photovoltaic generator as an input source for power

3028 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 6, JUNE 2013

Photovoltaic Generator as an Input Source for PowerElectronic Converters

Lari Nousiainen, Student Member, IEEE, Joonas Puukko, Student Member, IEEE, Anssi Maki, Student Member, IEEE,Tuomas Messo, Student Member, IEEE, Juha Huusari, Student Member, IEEE, Juha Jokipii, Student Member, IEEE,

Jukka Viinamaki, Diego Torres Lobera, Student Member, IEEE, Seppo Valkealahti, Member, IEEE,and Teuvo Suntio, Senior Member, IEEE

Abstract—A photovoltaic (PV) generator is internally a power-limited nonlinear current source having both constant-current-and constant-voltage-like properties depending on the operatingpoint. This paper investigates the dynamic properties of a PV gen-erator and demonstrates that it has a profound effect on the opera-tion of the interfacing converter. The most important properties aninput source should have in order to emulate a real PV generatorare defined. These properties are important, since a power elec-tronic substitute is often used in the validation process instead of areal PV generator. This paper also qualifies two commercial solararray simulators as an example in terms of the defined properties.Investigations are based on extensive practical measurements ofreal PV generators and the two commercial solar array simula-tors interfaced with dc–dc as well as three- and single-phase dc–acconverters.

Index Terms—Converter, inverter, photovoltaics (PVs), solararray simulator, validation.

I. INTRODUCTION

INSTALLED capacity of photovoltaic generator (PVG)-based energy systems is rapidly growing due to advantageous

public and political climates [1]. Such systems are interfaced todc or ac loads with power electronic devices, which have beenshown to cause, e.g., harmonic distortion, reduce damping inthe utility grid, and suffer from reliability problems [2]–[5].These phenomena can even lead to instability or productionoutages and are expected to increase as the penetration depthof distributed generation grows [6], [7]. Therefore, an extensivevalidation process, which characterizes dynamic properties ofthe proposed interfacing converters, is of utmost importance toovercome or minimize the problems.

The input source has a significant effect on converter dynam-ics, as discussed in detail in [8]–[10]. A PVG is internally a

Manuscript received April 10, 2012; revised June 12, 2012; accepted July 10,2012. Date of current version December 7, 2012. Recommended for publicationby Associate Editor Q.-C. Zhong.

L. Nousiainen and J. Puukko were with the Department of ElectricalEnergy Engineering, Tampere University of Technology, Finland. They arenow with ABB Drives, Helsinki, Finland (e-mail: [email protected];[email protected]).

A. Maki, T. Messo, J. Jokipii, J. Viinamaki, D. T. Lobera,S. Valkealahti, and T. Suntio are with the Department of Electrical EnergyEngineering, Tampere University of Technology, Tampere, Finland (e-mail:[email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

J. Huusari is with ABB Corporate Research, Baden-Dattwil, Switzerland(e-mail: [email protected]).

Digital Object Identifier 10.1109/TPEL.2012.2209899

power-limited nonlinear current source having both constant-current (CC) and constant-voltage (CV) like properties depend-ing on the operating point [11], which implies that the dynamicsof a photovoltaic interfacing converter (PVIC) cannot be vali-dated solely by using a voltage or current source as the inputsource. Therefore, the validation should be performed using areal PVG as the input source.

If a real PVG is to be used in the PVIC validation process, anartificial light source providing controllable illumination shouldbe used to guarantee the repeatability of the measurements.This can be accomplished cost effectively in small scale, e.g.,for a single PV module, but is impractical for larger systems.Therefore, a PVG is usually replaced with a power electronicsubstitute, i.e., a solar array simulator, so that time-invariantconditions can be guaranteed in the validation.

This paper presents the dynamic properties of a real PVG,defines the most significant parameters that will have an ef-fect on PVIC dynamics, and demonstrates these effects by ex-perimental measurements based on dc–dc as well as single-and three-phase dc–ac converters. This paper also qualifies twocommercial solar array simulators as an example in terms ofthe defined properties and analyzes the differences between thesolar array simulators and real PVGs both in time and frequencydomains.

The rest of the paper is organized as follows. The dynamicproperties of PVGs are reviewed in Section II. The effects ofPVG on the interfacing converter dynamics are presented inSection III. Section IV compares the dynamic properties of thecommercial solar array simulators with real PVGs and definesthe characteristics an input source should have in order to emu-late a real PVG. Conclusions are drawn in Section V.

II. DYNAMIC PROPERTIES OF A PV GENERATOR

A simplified electrical equivalent circuit of a PV cell com-poses of a photocurrent source with parallel-connected diodeand parasitic elements, as depicted in Fig. 1 [11], [12]. In Fig. 1,ipv and upv are the output current and voltage of the PV cell,respectively, iph is the photocurrent, which is linearly propor-tional to the irradiance, icpv is the current through the shuntcapacitance cpv , and irsh is the current through the shunt resis-tance rsh . The shunt and series resistances rsh and rs representvarious nonidealities in a real PV cell. The relation betweendiode current id and voltage ud can be modeled with an ex-ponential equation, yielding a nonlinear resistance rd that canbe used instead of the diode symbol in Fig. 1 [11], [13]. The

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NOUSIAINEN et al.: PHOTOVOLTAIC GENERATOR AS AN INPUT SOURCE FOR POWER ELECTRONIC CONVERTERS 3029

phi

di cpvi rshi

shrpvc

sr

pvi

du pvudr

Fig. 1. Simplified electrical equivalent circuit of a photovoltaic cell.

