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Integrating photovoltaic and power converter characteristics for energy extractionstudy of solar PV systems

Shuhui Li*, Timothy A. Haskew, Dawen Li, Fei HuDepartment of Electrical and Computer Engineering, University of Alabama, Tuscaloosa, AL 35487, USA

a r t i c l e i n f o

Article history:

Received 17 June 2010Accepted 21 February 2011Available online 25 May 2011

Keywords:

Solar powerPhotovoltaic cellPower converterMaximum energy extractionGrid interfaceModeling and simulation

a b s t r a c t

Solar photovoltaic (PV) energy is becoming an increasingly important part of the world s renewableenergy. A grid-connected solar PV system consists of solar cells for energy extraction from the sun andpower converters for grid interface. In order for effective integration of the solar PV systems with theelectric power grid, this paper presents solar PV energy extraction and conversion study by combiningthe two characteristics together to examine various factors that may affect the design of solar PV systems.The energy extraction characteristics of solar PV cells are examined by considering several practicalissues such as series and parallel connections, change of temperatures and irradiance levels, shading ofsunlight, and bypassing and blocking diodes. The electrical characteristics of power converters arestudied by considering physical system constraints such as rated current and converter linear modulationlimits. Then, the two characteristics are analyzed in a joint environment. An open-loop transientsimulation using SimPowerSystem is developed to validate the effectiveness of the characteristic studyand to further inspect the solar PV system behavior in a transient environment. Extensive simulationstudy is conducted to investigate performance of solar PV arrays under different conditions.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

Investment in solar photovoltaic energy is rapidly increasingworldwide[1]. A grid-connected solar photovoltaic (PV) systemconsists of a PV generator that produces electricity from sunlightand power converters for energy extraction and grid interfacecontrol[2,3]. The smallest unit of a PV generator is a solar cell anda large PV generator is built by many solar cells that are connectedtogether through certain series and parallel connections[4]. Unlikethe traditional power generation, the operation of a grid-connectedsolar PV system depends on the coordination of the electricalsystem and PV cells under variable weather and system conditions.In order for an optimal design of the integrated system, it is

important to investigate how the electrical characteristics of thepower converter and the physics characteristics of the solar cellsaffect the design, energy extraction and grid integration of a solarPV system.

Traditionally, solar cell and power converter characteristics areusually inspected in separate environments at the PV generatorand grid integration levels, respectively [2,4,5]. Different fromprevious studies [4e8], the main features of this paper are 1)

a study of power converter electrical characteristics using a d-qsteady-state model, 2) an examination of extracted solar powercharacteristics under different weather and system conditions, 3)an integration of PV generator characteristics with powerconverter characteristics in a joint environment, and 4) a transientsimulation assessment for comparison with the characteristicevaluations.

In the sections that follow, the paper rst introduces the generalcongurations of a grid-connected solar PV system as well as thecontrol strategies at the PV generator and power converter levels inSection2. Section3presents a d-q steady-state model of the grid-connected power converter system and electrical characteristics ofthe power converter under different d-q control conditions. A solar

cell model is presented in Section 4, which is used for energyextraction and grid integration study of the solar PV system byincorporating electrical characteristics of the power converter andextracted power characteristics of the PV generator together.Section5studies how temperature and insolation level variationswould affect the power converter and PV generator. Section 6investigates how the integrated PV generator and powerconverter are inuenced when uneven sunlight is applied to solarcells. Section7presents integrated transient simulation evaluationof various parametric data of the PV system concurrently underdifferent operating conditions. Finally, the paper concludes withthe summary of main points.

* Corresponding author.E-mail address:[email protected](S. Li).

