at the knee of theP-Vcurvewhere ∂P/∂V=0.

In eq. (2) the cell shunt resistance RP is relativelyhigh, thus thecurrent through it can be neglected. So eq. (2) becomes

So the panel output power becomes

the relationship between themaximum power voltage Vmp andthe maximum powercurrent Imp can be expressed as:

∂P ∂V=0

From (14) at VOC,thepanel current(I)equal zero so

From Eq. (16) and (17) we find

VDO

The term named Differential Offset Voltage (VDO) has beenimplicitly defined. We will now introduce thehypothesis,which we will verify in the immediate following,that VDOvariations with irradiation can be neglected, and hence,thedifference between Voc and Vmp, expressed by (18),increaseslinearly with Imp. [12]

Since VOC is a logarithmic function of Ig, therelationshipbetween VMP and IMP with respect to irradiationisnot linear. However, it is possible to linearize thisrelationshipfor an interval where the value of VOC issufficientlyinsensitive to irradiation [7]. So it is possible toderive the sensitivity of VOCto Ig(SVOC, Ig)as:

If we predefine a threshold value for SVOC,Ig(e.g., 5%),from (19),we can calculate a minimum irradiation

condition,corresponding to a photo generated current ,above whichthe sensitivity is lower than the selected threshold,at a giventemperature T*.The desired linear relation,approximating the MPP, will be defined as the tangent to theMPP locus curve for Ipv= I*

pv. The tangent line is namedVoltage Linear Reference (VLR), and is shown in Fig.7.TheVLR can also be analytically derived from (18) as

WhereConsidering that Impis roughly proportional to Ipv So

So Eq.(20) can be simplified as:

Based on the previous analysis, it ispossible to implement aMPPT method by forcing the PV panel to operate over theVAL.



Fig. 7 I–V curves of the solar panel under different irradiation levels and thevoltage approximation line.

The MPPlocus can be better modeled as two linear sectionsthanone straight line as shown in fig. 8. That is, the slope k andthe offset pointVOFFSET should be different for high and lowirradiationconditions.In summary, from section G we can draw the I–Vcharacteristics for anyPV panelunder different irradiationlevels.The parameter of VAL (kHIGH,kLOW, VOEESET,H andVOFFSET,L) which approximating theMPP locus can becalculated using the polynomial curvefitting function providedby MATLAB accordingly as shown in fig. 8.Using this concept, Eq. (22) can be rewritten as

V HIGH high irradiation level

V low low irradiation level(23)

Fig. 8 I–V curves of the solar panel under different irradiation levels andtwovoltage approximation lines.

Fig. 9 Detailed implementation of the proposed method.

I.The proposed Analog MPPT system

PV-connected converter is used to transmit electricity fromphotovoltaic array (variable) to the dc load (constant). Fig.9shows the circuit of the PV-connected converter. It is a dc-dcbuck converter consisting of two switches with anti-paralleldiode, an inductor and two capacitors [13]. The task of MPPTalgorithm is to determineVref (Vmp) only. Then, there isanother control loop (PWM) that the proportional and integral(PI) controller regulates the input voltage of converter. Its taskis to minimize error betweenVref and the measured voltage byadjusting the duty cycle. The PI loop operates with a muchfaster rate and provides fast response and overall systemstability. [4]The analog MPPT circuit shown in Fig. 9 can be realizedusinglow power operational amplifiers (OPAMP)and an analogswitch. Fig. 10 shows the detailed implementation of theanalog MPPT circuit with respect to Eq. (23).The turningpoint voltage (VTP) is the point between the twoVAL lines as shown in Fig. 8. So the high irradiation lineshould be employed when PV panel voltage is greater than theturning point voltage VTP, otherwise the low irradiation lineshould be used. To select the correct approximation line, acomparator and an analog switch is utilized.

J.Simulation and resultThe parameters of the utilized PV panel are listed in Tables Iand II. Fig. 12 shows the simulation model of the proposedsystem. We can get the two VAL equations (23) by usingMATLAB algorism that we discuss before. So the output of thealgorism as shown in fig.11. From this figure we get theparameters of the two VAL lines (kHIGH, kLOW, VOEESET,H andVOFFSET,L).We put this parameter in the simulated model and we can draw

the output power and we calculate the method efficiencyηwhich defined as:

Where PO is the averaged output power obtained under steadystate and PMAX is the maximum available power of the PVpanel under certain irradiation conditions (datasheets).So if we run the simulated model with the two PV modules(KC200GT solar array and BP Solar MSX-60 solar array)which we calculate its parameter before, the output power isshown in fig. 13. Table III illustrate the VAL parameters andthe efficiency of the two PV modules.



Fig.10 Detailed implementation of the proposed analog MPPT.

Fig.11 I-V and P-V curves with VAL as a result of MATLAB algorism

Fig.12 Simulation model of the proposed system.