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.2

0.4

0.6

0.8

1.0

1.2

Voltage (p.u.)

Cur

rent

, pow

er, r

esis

tanc

e

ipv

ppv

rpv

cpv

CC

MPP

CV

and

capa

cita

nce

(p.u

.)

Fig. 2. Static and dynamic terminal behavior of a PVG.

one-diode model can also be used to model the operation ofa PV module, i.e., a series connection of PV cells, by scalingmodel parameters, as presented in [12].

The measured static and dynamic characteristics of a PV mod-ule are shown in Fig. 2 as normalized (p.u.) values. The mea-surement setup has been reported earlier in detail in [14]. Thestatic current–voltage and power–voltage characteristics showthat the PV module is a highly nonlinear current source havinglimited output voltage and power. In order to maximally utilizethe energy of solar radiation by using a PVG, the operating pointhas to be kept at the maximum power point (MPP) in which

dppv

dupv=

d(upv ipv)dupv

= Ipv + Upvdipv

dupv= 0 (1)

where Ipv and Upv are the MPP current and voltage,respectively.

The dynamic behavior of the PV module is shown in Fig. 2 interms of its dynamic resistance rpv = rd‖rsh + rs and capac-itance cpv , which are nonlinear and dependent on the operat-ing point. The dynamic resistance represents the low-frequencyvalue of the impedance shown in Fig. 3 and is the most signif-icant variable that will have an effect on the PVIC dynamics,as presented in more detail in Section III. The dynamic capaci-tance, in turn, can be approximated from PVG impedance (see

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nitu

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dBΩ

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106

−90

−45

0

45

90

Phas

e (d

eg)

Frequency (Hz)

OC

MPP

OC

MPPSC

SC

Fig. 3. PVG impedances at short circuit (SC), MPP, and open circuit (OC).

Fig. 3) as

cpv ≈ 12πrpvf−3dB

(2)

where f−3dB is the cutoff frequency of the impedance magni-tude curve. Equation (2) gives a good estimate for cpv in theCC region, since rd‖rsh � rs . In CV region, (2) slightly un-derestimates cpv since rd‖rsh and rs are in the same order ofmagnitude, but is still sufficiently accurate.

According to Kirchhoff’s laws, the analyzed or measuredoutput impedance of a device is −Z, if the direction of positivecurrent flow is defined out of the device as in Figs. 1 and 2.Thus, the dynamic resistance rpv (or the incremental resistanceas named in [15]) is in fact positive since Δupv/Δipv in Fig. 2 isnegative and has to be multiplied by “−1” to obtain the correctimpedance.

III. DYNAMIC EFFECTS ON THE CONVERTER

Dynamic properties of a power electronic converter are deter-mined not only by the power stage but also by the type of sourceand load subsystems, which in turn define the possible feedbackvariables. It has been shown in detail in [8]–[10] that the inputsource has a profound effect on the dynamics of the converterconnected to it. The same power stage can be supplied either bya source that has current or voltage-source-like properties. Theconverter dynamics are completely different in these two cases.

According to circuit theory and control engineering princi-ples, the input variables are uncontrollable and only the out-put variables can be controlled. In practice, this means that aninput-voltage-controlled converter (as usually adopted in PVapplications for enabling maximum power transfer [16]) has tobe analyzed as a current-fed system (i.e., input current is anuncontrollable input variable and input voltage is a controllableoutput variable) as will be done in the following sections.

A. DC–AC Interfacing

Figs. 4 and 5 show conventional single- and three-phase VSI-type PV inverters usually applied in interfacing PVGs to the


ou

L

C

inu

Lr

Cr

N

Ci Pi Lu

Cu

Liini

oi

P

Fig. 4. VSI-type single-phase PV inverter.

cu

bu

au

n

aL

bL

cL

C

oai

obi

ociinu

Lar

Lbr

Lcr

CrA

B

C

P

N

Ci

Pi

LuCu

Lai

Lbi

Lci

ini

Fig. 5. VSI-type three-phase PV inverter.

+

_

d

+

_inSi

inu ou

ou

oi

inZ

oi oˆT u

ciˆG d io in

ˆG i coˆG d oY

ini

SY

Fig. 6. Linear small-signal model of a single-phase inverter [17].

utility grid. Dynamic properties of these inverters can be an-alyzed by constructing small-signal models that describe thedynamics between the uncontrollable input variables and thecontrollable output variables, as presented in Figs. 6 and 7, aslinear small-signal models. Detailed modeling procedures forthe single- and three-phase inverters can be found, e.g., from [10]and [17].