Contents lists available at ScienceDirect

Renewable Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ l o c a t e / r e n e n e

0960-1481/$e see front matter 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.renene.2011.02.016

Renewable Energy 36 (2011) 3238e3245
mailto:[email protected]://www.sciencedirect.com/science/journal/09601481http://www.elsevier.com/locate/renenehttp://dx.doi.org/10.1016/j.renene.2011.02.016http://dx.doi.org/10.1016/j.renene.2011.02.016http://dx.doi.org/10.1016/j.renene.2011.02.016http://dx.doi.org/10.1016/j.renene.2011.02.016http://dx.doi.org/10.1016/j.renene.2011.02.016http://dx.doi.org/10.1016/j.renene.2011.02.016http://www.elsevier.com/locate/renenehttp://www.sciencedirect.com/science/journal/09601481mailto:[email protected]

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2. Grid-connected solar PV systems

A grid-connected solar PV system consists of three parts: anarray of solar cells, power electronic converters, and an integratedcontrol system [9]. A solar cell is a semiconductor device thatconverts sunlight into direct-current electricity. Normally, solarcells are connected in series to form a module that gives a stan-dard dc voltage. For an application, modules are connected into anarray to produce sufcient current and voltage to meet a demand[4]. There are generally two ways to connect PV modules into anarray. The rst approach connects modules in series into stringsand then in parallel into an array. The second approach rst wiresmodules together in parallel and then those units are combined inseries. For practical applications, PV system optimization methodsare normally employed [10]. In practice, sizing the systems hasbeen established based on system performance, componentmodeling, technical-economical considerations and system reli-ability [11]. Techniques of PV array optimization are especiallyuseful for manufacturers who do not have detailed informationabout the future implementation of their products. The optimumconguration depends on the general radiative characteristics ofthe place, showing a clear dependence on latitude [12]. Several

other PV array interconnection schemes known in practice are alsoreviewed in[13].

Ideally, both series-parallel and parallel-series connections areequivalent if all the cells and modules are identical and work at thesame condition. But, if sunlight is applied unevenly to different PVcells as well as shading or other impacts, the second connectionapproach could cause many very bothersome problems [2]. Thecontrol system of a solar PV system contains two parts: one formaximum power point tracking (MPPT) and the other for gridinterface control [14e17]. Both control functions are achievedthrough power electronic converters. There are three typical powerconverter congurations[18]: 1) a dual-stage converter congu-ration including a dc/dc boost converter performing the MPPT anda grid-connected dc/ac converter performing grid interface control,

2) a conguration with multi-string dc/dc converters and a grid-connected dc/ac converter, and 3) a single-stage dc/ac converterhandling all the tasks such as MPPT and grid interface control.Fig. 1shows a PV array with converter conguration 2.

For converter congurations 1 and 2, the voltage applied to eachstring is

Vs 1 D$Vdc (1)whereVdcis the dc-link voltage andDis the duty ratio of the boostdc/dc converter. For conguration 3, the dc-link voltage is applied

to the parallel strings directly. In general, the MPPT control isachieved by varying the dc voltage applied to the PV generator.Typical MPPT strategies include Perturb and Observe, IncrementalConductance, Voltage-Based MPPT and Current-Based MPPT.

In the Perturb and Observe approach, a slight dc voltageperturbation is introduced. If the output power of the PV generatorincreases, then the perturbation is continued in that direction.Otherwise, the perturbation is changed to the opposite direction.The process continues until the maximum power point (MPP) isreached[19,20].

In the Incremental Conductance approach, the perturbationvoltage is calculated through the derivative of the output powerover the PV generator dc voltage [21]. Hence, compared to thePerturb and Observe approach, the Incremental Conductanceapproach is faster and more stable to get to the MPP.

In the Voltage-Based MPPT approach, it is assumed that an MPPof a particular solar PV module lies at about 0.8 times the opencircuit voltage of the module. Then, based on this relationship,a feed forward voltage control scheme can be implemented to bringthe solar PV module voltage to the MPP [22]. However, the opencircuit voltage and the MPP of the module vary with temperatureand other factors so that the MPP for a practical PV application is

hard to get by using this technique.In the Current-Based MPPT approach, it is assumed that an MPP

of a PV module lies at the point about 0.9 times the short circuitcurrent of the module. Similar to the Voltage-Based approach, theshort circuit current and the MPP of the module may be affected byinsolation levels so that the MPP for a practical PV application isalso hard to get by using this method[23].