KC200GTsolar array

BP SolarMSX-60 solar

array

HIGH0.167081 0.259886

25.195921 15.877021

low0.971941 1.915239

23.162405 14.157949199.17 58.665717

200.142935 59.849221

% 99.5 98.022

Table III, the efficiency of the proposed system with two types of PV system.

From fig 13 we observe that the efficiencyis greater than98%.So from these results this method is fast, accurate and lowcostfor standalone Photovoltaic Arrays.

I.CONCLUSIONS:

In this paper, the development of a method for themathematical modeling of photovoltaic arrays is analyzed. Themethod is used to obtain the parameters of the array modelusing its datasheet information. This method called simulatedannealing optimization is utilized to calculate the twoparameters Rp and Rs to reach to the accurate model ofphotovoltaic arrays. This paper has presented in details theequations that constitute the single-diode photovoltaic I-Vmodel and the algorithm necessary to obtain the parameters ofthe equation. For Plotting the P-V and I-V curves the Newton-Raphsonmethod is chosen for rapid convergence of the answer.In this paper, a fast and low cost analog MPPT methodfor lowpower PV system is proposed. By using two VAL linesto



approximate the MPP locus, high tracking efficiency canbeachieved. Simulation results are alsoprovided to demonstratethe effectiveness of the proposedtechnique. The efficiency canbe very high because, at steady-state, thereis no oscillationaround the MPP.

Fig.13the output power of both PV arraysunder STC.

REFERENCES[1] KashifIshaque, Zainal Salam, and HamedTaheri, “Accurate MATLAB

Simulink PV System Simulator Based on a Two-Diode Model,” Journalof Power Electronics, Vol. 11, No. 2, March 2011

[2] M. G. Villalva, J. R. Gazoli, E. Ruppert F, “MODELING ANDCIRCUIT-BASED SIMULATION OF PHOTOVOLTAIC ARRAYS,”Brazilian Journal of Power Electronics, 2009 vol. 14, no. 1, pp. 35--45,ISSN 1414-8862.

[3] R.Sridhar, Dr.Jeevananathan, N.ThamizhSelvan,Saikat Banerjee,“Modeling of PV Array and Performance Enhancement by MPPTAlgorithm,” International Journal of Computer Applications (0975 – 8887)Volume 7– No.5, September 2010

[4] Akihiro Oi,“ DESIGN AND SIMULATION OF PHOTOVOLTAICWATER PUMPING SYSTEM,” Faculty of California Polytechnic StateUniversity ,San Luis Obispo September 2005.

[5] Francisco M. González-Longatt, “Model of Photovoltaic Module inMatlab,” 2DO CONGRESO IBEROAMERICANO DE ESTUDIANTESDE INGENIERÍA ELÉCTRICA, ELECTRÓNICA Y COMPUTACIÓN(II CIBELEC 2005)

[6] NandKishor, Marcelo GradellaVillalva, SoumyaRanjanMohanty, ErnestoRuppert, “Modeling of PV Module with Consideration of EnvironmentalFactors,” IEEE,

[7] Yi-Hua Liu, Jia-Wei Huang, “A fast and low cost analog maximum powerpoint tracking methodfor low power photovoltaic systems”,Solar Energy85 (2011) 2771–2780

[8] BasimAlsayid,JafarJallad,“Modeling and Simulation of PhotovoltaicCells/Modules/Arrays,” International Journal of Research and Reviews inComputer Science (IJRRCS) Vol. 2, No. 6, December 2011, ISSN: 2079-2557

[9] KashifIshaque, ZainalSalam, HamedTaheri, “Simple, fast and accuratetwo-diode model for photovoltaic modules”, Solar Energy Materials&Solar Cells95 (2011)586–594.

[10]OrhanEkren, Banu Y. Ekren, “Size optimization of a PV/wind hybridenergy conversion system with battery storage using simulated annealing”,Applied Energy 87 (2010) 592–598.

[11]KashifIshaque, Zainal Salam , HamedTaheri, Amir Shamsudin., “A criticalevaluation of EA computational methods for Photovoltaic cell parameterextraction based on two diode model”,Solar Energy 85 (2011) 1768–1779

[12]Vladimir V. R. Scarpa, Simone Buso, Giorgio Spiazzi, “Low-ComplexityMPPTTechnique Exploiting thePV Module MPP LocusCharacterization”,IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL. 56, NO. 5, MAY 2009.

[13]Sangmin Han, “PHOTOVOLTAIC SYSTEM FORSTANDALONE/GRID-CONNECTED APPLICATIONS”, MichiganState University in partial fulfillment of the requirements for the degree ofMASTER OF SCIENCE, Electrical Engineering, 2010.

Simulated Annealing Modeling and Analog MPPT …Simulated Annealing Modeling and Analog MPPT Simulation for Standalone Photovoltaic Arrays G.El-Saady, El-NobiA.Ibrahim, Mohamed EL-Hendawi

Documents