The operating-point-dependent dynamic effect of a PVG canbe taken into account by considering the source as a parallel con-nection of a current source iinS and source admittance YS . Ac-cording to Fig. 3, PVG impedance behaves as an RC circuit upto typical converter switching frequencies (c.a. 1 . . . 100 kHz).The source impedance ZS can be given according to Fig. 1 by

ZS = rs + rd‖rsh‖1

scpv=

rpv︷︸︸︷

rs + rd‖rsh +scpvrs (rd‖rsh)1 + scpvrs (rd‖rsh)

(3)

+

_

inSi

io-q inˆG i

oi-d odˆT u

oi-q oqˆT u

ci-d dˆG d

ci-q qˆG d

inZ

cr-dq odˆG uco-dq d

ˆG d co-q qˆG d o-qY

io-d inˆG i cr-qd oqˆG u

co-d dˆG d

inu

odu

oqu

odi

oqi

dd qd

co-qd qˆG d

o-dY

SY

ini

Fig. 7. Linear small-signal model of a three-phase inverter in synchronousreference frame [10].

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de (

dBA

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103

104

−360−270−180−90

090

180270

Phas

e (d

eg)

Frequency (Hz)

CCMPPCV

CVCCMPP

Fig. 8. Three-phase inverter control-to-output-current transfer functionGco-d . Measurements with solid lines, prediction using measured sourceimpedance with dotted lines, and prediction using (5) with dashed line.

which can be approximated by considering rs = 0 and rpv =rd‖rsh + rs as

ZS ≈ rd‖rsh‖1

scpv≈ rpv‖

1scpv

(4)

and further at low frequencies by

ZS ≈ rpv . (5)

The use of (5) instead of (4) is justified if the interfacing con-verter input capacitance Cin � cpv , which typically applies.Fig. 8 shows measured three-phase inverter control-to-output-current transfer functions Gco-d compared with predictions ob-tained using either the measured source impedances or theirlow-frequency values, i.e., (5), to model the effect of the source.The results show high correlation, which confirms the analysis.

According to the notations of Figs. 4 and 5 as wellas using YS = 1/ZS = 1/rpv , the control-to-output transferfunctions Gco and Gco-d without the parasitic elements for


single- and three-phase inverters can be given by

Gco =U inL

[

s − 1C

(

I i nU i n

− 1rpv

)]

s2 + 1rpv C s + D 2

LC

(6)

Gco-d =U i nL s

[

s − 1C

(

I i nU i n

− 1rpv

)]

s(

s2 + 1rpv C s + 3

2D 2

d +D 2q

LC + ω2)

+ ω 2

rpv C

.

(7)

Analysis of (6) and (7) reveals that a right-half-plane (RHP)zero appears and the sign of the transfer function changes whenthe operating point moves from the CV to the CC region of aPVG. This is due to the fact that at MPP, the dynamic resistanceof the PVG rpv coincides with the equivalent static loadingresistance (i.e., the static input impedance of the PVIC) accord-ing to the maximum power transfer theorem [18] and (1). Thedynamic resistance rpv is greater in magnitude than the staticresistance in the CC region (CCR) and smaller in the CV region(CVR) of a PVG, which will change the location of the Gco andGco-d zero in the complex plane as presented in (8) and verifiedby the experimental measurements from three-phase inverterpresented in Fig. 8

CVR: rpv < Uin/Iin ⇒ ωz < 0 LHP

MPP: rpv = Uin/Iin ⇒ ωz = 0 Origin

CCR: rpv > Uin/Iin ⇒ ωz > 0 RHP. (8)

Appearance of the RHP zero and the change of sign of thecontrol-to-output-current transfer function means that the outputcurrent control cannot be stable both in the CC and CV regionsof a PVG. Therefore, a cascaded control scheme (input-voltageoutput-current) is needed to enable the operation at all PVGoperating points and to transfer maximum power in a reliablemanner, as shown in detail in [8]–[10], and [17]. The RHP zeroin the output-current-control loop will actually turn into an RHPpole in the input-voltage-control loop when the operating pointis in the CC region of a PVG. This will naturally cause designconstraints in the input-voltage control, as discussed in [19]and [20].

B. DC–DC Interfacing

Fig. 9 shows a dc–dc converter based on a conventional boosttopology with an additional input capacitor. The dc–dc convertercan be used as an upstream converter between a PVG and aninverter resulting in a two-stage conversion scheme, as presentedin Fig. 10. The dc–dc converter is responsible for the maximum-power-point-tracking (MPPT) function by controlling its owninput voltage. The VSI-type inverter has a similar cascadedcontrol structure as in the single-stage conversion scheme, thusenabling maximum power transfer. Accordingly, both the dc–dc and the dc–ac converters in PV applications control its owninput voltage. Therefore, they must be analyzed as current-fedcurrent-output converters as previously discussed.

ou

L

1C

inu

Lr

C1r

C1i Lu+ −

+

−C1u

Li

+

−

inioi

+−

2C

C2r

C2i

+

−C2u

Fig. 9. Boost-type dc–dc converter with an input capacitor.

+ DC

DC

DC

ACacu

invi

pvu

pvi

invu

invu

aci

aci

+

_

refpvu

ACgrid_

pvuMPPT

Fig. 10. Typical two-stage grid interface for a PVG.