3. Power control characteristics of grid-connected dc/ac

converter

For all the three converter congurations, the dc/ac inverteroperates on a similar principle, i.e., a control goal to assure theactive power from the solar array being transferred to the ac gridand the reactive power of the ac system at a desired value whilemaintaining a high power quality in terms of harmonics andunbalance.Fig. 2shows the schematic of the grid-connected dc/acconverter system, in which a dc-link capacitor is on the left, a three-phase voltage source representing the grid voltage at the Point ofCommon Coupling (PCC) is on the right, and a grid lter is inbetween.

In the d-qreference frame, the voltage balance across the gridlter is[16,17]

Fig. 1. Dual stage multi-string converter con

guration of grid-connected photovoltaic systems.

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vd1vq1

R

idiq

Ld

dt

idiq

usL

iqid

vdvq

(2)

where usis the angular frequency of the grid voltage, and L and Rare the inductance and resistance of the grid lter. Using spacevectors, Eq.(2)can be expressed by a complex Eq.(3)in whichvdq,idq, and vdq1 are instantaneous space vectors of PCC voltage, linecurrent, and converter injected voltage to the grid.

vdq1 R$idq Lddtidq jusL$idq vdq (3)Under the steady-state condition,(3)becomes:

Vdq1 R$Idq jusL$Idq Vdq (4)

whereVdq, Idqand Vdq1stand for the steady-state space vectors ofPCCvoltage,grid current, and converterinjected voltage to the grid.

The general approach used in the controller design of the grid-connected dc/ac converter is the PCC voltage oriented frame[16,17,24], i.e., thed-axis of the reference frame is aligned along thePCC voltage position. Hence, in terms of the steady-state condition,Vdq Vd j0. Assuming Vdq1 Vd1 jVq1 and neglecting thelter resistance, then, the steady-state current owing between the

PCC and the converter according to Eq.(4)is:

IdqVdq1 Vdq

jXL Vd1 Vd

jXL Vq1

XL(5)

in which XLstands for the grid lter reactance.Supposing generator convention is applied, i.e., power owing

toward the grid as positive, then, the power transferred from theconverter to the grid can be achieved from the basic complex powerequation,PgjQg VdqI*dq VdI*dq. By solving this powerequationtogether with Eqs.(5), (6)is obtained,

PgVdVq1

XL; Qg Vd

XLVd1 Vd (6)

According to Eq. (6), the active and reactive powers arecontrolled through q and d components Vq1 and Vd1 of the converterinjected voltage to the grid, respectively. If the lter resistance isconsidered, the similar power control characteristics of the grid-connected converter still exist as shown by[25]. For any powercontrol conditions, though, the converter must operate within therated current and converter linear modulation limits as shown byEq.(10)whereIratedis the rated phase rms current of the converterand Vconv is the phase rms voltage of the converter outputvoltage[26].

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiI2d I2q3

s Irated; Vconv

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2

d1 V2q13

s Vdc

2 ffiffiffi2p (10)

4. Characteristics of solar PV arrays

Control of power converters in a solar PV system relies stronglyon the PV generator characteristics. In most existing grid integra-tion study of a solar PV array, a solar cell is modeled by a currentsource, representing the photogenerated currentIL, in parallel witha diode. For a practical solar cell, however, two additional effectsmust be considered, i.e., 1) current leaks proportional to theterminal voltage of a solar cell and 2) losses of semiconductor itselfand of the metal contacts with the semiconductor[2,4,27]. The rstis characterized by a parallel resistance Rpaccounting for currentleakage through the cell, around the edge of the device, andbetween contacts of different polarity (Fig. 3). The second is char-acterized by a series resistance Rs, which causes an extra voltagedrop between the junction voltage and the terminal voltage of thesolar cell for the same ow of current.

The relationship between the currentIcproduced by a solar celland the output voltage Vcof the cell is

Ic IL I0

0

@e

qVdmkT 1

1

A Vd

Rp; Vc Vd Ic$Rs (11)

where the photocurrent IL is proportional to the illuminationintensity, the diode reverse saturation current I0 depends ontemperature, m is diode ideality factor (1 for an ideal diode), q is theelementary charge,kis the Boltzmanns constant, andTis absolutetemperature[2,4].