The additional dc–dc stage enables the use of less series-connected PV modules compared to the single-stage inverters(see Figs. 4 and 5), which may be beneficial in case of partialshading conditions [21]. The dc–dc stage can also regulate itsinput voltage to practically pure dc (i.e., provides perfect powerdecoupling), which can increase the energy yield compared tosingle-stage single-phase inverters where the dc power fluctuatesat twice the grid frequency [22].

The dynamics of the dc–dc converter, when loaded by avoltage-type load (i.e., an inverter controlling its input voltage,uo in Fig. 9), can be obtained by linearizing the switching-frequency-averaged model presented in [23] and solving thetransfer functions between the input and output variables in thefrequency domain.

The control-to-input-voltage transfer function for the con-verter in Fig. 9 without the parasitic elements can be given by

Gci-dc = − Uo

LC1

1s2 + 1

rpv C1s + 1

LC1

. (9)

According to (9) and Fig. 11, there exist no operating-point-dependent phase shift or zeros that would move between theleft and right halves of the complex plane causing control sys-tem design constraints as discussed earlier. The only differ-ence between different PVG operating points is the change inthe damping of the resonance of Gci-dc , as can be seen fromFig. 11.

The input-voltage control should be designed so that thebandwidth exceeds the MPPT-algorithm execution frequency.In addition, a bandwidth over twice the grid fundamental fre-quency would be beneficial in single-phase applications in orderto prevent the low-frequency dc-link-voltage (i.e., inverter in-put voltage) ripple from reflecting to the input terminals of thedc–dc converter and, therefore, to the PVG.


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dBV

)

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103

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−90

0

90

180

Phas

e (d

eg)

Frequency (Hz)

CCCVpred.

Fig. 11. Control-to-input-voltage transfer function.

Some researchers claim that the dc–dc converter in the two-stage conversion scheme could be used to control the dc-linkvoltage [24]–[26], which means that the inverter controls onlyits output current, because two converters cannot control thesame voltage. This control scheme does not work when theintention is to deliver maximum power from the input sourcewithout compromising the stability of the system, which willbe proven next. The transfer functions presented in [23] can beused to compute the control-to-output-voltage transfer functionusing the method presented in [27] as

GZco-dc =

uo

d=

io/d

io/uo=

GHco-dc

Y Ho-dc

(10)

where the superscript “H” denotes an H-parameter model(current-to-current converter) and “Z” denotes a Z-parametermodel (current-to-voltage converter) [28]. According to (10), thecontrol-to-output-current and voltage transfer functions sharethe same zeros and the following analysis is valid for both ofthe transfer functions. The source-affected control-to-output-voltage transfer function Gco-dc can be given according to [23]by

GZco-dc =

− I inC2

[

s2 +(

1C1 rpv

− U i nI i n L

)

s +(

1C1 L − U i n

I i n C1 Lrpv

)]

s3 + 1C1 rpv

s2 + C1 D ′2 +C2C1 C2 L s + D ′

C1 C2 Lrpv

.

(11)

Analyzing (11) and Fig. 12 reveals that the transfer functionhas a low-frequency zero located on the RHP when the PVGis operating at voltages lower than the MPP. Accordingly, theoutput control (whether output voltage or current) of the inter-facing dc–dc boost converter cannot be designed to be stable atall PVG operating points, because the Gco-dc changes its signbetween different operating regions and a low-frequency RHPzero appears.

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101

102

103

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090

180

Phas

e (d

eg)

Frequency (Hz)

CCCVpred.

Fig. 12. Control-to-output-voltage transfer function.

This implies that if the output of the dc–dc converter is tobe controller, it needs to control also its input. But a cascadedinput-voltage output-voltage control scheme for the dc–dc con-verter cannot guarantee proper dc-link voltage for the VSI-typeinverter. Also, determining the grid current reference will beproblematic. Therefore, it can be concluded that each converterin the power processing chain have to control its input termi-nals if maximum power is to be supplied into the utility grid. InPV applications, the input-current control is prone to saturation,since the MPP current is close to the short-circuit current thatis dependent on the irradiation level with relatively fast dynam-ics. The open-circuit voltage, on the other hand, is dependentmostly on the temperature with negligibly slow dynamics; thus,input-voltage control can be realized in a reliable manner [16].

Based on the previous analysis regarding dc–ac and dc–dcinterfacing, few key points can be outlined: 1) the dc–dc con-verter in the two-stage conversion scheme is responsible forthe MPPT, where input-voltage control is preferred over theopen-loop-based MPPT [23]; 2) the dc–ac converter has a cas-caded input-voltage output-current control structure both in thesingle- and two-stage conversion schemes; 3) therefore, the dc–dc and dc–ac converters in PV applications have to be analyzedas current-fed current-output converters, where the input cur-rent is the source-side input variable and the input voltage isthe source-side output variable; and 4) the practical tests haveto be carried out by using input source emulating properly thebehavior of real PVG.

IV. EXAMPLE SOLAR ARRAY SIMULATORS

Properties of two different commercial solar array simulatorsfrom two different manufacturers were evaluated. Two artificiallight units were used to illuminate the reference PV modules.The first light unit is a based on fluorescent lamps and is de-signed to produce radiation intensity of 500 W/m2 for a 30-WPV module. The second light unit based on halogen lamps isdesigned to produced the same intensity for a 190-W PV mod-ule. Both of the modules operate at half the nominal power. The


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30

40

50

60

70

Voltage (V)

Res

ista

nce

(dB

Ω)

PVG

SAS

Table

Fig. 13. Measured dynamic resistances.

0 5 10 15 20−30

−20

−10

0

10

20

30

Voltage (V)

Cap

acita

nce

(dB

μF)

PVGSASTable

Fig. 14. Measured dynamic capacitances.

first solar array simulator, device A, was evaluated by using the30-W and 190-W modules as references. The second solar arraysimulator, device B, was evaluated by using the 190-W moduleas a reference.

A. 30-W Module Emulation

The evaluated commercial power electronic substitute(device A) has three different modes of operation: SAS, tableand fixed modes. In the SAS mode, the simulator is programmedusing three reference points: short-circuit current, open-circuitvoltage, as well as current and voltage at the MPP. In the tablemode, the I–V curve is represented by voltage–current pairswith a limitation that the voltage points must be ascending andthe current points descending. In the fixed mode, a maximumvoltage is given and the simulator operates as a voltage limitedcurrent source having rectangular I–V curve characteristics.

Measured dynamic resistances and capacitances from thecommercial PVG and device A are shown in Figs. 13 and 14.Later on in the figures, the device A at the two different oper-

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Voltage (V)

Cur

rent

(A

)

SASTable

Fig. 15. Solar array simulator I–V curve comparison.

ating modes will be referred to as “Table” and “SAS.” Basedon rpv of the real PVG, it can be seen that the curve has twodistinct slopes. Because rpv is presented in dB·Ω, it is clear thatrpv would be best approximated with a two-diode (i.e., doubleexponential) model as opposed to the one-diode model of Fig. 1.The same double exponential characteristics are also visible inFig. 14, which presents the measured dynamic capacitances.

Based on Fig. 13, the device A produces similar double ex-ponential characteristics in respect to rpv when it is used in thetable mode. However, the dynamic resistance of the device Aused in the SAS mode is constant in the CV region, as can beseen from Fig. 13. This indicates that the dynamic resistanceof a real PVG can be emulated with higher precision by usingthe table mode. The operating mode of device A does not affectthe emulated dynamic capacitance, as can be seen from Fig. 14.The capacitance of the device A is considerably higher (up to30 dBμF higher) than the capacitance of the real PVG and itdoes not show double exponential characteristics.

Fig. 15 presents the I–V curves of solar array simulator inSAS and table modes. It was stated earlier that the dynamicresistance of device A in the SAS mode is constant in the CVregion. Constant dynamic resistance implies that the I–V curveis a straight line in the CV region, as can be noticed fromFig. 15. In the table mode, the device A produces I–V curvecorrectly, and thus also the dynamic resistance as was analyzedin Section II. It is worth noting that a solar array simulator canproduce the dynamic resistance of a PVG correctly only if thesimulator produces the I–V curve correctly when loaded withthe specific power electronic device under test.

Figs. 16 and 17 present step-like load change from CV to CCregion so that the power at initial and final operating points isthe same. The short-circuit current for the PVG and the deviceA model was 1.0 A. The generator current exceeds the short-circuit current value (which should be impossible based on thestatic I–V curve) because of the stored energy in the dynamiccapacitance. The overshoot is considerably smaller with the realPVG (peak current 1.222 A) than with the device A (peak current


100 µs

0.5 A divi

5 V divu

0 A

0 V

Fig. 16. Load step change in case of the PVG.

100 µs

0.5 A divi

5 V divu

0 A

0 V

Fig. 17. Load step change in case of the device A in the table mode.

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eg)

Frequency (Hz)

Table

SAS

PVGCC

CV

Fig. 18. Impedance comparison.

1.526 A) since the dynamic capacitance of PVG is considerablysmaller than that of the device A as discussed earlier. This effectshould also be taken into account when validating time-domainbehavior of interfacing converters. The high-frequency ripple inPVG current (see Fig. 16) is due to the resonant inverters drivingthe fluorescent lamp unit.

Figs. 13–16 compared the PVG and the electronic substitute interms of rpv , cpv , and time-domain responses. Fig. 18 presentsthe measured PVG and device A impedances in CC and CVregions of the I–V curve. By considering the impedance in the

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PVG

Table

CV

CV

CC

CC

Fig. 19. Control-to-output current transfer function comparison.

1L

1C

inu

L1r

C1r

C1i L1u

C1u

L1iini

ou

oi

2C

C2r

C2i

C2u

dC

dR

Cdi

Cdu

2L L2r

L2u

L2i

Fig. 20. Boost–buck-type dc–dc converter.

CC region, device A shows PVG-like characteristics but with ahigher capacitance up to c.a. 2 kHz. The impedance in the CVregion correlates up to the same frequency range. After the c.a.2-kHz frequency, the device A impedance does not show similarresistive–capacitive characteristics as the real PVG does.