Important characteristics fora solar cell areoutput current Icandoutput power Pc versus output voltage Vccharacteristics. Whenconsidering both Rp and Rs, the characteristics of a solar cell areobtained by varying the voltage Vdapplied to the diode and thencomputingIcandVcfor eachVdvalue Eq.(11). The characteristics ofa solar array are integration of all the solar cell characteristics. Ifassuming allthe cellsof a solararrayareidentical andfunction underthe same conditions of illumination and temperature, then, the

currentI

aand terminal voltageV

aproduced by the solar array areIa NpIc Va NsNcVc (12)whereNcis the number of cells connected in series in a module,Nsis the number of modules connected in series in a string, and Npisthe number of strings connected in parallel (Fig. 1). For a givennumber of total modules in an array, the characteristics of a solararray depend on Np and Ns. In general, for modules in series, the IeVcurves are added along the voltage axis; for modules in parallel, theIeVcurves are added along the current axis. Regarding the PeVcharacteristics, the maximum extracted power is almost notaffected byNpand Ns. However, the PeVcharacteristics extend orshrink along the voltage axis depending on the number of modulesin a string. It is also found from the simulation study that if all the

cells operate at the same condition, the MPP voltage Vamaxof thesolar array can be estimated from the MPP voltage Vcmaxof a solarcell by

Vamax NsNcVcmax (13)

Rp

Rs Ic

+

- -

+

IL Id Vd Vc

Fig. 3. Solar cell equivalent circuit model.

Fig. 2. Grid-connected dc/ac converter schematic.

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Although the maximum extracted power does not change withNpand Ns, how to select the values ofNpand Nsaffects the powerconverters for MPPT and grid interface control. Assuming themaximum extracted power from a solar array is Pamaxand the gridreactive power should be zero, then, according to Eq.(6)theqanddcomponents of the converter output voltage should be:

Vq1 XLPamax

Vd ; Vd1 Vd (14)Therefore, to meet the converter linear modulation constraint,

the dc capacitor voltage according to Eq. (10)should satisfy thefollowing condition:

Vdc Vdcmin 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

23

V2d

XLPamax

Vd

2!vuut (15)Hence, for converter congurations 1 and 2, the dc-link voltage

Vdcmust be maintained, through the control of the grid-connecteddc/ac converter, at a reference value Vdc_ref that is larger thanVdc_min. If a Vdc_refis selected, then, the MPPT control by the dc/dcconverters requires that the number of the series modules in

a string according to Eqs.(13) and (1)should satisfy

NsVdcref

NcVcmax(16)

Nevertheless, thissituationis different forconverter conguration3 since the dc/ac converter is used for both the MPPT and grid inter-face control. From the converter linear modulation standpoint,control of thegrid-connected dc/ac convertermustmaintain a dc-linkvoltage that satises Eq.(15). Since this dc voltage is also used forMPPT control of the solar PV array, the number of series modules ina string must be large enough so that Vamax> Vdc_minfrom the MPPTcontrol requirement perspective. Therefore, different from convertercongurations 1 and 2, Ns must meet the following condition forconverter conguration 3 according to Eqs.(13) and (15).

Ns 2NcVcmax

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi23

V2d

XLPcmax

Vd

2!vuut : (17)

5. Temperature and insolation impact to converter and PV

array integration

5.1. Effect of temperature

Temperature affects the characteristic Eq. (11) of a solar cellprimarily in thefollowing twoways: directlyvia Tin the exponential

term of Eq. (11)and indirectly via its effect on the reverse-biassaturation currentI0. The impact of temperature to photocurrentILis small and can be ignored[2]. The dependence of the reverse-biassaturation currentI0on temperature for a silicon solar cell is

I0T K$T3$eEGOkT (18)

where K and EGO (the bandgap at 0 K) are both approximately

constant with respect to temperature [2,4]. The overall effect oftemperature on solar PV array characteristics can be studied byconsidering Eq. (18) in Eqs. (11) and (12). In general, as thetemperature increases, the MPP voltage reducesand the MPP powerdrops signicantly, indicating that photovoltaic cells perform betteron cold days than hot ones. Therefore, the temperature affects theintegration of PV generator with power converters. Fig. 4showsVamax vs. Ns characteristicsas wellas Vdc_min calculatedusing Eq. (15)for four different temperatures. As it can be seen from the gure,underthesame Ns value, the higherthe temperature, the smaller theMPP voltage. But, Vdc_minchanges very little. Thus, for convertercongurations 1 and 2, if the MPP voltage is above the dc-linkvoltage due to a low temperature, the MPPT control effectivenesswill be affected; for converter conguration 3, if MPP voltage is

belowVdc_mindue to a high temperature, the dc/ac converter maynot be able to maintain the effectiveness of both MPPT and gridinterface controls. Those factors must be considered in designinga solar PV system. Otherwise, the efciency and stability of theoverall system could be affected in a feedback control environment.