This difference is visible in Fig. 19, which presents the mea-sured control-to-output-current transfer function for the con-verter in Fig. 9. The measurements are performed at the sameoperating points as the impedances in Fig. 18. It can be con-cluded by considering Figs. 18 and 19 that the low-frequencyvalue of the PVG impedance rpv is the major factor in deter-mining the dynamic properties of the converter connected to aPVG as was discussed in Section III-A. However, if the inputcapacitance of the converter and the dynamic capacitance ofthe solar array simulator are in the same order of magnitude orsmaller, the considerably higher capacitance of the solar arraysimulator has to be taken into account.

Figs. 3 and 18 show that the phase of the PVG impedancelies between ±90◦. A solar array simulator should have similarpassive-circuit-like characteristics, as in Fig. 18, in order to bejustified as a substitute for the real PVG.

B. 190-W Module Emulation

The 190-W module and the devices A and B were interfacedwith a boost–buck-type dc–dc converter shown in Fig. 20, op-erating under input-voltage-feedback control. A low-bandwidth(75 Hz) integral controller was used yielding a phase margin of


101

102

103

104

105

106

−200

204060

Mag

nitu

de (

dB)

101

102

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104

105

106

−180

0

180

360

540

Phas

e (d

eg)

Frequency (Hz)

PVGAB

CV

CC

CV for device B

Fig. 21. Impedance comparison.

200 ms

1 A divi

5 V divu

0 A0 V

5 V divu

1 A divi

Fig. 22. Input-voltage-reference ramp with the PVG.

88◦ in the input-voltage-control loop. A parallel damping circuitcomprising series connection of a capacitor Cd and a resistorRd was connected in parallel with the converter input in orderto minimize the resonant behavior of the converter.

The measured output impedances of the PVG and the devicesA and B are shown in Fig. 21. It can be observed that both ofthe devices reproduce the dynamic resistance accurately (i.e.,low-frequency impedance). The capacitance of the device B ishigher than the capacitance of device A, which again is higherthan the capacitance of the real PVG, as was the case also earlier.It can be also observed that the phase of the PVG and deviceA impedances lies between ±90◦ within the whole operatingregion, as in Fig. 18. The phase of the device B impedance issimilar to the CC region. However, the behavior of the device Bchanges dramatically when the operating point moves to the CVregion. A resonance with 270◦ phase shift occurs approximatelyat 250 Hz, which can lead to impedance-based stability problemswhen the interfacing converter is connected.

It is known that the stability and load interaction issues in avoltage-fed system can be studied by applying Nyquist stabilitycriterion to the impedance ratio of the load and source subsys-tems known as minor-loop gain (Zo/Zin ) [29]. In current-fedsystems, the stability is studied based on inverse minor-loop gain

200 ms

1 A divi

5 V divu

0 A0 V

5 V divu

1 A divi

Fig. 23. Input-voltage-reference ramp with the device A.

101

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)

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Zin

> Zo−B

< 180°

≥ 180°

CC

CV

CV

CC

Fig. 24. Input impedance of the converter and output impedance of the deviceB.

(Zin/Zo) [30]. If the impedance ratio of an interconnected stablesource and load subsystems does not satisfy the Nyquist stabil-ity criterion, the interconnected system is unstable. It can bededuced that the stability criterion will be violated in a PV sys-tem if |Zin/Zo | ≥ 1, while the phase difference exceeds 180◦.The concept of minor-loop gain is typically used to study gridinteractions between the inverters and the utility grid [6], butapplies also in the PVG/converter interface.

A triangular input-voltage-reference ramp sweeping the op-erating points between the CC and CV regions was applied inthe control system of the converter in Fig. 20. In Figs. 22 and23, the ramp was applied with the PVG and device A. As canbe seen, the system is stable within the whole operating rangeand the reference ramp is reproduced nicely. This is due to thefact that both the source and load impedance (the converter in-put impedance is shown in Fig. 24) phase lies between ±90◦.Accordingly, a phase difference of 180◦, and thus, violation ofthe stability criterion does not take place.


200 ms

1 A divi

5 V divu

0 A0 V

5 V divu

1 A divi

Fig. 25. Input-voltage-reference ramp with the device B.

Fig. 24 shows the converter input impedance Zin and theoutput impedance of the device B Zo-B in the CC and CVregions. The magnitude of the converter input impedanceexceeds the source impedance magnitude after 100 Hz in theCV region; thus, instability is predicted to occur in the CVregion since phase difference of 180◦ is found at a higherfrequency. A frequency range is found where Zin > Zo also inthe CC region, but a phase difference of 180◦ does not exist,indicating stable operation in the CC region. This informationis verified in the time domain in Fig. 25. It can be seen that thesystem is stable in the CC region but oscillates at the CV regionwhen the same input-voltage-reference ramp was applied, asshown in Figs. 22 and 23.

V. CONCLUSION

In this paper, the properties of a PV generator have beenanalyzed analytically and with experimental measurements. APV generator is internally a power- and voltage-limited non-linear current source having both CC- and CV-like propertiesdepending on the operating point. The dynamic properties ofthe generator, which include the dynamic resistance and capac-itance, are also operating-point-dependent nonlinear quantities.