5.2. Effect of illumination intensity

Over a wide operating range, the photocurrent of a solar cell isdirectly proportional to the intensity of irradiance levels. If thephotocurrent at the level of irradiance dened asunity is IL1, then, thephotocurrentatalevelofirradianceXcanbeapproximatedby IL X,IL1[2]. Although this approximation behaves worse with increasingconcentration, the photocurrent usually increases with the increaseof

the level of irradiance. Therefore, conclusions obtained based on thisapproximation should still be applicable to common cases. Fordifferent irradiance levels, theIeVandPeVcharacteristics of a solararray can be investigated by considering the property ofIL X,IL1inEqs.(11) and (12). In general, as the irradiance level decreases, themaximum power drops greatly but the MPP voltage remains almostunchanged. Similar toFig. 4,the required minimum dc-link voltageVdc_min calculated using Eq. (15)does not change much. Hence, unlikeresults obtained in Section 5.1, the change of irradiance levelshas verylittle impact to MPPT and grid interface control of a solar PV system.

The study presented above shows that as the temperature orillumination intensity varies, the MPP voltage may change and themaximum extracted solar power may change[28]but the requiredminimum dc-link voltage Vdc_min does not change much.

5 10 15 20 25 30 35 40 45 500

200

400

600

800

1000

1200

# of modules in a string

PVa

rrayvoltage(V)

0 C

25 C

50 C

75 C

Vdcmin

Fig. 4. Vdc_min and MPP voltage vs.Ns characteristics for PV array varying cell temperatures ( Np

10,Ns

20, Nc

36).


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Traditionally, control goals of the grid-connected dc/ac converterinclude (i) assuring active power to be transferredfrom the solar PVarray to the grid, and (ii) compensating the reactive power absor-bed from the grid by the converter completely. However, under theconstraint of Eq.(10), it may be impossible to ndVd1andVq1thatsatisfy both control requirements at the same time, particularly astemperature changes (Fig. 4). Hence, due to the converter ratedpower and linear modulation constraints, it is appropriate todevelop a new control strategy, in which the primary control goalshould be to maintain active power control effectiveness, i.e.,keeping the maximum power extracted by the PV array (Pamax)equal to the power transferred to the grid through the converter(Pgrid) when neglecting the converter losses, and the secondary

control goal should be to keep the resultant reactive powerabsorbed fromthe grid by the PV system Qgrid as close as possible tothe reactive power reference Qgrid*. This results in a nonlinearprogramming or an optimal control strategy as illustrated below.

Minimize :Qgrid Q*grid

Subject to : Pgrid Pamax;ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

I2d I2q3

s Irated;

Vconvffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

V2d1 V2q1

3

s Vdc

2ffiffiffi2p

6. Shading impacts to PV array and power converter

integration

The analysis in the above sections is based on the assumptionthat all the cells and modules making up the PV generator areidentical and work under the same condition. But in reality, thecharacteristics of the cells and modules are subject to some varia-tions. This may happen when uneven sunlight is applied to a solarPV array, unclean PV cells, variation of the cell parameters to beexpected from manufacturing process, or other conditions [2,4].When a PV cell is shaded, for example, the photocurrent ina module or a string has to pass through the parallel resistance Rp ofthe cell as shown inFig. 3. This means that the shaded cells, instead

of adding to the output voltage and power, actually reduce it.Therefore, even a single shaded cell in a long string of cells caneasily cut output power by more than half and create potentialdamaging hot spots in the shaded cell[2,4]. Thus, external bypassdiodes are normally utilized to mitigate the impacts of shading onPeVcurves as shown byFig. 5. In addition, blocking diodes are alsoused at the top of each string to prevent a shading or malfunc-tioning string from withdrawing current from the rest strings thatare wired together in parallel.

The shading inuence to thePeVcharacteristics of a solar arraydepends on the distribution of the shaded cells within the PV array.Assuming the bypass diodes are ideal, then, the diode of a moduleturns on when the photogenerated voltage of the module is lessthan the voltage drop over Rpof the shaded cells in the module.

Hence, output power from a series string should be computed by

Fig. 5. Bypass and blocking diodes in a solar PV generator.

Fig. 6. Solar array characteristics under shading condition ( T

25

C,Np

10,Ns

20, Nc

36).


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considering whether the voltage drops of the shaded cells withina module cause the bypass diode turning on or off. If there are ncells that are 100% shaded within one module while the rest cellswithin the module is in full sun, the current, voltage and powerequations of one string containing the shaded module are:

8>>>>>>>>>:

Is Ic IL I0

e

qVdmkT1

!Vd

RpVs NsNcnVd Ic,Rsn,IcRp; bypassdiodeisoffVs Ns 1NcVd Ic,Rs; bypassdiodeisonPs IsVs

(19)

where Is, Vs, and Psare output current, voltage and power of thestring. It can be calculated from Eq. (19) that with the bypassdiodes, the output power of a single PV string can be improvedconsiderably if all the shaded cells only exist in one module. But, ifthere are more modules containing shaded cells, the IeVand PeVcharacteristics are more complicated. In general, the IeVor PeVcharacteristics of a string when considering shading impact depend

on howmany modules areshaded, howmanycells within a moduleare shaded, and how much each cell is shaded. For an array of PVmodules, theIeVandPeVcharacteristics of the array also dependon how many strings contain shaded cells.

For a solar PV array with Ns 20 andNp 10,Fig. 6a shows thePeVcharacteristics of the array under the conditions that 1) none ofthe cells in the array are shaded, 2) only four modules in one stringcontain 100%shadedcells and the rest cells of the PVarray are in fullsun, and 3) only eight modules in one string have 100% shaded cellsandtherestcellsofthePVarrayareinfullsun.Fig.6bshowsthe PeVcharacteristics of the solar array under the condition that fourmodules in one string contain 100% shaded cells, eight modules inanother stringcontain100%shadedcells, andthe rest modules of thePVarrayareinfullsun.AsshownbyFig.6,underashadedcondition,

thePe

Vcharacteristics may have multiple peaks depending on theshading distributionoverthe cells in thePV array. This resultimpliesthat using conventional MPPT control mechanisms (Section2), it ispossible to get into a local MPP under a shading condition for a PVsystem using converter congurations1 and3, which would greatlyreduce the efciency of the solar PV array when a local MPP isreached. In order to get to the global MPP, new control strategiesmust be developed if converter congurations 1 and 3 are adopted.For converter conguration 2, however, MPPT control is obtainedseparately for each individual string by controlling the dc/dcconverter of each string so that the maximum output power of thesystem is the summation of MPP powers of all the strings.

It is necessary to point out that the global MPP power obtainedfor converter congurations 1 and 3 is different from the summa-tion of MPP powers obtained for converter conguration 2.

In general, the ratio of global MPP power of a PV array over thesummation of MPPpowers of all the PV strings varies depending onthe shading distribution. For a PV array having only two strings ofPVmodules in parallel, in which PVcells in one string operate in fullsun while the PV cells in the other string may be shaded, it was

found that the lowest ratio occurs around a point that half of themodules contain 100% shaded cells in one string while all the PVcells in the other string operate in full sun.

7. Integrative study of solar PV system

The solar PV system is further investigated and veried throughan integrative transient simulation method. The transient simulationof the solar PV system is developed by using MatLab SimPo-werSystens. In the transient environment, characteristicsof the solar

Fig. 7. Solar PV generator under the control of a dc/dc power converter using SimPowerSystems.

Fig. 8. Transient simulation results of a PV array when all cells operate at the same

condition: a) Voltage applied to the PV array, b) Photogenerated current, c) PV array

output power.