The dynamic resistance of a PV generator has profound ef-fects on dynamic behavior of the interfacing converter. Thedynamic resistance is known to equal the static resistance atthe MPP. The current- and voltage-source properties of the PVgenerator can also be justified by considering the dynamic re-sistance. The dynamic resistance is greater in magnitude thanthe static resistance in the current region and lower in magni-tude in the voltage region. This property moves operating-point-dependent zeros and poles in the converter dynamics betweenthe right and left halves of the complex plane according to theoperating point of the PV generator. The appearance of RHPzeros and poles and their effect on the control dynamics of PVconverters are important to be taken into account if robust andstable PV power systems are to be designed.

Key points for the analysis, design, and testing of PV con-verters can be summarized as follows: 1) in order to transfermaximum power, an input-side variable (current or voltage)must be controlled, or the converter has to operate at open loop;2) input-voltage-feedback control is the most feasible method

to control a PV converter; 3) in case of input-voltage-controlledconverter, the converter must be analyzed in such a way thatit is fed by a current source; and 4) the nonideal PV generatorsource impedance has to be considered because of its profoundeffect on the interfacing converter dynamics.

A real PV generator is usually replaced with a power elec-tronic substitute, known as a solar array simulator, so that time-invariant and controlled testing conditions can be guaranteed inthe converter validation process without the need to invest ina large PV power plants. This paper also qualified two com-mercial solar array simulators as an example in terms of thedefined dynamic properties and analyzed the differences bothin time and frequency domains between the substitutes and realPV generators.

The measured substitutes were shown to reproduce the dy-namic resistance accurately although the dynamic capacitanceswere considerably higher and did not show similar properties asthe PV generator capacitance. It was also noticed that in orderto reproduce the PV generator characteristics with the high-est precision, the I–V curve of the electronic substitute shouldbe programmed using several current–voltage pairs if possible.The output impedance of one of the substitutes was such thatit made the solar array simulator/converter interface unstable.The properties of electronic substitutes should always be testedproperly so that the same converter dynamics is reproduced withthe substitute and the real PV generator.

Based on the investigations presented in this paper, the mostimportant properties the solar array simulator shall have in orderto properly emulate a real PVG can be summarized as follows:1) The low-frequency impedance, i.e., the dynamic resistanceand the I–V curve have to be emulated as accurately as possible.2) The dynamic capacitance should be also emulated accuratelyenough though it is not as important as the emulation of thedynamic resistance. The capacitance of the simulators are typi-cally higher than the capacitance of the PV generator. This canaffect the behavior of the converters having small input capaci-tor. 3) The real PV generator shows passive-circuit-like behav-ior, which means that the phase of its output impedance stayswithin ±90◦. The emulator has to follow the same behavior.

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[29] R. D. Middlebrook, “Input filter considerations in design and applicationsof switching regulators,” in Proc. IEEE Ind. Appl. Soc. Annu. MeetingRec., Chicago, IL, Oct. 1976, pp. 366–382.

[30] J. Leppaaho, J. Huusari, L. Nousiainen, J. Puukko, and T. Suntio, “Dy-namic properties and stability assessment of current-fed converters in pho-tovoltaic applications,” IEEJ Trans. Ind. Appl., vol. 131, no. 8, pp. 976–984, Aug. 2011.

Lari Nousiainen (S’09) was born in Nurmes,Finland, in 1984. He received the M.Sc. (Tech) degreein electrical engineering from the Tampere Univer-sity of Technology, Tampere, Finland, in 2009. He iscurrently working toward the Ph.D. degree in the De-partment of Electrical Energy Engineering, TampereUniversity of Technology. He completed writing hisdoctorate thesis on the analysis and design of grid-tied photovoltaic inverters in June 2012.

In July 2012, he started working at ABB Drivesin Helsinki, Finland, as a Design Engineer.

Dr. Nousiainen is a Member of the IEEE Power Electronics Society, theIEEE Industrial Electronics Society, and the IEEE Power and Energy Society.

Joonas Puukko (S’10) was born in Helsinki, Finland,in 1983. He received the M.Sc. (Tech.) degree (withdistinction) in electrical engineering from the Tam-pere University of Technology, Tampere, Finland, in2008, where he also received the Ph.D. degree fromthe Department of Electrical Energy Engineering. Hecompleted writing his doctorate thesis in May 2012.

In July 2012, he started working at ABB Drivesin Helsinki, Finland, as a Design Engineer. His re-search interests included power electronics, three-phase dc/ac power supplies, dynamic modeling, and

interfacing of renewable energy systems.Dr. Puukko is a Member of the IEEE Power Electronics Society, the IEEE

Industrial Electronics Society, and the IEEE Power and Energy Society.

Anssi Maki (S’09) was born in Kauhava, Finland,1985. He received the M.Sc. (Tech.) degree in electri-cal engineering from the Tampere University of Tech-nology, Tampere, Finland, in 2010, where he has beenworking toward the Ph.D. degree in the Departmentof Electrical Energy Engineering as a Researcher.

His current research interests include the operationof photovoltaic power generators and the develop-ment of maximum-power-point-tracking algorithms.

Mr. Maki is a Member of the IEEE Power andEnergy Society.