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PV system are investigated under more realistic conditions, whichinclude 1) actual circuit connection of the solar PV array, 2) highswitching frequency power converters, 3) blocking and bypassingdiodes, and 4) losses of the power converters and the system. Fig. 7shows the transient simulation schematics of the solar PV system inan open-loop control condition for converter congurations 1 and 2.The dc voltage source represents the dc-link voltage between thedc/dc converterand the dc/ac inverter. The dc/dc converter is a boostconverter, i.e., power ows from the PV array to the dc voltagesource. Each string of PV modules is represented by a subsystemcontaining all the PV modules in series with a blocking diode on thetop. The number of series and parallel PV modules are 20 and 10,respectively. Major measurements include current and voltage ofeach PV module, current and voltage of the PV array, and the pho-togenerated power of the PV array. For the power measurement,generator sign convention is used, i.e., power generated by the PVarray and transferred to the dc source is positive.

Fig. 8demonstrates transient results when all the PV cells are inthe sun and operate at the same condition. The dc source voltage is500V.Before t 2s,thedutyratioDofthedc/dcconverteris0.6.Afterthe system is stable, the dc voltage applied to the PV array is 200.7 V(Fig. 8a) which is veryclose to thetheoretical calculation of (1-D),Vdcforthedc/dc converter. The photogeneratedcurrentand powerof thePV array are around 33.6 A and 6.7 kW, respectively, which areconsistent with the steady-state results that can be obtained bysolving(19). At t 4 s,the duty ratioof the dc/dc converterchangesto0.4causingtheterminalvoltageoftheboostdc/dcconverterrisingup.However, the output current of the PV array does not change much(Fig. 8b), reecting that the PV cells still operate near the constantcurrent region. At t 6s,thedutyratioofthedc/dcconverterchangesto 0.2and thevoltage applied to thePV array increases to 400. At thisvoltage level, the output current of the PV cells decrease due to theequivalentdiodeeffectandtheoutputpowerofthePVarraydropstoo(Fig. 8c). All thetransientresultsafter thePV system is stable foreachcontrol condition change are consistent with the steady-state resultsthat can be calculated from Eq. (19), demonstrating the effectiveness

of both transient and steady-state computations.

8. Conclusions

This paper presents an energy extraction and grid interfacecontrol study of a solar PV system by combining the energyextraction characteristics of the PV generator and the electricalcharacteristics of the power converters jointly in one environmentfor an integrative investigation.

Through the integrated study, it is found that the operation ofa solar PV system is determined by the PV generator, the dc-linkvoltage and the power converters. If an ac/dc/dc converter cong-uration is used between the grid and the PV array, the dc-linkvoltage must be designed to be larger than the highest of the

following two voltage values: 1) the maximum MPP voltage of thePV array for all the possible temperatures and irradiance levels, and2) the dc-link voltage that can meet reactive power compensationrequirement under the highest possible power transferred from thePV array to the grid. If only an ac/dc converter is used between thegrid and the PV array, the series number of solar PV array must beselected in such a way that the minimum MPP voltage of the PVarray for all the possible temperatures and irradiance levels mustbe large enough so that the ac/dc converter can meet reactivepower compensation need under the highest possible powertransferred from the PV array to the grid. Otherwise, maximumpower extraction of the PV array and/or the proper operation of theac/dc converter may be affected. To assure stable and reliableoperation of a solar PV system while maximizing the power

transferred from the PV generator to the grid for all conditions, it is

benecial to develop an optimal control mechanism for the grid-connected dc/ac converter.

Under uneven shading situations, the PeVcharacteristics of a PVarray may exhibit multiple peaks because the peak power of eachPV string does not appear at the same external voltage applied tothe PV array. Thus, if using an ac/dc converter or an ac/dc/dcconverter between the grid and PV array, the MPPT control strategymust be designed to be able to locate the highest peak powerproduction of the PV array. But, if using an ac/dc converter plusmultiple dc/dc converters, each dc/dc converter connected toa string of PV modules is able to nd the peak power production ofthat PV string, and the total power production of all the strings isthe summation of the peak powers of all strings, making themultiple dc/dc converter structure has the highest efciencycompared to the other two converter congurations.

Acknowledgment

This work was supported in part by the U.S. National ScienceFoundation under Grant 1059265.

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