Tuomas Messo (S’11) was born in Helsinki, Finland,in 1985. He received the M.Sc. (Tech.) degree inelectrical engineering from the Tampere Universityof Technology, Tampere, Finland, in 2011, where heis currently working toward the Ph.D. degree in theDepartment of Electrical Energy Engineering, as aResearcher.

His research interests include power electronics,three-phase dc/ac power supplies, dynamic modeling,control design, and interfacing of photovoltaic energysystems.


Juha Huusari (S’09) received the M.Sc. (Tech.)degree in electrical engineering from the TampereUniversity of Technology, Tampere, Finland, in 2009.He is currently working toward the Ph.D. degree inthe Department of Electrical Energy Engineering,Tampere University of Technology.

As of August 2012, he will be with ABB CorporateResearch in Baden-Dattwil, Switzerland, working asa Scientist with photovoltaic electricity systems. Hehas authored and co-authored 12 conference publica-tions and five journal publications. He also has one

international patent application. His current research interests include analy-sis and design of distributed maximum-power-point-tracking dc–dc converters,issues related to interfacing of photovoltaic generators, as well as practicalswitching-power-supply design issues.

Dr. Huusari is a Member of the IEEE Power Electronics Society, the IEEEIndustrial Electronics Society, and the IEEE Power Engineering Society.

Juha Jokipii (S’11) received the M.Sc. (Tech.)degree in electrical engineering from the Tam-pere University of Technology, Tampere, Finland,in 2011, where he is currently working toward thePh.D. degree in the Department of Electrical EnergyEngineering.

His research interests include power electronics,three-phase dc/ac power supplies, dynamic model-ing, and interfacing of renewable energy systems.

Jukka Viinamaki received the B.Sc. (Tech.) degreein embedded systems from the Tampere University ofApplied Sciences, Tampere, Finland, in 2009. He iscurrently working toward the M.Sc. in electrical en-gineering at the Tampere University of Technology.

Since 2012, he has been a Research Assistant in theDepartment of Electrical Energy Engineering, Tam-pere University of Technology. His research interestsinclude dc/dc converters and dc/ac inverters in pho-tovoltaic applications.

Diego Torres Lobera (S’10) was born in Palmade Mallorca, Spain, in 1985. He received the M.Sc.degree in industrial engineering from the Universityof Zaragoza, Zaragoza, Spain, in 2010.

Since the beginning of 2011, he has been aResearcher with the Department of Electrical EnergyEngineering, Tampere University of Technology,Tampere, Finland. His current research interests in-clude operation and modeling of photovoltaic powergenerators and maximum-power-point-trackingtechniques.

Seppo Valkealahti (M’10) was born in Alavus,Finland, 1955. He received the M.Sc. and Ph.D. de-grees in physics from the University of Jyvaskyla,Jyvaskyla, Finland, in 1983 and 1987, respectively.

From 1982 to 1997, he was a Teacher and Re-searcher of physics at the University of Jyvaskyla, inthe Riso National Laboratory in Denmark, and in theBrookhaven National Laboratory in NY. From 1997to 2004, he worked in ABB heading research andproduct development activities. In the beginning of2004, he joined the Tampere University of Technol-

ogy, Tampere, Finland, where he is currently a Professor in the Department ofElectrical Energy Engineering. His research interests include electric-power-production- and consumption-related technologies, solar energy, and multisci-entific problems related to power engineering.

Prof. Valkealahti is a Member of the IEEE Power and Energy Society.

Teuvo Suntio (M’98–SM’08) received the M.Sc.(Tech) and D.Sc. (Tech) degrees in electrical engi-neering from the Helsinki University of Technology,Espoo, Finland, in 1981 and 1992, respectively.

From 1977 to 1991, he worked at Fiskars PowerSystems as a Design Engineer and R&D Manager.From 1991 to 1992, he worked at Ascom Eergy Sys-tems Oy as an R&D Manager. From 1992 to 1994, hewas an entrepreneur in power electronics design con-sultancy, and from 1994 to 1998 he worked at EforeOyj as a Consultant and Project Manager. Since 1998,

he has been a Professor specializing in switched-mode power converter tech-nologies first at the University of Oulu, Electronics Laboratory, and from August2004 in the Department of Electrical Energy Engineering, Tampere Universityof Technology, Tampere, Finland. He holds several international patents and hasauthored about 180 international scientific journal and conference papers, thebook Dynamic Profile of Switched-Mode Converter—Modeling, Analysis andControl (Weinhein, Germany: Wiley-VCH, 2009) as well as two book chapters.His current research interests include dynamic modeling, control design, opti-mal electromagnetic interference design of switched-mode power converters, aswell as interfacing of renewable energy sources.

Prof. Suntio is a Member of the IEEE Power Electronics Society, the IEEEIndustrial Electronics Society, and the IEEE Circuits and Systems Society aswell as a Member of the European Power Electronics and Drives Association.From the beginning of 2010, he has served as an Associate Editor for the IEEETRANSACTION ON POWER ELECTRONICS. He has also served as a Guest Editor-In-Chief of the special issue on power electronics in photovoltaic applicationsin the IEEE TRANSACTION ON POWER ELECTRONICS.

photovoltaic generator as an input source for power

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